While the mobile phone is the world’s most popular media device, it is actually not one single medium, but is effectively used as a different medium by different user groups. The article characterizes polymodal differences in mobile apps usage among different user groups, including gender, education, occupation, screen size, and price. We monitored the complete app usage of 10,725 smartphone users for one month each (56 million sessions, recording almost 1 million hours). Our key contribution consists in developing and analyzing a theoretical framework to classify the over 16,000 apps used into five categories. Exploring nine research questions we provide a broad characterization by asking who, with which characteristics, uses which kinds of apps in what extensity and intensity? For example, it is not the young and high occupational grades that use the mobile phone as a human-to-machine computer (including gaming and artificial intelligence tools). Large screen size is related to extensive long sessions, while a small screen size is related to intensive frequent usage. The results go beyond providing ample empirical evidence for the inherently polymodal nature of the mobile phone, but also proposes a framework on how to possibility deal with it analytically.

We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t

Tree ordinances can be an effective means of preserving urban forests in the face of development pressures. Despite this, they also have the potential to be divisive among the public - especially when applied to privately-owned land. In this study we surveyed 1,716 Florida urban residents to understand how they value regulation and management of the urban forest. Specifically, we asked about: tree protection ordinances, incentive programs to manage or plant trees, justification for tree removal, and development. Most respondents supported tree protections, even when applied to trees on their own property or when they had the potential to limit development activities. Additionally, there was limited support for removing healthy trees for development. Respondents supported the use of funds for urban forestry efforts – particularly at the local or state level.

In this study, we prove the norm separating property for the composition of Cesàro 1 and Gamma matrices with their transpose. As a result, we compute the ℓp-norms of six classes of operators that commute with the infinite Hilbert operators. Additionally, we find the norm of 3 Hilbert’s commutants on some well-known sequence spaces.

Let $(Omega, mu)$ be a measure space and $\{\tau_\alpha\}_{\alpha\in \Omega}$ be a normalized continuous Bessel family for a real Hilbert space $\mathcal{H}$. If the diagonal $\Delta \{(\alpha, \alpha):\alpha \in \Omega\}$ is measurable in the measure space $\Omega\times \Omega$, then we show that \begin{align}\label{CRBA} \sup _{\alpha, \beta \in \Omega, \alpha\neq \beta}\langle \tau_\alpha, \tau_\beta\rangle \geq \frac{-(\mu\times\mu)(\Delta)}{(\mu\times\mu)((\Omega\times\Omega)\setminus\Delta)}. \end{align} We call Inequality (1) as continuous Rankin bound. It improves 76 years old result of Rankin [Ann. of Math., 1947]. It also answers one of the questions asked by K. M. Krishna in the paper [Continuous Welch bounds with applications, Commun. Korean Math. Soc., 2023]. We also derive Banach space version of Inequality (1).

The aim of this paper is to determine a suitable definition for the concept of fuzzy Hilbert space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Then we considered another approach to the notion of fuzzy inner product and analysed its properties.

The continuous casting process of helical fiber reinforced metal matrix composites was proposed, and the experimental equipment was designed and manufactured. The relationship model be-tween the process parameters and the helical shape of the fibers in the metal matrix is analyzed by differential geometry. Helical carbon fiber reinforced lead matrix composites were prepared under different conditions. When the melting temperature and cooling intensity were increased, the helical radius of helical carbon fiber in lead matrix was increased. When the fiber rotation speed was increased, the helical radius was decreased, and the helical pitch was de-creased proportionally. The experimental results are consistent with the process model. Carbon fiber rein-forced aluminum composites were prepared. Scanning electron microscopy showed that the infiltration between the aluminum matrix and the carbon fiber was not complete. As the volume fraction of carbon fiber which was added in composites is too small, the mechanical properties of the composites have not been significantly improved.

Lignin fibers typically influence the mixture performance of stone matrix asphalt (SMA), such as strength, stability, durability, noise level, rutting resistance, fatigue life, and water sensitivity. However, limited studies were conducted to analyze the influence of fibers on the percent voids in mineral aggregate in bituminous mixture (VMA) during the mixture design. This study analyzed the effect of different fibers and fiber contents on the VMA in SMA mixture design. A surface-dry condition method test and Marshall Stability test were applied on the SMA mixture with four different fibers (i.e., flocculent lignin fiber, mineral fiber, polyester fiber, blended fiber). The test results indicated that the bulk specific gravity of SMA mixtures and asphalt saturation decreased with the increasing fiber content, whilst the percent air voids in bituminous mixtures (VV), Marshall Stability and VMA increased. Mineral fiber had the most obvious impact on the bulk specific gravity of bituminous mixtures, while flocculent lignin fiber had a minimal impact. The mixture with mineral fiber and polyester fiber had significant effects on the volumetric properties, and, consequently, exhibited better VMA over the conventional SMA mixture with lignin fiber. Modified fiber content range was also provided, which will widen the utilization of mineral fiber and polyester fiber in the applications of SMA mixtures. The mixture evaluation suggested no statistically significant difference between lignin fiber and polyester fiber on the stability. The mineral fiber required a much larger fiber content to improve the mixture performance than other fibers. Overall, the results can be a reference to guide SMA mixture design.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

In a previous paper (https://dx.doi.org/10.2139/ssrn.3648127 ), an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it.

While the number of publications on wine and health is steadily increasing, ranging from molecular level to epidemiological studies, often with contradictory results, little attention has been given to an holistic approach. In this review some unusual concepts are considered, such as phytocomplex, vehicle and the Matrix effect. As an example, three mono/polyphenols present in wine, Tyrosol, Hydroxytyrosol and Resveratrol, have been selected and the consequences of respecting, disregarding or ignoring the Matrix effect are shown. Underestimation of the wine Matrix effect could lead to deceiving results, as in the case of de-alcoholized wine or wine-compound-based nutritional supplements,or in emphasizing a single component toxic activity, in this case alcohol, ignoring the specific protective action at molecular level of other compounds (polyphenols) present in the same Matrix. The dark side of Matrix effect is also discussed. It is suggested that specificity of wine should be always taken in consideration by public health Authorities.

While many practitioners and experts understand the risks associated with low urban tree diversity, they often lack the ability to rectify issues they encounter on their own. The current system of tree production and procurement is complex – shaped by market pressures, nursery and site constraints, local governance, and differing professional objectives among those who grow, specify, and plant trees. To understand this complexity as well as constraints to- and opportunities for increasing urban tree diversity, we conducted a series of focus groups comprised of nursery growers, landscape architects, and urban foresters. Our results highlight a significant list of considerations and constraints to diversity (both shared among green industries and some specific to growers or purchasers). More importantly, in discussing our findings we outline actionable strategies for increasing urban tree diversity.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

This study provides an in-depth review of the available literature on metal composite material machining, focusing on traditional machining operations such as turning, milling, shaping, drilling, and grinding. The motivation for the study is that this composite type has emerged as a vital material in applications requiring functionality, resilience, cost-effective operation, low consumption of energy and lightweight. Despite its superior characteristics, the manufacturing complexity and poor machinability of metal matrix composites have been the primary barriers to its adoption. Nevertheless, there is a reduction of exceptional efficiency, increase in surface roughness, tool wear and so on in metal matrix composites throughout machining. As a result, this review gives a comprehensive investigation of metal matrix composite machining and effect on process parameters and procedures. Furthermore, this study distinguishes metal matrix composites towards sustainable manufacturing and the metals employed by the researchers, as well as the gaps discovered for future recommendations in metal-based composites.

Inspired by works of W. H. Zurek and others, a mathematical, physical theory, entirely within a quantum mechanical formalism, is proposed for cognitive processes in terms of an abstract Hilbert-space for the conscious state that is an exact replica of the Hilbert-space for the neuronic physical state. Thus, any actual state of consciousness arises by its formal alignment (identification) with some-one in the set of the neuronic states, with the latter undergoing perpetual changes in the wake of life-long experiences. It is posited that these changes become expressed by an increase in the number of ordered, coherent neuronic states at the expense of the pre-ordinal random neuronic states. Changes, transitions between states are induced by a Gorini-Kossakowski-Sudarshan-Lindblad formalism, which is also instrumental in the effect of the conscious state on bodily actions. The paradigmatic findings of R.N. Shepard (1958 - 2011) and of S. Sternberg (1966 - 2016) for long- and short-term recalls are interpreted within the model.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom [J. Funct. Anal., 2021], we introduce the notion of p-absolutely summing morphisms between Hilbert C*-modules over commutative C*-algebras. We show that an adjointable morphism between Hilbert C*-modules over monotone closed commutative C*-algebra is 2-absolutely summing if and only if it is Hilbert-Schmidt. We formulate version of Pietsch factorization problem for p-absolutely summing morphisms and solve partially.

Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

Background: This study attempted to construct musculoskeletal JEM using KWCS data and use it to evaluate the burden of these disorders in Korean workers. Methods: This study was conducted using data from the second to the sixth KWCS, and a total of 210,500 people were included. The jobs of the subjects were reclassified based on the unit groups of the 7th Korean Standard Classification of Occupation (KSCO). The intensity of exposure to work-related risk factors for musculoskeletal disorders was classified into ‘high’, ‘moderate’, and ‘low’ for the body segments involving the ‘upper extremities and neck’, ‘lower back’, and ‘lower extremities’. Results: The time of exposure was longest in the standing posture and repetitive hand and arm movements. An analysis of the intensity of exposure by body segments revealed that the highest intensity of exposure was to the upper extremities. For the upper extremities and neck, and the lower back, there was a exposure-response relationship in the association between intensity of exposure and musculoskeletal symptoms. However, for the lower extremities, there was a exposure-response relationship only at high exposure. Conclusion: In this study, a JEM for work-related risk factors for musculoskeletal disorders was constructed for the first time in Korea. The intensity of exposure to musculoskeletal risk factors was estimated for each occupation. The JEM constructed in this study is expected to have high applicability for assessing the risk of musculoskeletal disorders for each job with respect to the upper extremities and neck, and lower back.

The ECM is composed of a considerable number of biochemically and structurally diverse constituents. ECM is a highly dynamic system that constantly receives and sends biological, chemical and mechanical signals. Several studies suggest that mechanical signals derived from the extracellular microenvironment regulate skin regeneration and wound healing. We evaluated effects of a mixture of biomolecules extracted and purified from bovine colostrum on restoring the mechanical properties of ECM. Test measuring collagen contraction showed a significant difference in contraction activation in samples treated with the 2% colostrum derivative mixture compared to the control. The analysis of the supernatant showed an inhibition of metalloproteinase-2 expression and an increase in collagen secretion by fibroblasts in treatment samples. Our hypothesis is that the molecules extracted and purified from bovine colostrum restore the ECM environment qualitative and quantitative characteristics, thus guaranteeing through a mechanical action the restoration of the wound due to the transduction of the signal activated by the integrins.

The release of the active substance from the matrix modified-release tablets based on Kollidon®SR and chitosan depends on its solubility in the dissolution medium and on the composition of the matrix-forming polymers. The study is based on new oral matrix tablets based on Kollidon®SR and chitosan, formulated to optimize the low oral bioavailability of chlorzoxazone, a non-steroidal anti-inflammatory drug, a class II Biopharmaceutical Classification System. Nine types of chlorzoxazone matrix tablets were obtained using the direct compression method, and their combination at 1:1, 1:2, 1:3 chlorzoxazone/ excipients, 20%-40% (w/w) Kollidon®SR, 3-7% (w/w) chitosan and the auxiliary substances were formulated in constant concentrations. Pharmaco-technical characterization included the analysis of flowability and compressibility properties (flow time, friction coefficient, angle of repose, Hausner ratio, Carr Index), and of pharmaco-chemical characteristics (mass and dose uniformity, thickness, diameter, mechanical strength, Friability, degree of softening, in vitro release profile) of the tablets. Based on the initial evaluation of the pharmaco-technical analysis, pharmaco-chemical characteristics, and in vitro release profile, only three matrix tablet formulations (F1b, F2b, and F3b) were further tested. They were evaluated through Fourier-transform infrared spectrometry, X-ray Diffraction, thermogravimetry, differential scanning calorimetry, and in vitro dissolution tests. The three formulations were comparatively studied regarding the release kinetics of active substances using in vitro release testing. The results were analyzed by fitting into four representative mathematical models for the modified release oral formulations. In vitro kinetic study reveals a complex mechanism of release occurring in the first (0 - 2 hours) and second (2.0 hours – 36 hours) steps of drug release. Two factors have been calculated to assess the release profile of chlorzoxazone: f1 - the similarity factor and f2 - the factor difference. The results have shown that both Kollidon®SR and chitosan may be used as matrix-forming agents when combined with chlorzoxazone. In vitro dissolution tests revealed the F2b sample, data suggesting a faster drug release. The three formulations showed optimum pharmaco-technical properties and in vitro kinetic study, and they had tremendous potential to be used in oral pharmaceutical products for the controlled delivery of chlorzoxazone.

Sesquiterpene lactones (STLs) are a large group of terpenoids most commonly found in plants of the Asteraceae family, e. g. in chicory plants, displaying a wide range of interesting biological activities. However, further studies on the biological potential of chicory derived STLs and analogues are challenging as only four of these molecules are commercially available (as analytical standards), and to date there are no published or patented simple extraction-purification processes capable of large scale STLs isolation. In this work we describe a novel three-step large scale extraction and purification method for the simultaneous purification of 11,13-dihydrolactucin (DHLc) and lactucin (Lc) starting from a chicory genotype rich in these STLs and in the corresponding glycosyl and oxalyl conjugated forms. After a small-scale screening on 100 mg of freeze-dried chicory root powder, the best results were achieved with a 17 h water maceration at 30°C. With these conditions we managed to increase the content of DHLc and Lc, at the same time favouring the hydrolysis of their conjugated forms. On a larger scale, the extraction of 750 g of freeze-dried chicory root powder, followed by a liquid-liquid extraction step and a reversed-phase chromatography, allowed the recovery of 642.3 ± 76.3 mg of DHLc and 175.3 ± 32.9 mg of Lc. The two pure STLs were subsequently used in the context of semi-synthesis to generate analogues for biological evaluation as antibacterial agents. In addition, other described chicory STLs that are not commercially available were also synthesized or extracted to serve as analytical standards for the study. In particular, lactucin-oxalate and 11,13-dihydrolactucin-oxalate were synthesized in two steps starting from Lc and DHLc, respectively. On the other hand, 11β,13-dihydrolactucin-glycoside was obtained after a MeOH/H₂O (70/30) extraction, followed by a liquid-liquid extraction step and a reversed-phase chromatography. Together, this work will help facilitate the evaluation of the biological potential of chicory derived STLs and their semisynthetic analogues.

In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As special cases of our results (when T = N and T = R), we get the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scale, like T = q^Z, q > 1.

Integrated Kerr micro-combs, a powerful source of many wavelengths for photonic RF and microwave signal processing, are particularly useful for transversal filter systems. They have many advantages including a compact footprint, high versatility, large numbers of wavelengths, and wide bandwidths. We review recent progress on photonic RF and microwave high bandwidth temporal signal processing based on Kerr micro-combs with spacings from 49-200GHz. We cover integral and fractional Hilbert transforms, differentiators as well as integrators. The potential of optical micro-combs for RF photonic applications in functionality and ability to realize integrated solutions is also discussed.

Electrowetting display (EWD) device is a new type of electrowetting-on-dielectric (EWOD) equipment which can achieve a paper-like display effect under the control of electric field. In this microfluidic system, the stability of grayscale could be affected by various factors, such as the physicochemical properties of materials, device structure, and electric field distribution. To improve the grayscale stability of active matrix electrowetting displays (AM-EWDs), the impact of different polarities of driving voltage on oil backflow was investigated in this study. Based on the driving principles of AM-EWD, an optimized inter-frame bipolar reset driving waveform was designed to overcome oil backflow. The proposed driving waveform maintained the stability of the oil state by periodically and rapidly releasing trapped charges in the dielectric layer through a reverse driving voltage. Additionally, the effect of feed through voltage on the pixel driving voltage was eliminated by compensating for the driving voltage on common electrode. Finally, the performance of the designed driving waveform was evaluated with a 6-inch AM-EWD driving platform. Compared to the conventional unipolar reset driving waveform, the backflow speed decreased by 2.70 a.u./s. The standard deviation of the display luminance was also reduced by 11.24 a.u. Experimental results indicated that both the oil backflow speed and the fluctuation range of luminance were effectively suppressed by the proposed driving waveform.

This investigation mainly focused on the microstructural analysis of Al based hybrid metal matrix composites. Aluminium as base metal and reinforced with 2% B4 C, ZrO2 (2%,4%,6%), SiC (4%,8%,12%). Specimens were manufactured by using conventional stir casting technique. Hybrid metal matrix composites were examined by using Scanning electron microscope. This research explained XRD, EDS and Fractography analysis. This investigation shows the reinforced material has given better results in all aspects than pure Al6061 alloy and homogeneous dispersion of particles inside the matrix. Porosity, delamination, cracks, particle distributions were observed through microstructural analysis. Additionally determined the crystal size of pure Aluminium 6061 alloy and hybrid composites.

Despite the abundance of tree diversity in the natural world, and generally high tree species richness in urban areas, urban forests continue to be dominated by a limited number of species. As socio-ecological systems, urban forests are shaped by historical and current management efforts and decision-making of a wide range of human actors. Drawing on past research, we offer a conceptual framework for describing the complex interactions among tree producers and consumers as trees are selected, grown, specified, and planted in private and public urban areas. We illustrate how multiple layers of selection criteria filter down the entirety of potential local tree diversity to a handful of commonly used and accepted tree species. We detail the actors and decision makers who impact tree composition and diversity across several land types. Finally, we identify research, education and outreach needs as they relate to creating more diverse and resilient urban forest ecosystems.

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought.

To enhance the overall reliability of the power system, engineers have redirected their focus toward health monitoring and early detection of faults in transformers. Among these faults, transformer core defects demand particular attention. While fault simulation using software has traditionally been the preferred approach, these methods suffer from data inaccuracies in real-world conditions. Consequently, conducting actual experimental setups with induced faults is imperative to investigate core issues. This study uses Hilbert Transform (HT) as a signal processing technique to extract crucial data characteristics, thereby enhancing the performance of the classifier model. The research involves analyzing electric current signals from a single-phase 1kVA transformer. A comparative assessment of our proposed model was conducted using raw data and Fast Fourier Transform (FFT), evaluating accuracy, precision, recall, F1-score, and computational time. The results demonstrate a significant improvement in all metrics for the classifier models, particularly the k-nearest neighbor (KNN) algorithm, which exhibited values of 83.89%, 84.39%, 83.89%, 83.79%, and 0.0156 seconds, respectively. Future work aims to extend this analysis under different loading conditions.

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

Titanium-based metal-matrix composites manufactured by additive manufacturing offer tremendous lightweighting opportunities. However, processing high reinforcement content remains challenging. This study reports an improved manufacturing process for Ti-TiC enabling high reinforcement content and significant fracture strain concurrently: mechanical blending, followed by laser powder bed fusion and a single heat treatment. As-built microstructure shows both un-melted TiC particles and sub-stoichiometric TiC dendrites resulting from a partial dissolution of TiC particles. The heat treatment is shown to fully convert TiC dendrites into equiaxed TiC grains. Reduction of the C/Ti ratio in TiC during the process results in an increase in the reinforcement content, from a nominal 12 vol% to an effective 21.5 vol%. Ti-TiC tensile samples reached fracture strains of up to 1.7%, Young’s moduli of up to 149 GPa and ultimate tensile strengths of up to 827 MPa. Lower TiC initial powder size distributions displayed the best mechanical performance.

This article aims to analyze household energy data to predict electricity self-sufficiency and identify the key features that impact it. For this purpose, we use SHAP (Shapley Additive Explanations), LightGBM (Light Gradient Boosting Machine), and a correlation heatmap-based framework to analyze 12 months of energy and questionnaire survey data collected from over 200 smart houses in Kitakyushu, Japan. We use the SHAP summary plot to identify the impact-wise order of key features influencing the electricity self-sufficiency rate (ESSR). Using SHAP, we demonstrated that key features are; housing types, average monthly electricity bill, floor heating, electric capacity, number of washing and drying machines, fee plans, occupation of household head, total floor area, average monthly gas bill, cooking equipment, etc. Furthermore, we adopted the LightGBM classifier with $\ell^1$ regularization to extract the most significant features and predict the electricity self-sufficiency rate of households. This LightGBM-based model can also predict the electricity self-sufficiency rate of households that did not participate in the questionnaire survey. A heat map is also used to analyze the correlation among household variables. The findings discussed in this article offer valuable insights for energy policymakers to achieve the targets of energy self-sufficient houses.

Development and redevelopment are important drivers of tree removal and canopy loss in urban landscapes. Local ordinances are often used to curtail tree removal, but punitive regulations alone may not be enough to reduce urban tree canopy loss in land development. In Florida (US), efforts to balance trees and development have so far focused on fees and fines, but with a recent backlash against tree regulations and the fast pace of urban growth, we explored the possible role of incentives in urban tree policies. We interviewed 20 land developers across Florida to understand their perspectives on current barriers and potential incentives for tree preservation and planting. We collected data from developers, whose perspectives on tree preservation are often unknown or overlooked, despite their significant role in tree planting, removal, and retention in and around cities. Our results show that major barriers to tree preservation and planting include requirements to grade sites for stormwater management, site constraints, and monetary costs. Most developers did not know of any existing incentives beyond intrinsic motivations but said that financial incentives would be most appealing to them. Top incentive suggestions include increasing building density, reducing impact fees and tax liability, and changing tree mitigation policies. Another promising finding is that developers are willing to work with regulators to find solutions that benefit both parties. Future research should consider evaluating the level of support and viability of different incentives by gathering feedback from policymakers, land developers, and the public.

As urban development increases in density, the space to grow urban trees becomes more constrained. In heavily developed areas, small stature trees can be planted to reduce both above- and below-ground conflicts with infrastructure elements. However, even these species have their limits when placed in extremely confining conditions. In this study, we build on past work to determine the minimum planting widths of small stature urban trees. We found that species, stem diameter, and the height at which stem diameter measurements occurred were all strong predictors of trunk flare diameter (adjusted R² of 0.843). Additionally, we modelled the relationship between planting space and the presence or absence of hardscape conflicts – using the predictions derived from this effort to project the potential cost savings in two United States cities. Study results provide a guideline to create sufficient space for urban trees and minimize infrastructure damage and associated cost savings.

Several Lung diseases can result in lung damage structural changes, with lung transplantation as a only therapeutic option when the disease reaches an advanced progression, unfortunately, the success of lung transplantation is limited. In this context, lung bioengineering is considered a potential therapeutic alternative and the current approach is based on the use of the natural extracellular matrix (ECM) of the decellularized lung. The use of undifferentiated cells to seed an ECM can be a more practical strategy for lung bioengineering but the sterilization of the organ for this recellularization process is still a challenge. In this sense, Low-Level Laser Therapy (LLLT) can emerge as a potential treatment alternative. Therefore, the objective of this study was to verify if LLLT, can optimize lung recelularization with mesenchymal stem cells by cytokine modulation. For this, we decellularized lungs from C57BL/6 mice perfusing SDS 1% via pulmonary artery, sterilized with LLL (660nm, 100mW, 30s). Whole lung scaffolds were recellularized: (1) Recellularized Lung (2) Recellularized Lung + LLLT. Mesenchymal stem cells derived from human tooth pulp (DPSc) were seeded into lungs and incubated for 24 hours at 37ºC, 5% CO₂, in a bioreactor-like conditions, maintaining CPAP at 20cmH2O, 90% O2, and LLL at wavelength of 808nm, 100mW, 30s. Culture medium were analyzed at 24 hours. H&amp;E, immunostaining, SEM and ELISA assay were performed. We produced viable biological scaffolds absent of DNA content, preserving glycosaminoglycans and collagen I, III and IV, fibronectin, laminin and elastin and lung structure (SEM). The levels of IL-6 and IL-8 were stable during the 24 hours of culture. IFN-γ levels showed significant difference in the DPSc and DPSc+LLLT group in the 24-hour evaluation. The levels of IL-10 decreased after LLLT. These findings highlight LLLT's role in cytokine regulation and contamination prevention during lung recellularization with mesenchymal stem cells. Overall, these results demonstrated that LLLT's modulated cytokine levels and could prevent contamination during the lung recellularization process with mesenchymal stem cells, offering promise for enhanced therapeutic strategies in lung bioengineering.

In Indonesia, types of meat are still identified manually due to increasing prices for beef and buf-falo ahead of Idul Fitri. Traders mix beef with pork to thwart the beef scam. Haar wavelet and GLCM, GLCM with angles of 0°, 45°, 90°, and 135°, as well as matrices using contrast, correlation, energy, homogeneity, and entropy, are used in feature extraction. The following are the results of meat image classification testing using k-NN, Haar wavelet, and GLCM: The k-NN algorithm shows superiority in identifying fresh (99%), frozen (99%), and rotten (96%) meat texture images with the most fantastic accuracy results in every situation. Meanwhile, GLCM routinely provides good results, especially regarding the texture image of fresh meat (183.21) and rotten meat (115.79). However, despite delivering less throughput than k-NN and GLCM, Haar wavelets are still helpful, especially when dealing with fresh meat texture images (89,96).

We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity. Tan, and D. J. Moss are with the Optical Sciences Centre, Swinburne University of Technology, Hawthorn, VIC 3122, Australia. (Corresponding e-mail: [email protected]). Xu is with the Electro-Photonics Laboratory, Department of Electrical and Computer System Engineering, Monash University, Clayton, 3800 VIC, Australia

Thin people who undergo implant insertion into the chest wall face a high risk of implant exposure to the external environment. Five months after an 8-year-old boy underwent implantable cardioverter-defibrillator (ICD) implantation in a subcutaneous pocket in the left anterolateral chest wall to manage long QT syndrome, ICD replacement became necessary owing to exposure risk from distal and lateral thinning of the ICD pocket. Pocket rupture and exposure would increase the risk of infection; therefore, we performed ICD removal and primary pocket closure. Two weeks later, a new suprafascial pocket was created, acellular dermal matrix (ADM) was attached to the inner wall to prevent ICD protrusion, and a new ICD was inserted. One year postoperatively, the ADM was engrafted, and no complications were observed. A thin subcutaneous layer increases the risk of ICD implantation complications. Inner wall strengthening with ADM can help prevent pocket rupture.

The transformation of the states of polarization of electromagnetic waves that interact with polarimetrically linear media can be represented by means of the associated Mueller matrix. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as a distance of the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

This study outlines a 3-step production process for Ti-TiC Metal Matrix Composite (MMC) employing powder Mechanical Blending, Laser Powder Bed Fusion (LPBF), and a heat treatment. A TiC fraction of more than 20 vol% was formed in-situ through the reaction of titanium with carbon during the LPBF process. The manufactured MMC pieces showed a record stiffness and fracture strain combination. The LPBF energy density impacted strongly porosity type. The as-built microstructure displayed an homogeneous distribution of sub-stoichiometric TiC dendrites which were fully converted into equiaxed TiC grains during the heat treatment. The TiC C/Ti ratio was found to be close to 0.5, resulting in an effective reinforcement content nearly twice the one expected for stoichiometric TiC, leading to stronger reinforcement. The mechanical analysis revealed a Young’s modulus of up to 149 GPa and an ultimate tensile strength of up to 770 MPa, indicating a 27% and 34% improvement, respectively, compared to commercially pure Titanium produced by LPBF and heat treated in the same conditions. A fracture strain of up to 2.8% was achieved. The combination of in-situ formation of defect-free TiC reinforcement and subsequent heat treatment enables to reach an exceptional ductility, considering the 20 vol% reinforcement content.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

Uterine tube extracellular matrix is a key component that regulates tubal tissue physiology, and it has a region-specific structural distribution, which are directly associated to their functions. Considering this, application of biological matrices in culture systems is an interesting strategy to develop biomimetic tubal microenvironments and enhance their complexity. However, there are no established protocols to produce tubal biological matrices that consider the organ morphophysiology for such applications. Therefore, this study aimed to establish region-specific protocols to obtain decellularized scaffolds derived from porcine infundibulum, ampulla, and isthmus to provide suitable sources of biomaterials for tissue-engineering approaches. Porcine uterine tubes were decellularized in solutions of 0.1% SDS and 0.5% Triton X-100. Decellularization efficiency was evaluated by DAPI staining and DNA quantification. We analyzed ECM composition and structure by optical and scanning electronic microscopy, FTIR and Raman spectroscopy. DNA and DAPI assays validated the decellularization, presenting significative reduction of cellular content. Structural and spectroscopy analyses revealed that produced scaffolds remained well structured and with ECM composition preserved. YS and HEK293 cells were used to attest cytocompatibility, allowing cell survival and successful interaction with the scaffolds. These results suggest that such matrices are applicable for future biotechnological approaches in the reproductive field.

Background: Public engagement is needed to make sure urban forestry management efforts align with the values of the public being served. Noting this, we determined current and desired urban forest access of Florida (United States) residents using the criteria from the 3-30-300 rule (i.e., 3 trees visible from home, 30% canopy in neighborhood, and a green space within 300 meters of home). Methods: A survey of 1,716 Florida residents was conducted to assess canopy coverage and green space access. Respondents were then asked if this level of urban forest access was sufficient for their needs. We also asked their perceptions of the benefits and drawbacks of urban trees and whether they had any negative interactions with trees in the past. Results: We found that 37.3% of Florida residents met all three criteria of the 3-30-300 rule. Despite this, half the respondents would prefer more trees in their neighborhoods. When asked to name the top benefits provided by trees, the most common responses were shade, beauty, and attracting wildlife. The most common drawbacks to urban trees included risk to property, leaves/debris, and fears regarding storms and hurricanes. Conclusions: Florida residents largely value their urban forest and would like to see it maintained or enhanced. Improving access to greenspaces for recreation is the most pressing concern for urban forest managers in Florida looking to meet the requirements of the 3-30-300 rule. Results from this study can inform and test urban forest management at national and global scales.

In this study, in order to determine the effect of matrices shape on percolation threshold values, computer simulations were performed using the Monte Carlo method for a 200x200 square-shaped matrix and rectangular matrices containing the same number of nodes as the square matrix. Based on the simulations, the average values of percolation thresholds and standard deviations for current flow along and across the matrices were determined. It was determined that for a square-shaped matrix, the average values of percolation thresholds in both directions of current flow were the same. Extending the rectangular matrix while reducing its height causes the average value of the percolation threshold in the direction of current flow along the matrix to increase from 0.592740 to 0.759847, while in the transverse direction it decreases from 0.592664 to 0.403614. The values of the classical asymmetry coefficients of the probability distributions of percolation thresholds for both directions of current flow were determined. Histograms of the probability distributions of percolation threshold values for square-shaped matrix and rectangular matrices were made and compared with normal distributions. It was found that the occurrence of two percolation thresholds in rectangular layers should be considered when analyzing electrical conductivity measurements of nanocomposite thin films.

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

Hydrogels can be considered as mimics of extracellular matrix (ECM).Cytoskeleton through integrins is connected with ECM and cytoskeleton tension depends on ECM stiffness.A number of age-related diseases depend on cellular processes related with cytoskeleton function.Some examples of cancer initiation and progression and heart disease in relationship with ECM stiffness has been analysed.Incorporation of rigid particles in ECM can increase ECM stifness and to promote formation of internal residual stresses. Water migration, changes of water binding energy to biomactomolecules, changes of the state of water from tightly bound water to free and loosely bound water changes stiffness of ECM. Risks related with rigid particles incorporation into ECM have been also iscussed.

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulate morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin density independent increase of the projected cell area until 12 kPa. Additionally, changes in the fibronectin density led to an area optimum at about 2.6 μg/cm, which was confirmed by an independent F-actin analysis, revealing a maximum actin filament to cell area ratio of 7.5 %. The proliferation evaluation showed an opposite correlation between cell spreading duration and speed to the matrix elasticity and protein density, which did not affect the cell cycle duration. In summary, we identified an optimized ECM composition, while independent matrix properties regulate distinct cell characteristics.

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

In recent years, the abundance of streaming data has posed significant challenges for traditional machine learning algorithms due to the dynamic nature and high volume of data. To address these challenges, this paper presents an adaptive supervised learning framework designed for data streams, leveraging the power of reproducing kernel Hilbert spaces (RKHS) while incorporating a data sparsity constraint. The proposed framework aims to adaptively update the model to efficiently handle the continuous arrival of streaming data while ensuring accurate and reliable predictions. The primary objective is to exploit the RKHS framework, which provides a rich mathematical structure for learning in high-dimensional feature spaces. By utilizing RKHS, the model can capture complex patterns and nonlinear relationships in the streaming data. Furthermore, the framework incorporates a data sparsity constraint to address the issue of limited resources and computational efficiency. The constraint promotes the selection of a subset of relevant features, reducing the dimensionality of the problem and enhancing the scalability of the learning algorithm. This constraint not only improves computational efficiency but also mitigates the effects of noisy or irrelevant features, leading to more robust and accurate predictions. To achieve adaptability, the proposed framework employs an online learning approach that incrementally updates the model parameters as new data arrives. This allows the model to adapt to concept drift and changing data distributions, ensuring its relevance and effectiveness over time. The adaptation process is guided by a mechanism that balances the exploitation of current knowledge with the exploration of new information, enabling the model to gradually evolve and refine its predictions. Experimental evaluations on various benchmark datasets demonstrate the efficacy of the proposed framework in handling streaming data. The results indicate that the adaptive supervised learning approach in RKHS with a data sparsity constraint outperforms traditional batch learning methods and exhibits superior accuracy, scalability, and adaptability in dynamic data stream scenarios. Overall, this research contributes to the development of adaptive supervised learning methods for data streams, highlighting the effectiveness of RKHS and the significance of incorporating a data sparsity constraint. The proposed framework offers a promising solution to handle the challenges posed by streaming data, paving the way for real-time, efficient, and accurate learning in diverse application domains.

Eight lesions were analyzed using some algorithms of Intelligence Artificial: basal cell carcinoma (BCC), squamous cell carcinoma (SCC), melanoma (MEL), actinic keratosis (AK), benign keratosis (BKL), dermatofibromas (DF), melanocytic nevi (NV), and vascular lesions (VASC). This manuscript presents the possibility of using concatenated signatures (instead of images) obtained from different integral transforms, such as Fourier, Mellin, and Hilbert, to classify skin lesions. Eleven other Artificial Intelligence models were applied so that eight skin lesions could be classified by analyzing the particular signatures of each lesion. The database was randomly divided into 80%–20% for the training and test datasets images, respectively. The metrics that are being reported are accuracy, sensitivity, specificity, and precision. Each case was repeated 30 times to avoid bias, according to the central limit theorem in this work, and the average and ±standard deviation were reported. Although all the results were very satisfactory, the best average mark for the eight lesions analyzed was obtained using the Subspace KNN model, where the metrics for the test were 99.98% accuracy, 99.96% sensitivity, 99.99% specificity, and 99.95% precision.

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δ_p, ϑ_p and the real norms η_r,p and θ_r,p are provided as well.

The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

Matrix metalloproteinases (MMPs) have been demonstrated to have both detrimental and protective functions in inflammatory diseases. Several MMP inhibitors, with the exception of Periostat®, have failed in Phase III clinical trials. As an alternative strategy, recent efforts have been focussed on the development of more selective inhibitors or targeting other domains than their active sites (e.g., exosites, ectosites) through specific small molecule inhibitors or monoclonal antibodies. Here, we present some examples that aim to better understand the mechanisms of conformational changes/allosteric control of MMPs functions. In addition to MMP inhibitors, we discuss unbiased global approaches such as proteomics and N-terminomics to identify new MMP substrates and achieve a better understanding of the roles of these proteases in diseases.

Human disturbance, such as trampling, is an integral component of global change, yet we lack a comprehensive understanding of its effects on alpine ecosystems. Many alpine systems are seeing a rapid increase in recreation, and in understudied regions, such as the Coast Mountains of British Columbia, disturbance impacts on alpine plants remain unclear. We surveyed disturbed (trail-side) and undisturbed (off-trail) transects along elevational gradients of popular hiking trails in the T’aḵ’t’aḵ’múy̓in tl’a In̓inyáx̱a7n region (Garibaldi Provincial Park), Canada, focusing on dominant shrubs (Phyllodoce empetriformis, Cassiope mertensiana, Vaccinium ovalifolium) and graminoids (Carex spp). We used a hierarchical Bayesian framework to test for disturbance by elevation effects on total plant percent cover, maximum plant height and diameter (growth proxies), and buds, flowers, and fruits (reproduction proxies). We found that trampling reduces plant cover and impacts all species, but that effects vary by species and trait, and disturbance effects only vary with elevation for one species’ trait. Growth traits are more sensitive to trampling than reproductive traits, which may lead to differential impacts on population persistence and species level fitness outcomes. Our study highlights that disturbance responses are species-specific, and this knowledge can help land managers minimize disturbance impacts on sensitive vegetation types.

Introduced in 1967 by Lov\'{a}sz, graph exponentiation has received little attention over the past several decades. Since graph exponentiation produces large graphs and any graph can be constructed utilizing its adjacency matrix, we provide a four step linear construction algorithm that generates the adjacency matrix for the graph exponential.

Biofilm matrix is akin to bacterial abodes, primarily composed of proteins, polysaccharides, extracellular DNA, and lipids, providing essential structural support to bacteria. While some biofilm matrix offers significant benefits, such as engineered biofilm reactors that assist in water pollutant removal, others pose risks to human health, potentially leading to conditions like lung infections. Realizing the potential of advantageous biofilm matrix and mitigating the harmful effects of detrimental ones necessitates a comprehensive and systematic exploration of this intricate domain. To facilitate this examination, our study leveraged a dataset of the 1000 most pivotal papers in the field and conducted an exhaustive bibliographic review. This paper serves as a valuable resource for understanding the current progress in biofilm matrix research and delving into vital avenues for future exploration in this dynamic field.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

Metal matrix composite are used in such fields of technology, such as: aerospace, electronics, energy, industry, defense, automotive, aviation, shipbuilding, and more. Composite coatings of ceramic - metals is used primarily to enhance the durability of machine parts. Therefore, new materials are permanently looked for, what has resulted in the past in development of composite materials. The coatings dispersed are consisting of metallic matrix (metals and their alloys) and small non-metallic particles. The deposition of ceramic particles simultaneously with metallic matrix leads often to composite coatings possessing properties much better than those of metallic coating. The nickel and less often, other iron group elements are usually used as a matrix and Al2O3 as tough particles. The welding technology of applying alloy and composite coatings is widely used. The technology of infrasound thermal spraying of metal matrix composite coatings was presented. It is a simple technology and a very useful one in ship machinery regeneration during the cruise craft (e.g. internal combustion engines, torque pumps, separators). The metal matrix composite coatings must undergo finishing due to high surface roughness after application. In the article to used finishing by plastic working and machining of coatings nickel matrix composite was proposed.

Before calcification begins, the early embryonic and fetal skeletal development of both mammalian Homo sapiens and the chondrichthyan fish Raja asterias consists exclusively of cartilage. This cartilage is formed and shaped through processes involving tissue segmentation and the frequency, distribution, and orientation of chondrocyte mitoses. In the subsequent developmental phase, mineral deposition in the cartilage matrix conditions the development further. The stiffness and structural layout of the mineralized cartilage have a significant impact on the shape of the anlagen (early formative structures of organs or tissues) and the mechanical properties of the skeletal segments. The fundamental difference between the two studied species lies in how calcified cartilage serves as a scaffold for osteoblasts to deposit bone matrix, which is then remodeled. In contrast, chondrichthyans retain the calcified cartilage as the definitive skeletal structure. This study documents the distinct mineral deposition pattern in the cartilage of the chondrichthyan R. asterias, in which calcification progresses with the formation of focal calcification nuclei or “tesserae”. These are arranged on the flat surface of the endo-skeleton (crustal pattern) or aligned in columns (catenated pattern) in the radials of the appendicular skeleton. This anatomical structure is well adapted to meet the mechanical requirements of locomotion in the water column. Conversely, in terrestrial mammals, endochondral ossification (associated with the remodeling of the calcified matrix) provides limb bones with the necessary stiffness to withstand the strong bending and twisting stresses of terrestrial locomotion. In this study, X-rays of marine mammals (reproduced from previously published studies) document how the endochondral ossification in dolphin’s flipper adapts to the mechanical demands of aquatic locomotion. This adaptation includes the reduction in the length of the stylopodium and zeugopodium and an increase in the number of elements in the autopodium’s central rays.

Novel tetragonal matrix Ba0.5Gd0.5-xNaxF2.5-x, where x = 0.05, doped by Yb3+, Ho3+, Er3+, was synthesized by molten salt synthesis (MSS) from nitrate flux. XRD data show that tetragonal phase with a = 4.122(1) Å, c = 17.672(1) Å is stable in argon atmosphere up to 960 °C. Luminescence spectra recorded in 500-900 nm and 1050-1700 nm upon 974 nm pumping demonstrated the characteristic luminescence at 1550 nm (4I13/2 → 4I15/2) for Er3+ and 1150 nm (5I6 → 5I8) for Ho3+. The relative thermal sensitivity (Sr) at 296-316 K were 0.3 %*K-1 and 5.5%*К-1 in shortwave infrared (SWIR) and visible range, respectively. Synthesized luminophores can be used as dual-range optical temperature sensors, which simultaneously operating in visible and SWIR ranges.

It is shown that a Mueller quaternion can be formulated as a quaternion with matrix coefficients, and this Mueller quaternion transforms the Stokes quaternion for depolarizing process as well as for nondepolarizing process. Mueller quaternion keeps track of the phase acquired by the Stokes quaternion and, in general, quaternion states of optical media comprises all properties of Jones, Mueller-Jones and Mueller matrices.

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results (e.g., classical chaos) by means a pure-state density matrix.

Portfolio weights solely based on risk avoid estimation error from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation and the Exponential Weighted Moving Average target matrices. By an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance, Inverse Volatility, Equal-risk-contribution and Maximum Diversification portfolios. We find out that the Identity and Variance Identity have very good statistical properties, being well-conditioned also in high-dimensional dataset. In addition, the these two models are the best target towards to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps reducing weights misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification, hence they benefit less from shrinkage.

This article is devoted to the results of in-depth analysis of the system of binary-oppositional structures in DNA n-plet alphabets and their algebraic-matrix representations. These results show that the molecular complementary replication of DNA strands is accompanied by the presence of an algebraic version of the principle "like begets like" in matrix representations of DNA alphabets having internal structures. This algebraic version is based on binary-oppositional structures in the genetic molecular system, which can be represented by binary numbers and corresponding matrices of DNA alphabets. The received results allow thinking that the phenomenon "like begets like" (or a complementary replication in a wide sense) is systemic in the genetic organization and is connected with algebraic features of biological organization. Correspondingly, the biological principle "like begets like" can be additionally modeled by algebraic-matrix methods and approaches. Such algebra-matrix modeling of the genetic coding system gives new ways for studying and understanding the key role of the named principle in genetic and other inherited physiological complexes. On this way, the author discovered general rules of stochastic organization of information binary sequences of genomic DNAs of eukaryotes and prokaryotes. The presented rules are connected with information dichotomies of probabilities and corresponding fractal-like trees of probabilities, which fundamentally differ from constructional dichotomies in biological bodies. The received phenomenological data and rules lead to new biological ideas.

The extracellular matrix (ECM) is a ubiquitous member of the body and is key to the maintenance of tissues and organs integrity. Initially thought to be a by-stander in many cellular processes, the extracellular matrix has been shown to have diverse components that regulate and activate many cellular processes and ultimately influence cell phenotype. Importantly, the ECM composition, architecture, and stiffness/elasticity influence cellular phenotypes. Under normal conditions and during development, the synthesized ECM is constantly undergoing degradation and remodeling processes via the action of matrix proteases that maintain tissue homeostasis. In many pathological conditions including fibrosis and cancer, the ECM synthesis, remodeling, and degradation is dysregulated causing its integrity to be altered. Both physical and chemical cues from the ECM are sensed via receptors including integrins and play key roles in driving cellular proliferation and differentiation and in various disease progression such as cancers. Advances in ‘omics’ technologies have seen an increase in studies focussing on bi-directional cell-matrix interactions and here we highlight emerging knowledge on the role played by the ECM during normal development and in pathological conditions. This review summarizes current ECM-targeted-therapies that can modify tumor ECM to overcome drug resistance and better cancer treatment.

By constructing a static map, the library robot can navigate and access documents autonomously, which greatly improves efficiency; however, for libraries where shelves can be moved, map changes do not allow for direct navigation, and also sensors such as radar and camera are relatively expensive, so we propose a low-cost navigation algorithm based on real-time ranging data and map matrices, and designed a mobile archive access robot. In order to obtain real-time distance data, nine near/long range sensors were mounted on the chassis and a composite digital filtering algorithm was designed based on different moving area characteristics; then the access task matrix and map matrix were designed based on the archive access task and the location characteristics of the archive shelf placement, the robot can rely on the range data to update the map matrix during the moving process, complete its own positioning, and use the task matrix The robot can use the task matrix to complete autonomous navigation and access to multiple files. Experiments show that the filtered positioning accuracy can reach 1cm, while the robot can move to the target shelf autonomously, which is more practical and less costly.

The paper summarizes in a step by step ‘recipe’ format a model of developing new ideas (Ideation) that can be used to form a new venture or develop a new product. The proposed ‘recipes’ are widely used and can be applied in tandem with other prevalently available models or tools. The intention of the paper is also to serve as a resource for entrepreneurs and innovators, and the links and references munificently used in the paper are serving this purpose. The author has used the outline and the tools described here in numerous Ideation classes taught for over a decade in several countries around the world. The paper’s intention is not to conduct a systematic review on the subject of new venture creation or propose new research agenda (for that, see for example Shepherd et al., 2021). The purpose is to provide an effective and efficient set of tools, models and techniques that can assist the entrepreneur in her journey to create and achieve her dreams. One such tool is the matrix of Reasonings-Outcomes introduced here for the first time.

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

Abstract: Congenital cytomegalovirus (cCMV) infection poses significant risks to fetal development, particularly affecting the nervous system. This study reports a fetal autopsy case, examining cCMV infection and focusing on CMV DNA measurements in various fetal organs before formalin fixation, a novel approach for comprehensive CMV DNA evaluations in fetal organs affected by cCMV. A 20-week-old male fetus was diagnosed with cCMV following the detection of CMV DNA in ascites obtained via abdominocentesis in utero. After termination of pregnancy, multiple organs of the fetus, including the cerebrum, thyroid gland, heart, lungs, liver, spleen, kidneys, and adrenal glands, were extracted and examined for CMV DNA loads using real-time polymerase chain reaction. Histopathological examination involved hematoxylin-eosin and CMV-specific immunostaining. A correlation was found between CMV DNA loads and pathology, with higher CMV-infected cell numbers observed in organs positively identified with both staining methods, exhibiting CMV DNA levels of ≥1.0 × 104 copies/mL, compared to those detected solely by CMV-specific immunostaining, where CMV DNA levels ranged from 1.0 x 103 to 1.0 x 104 copies/mL. These results highlight a quantifiable relationship between organ infection extent and CMV DNA concentration, providing insights into cCMV pathogenesis and potentially informing future diagnostic and therapeutic strategies for cCMV infection.

This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, particularly susceptible to instability. To address this challenge, we combine a data preprocessing technique based on the Hilbert transformation of returns with RMT to refine the accuracy and robustness of correlation matrix estimation. By contrasting empirical correlations with those derived from random matrices, we uncover non-random properties and underlying relationships within financial data. We then utilize this methodology to construct the correlation network dependence structure used in portfolio optimization. The empirical analysis presented in this paper validates the effectiveness of RMT in enhancing portfolio diversification and risk management strategies. This research contributes by offering investors and portfolio managers with methodological insights to construct portfolios that are more stable, robust, and diversified. At the same time, it advances our comprehension of the intricate statistical principles underlying multivariate financial data.

Matrix-variate Gaussian type or Wishart type distributions in the real domain are widely used in the literature. When the exponential trace has an arbitrary power and when a factor involving a determinant enters into the model or a matrix-variate gamma type or Wishart type model with exponential trace having an arbitrary power, is extremely difficult to handle. Evaluation of the normalizing constant in such a model is the most important part because when studying the properties of such a model, the method used in the evaluation of the normalizing constant will be the relevant steps in all the computations involved. One such model with a factor involving a trace and the exponential trace having an arbitrary power, in the real domain, is known in the literature as Kotz' model. No explicit evaluation of the normalizing constant in the model involving trace with an exponent and determinant with an exponent entering into the model and at the same time the exponential trace having an arbitrary exponent seems to be available in the literature. The normalizing constant widely used in the literature and interpreted as the normalizing constant in the general model and refers to as a Kotz' model does not seem to be correct. Corresponding model in the complex domain, with the correct normalizing constant, does not seem to be available in the literature. One of the main contributions in this paper is the matrix-variate distributions in the complex domain belonging to Gaussian type, gamma type, type-1 and type-2 beta type when the exponential trace has an arbitrary power. All these models are believed to be new. A second main contribution is the explicit evaluation of the the normalizing constants, in the real and complex domains especially in the complex domain, in a matrix-variate model involving a determinant and a trace as multiplicative factors and at the same time the exponential trace having an arbitrary power. Another main contribution is the introduction of matrix-variate models with exponential trace having an arbitrary exponent, in the categories of type-1 beta, type-2 beta and gamma distributions or in the family of Mathai's pathway models [1], both in the real and complex domains. Another new contribution is the logistic-based extensions of models in the real and complex domains with exponential trace having an arbitrary exponent and connecting to extended zeta functions introduced by this author recently. Some properties of such models are indicated but not derived in detail in order to limit the size of the paper. The techniques and steps used at various stages in this paper will be highly useful for people working in multivariate statistical analysis as well as people applying such models in engineering problems, communication theory, quantum physics and related areas, apart from statistical applications.

Matrix metalloproteinases are involved in extracellular matrix remodeling through the degradation of extracellular matrix components and are involved in the inflammatory response by regulating the activities of TNF-alpha and IL-1beta, which are pro-inflammatory cytokines, in addition to extracellular matrix components. Since the regulation of inflammatory response and changes in the extracellular matrix by MMPs are related to the development of various diseases including lung and cardiovascular diseases, many studies have been conducted on the role of MMPs in pathogenesis. In addition, various studies have demonstrated that MMPs are involved in the pathogenesis of infectious diseases by regulating the expression and activity of MMPs by infection with pathogens. In this review, we discuss the role of MMPs in infectious diseases and the role of MMPs in inflammatory responses and present their potential as therapeutic targets in infectious diseases.

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science using the Dirac-Fock formalism. A direct comparison of the Wigner-Smith-Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the Relativistic Random Phase Approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as Argon, show negligible relativistic effects, while heavier elements, such a Krypton and Xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notable close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner-Smith-Eisenbud delay and a universal continuum--continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

The matrix converter converts the input line voltage into a variable voltage with an unrestricted output frequency without using an intermediate circuit, dc link circuit. A pure sine in and pure sine out is the unique feature of the matrix converter. This research paper also analyzes the basic operating principle and the simulation modeling of the direct matrix converter, which is controlled by the Space Vector Pulse Width Modulation technique by using the software which is known as MATLAB/Simulink. The most desirable features in the power frequency changes can be fulfilled by using the matrix converters, and this is the reason for the tremendous interest in the topology. Since the power electronic circuits which is known as the motor drives are used to operate the AC motors at the frequencies other than that of the supply.

An oil and vinegar scheme is a signature scheme based on multivariate quadratic polynomials over finite fields. The system of polynomials contains $n$ variables, divided into two groups: $v$ vinegar variables and $o$ oil variables. The scheme is called balanced (OV) or unbalanced (UOV), depending on whether $v = 0$ or not, respectively. These schemes are very fast and require modest computational resources, which make them ideal for low-cost devices such as smart cards. However, the OV scheme has been already proven to be insecure and the UOV scheme has been proven to be very vulnerable for many parameter choices. In this paper, we propose a new multivariate public key signature whose central map consists of a set of polynomials obtained from the multiplication of block matrices. Our construction is motivated by the design of the Simple Matrix Scheme for Encryption and the UOV scheme. We show that it is secure against the Separation Method, which can be used to attack the UOV scheme, and against the Rank Attack, which is one of the deadliest attacks against multivariate public-key cryptosystems. Some theoretical results on matrices with polynomial entries are also given, to support the construction of the scheme.

This paper attempts to extend the Riemann Zeta function of a complex number to a function of a matrix and/or a tensor $A$, namely $$\zeta (A)=\sum _{n=1}^{\infty} \frac{1}{n^{A}}= \sum _{n=1}^{\infty} \sum_{k=1}^n\lambda_k A^k$$ and inverse $$A=\sum _{n=1}^{\infty} \sum_{k=1}^n \mu(n)\lambda_k \zeta(A^k)$$ where $\mu(n)$ is the M\"obius function, $A$ is a complex matrix or tensor with any order, and $\lambda_k$ is eigenvalue of the matri/tensor $A$. This kind of calculations on the Riemann Zeta function has never been seen in the literature. Some examples are provided.

Epoxy matrix composites reinforced with high-performance fibers such as carbon, Kevlar, and glass, exhibit excellent specific stiffness and strength in many mechanical applications. However, these composites are disappointingly non-recyclable and are usually disposed of in landfill sites, with no realistic prospect for biodegradation in reasonable time. In contrast, moldable composites with carbonized elastomeric matrices developed in the last decades possess attractive mechanical properties in final net-shape products and can also be incinerated or recycled. Many carbon and inorganic fillers have recently been evaluated to adjust the properties of carbonized elastomeric composites. Renewable organic fillers such as human or animal hair offer an attractive fibrous material with substantial potential for reinforcing composites with elastomeric matrices. Samples of unidirectional fiber composites (with hair volume fraction up to 7 %) and quasi-isotropic short fiber composites (with hair volume fraction up to 20 %) of human hair-reinforced nitrile butadiene rubbers (HH-NBR) were produced in the peroxide-cured and carbonized states. The samples were characterized using SEM, Raman spectroscopy and photoacoustic microscopy. Mechanical tests were performed in tension using a miniature universal testing machine. The expected effect of fiber reinforcement on the overall mechanical performance has been demonstrated for both cured and carbonized composites. Considerable enhancement of the elastic modulus (up to 10 times), ultimate tensile strength (up to 3 times) and damage tolerance was achieved. The evidence of satisfactory interfacial bonding between hair and rubber was confirmed by SEM imaging of fracture surfaces. The suitability of photoacoustic microscopy was assessed for 3D reconstruction of the fiber sub-system spatial distribution and non-destructive testing.

(1) Background: Breast cancer is a frequent heterogeneous disorder diagnosed in woman and is a high cause of mortality of them in reason to rapid metastasis and disease recurrence. Ferroptosis can inhibit breast cancer cell growth, improve the sensitivity of chemotherapy and radiotherapy and inhibit distant metastases so potentially acts on tumor micro-environment; (2) Methods: Ferroptosis/Extracellular matrix remodeling literature text-mining results were integrated in breast cancer transcriptome cohort according their distant relapse free survival (DRFS) under adjuvant therapy (anthracyclin+taxanes) and also in MDA-MB-231 transcriptome functional experiments with ferroptosis activations (GSE173905); (3) Results: Ferroptosis/Extracellular matrix remodeling text-mining identified 910 associated genes in at list 10 articles. Univariate Cox analyses censored on breast cancer (GSE25066) selected 252 individual significant genes and 171 of them found with an adverse expression. Functional enrichment of these 171 adverse genes predicted basal breast cancer signatures. By text-mining some ferroptosis significant adverse selected genes shared citations in domain of ECM remodeling such as: TNF, IL6, SET, CDKN2A, EGFR, HMGB1, KRAS, MET, LCN2, HIF1A, TLR4. A molecular score based on expression the eleven genes was found predictive of worst prognosis breast cancer at univariate level: basal subtype, short DRFS, high grade values 3 and 4, estrogen and progesterone receptors negative and nodal stages 2 and 3. This eleven gene signature was validated as regulated by ferroptosis inductors (erastin and RSL3) in triple negative breast cancer cellular model MDA-MB-231.; (4) Conclusions: Crosstalk between ECM remodeling-Ferroptosis functionalities allowed to define a molecular score which have been characterized as an independent adverse parameter in prognosis of breast cancer patients. Gene signature of this molecular score have been validated to be regulated by erastin/RSL3 ferroptosis activators. This molecular score could be promising to evaluate ECM impact of ferroptosis target therapies in breast cancer.

This paper seeks to optimize the mechanical and durability properties of ultra-high performance concrete (UHPC). To meet this objective, concrete specimens were manufactured by using 1,100 kg/m3 of binder, water/binder ratio 0.20, silica sand and last generation of superplasticizer. Silica fume, metakaolin and two types of nano silica were used for improving the performances of the concrete. Additional mixtures included 13mm long OL steel fibers. Compressive strength, electrical resistivity, mercury intrusion porosimetry tests and differential and thermogravimetric thermal analysis were carried out. The binary combination of nano silica and metakaolin, and the ternary combination of nano silica with metakaolin and silica fume, led to the best performances of the UHPC, both mechanical and durable performances.

A complex square matrix $A$ is said to be Hermitian if $A= A^{\ast}$, the conjugate transpose of $A$. The topic of the present note is concerned with the characterization of Hermitian matrix. In this note, the we show that each of the two triple matrix product equalities $AA^{\ast}A = A^{\ast}AA^{\ast}$ and $A^3 = AA^{\ast}A$ implies that $A$ is Hermitian by means of decompositions and determinants of matrices, which are named the two-sided removal and cancellation laws associated with Hermitian matrix, respectively. We also present several general removal and cancellation laws as the extensions of the preceding two facts about Hermitian matrix.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

In this paper, we introduce ResNetMF, a groundbreaking approach that harnesses the power of residual network matrix factorization to revolutionize recommendation systems. ResNetMF integrates residual networks, renowned for their ability to capture intricate patterns and features, with matrix factorization techniques that excel in modelling user-item interactions. This fusion presents a novel solution that surpasses the limitations of traditional recommendation systems. Through comprehensive experimentation and evaluation of diverse datasets, ResNetMF demonstrates remarkable enhancements in recommendation accuracy and efficiency. By effectively capturing both linear and nonlinear relationships in user-item interactions, ResNetMF provides superior recommendation quality. The outcomes from experiments unequivocally highlight the superiority of ResNetMF over existing state-of-the-art recommendation approaches, thereby validating its innovative nature and underscoring its potential to shape the future of recommendation systems. Through the integration of the deep residual network, ResNetMF approach facilitates the training of neural networks, enabling them to explore the underlying data layers more comprehensively. Extensive experimentation and evaluation across various datasets provide compelling evidence for the superiority of ResNetMF. Moreover, the proposed method utilized natural language processing (NLP) techniques for targeted information dissemination in recommendation systems, emphasizing the importance of personalized and relevant recommendations for user satisfaction and engagement.

There is need to address the challenges of organ shortage, through development of tissues and organs with alternatives to those of the allograft-kind. This illustrates the quest behind novel biofabrication strategies such as 3D bio-printing, which is necessary to create artificial multi-cellular tissues/organs. Several findings have been reported in this review. First, the role of ECM components in tissue regenerative medicine is presented. Different ECM components such as collagen, gelatin, elastin, fibronectin, laminins and glycosaminoglycans are concisely examined for their tissue regenerative medicine applications. Next, current state of research on extrusion-based 3D bio-printing techniques and their limitations are reviewed. For example, we show that cell viability is still a challenge with extrusion, while the use of natural polymers such as collagen in improving composites’ mechanical properties is limited. Lastly, we examine unresolved research questions necessary to advance the present state of research in the field.

This article shows how to establish expansion formulas for calculating the mixed operations $(A^{\dag})^{\#}$, $(A^{\#})^{\dag}$, $((A^{\dag})^{\#})^{\dag}$, $((A^{\#})^{\dag})^{\#}$, $\ldots$ of generalized inverses, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of a matrix and $(\cdot)^{\#}$ denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above mixed operations, and derives necessary and sufficient conditions for them to hold.

In order to meet the diversified rehabilitation needs of people, it is necessary to design a product for active rehabilitation of patients. Existing rehabilitation chairs use intelligent massage, which can cause problems such as large massage area, inability to local massage, large chair size, and inability to meet the continuous use of the damaged parts. In this paper, modular design method and multi-layer evaluation method are used to solve the problems related to rehabilitation chairs. The authors use the questionnaire survey method and the functional technology matrix method to determine the functional requirements of the rehabilitation chair, and then use the multilevel evaluation methods, including the AHP method, entropy weight method main and grey correlation analysis, to optimize the functional solutions of the rehabilitation chair, and finally obtain a chair for the rehabilitation of patients with upper and lower limb disorders. Problems such as generalisation of rehabilitation scope and non-durable use of components were solved, and the purpose of active exercise was achieved. This study verifies that the use of multilevel decision evaluation method can effectively improve the efficiency of programme decision-making, and provides theoretical and practical basis for the design of similar products.

Uterine fibroid (UF) is a tumour in some parts of the uterus, which introduces health challenges or death due to failed surgery among women globally. This study was designed to ascertain the involvement of micro-nutrients, inflammation, and antioxidant enzymes in the UF development to gain further insights and provide a strategy for managing the disease. One hundred ninety reproductive-aged women were recruited and classified equally into case and control subjects. The supernatant obtained from excised tissues from the fibroid and the normal samples from the adjacent myometrium were assessed for the selected biochemical parameters with standard methods. The levels of vitamin A and sodium between 26-35 years; vitamins D, E, zinc, and selenium between 46-55 years; and vitamin E at 56 years and above significantly decreased (p&lt;0.05). Interleukin-2 (IL-2) level significantly increased (P &lt; 0.05) among the case between 36-45 years. An increase in the activity of glutathione-s-transferase and the reduction in glutathione peroxidase activity and vitamin A level in the uterus between 26-45 years were the most pronounced significant findings (p&lt;0.05) recorded. Prolonged vitamin A deficiency coupled with excess sodium salts facilitating inflammation induced by IL-2 are critical factors for UF development.

Computation of Discrete Fourier Transform (DFT) is a challenging task. Especially, on computational machines/embedded systems where resources are limited. The importance of Fourier Transform (FT) cannot be denied in the field of signal processing. This paper proposes a technique that can compute Discrete Fourier Transforms for a matrice or vector with the help of matrix multiplication. Moreover, this paper discusses the trivial methods used for computation of DFT along with methods based on matrix multiplication used to compute discrete Fourier Transform in addition to the shortcomings. The proposed method can help in the calculation of a Discrete Fourier Transformation matrix by truncation of values from the proposed generic method which can help in computing DFT of varying lengths of vectors. On legacy computing machines and programming environments, having support for matrix multiplication, the proposed methodology can be implemented.

Tenascin C (TNC) is an element of the extracellular matrix (ECM) of various tissues, including the skin, and is involved in modulating ECM integrity and cell physiology. Although skin aging is apparently associated with changes in the ECM, little is known about the role of TNC in skin aging. Here we found that Tnc mRNA level was significantly reduced in the skin tissues of aged mice compared with young mice, consistent with reduced TNC protein expression in aged human skin. TNC-large (TNC-L; 330-kDa) and -small (TNC-S; 240-kDa) polypeptides were observed in conditional media from primary dermal fibroblasts. Both recombinant TNC polypeptides, corresponding to TNC-L and TNC-S, increased the expression of type I collagen and reduced the expression of matrix metalloproteinase-1 in fibroblasts. Treatment of fibroblasts with a recombinant TNC polypeptide, corresponding to TNC-L, induced phosphorylation of SMAD2 and SMAD3. TNC increased the level of TGF-β1 mRNA and upregulated the expression of type I collagen by activating the TGF-β signaling pathway. In addition, TNC also promoted the expression of type I collagen in fibroblasts embedded in a three-dimensional collagen matrix. Our findings suggest that TNC contributes to the integrity of ECM in young skin and to prevention of skin aging.