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.

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 This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

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.

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.

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

The electroencephalogram (EEG) is a record of brain activity. Brain Computer Interface (BCI) technology formed by the EEG signal has become one of the hotspots at present. How to extract the feature signal of EEG is the most basic research of BCI technology. In this paper, A new method of recognizing fatigue, conscious, concentrated state of human brain is proposed by the combination of discrete wavelet transform and the neural network based on EEG signal. First of all, the law signal is preprocessed by the wavelet denoising method because the law EEG signal contains a large number of high frequency noise, which is decomposed into multi-layer high frequency signal and low frequency signal. thus, δ wave, θ wave, α wave, β wave are obtained by the wavelet transform. And then, frequency band energy of the different wave is regards as the feature signal of EEG. In the experiment, the feature signal is classified by radial basic function (RBF) and annealed chaotic competitive learning network (ACCLN). RBF and ACCLN networks are trained with 500 sets of sample data and are tested by 100 sets of samples in different mental states. The experimental results show that the average accuracy of RBF network under three conditions are 88.75%, 88.25%, 88.5%, respectively, and the correct rate of ACCLN network is 97%, 98%, 98%, respectively.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

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.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

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.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

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.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

This paperfocusesontheoscillatorypropertiesofthesemi-canonicalnonlineardelaydifferential equation ofthird-order (δ2(t)(δ1(t)ζ′(t))′)′ + η(t)ζα(τ(t))= 0, t ≥ t0, under theconditions ∞t01δ2(t)dt = ∞ andZ ∞t01δ1(t)dt < ∞. Using the new canonical transform method, we transformed the studied equation into a canonical type equation and then we find the conditions for the oscillation of the studied equation from the canonical equations. The obtained results are new and complement to the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

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.

The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration experiments.

Elbow dislocation and instability present significant clinical challenges, necessitating a thorough understanding of the underlying bio-mechanical mechanisms. In this study, a quasi-static three-dimensional finite element model of the human elbow joint is developed to investigate stress distribution and stages of dislocation in the human elbow under various loading conditions. The model simulates the elbow joint in different degrees of flexion (30°, 45°, 60°, and 90°) and forearm positions (pronation and supination), providing detailed insights into the progression of dislocation. Significant findings include the identification of high stress concentrations on the humerus at 90° flexion and on the radial and coronoid processes at 30°, 45°, and 60° flexion. Three reproducible stages of dislocation were observed, particularly in flexed positions with forearm pronation or supination. These stages align with experimental observations and highlight the initial occurrence of bony failures, such as radial head and ulnar coronoid fractures, preceding soft tissue tears. Clinically, the study underscores that early-stage low-impact posterior elbow dislocations retain enough stability to be managed with closed reduction and early mobilization. However, as dislocations progress, significant damage to the medial and lateral collateral ligaments is expected, necessitating more invasive treatments. This research provides valuable bio-mechanical insights into elbow dislocation, aiding in the development of improved treatment strategies and enhancing patient outcomes through precise and timely clinical interventions. The validated FEM serves as a powerful tool for pre-surgical planning offering a comprehensive understanding of elbow joint mechanics.

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

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.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

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 Finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990’s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second order velocity structure function.

One of the relevant goals in forging technologies is simplifying the existing process and developing new processes that can retain the original or very close to the original dimensions and billet shape after the end of the deformation cycle. This study attempts to develop a forging equipment design that provides alternating cyclic loading; the alternate cyclic forging (ACF) method is proposed. To preliminary evaluate the ACF and study the plastic deformation behavior, numerical simulation via finite element modeling (FEM) was conducted using DEFORM-3D. The main attention was paid to the metal flow characteristics, effective strain and stress distribution, and the forging load. The ACF results in non-uniform metal flow with the formation of diagonal and vortex flows were demonstrated. Maximum effective strains and stresses zones are localized at two points of the billet contact with the surface of the tooling container and at two points of the interface between the punches. It was also assumed that reducing the contact area between the punch and the billet using separate semi-cylindrical punches can reduce the forging load. Preliminary finite element analysis (FEA) results of the proposed process after four successive steps of the deformation cycle confirmed the feasibility of its general implementation.

Currently, in some domestic and foreign mines, the backfill drilling pipeline experience a rupture phenomenon even when the wear degree is low. This results in a delay in production due to the filling becoming 'sick'. This paper presents, for the first time, the damage mechanism from a mechanical perspective and re-derives the anti-extrusion strength model of the backfill drilling pipeline. We investigate the influence of law on the anti-extrusion strength of pipelines from the perspective of stratum and cement ring. We then verify the theoretical and simulation results through engineering examples. The results demonstrate that the Mises stress criterion is a suitable modification principle for the anti-extrusion strength model of the backfill drilling pipeline. The anti-extrusion strength of the pipeline is related to the elastic modulus and Poisson's ratio of the stratum, and the thickness of the cement ring. It is negatively affected by the depth of the stratum. For hard strata, a cement ring with a smaller elastic modulus is suitable, while for soft stratum, a cement ring with a larger elastic modulus is recommended. When the missing angle of the cement ring is less than 60°, the stress concentration factor increases up to 2.2. The stress unloading capacity of the cement ring ranges from 32.7% to 37.8%, and optimal performance of the cement ring is achieved when it has high strength and low rigidity. The backfill filling pipeline of a copper mine abroad was destroyed due to external extrusion force exceeding its anti-extrusion strength value. The modified pipeline anti-extrusion strength model is 18.2% higher than the casing API strength value. This finding can inform the design of the backfill filling pipeline for China's kilometer-deep wells in the future.

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.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

Concrete is more stable than filler as a false roof in a downward approach type infill quarry, but the mechanical model of a concrete false roof is not clear. As a result, there has been limited application. Therefore, it is necessary to establish the mechanical model of a concrete artificial false roof to enhance the stability of the downward approach infill quarry. This paper combines theoretical analysis, model derivation, finite element analysis and field application methods. Firstly, the basic assumptions of thin plate theory and elasticity mechanics are used as the premise to establish the differential equations of the deflection curve of the concrete thin plate false roof. Then, the three types of bending moment generation of the concrete thin plate false roof are explored. Secondly, the relationship between the location of dangerous surface and dangerous point in hard-supported weak-slab structure and soft-supported weak-slab structure is analyzed, and the type of uniform load and calculation model of concrete thin-slab false roof are improved. Finally, according to the established mechanical model of thin slab false roof, finite element analysis and field application were carried out. The results show that there are three types of deflection curve differential equations in the concrete thin slab false roof perpendicular to the strike, and three extreme points exist in the middle section of the thin slab and on both sides of the surrounding rock. The hazardous surface of the hard-supported weak-slab structure is present at the intersection of the encircling rock and the thin-slab fake ceiling, with the perilous point situated on the top of this surface. The hazardous surface of the soft-supported weak-slab structure can be found in the centre section of the thin-slab fake ceiling, with the perilous point being located at the bottom of this surface. Moreover, the damage mode for both structures is that of maximum tensile stress damage. Upon conducting a finite element analysis, the results indicate that the concrete's maximum tensile stress is significantly high.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

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 many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

Recently Candida auris has emerged as a multi-resistant fungal pathogen, with a significant clinical impact, and has become a critical issue in WHO fungal priority list, due to its unique ability to persist for long time on human skin and hospital environments. It is therefore fundamental to reinforce hospital surveillance protocols to limit nosocomial outbreaks. The study purpose was the Fourier-Transform Infrared Spectroscopy (FT-IR) application to investigate the phylogenetic relationships between isolated strains within the C. auris outbreak at the university Intensive Care Unit of a Tertiary University hospital in Turin (Italy). In order to calculate a clustering cut-off, intra- and inter-isolates distance values were analysed. Data showed the presence of a major cluster Alfa and a minor cluster Beta with a defined C. auris clustering cut-off. The results were validated by an external C. auris strain and Principal Component and Linear Discriminant Analysis. The application of FT-IR technology had allowed to obtain important information about the phylogenetic relationships between the analysed strains, defining for the first time a “not WGS-based” clustering cut-off with a statistical-mathematical approach. FT-IR could represent a valid alternative to molecular methods for rapid and cost saving typing of C. auris strains with important clinical implications.

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.

The development of the finite element method (FEM) combined block polynomial interpolation with the concepts of finite difference formats and the variation principle. Because of this combination, FEM overcomes the shortcomings of traditional variation methods while maintaining the benefits of current variation methods and the flexibility of the finite difference method. As a result, FEM is an advancement above the traditional variation methods. The aim of the study is to experimentally determine the thermal behavior of two stomatognathic systems, one control and the other presenting orthodontic treatment by means of a fixed metallic orthodontic appliance, both being subjected to several thermal regimes. In order to carry out this experimental study, we examined the case of a female subject, who was diagnosed with Angle class I malocclusion. The patient underwent a bimaxillary CBCT investigation before initiating the orthodontic treatment. A three-dimensional model with fully closed surfaces was obtained by using the InVesalius and Geomagic programs. Like the tissues examined in the patient, bracket and tube-like components, as well as orthodontic wires, can be included to these models. Once it is finished and geometrically accurate, the model is exported to a FEM-using program, such as Ansys Workbench. The intention was to study the behavior of two stomatognathic systems (with and without a fixed metallic orthodontic appliance) subjected to very hot food (70 ⁰C) and very cold food (-18 ⁰C). From the analysis of the obtained data, it was concluded that, following the simulations carried out in the presence of the fixed metallic orthodontic appliance, significantly higher temperatures were generated in the dental pulp.

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.

The paper presents the problem of damage detection in steel girders. Static displacements at the selected point of the structure play the role of measured variables. Structural response signal decomposition is performed according to the Mallat pyramid algorithm, which is used to perform the discrete wavelet transform (DWT). This procedure allows us to quite well determine the location of structural damage. The geometry and the placement of any defective part of the structure may have a random character. It can be assumed that the random processes occurring in the broadly understood structure mechanics are Gaussian in nature. The first four probabilistic moments are estimated using three approaches independent: semi-analytical (SAM), perturbative (SPT), and Monte-Carlo simulations (MCS). The semi-analytical random approach seems to be the most optimal due to the necessary computation time. The incorporation of the mathematical stochastic apparatus into the classical (deterministic) analysis of the statics of the structure makes it possible to estimate the reliability measures of the analyzed girder.

In this paper, we study the semilinear pseudo-parabolic equations $\displaystyle u_{t} - \triangle_{\mathbb{B}}u - \triangle_{\mathbb{B}}u_{t} = \left|u\right|^{p-1}u$ on a manifold with conical singularity, where $\triangle _{\mathbb{B}}$ is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary $x_{1} = 0$. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence and nonexistence of global weak solution: for the low initial energy $J(u_{0})<d$, the solution is global in time with $I(u_{0}) >0$ or $\displaystyle\Vert \nabla_{\mathbb{B}}u_{0}\Vert_{L_{2}^{\frac{n}{2}}(\mathbb{B})} = 0$ and blows up in finite time with $I(u_{0}) < 0$; for the critical initial energy $J(u_{0}) = d$, the solution is global in time with $I(u_{0}) \geq0$ and blows up in finite time with $I(u_{0}) < 0$. The decay estimate of the energy functional for the global solution and the estimates of the lifespan of local solution are also given.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

Every finite simple group P can be generated by two of its elements. Pairs of generators forP are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P . It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that a wealth of standard graphs and finite geometries G - such as near polygons and their generalizations - are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurationsdefined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G's have a contextuality parameterclose to its maximal value 1.

In this work we present a novel steganography algorithm, based on Fractal Transform domain, combined with the principles of Cryptography. The proposed method uses a private key, which will indicate which segment of the image will be taken and encoded with the Fractal Transform, to then insert the secret bits in the transformed coefficients, thus generating the stego image.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Bone drilling is a common procedure used to create pilot holes for inserting screws to secure implants for fracture fixation. However, dis process can increase bone temperature, teh excessive heat can lead to cell death and thermal osteonecrosis, potentially causing early fixation failure or complications. We conducted a three-dimensional dynamic elastoplastic finite element model to evaluate teh propagation and distribution of heat during bone drilling and assess teh thermally TEMPeffected zone (TAZ) dat may lead to thermal necrosis. dis model investigates teh parameters influencing bone temperature during bone drilling, including drill diameter, rotational speed, feed force, and predrilled hole. Teh results indicate dat our FE model is sufficiently accurate in predicting teh temperature rise TEMPeffect during bone drilling. Teh maximum temperature decreases exponentially wif radial distance. When teh feed forces are 40 and 60 N, teh maximum temperature does not exceed 45 °C. However, wif feed forces of 10 and 20 N, both teh maximum temperature exceeds 45 °C wifin a radial distance of 0.2 mm, indicating a high-risk zone for potential thermal osteonecrosis. Wif teh two-stage drilling procedure, where a 2.5 mm pilot hole is pre-drilled, teh maximum temperature can be reduced by 14 °C. dis suggests dat higher feed force and rotational speed and/or using a two-stage drilling process could mitigate bone temperature elevation and reduce teh risk of thermal osteonecrosis during bone drilling.

Background/Objectives: Dental implants have become a cornerstone of restorative dentistry, providing a long-lasting method for tooth replacement. The level of osseointegration has a big impact on the biomechanical stability at the bone-implant contact (BIC), which determines how long these implants will work. However, the exact consequences of changing osseointegration levels on different implant designs, especially in bones with variable densities, are not well known. Three short dental implants were tested in this study: BioMet 3iT3, Straumann® Standard Plus Short Regular Neck (SPS-RN), and Straumann® Standard Plus Short-Wide Neck (SPS-WN). 3D finite element analysis (FEA) was used to look at how well they worked biomechanically. This paper tests the implants at four stages of osseointegration: 25%, 50%, 75%, and 100% in both high-density (Bone Type III) and low-density (Bone Type IV) cancellous bone. It also created and examined realistic CAD models under static occlusal loading conditions to assess stress distribution and major strains at the bone-implant contact.; Results: The study discovered that as osteointegration increases, von Mises stress and principal strains go down significantly for all implant types. The SPS-WN implant had the lowest strain values, especially for bone with low density. These reductions demonstrate increased mechanical stability as the bone-implant inter-face becomes more capable of dispersing mechanical stresses, minimizing the potential for localized deformation and bone resorption.; Conclusions: The results highlight the importance of achieving optimum osseointegration to reduce mechanical stress and increase the lifespan of dental implants. The SPS-WN type implant performed better in biomechanical tests than the others, especially when bone conditions were not ideal. This makes it a great choice for clinical applications that need long-term implant success.

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.

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.

Predictive numerical models in the study of ground-borne vibrations generated by railway sys-tems have traditionally relied on the segmented approach of subsystems. In this approach, loads are individually applied, and the cumulative effect of rolling stock is obtained through superposi-tion. While this method serves to mitigate computational costs, it may not fully capture the com-plex interactions involved in ground-borne vibrations. Recent advancements in computational and software tools have enabled the development of more sophisticated vibrational pollution models. These advanced models encompass the entire dynamic system, from the rolling stock to the terrain, allowing for continuous simulations with a defined time step. Furthermore, the incorporation of computational contact tools between various ele-ments not only ensures temporal accuracy but also extends the analysis to the frequency domain. This paper explores the evolution of predictive numerical models in the context of ground-borne vibrations generated by trains on ballasted tracks. It highlights the shift from segmented models to continuous simulations, demonstrating the progressive advancement towards more comprehen-sive and accurate representations of railway-induced and generated vibrations in the track sur-roundings as an additional way of evaluate sustainability of infrastructures. In particular, this development of a numerical model from its inception aimed to expand upon ex-isting emission - prediction models by enriching the data with frequency-domain information. This approach has been driven by the aspiration to bridge the gap between numerical predictions and measured signals, striving for a higher level of accuracy in our obtained results. This model can predict the impact of a high-speed rail (HSR) vehicle passing on its own track. It possesses sufficient information in both the time and frequency domains to precisely characterize vibrations. This initiative marks a pivotal advancement, enabling us to more effectively capture the intricacies of ground-borne vibrations and their impact on the surrounding environment due to a deeper comprehension of the occurrences in the frequency domain, there's a heightened ca-pability to accurately characterize vibrations.

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.

During routine bridge maintenance, edge detection allows the partial condition of the bridge to be viewed. However, many edge detection methods often have unsatisfactory performances when dealing with images with complex backgrounds. Moreover, the processing often involves the manual selection of thresholds, which can result in repeated testing and comparisons. To address these problems in this paper, the wavelet transform modulus maxima method is used to detect the target image, and then the threshold value of the image can be determined automatically according to the OTSU method to remove the pseudo-edges. Thus, the real image edges can be detected. The results show that the information entropy and SSIM of the detection results are the highest when compared with the commonly used Canny and Laplace algorithms, which means that the detection quality is optimal. To more fully illustrate the advantages of the algorithms, images with more complex backgrounds were detected and the processing results of the algorithms in this paper are still optimal. In addition, the automatic selection of thresholds saves the operator’s effort and improves the detection efficiency. Thanks to the combined use of the above two methods, detection quality and efficiency are significantly improved, which has a good application in engineering practice.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

Modular steel buildings (MSBs) interlocking inter-module connections (IMCs) have piqued researchers’ interest. However, the existing literature has not yet studied the optimisation of its plate thicknesses. This paper, therefore, focuses on optimising interlocking (IMCs) plate thickness in (MSBs), leveraging previous experimental and numerical simulation methodologies. Various numerical models for four MSBs interlocking (IMCs) with plate thicknesses (4 mm, 6 mm, 10 mm, and 12 mm) were developed under compression loading conditions. The study’s novelty lay in its comprehensive parametric analysis, which evaluated the slip phenomenon in (MSBs) connections and introduced a slip prediction model validated against empirical data. Further innovative machine learning approach was utilised to predict slip values based on applied force through a random forest regression model trained using the 'Treebagger' function. Sensitivity analysis and comparisons with alternative methods were utilised to underscore the reliability and applicability of the findings. The results showed that 11.03 mm was the optimal plate thickness for interlocking (IMCs) in modular steel buildings, with up to 8.08% reduced material costs. Increasing plate thickness boosts its deformation resistance by up to 50.75%. ‘TreeBagger’ random forest for anomaly detection and machine learning improves slip prediction up to 7% at higher force levels.

This paper focuses on establishing boundedness properties and Parseval-Goldstein type relations for the generalized Mehler-Fock transform initially introduced by B. L. J. Braaksma and B. M. Meulenbeld (Compositio Math.,{18}(3):235-287, 1967. Also, we derive an inversion formula for this transform over Lebesgue spaces.

Abstract: The two-dimensional Fuzzy Transform was applied in image compression. The quality of the image compressed with this methodis better than that obtained using methods based on fuzzy relation equations and comparable with that of the JPEG method, with better compression execution times. In this paper we propose a variation of the method based on the two-dimensional Fuzzy Transform of image compression, in which the image is first partitioned into blocks and then each block is compressed with the higher compression rate. The advantage of this method consistsinto a greater compression of the image, guaranteeing a high quality of the reconstructed image.The results show that our method is better than the Fuzzy Transform method improving also the quality of the reconstructed image.

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

A multiscale model that enables quantitative understanding and prediction of the size effect on scattering properties of micro- and nanostructures is crucial for the design of LED surface textures optimized for high light extraction efficiency (LEE). In this paper, a hybrid process for combining full-wave finite-difference time-domain simulation and a ray-tracing technique based on a bidirectional scattering distribution function model is proposed. We apply this method to study the influence of different pattern sizes of a patterned sapphire substrate on GaN-based LED light extraction from the microscale to the nanoscale. The results show that near-wavelength–scaled patterns with strong diffraction are not expected to enhance LEE. By contrast, microscaled patterns with optical diffusion behavior have the highest LEE at a specific aspect ratio, and subwavelength-scaled patterns that have antireflection properties show marked enhancement of LEE for a wide range of aspect ratios.

Advances in machine learning (ML) and artificial intelligence (AI) are transforming the way we treat patients in ways not even imagined a few years ago. Cancer research is at the forefront of this movement. Infertility, though not a life-threatening condition, affects around 15% of couples trying for a pregnancy. Increasing availability of large datasets from various sources creates an opportunity to introduce ML and AI into infertility prevention and treatment. At present in the field of assisted reproduction, very little is done in order to prevent infertility from arising, with the main focus put on treatment when often advanced maternal age and low ovarian reserve make it very difficult to conceive. A shift from this disease-centric model to a health centric model in infertility is already taking place with more emphasis on the patient as an active participator in the process. Poor quality and incomplete data as well as biological variability remain the main limitations in the widespread and reliable implementation of AI in the field of reproductive medicine. That said, one of the areas where this technology managed to find a foothold is identification of developmentally competent embryos. More work is required however to learn about ways to improve natural conception, the detection and diagnosis of infertility, and improve assisted reproduction treatments (ART) and ultimately, develop clinically useful algorithms able to adjust treatment regimens in order to assure a successful outcome of either fertility preservation or infertility treatment. Progress in genomics, digital technologies and advances in integrative biology has had a tremendousimpact on research and clinical medicine. With the rise of ‘big data’, artificial intelligence, and the advances in molecular profiling, there is an enormous potential to transform not only scientific research progress, but also clinical decision making towards predictive, preventive, and personalized medicine. In the field of reproductive health, there is now an exciting opportunity to leverage these technologies and develop more sophisticated approaches to diagnose and treat infertility disorders. In this review, we present a comprehensive analysis and interpretation of different innovation forces that are driving the emergence of a system approach to the infertility sector. Here we discuss recent influential work and explore the limitations of the use of Machine Learning models in this rapidly developing area.

We have presented a controllable and human-readable polynomial neural network (CR-PNN) that is the first human-readable neural network. One can imagine its influence on system identification. Subsequently, we developed a relation spectrum in a medical application, which is likely to stand alongside the Fourier spectrum. However, the system analysis methodology is incomplete in contrast to signal processing methodology. Here, we presented the system filters for the first time. In this paper, we used the simulation system to verify the availability of the system analysis methodology. The system analysis methodology showed great properties in system identification and filter. The contribution of this paper is the system analysis methodology: transform method (CR-PNN), relation spectrum, and system filter design.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

Background: Good reduction of the articular surface and restoration of the congruent joint space are crucial for promoting positive outcomes in ankle fracture treatment. A good understanding of the mechanism of ankle fractures is indispensable to achieve these goals. Unfortunately, until now, the mechanism has still not been fully elucidated, particularly regarding the posterior malleolar fractures (PMFs). This study aims to provide insight into the mechanism of PMFs, thereby grasping the key to proceeding with PMFs reduction and fixation. Methods: An FE model of a normal ankle in tiptoe posture with 9 collateral ligaments was constructed from CT images. On the model, lateral malleolar fractures were made below, through, and above the syndesmosis; the medial malleolus was broken at its base; and ligaments were suppressed to simulate ligament rupture. A force of 1000 Newtons was applied on the talus head along talus axis. The posterior malleolar fragment (PMF) displacement, whether the talus impacts the posterior malleolus, and the initial mechanism displacing the PMF, were recorded. Results: A total of 15 tests were conducted. The tests, 'all collateral ligaments rupture', 'LMFB', 'LMFC+AITFL rupture', 'ATFL+CFL+PTFL rupture', 'ATTL+PTTL+TCL rupture', 'MMF', and 'MMF+AITFL rupture', presented significant PMF displacement. In tests 'MMF' and 'ATTL+PTTL+TCL rupture', the talus hit the medial edge of the PMF; but in tests 'ATFL+CFL+PTFL rupture' and 'all collateral ligaments rupture', the talus impacted the center part of the PMF. Except tests 'all collateral ligaments rupture' and 'ATFL+CFL+PTFL rupture', where PMF displacement was initially caused by talus impact, the other tests demonstrated PMF displaced following PITFL drag. Conclusions: This research discovered that rotation is the initial and major mechanism causing PMF displacement. The subsequent impact of the talus on the posterior malleolus may be the reason for large/blocky PMF. The talus impacting the posterior malleolus is always combined with talus rotation. Without the medial ankle structure being broken, big/blocky PMF may not occur. These findings suggest that, in clinical practice, reconstructing both the medial and lateral ankle structures is critical for achieving ankle stability, and this procedure even takes precedence over posterior malleolar fracture fixation itself.

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.

In this paper, a technique of image watermarking using multiple images as watermarks is presented. The technique is based on transform domain functions including discrete wavelet transform (DWT), discrete cosine transform (DCT) and singular value decomposition (SVD) with an image as the host signal i.e. the watermarks will be used as proofs of the authenticity of the host image. The technique is executed by performing multilevel DWT followed by applying DCT and SVD to both the host and watermark. Multiple watermarks are used for the insurance of better security level. The scheme is immune to common image processing operations & some attacks and exhibits PSNR of 108.3781dB, normalized cross correlation (NCC) over 0.99 and normalized correlation (NC) over 0.99.

High Efficiency Video Coding (HEVC) uses an 8-point filter and a 7-point filter, which are based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (IF) are proposed. The first proposed DST-based IFs (DST-IFs) use 8-point and 7-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. The final proposed DST-IFs use 12-point and 11-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. These DST-IF methods are proposed to improve the motion-compensated prediction in HEVC. The 8-point and 7-point DST-IF methods showed average BD-rate reductions of 0.7% and 0.3% in the random access (RA) and low delay B (LDB) configurations, respectively. The 12-point and 11-point DST-IF methods showed average BD-rate reductions of 1.4% and 1.2% in the RA and LDB configurations for the Luma component, respectively.

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.

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).

Euler sums are alternating (or level two) extension of multiple zeta values (MZVs). Kaneko and Tsumura initiated the study of multiple T-values (MTVs), another level two generalization, by restricting the summation indices in the definition of MZVs to a fixed parity pattern. In this paper, we shall study finite MTVs and their alternating versions which are level two and level four variations of finite MZVs, respectively. We conjecture that all finite MZVs are in the Q-span of finite MTVs which in turn apparently lie in the span of finite Euler sums, and the inclusions are both proper. We shall first provide some structural results for Euler sums of small weights, guided by the author's previous conjecture that the finite Euler sum space of weight w is isomorphic to a quotient Euler sum space of weight w. Then, by utilizing some well-known properties of the classical alternating MTVs, we shall derive a few important Q-linear relations among the finite alternating MTVs, including the reversal, linear shuffle and sum relations. We then compute the upper bound for the dimension of the Q-span of weight w finite (alternating) MTVs for w<9, both rigorously using the newly discovered relations and numerically aided by computers.

In this paper, we integrate the Finite Element Method (FEM) with orthogonal polynomial approximation in high-dimensional spaces to innovatively model the Moon’s surface gravity anomaly. Our aim is to approximate solutions to Laplace’s classical differential equations of gravity, employing classical Chebyshev polynomials as basis functions. Using classical Chebyshev polynomials as basis functions, the least-squares approximation was used to approximate discrete samples of the approximation function. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. The first application of this project is to substitute the globally-valid classical spherical harmonic series of approximations with locally-valid series of orthogonal polynomial approximations (i.e. using the FEM approach). With an error tolerance set at 10−9ms−2, we use this method to adapt the gravity model radially upwards from the lunar surface. The results showcase a need for a higher degree of approximation on and near the lunar surface, with the necessity decreasing as the radius increases. Notably, this method achieves a computational speedup of five orders of magnitude when applying the method to radial adaptation. More intrinsically, our second application involves using the methodology as an effective tool in solving boundary value problems. Specifically, we implement this approach to solve classical differential equations involved with high precision, long-term orbit propagation. This application provides a four-order of magnitude speedup in computational time while maintaining an error within the 10−10ms−2 error range for various orbit propagation tests. Alongside the advancements in orthogonal approximation theory, the FEM enables revolutionary speedups in orbit propagation without compromising accuracy.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

We derive a concentration inequality for the uncertainty in the mean computed by stratified random sampling, and provide an online sampling method based on this inequality. Our concentration inequality is versatile and considers a range of factors including: the data ranges, weights, sizes of the strata, the number of samples taken, the estimated sample variances, and whether strata are sampled with or without replacement. Sequentially choosing samples to minimize this inequality leads to a online method for choosing samples from a stratified population. We evaluate and compare the effectiveness of our method against others for synthetic data sets, and also in approximating the Shapley value of cooperative games. Results show that our method is competitive with the performance of Neyman sampling with perfect variance information, even without having prior information on strata variances. We also provide a multidimensional extension of our inequality and discuss future applications.

Ming-style round-backed armchairs as a classic Chinese chair design are renowned for the blend of ergonomics, practicality, and elegance. Although the Chinese armchair furniture industry has made strides in sustainability, there is still a need for further improvements in material selection, manufacturing processes, and supply chain management to fully support the development of sustainable furniture. Laminated bamboo lumber as new sustainable materials are becoming a popular option for furniture designers in the era of "sustainable design". This research aims to investigate the feasibility and application of laminated bamboo lumber in the design of Chinese armchair furniture and proposes innovative ideas for optimizing the armchair's design. First, an empirical study was conducted to comprehensively understand the classification of Ming-style round-backed armchairs’ structure to develop a 3D model. Secondly, an experimental research method was then employed to explore the parameters of laminated bamboo lumber for future studies. Additionally, a validation experiment was conducted to compare real-world scenarios with simulations using finite element analysis in Ansys. Finally, finite element analysis was used to test the feasibility and application of laminated bamboo lumber in furniture design, focusing on the material’s mechanical properties. Results indicated that laminated bamboo lumber has excellent mechanical properties as furniture design materials, subsequently, using the optimized results, the use of 0.6319 kg of steel was successfully reduced by 23.68% to ensure the armchair’s stability. This provides a reference for the future compter-assist and standardized innovative design of Chinese armchair. By incorporating compter-assist design and lightweight optimization, it is possible to save materials and make more efficient use of resources, thereby contributing to sustainable development goals in the field of furniture design.

Despite the increasing popularity of liquid chromatography-mass spectrometry (LC-MS)-based lipidomics, there is a lack of accepted and validated method for lipid extract quality and quantity assessment prior to LC-MS. Fourier-Transform Infrared Spectroscopy (FTIR) has been reported for quantification of pure lipids, however, the sample complexity and purity complex lipid extract quantification in lipidomics experiments could be impact quantification accuracy. Here, we report comprehensive assessment of the sample matrix on the accuracy of lipid quantification using Attenuated Total Reflectance Fourier-Transform Infrared Spectroscopy (ATR-FTIR). Pure lipids are characterized by CH-and C=O-stretching vibrations on FTIR, with quantitative range of 40–3000 ng and a limit of detection of 12 ng. Sample extraction method and local baseline subtraction during FTIR spectral processing significantly impact lipid quantification by CH-stretching. To facilitate sample quality screening, we developed the Lipid Quality (LiQ) score from a spectral library of common contaminants, using a ratio of peak heights between CH-stretching vibrations maxima and the collective vibrations from amide/amine, CH-stretching minima and sugar moieties. We evaluated LiQ score as a rapid sample quality control method by comparing to total LC-MS intensity of targeted lipidomics of 107 human plasma lipid extracts. Exclusion of poor-quality samples based on LiQ score improved the correlation between FTIR and LC-MS quantification. Finally, the uncertainty of absolute quantification by FTIR was estimated using a 795 ng SPLASH LipidoMix standard to be &lt;10%. In summary, this study identified key parameters for accurate FTIR-based quantification of complex lipid mixture, and developed a rapid workflow requiring only 1 µL of MS-ready sample and &lt; 5 minutes for routine lipidomics sample quality and quantity assessment.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.

Objective:The Glioma brain tumor detection and segmentation methods are proposed in this paper using machine learning approaches. Methods:The boundary edge pixels are detected using Kirsch’s edge detectors and then contrast adaptive histogram equalization method is applied on the edge detected pixels. Then, Ridgelet transform is applied on this enhanced brain image in order to obtain the Ridgelet multi resolution coefficients. Further, features are derived from the Ridgelet transformed coefficients and the features are optimized using Principal Component Analysis (PCA) method and these optimized features are classified into Glioma or non-Glioma brain images using Co-Active Adaptive Neuro Fuzzy Expert System (CANFES) classifier.Results:The proposed method with PCA and CANFES classification approach obtains 97.6% of se, 98.56% of sp, 98.73% of Acc, 98.85% of Pr, 98.11% of FPR and 98.185 of FNR, then the proposed Glioma brain tumor detection method using CANFES classification approach only.

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.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

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.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and increase rapidly with time $t$. This method can only be applied within a certain time range and the time range is relevant to fractional order and fractional expansions. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

Estimating the remaining useful life (RUL) of components is a crucial task to enhance the reliability, safety, productivity, and to reduce maintenance cost. In general, predicting the RUL of a component includes constructing a health indicator ( ) to infer the current condition of the component, and modelling the degradation process, to estimate the future behavior. Although many signal processing and data-driven based methods were proposed to construct the , most of the existing methods are based on manual feature extraction techniques, and need the prior knowledge of experts, or rely on a large amount of failure data. Therefore, in this study, a new data-driven method based on the convolutional autoencoder (CAE) is presented to construct the . For this purpose, the continuous wavelet transform (CWT) technique is used to convert the raw acquired vibrational signals into a two-dimensional image; then, the CAE model is trained by the healthy operation dataset. Finally, the Mahalanobis Distance (MD) between the healthy and failure stages is measured as the . The proposed method is tested on a benchmark bearing dataset and compared with several other traditional construction models. Experimental results indicate that the constructed exhibits a monotonically increasing degradation trend and has a good performance to detect incipient faults.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel Transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

(1) Background: This study aimed to compare the effect of polyetheretherketone (PEEK) and titanium abutments on implant prosthetic systems and supporting bone using three-dimensional finite element analysis (FEA); (2) Methods: A three-dimensional finite element analysis was conducted using CATIA and Abaqus software to model mandibular first molar implant systems with titanium and PEEK abutments. Under external loading conditions, finite element analysis was conducted for the stresses in implant components and surrounding bones of each group; (3) Results: The implant fixture of the PEEK model exhibited the highest von Mises stress (VMS). The lowest VMS was observed in the abutment screw of the titanium model. Both implant systems demonstrated similar stress distribution and magnitudes in cortical and cancellous bones; (4) Conclusion: PEEK abutments show similar stress distribution in surrounding bone compared to titanium. However, PEEK absorbs the stresses within the implant system and exhibits the highest VMS values due to its low mechanical and physical properties. Therefore, PEEK abutments need improved mechanical properties for better clinical application.

In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles. Additionally, we introduce two applications: estimating the common scale factor for the radii that makes the re-scaled disks intersects in a single point, this is the \v{C}ech scale, and constructing the minimal Axis-Aligned Bounding Box (AABB) that encloses the intersection of all disks in the system.

Drawing inspiration from a recent construction of a polyhedral structure associated with an icosahedrally-symmetric map on the Riemann sphere, the article shows how to build such "dynamical polyhedra" for other icosahedral maps. First, icosahedral algebra is used to determine a special family of maps with 60 periodic critical points. The topological behavior of each map is worked out and results in a geometric algorithm that constructs a system of edges---the dynamical polyhedron---in natural correspondence to a map's topology. It turns out that the maps' descriptions fall into classes the presentation of which concludes the paper.

Besides the Lagrangian and the Eulerian descriptions, the motion of a body can also be expressed relative to the present configuration of the body, known as the relative motion description. It is interesting to consider such a relative motion description in general to formulate the basic system of field equations for solid bodies. In doing so, when the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system becomes linear. This will be done for thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Relative Lagrangian formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. Some applications of such a formulation in numerical simulations are briefly reviewed.

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.