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.

In Functional Analysis as well as Topology, we frequently encounter sets, say $X$, that contain elements close to each other. These sets display a defining "finite-ness" property: for all open cover $\mathcal{O}$ of $X$, there exists a finite subcollection $\mathcal{U}\subseteq\mathcal{O}$ such that $\mathcal{U}$ covers $X$. Such spaces $X$ are called $\textbf{compact}$, and the above "finite-ness" property afford us great convenience, because we can always investigate $X$ by investigating its finite open cover $\mathcal{U}$Arzela-

To conduct high-precision and high-resolution numerical simulation of complex flow structures in turbomachinery, a high-order finite volume weighted essentially non-oscillatory (WENO) scheme for the large eddy simulation (LES) is improved and embedded into the three-dimensional viscous unsteady CFD solver NUAA-Turbo. Firstly, the spectral characteristics and unsteady convergence of the improved WENO scheme are studied. Compared with the classical WENO scheme, the improved WENO scheme has better dissipation and dispersion characteristics and faster convergence speed. Then, the coefficient CW of the Wall-Adapting Local Eddy-viscosity (WALE) model is calibrated by decaying homogeneous isotropic turbulence (DHIT) test case. Finally, the scheme is applied to conduct high-precision LES calculations of turbulent boundary layer flow, supersonic compression corner flow, and low-pressure turbine cascade separation flow. The numerical simulation results show that this WENO scheme has excellent shock wave capture ability and turbulence resolution and can capture more flow field details with less mesh size, greatly reducing the computational cost and laying a foundation for large-scale engineering application of LES.

This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully expressed with the Laplace transform of transition probability function of the birth-death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

The building envelope has the most significant contribution in the reduction of the building energy consumption. Application of new, alternative and improved materials and systems has an important impact on the buildings performances. This paper is focused on the thermal transmittance, as an indicator of the thermal conductance of the construction element. It includes comparisons of the U-values, calculated by software, with those measured in situ on three representative façade walls. The walls have been constructed with the new wall system Fragmat NZ-1, a new product in Macedonian buildings. This research provides basic information on the thermal transmittance of the system. The results of the analysis show that the in situ measuring is a useful tool in validation of the precision of analytically calculated values, since it was difficult to obtain precise results from the analytical calculations only, especially when the layers are with non-uniform thickness.

In this paper, a new axial-type magnetic gear with auxiliary flux-enhancing structure (AFS-AMG) is proposed. Compared to conventional AFS-AMG, it has the higher torque density and higher permanent magnet (PM) utilization factor. Firstly, the design rules and operating principles of proposed AFS-AMG are elaborated. Then, the mapping relation between the radial-type magnetic gears (RMGs) and AMGs are elucidated. Compared to its counterpart in RMGs, AFS-AMGs achieve small size. Then, the geometrical parameters of AFS-AMGs are optimized to obtain the better electromagnetic performances, where the torque density per volume and per PM volume is adopted as the evaluation standard. Finally, three different AMG topologies are constructed in finite element analysis (FEA) software for comparison. It is proven that the AFS-AMG has the largest torque density per volume and per PM volume.

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

The assortment of low-cost 3D printers for “in-practice” use, e.g., for clear aligner therapies, is ever increasing. To address concerns about the accuracy of orthodontic models produced on such printers when cost efficient modes of 3D printing are employed, this study examined the effect of print model body type and print angulation on accuracy. Six printing-configuration groups were included: 2 model types (solid or hollow shell) combined with 3 print angles (0°, 70°, or 90°) with 10 models/group; all models were printed with 100-µm layer thickness using a digital light processing-based 3-dimensional printer. Eleven selected structures and distances were measured on the printed models with a digital microscope and compared to the same measures on a digitized master model. The clinically-acceptability range was set at ±0.25 mm difference from the master model for single tooth measurements (intra-tooth) and ±0.5 mm for cross-arch measurements (inter-tooth). For individual measurements across all models, 98% fell within clinical acceptability. For mean measurements within each model group, only canine height for the shell-0° model had a mean difference (0.26 mm ± 0.03) outside the clinically acceptable range for intra-tooth measurements. Standard deviations for all intra-tooth measurements were within 0.07 mm. While none of the mean inter-tooth measurements exceeded the acceptability range, the standard deviations were larger (0.04 to 0.30 mm). Accuracy of orthodontic models for clear aligner therapies was not impacted beyond the clinically acceptable range when altering model body type and print angulation to improve efficiency of 3D printing. These findings suggest greater flexibility of the practitioner to alter print settings to address time and cost efficiency in various clinical scenarios and still maintain clinically acceptable model accuracy.

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.

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

An active power dispatch method for a microgrid (MG) with multi-type loads, renewable energy sources (RESs) and distributed energy storage devices (DESDs) is the focus of this paper. The MG operates in a grid-connected model, and distributed power sources contribute to the service for load demands. The outputs of multiple DESDs are controlled to optimize the active power dispatch. Our goal with optimization is to reduce the economic cost under time-of-use (TOU) price, and to adjust the excessively high or low load rate of distributed transformers (DTs) caused by the peak-valley demand and load uncertainties. To simulate a practical environment, the stochastic characteristics of multi-type loads are formulated. The transition matrix of system state is provided. Then, a finite-horizon Markov decision process (FHMDP) model is established to describe the dispatch optimization problem. A learning-based technique is adopted to search the optimal joint control policy of multiple DESDs. Finally, simulation experiments are performed to validate the effectiveness of the proposed method, and the fuzzification analysis of the method is presented.

The sexual reproduction of ascomycetes is controlled by the mating-type(MAT) locus. (Pseudo)homothallic reproduction has been hypothesized based on genetic data from Hirsutella sinensis (Genotype #1 of Ophiocordyceps sinensis). In this study, the differential occurrence of the mating-type genes in the MAT1-1 and MAT1-2 idiomorphs, which constitute the genetic control of O. sinensis reproduction, was analyzed in 237 strains and 5 genomes of H. sinensis. The mating-type genes were differentially transcribed in H. sinensis Strain L0106, and the MAT1-2-1 transcript in H. sinensis Strain 1229 was alternatively spliced, with an unspliced intron I containing stop codons; these findings constitute O. sinensis reproduction controls at the transcriptional and coupled transcriptional-translational levels. The occurrence of the mating-type genes and a-/α-pheromone receptor genes differed among the 5 H. sinensis genomes. The differential occurrence and transcription of these genes are inconsistent with self-fertilization under (pseudo)homothallism but suggest self-sterility of H. sinensis, which therefore needs a mating partner to achieve sexual outcrossing under heterothallism or hybridization. Consistent occurrence and transcription of the mating-type genes of both the MAT1-1 and MAT1-2 idiomorphs have been reported in natural and cultivated Cordyceps sinensis, but these findings are insufficient to determine the reproduction mode(s) because of the co-occurrence of >90 fungal species and multiple genomically independent genotypes of O. sinensis. The mutant MAT1-1-1 and α-pheromone receptor transcripts in natural C. sinensis result in the N-terminus or middle-truncated proteins, with changes in hydrophobicity and secondary structures of the proteins, suggesting heterogeneous fungal source(s) of the proteins and hybridization reproduction.

Nanocrystalline silicon oxide (nc-SiOx:H) is a multipurpose material with its varied application in solar cells as a transparent front contact, intermediate reflector, back reflector layer and even tunnel layer for passivating contacts, owing to easy tailoring of its optical properties. In this work, we systematically investigate the influence of gas mixture (SiH4, CO2, PH3 and H2), RF power and process pressure on the optical, structural and passivation properties of thin n-type nc-SiOx:H films prepared in an industrial, high throughput, plasma-enhanced chemical vapor deposition (PECVD) reactor. We provide a detailed description of the n-type nc-SiOx:H material develop-ment using various characterization techniques (SEM, EDX, Raman spectroscopy, and spectro-scopic ellipsometry) with a focus on the relationship between the material properties and the pas-sivation they provide to n-type c-Si wafers characterized by their effective carrier lifetime (τeff). Further, we also outline the parameters to be kept in mind while developing different n-type nc-SiOx:H layers for different solar cell applications. We report a tunable optical gap (1.8 – 2.3 eV) for our n-type nc-SiOx:H films as well as excellent passivation properties with τeff up to 3.5 ms (iVoc ~ 715 mV) before annealing. Oxygen content plays an important role in determining the crystallinity and hence passivation quality of the deposited nanocrystalline silicon oxide films.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

Spinocerebellar ataxia type 3 is a neurodegenerative disease caused by an abnormal expansion of CAG repeats in the disease gene ATXN3, leading to prolonged polyglutamine (polyQ) tracts in the respective protein ataxin-3. The polyQ-expanded protein forms polyQ-containing aggregates in several brain regions which leads to neuronal cell loss. Autophagy is thought to play a significant role in clearing these polyQ-containing protein aggregates. Therefore, the autophagy mechanism was investigated in SCA3 with focus on the autophagic protein p62/sequestosome-1. Human and mouse RNA sequencing data were analyzed to determine RNA expression level of autophagic genes. Additionally, autophagy was studied in the SCA3 304Q knock-in mouse model and through several cell culture experiments using HEK-293T cells transfected with ATXN3 of differ-ent polyQ lengths. For cell culture experiments, autophagy was induced with rapamycin treat-ment, proteasomal degradation was blocked with MG132 and degradation of autophagic pro-teins was investigated using cycloheximide treatment. Here, we report an increased autophagy impairment with SCA3 disease progression seen in HEK-293T cells transfected with ATXN3 plasmid with expanded polyQ tracts, higher aged 304Q-knock-in mice, or human post-mortem brain material. Furthermore, co-localized aggregation of the autophagic protein p62 and the dis-ease protein ATXN3 was observed in the course of SCA3 disease. Therefore, we suggest a signifi-cant role for p62 in aggregate formation seen in the neurodegenerative disease SCA3.

Existing research indicates that mineralization of Carlin-type gold deposit is related to geological structures, but current studies mostly focus on the qualitative association, and lack quantitative analysis of the relationship between mineralization and structural features, which limits the potential for predictive mineral exploration. In this study, the Nibao Carlin-type gold deposit was selected as the research area to conduct three-dimensional geological modeling, spatial analysis, and three-dimensional prospectivity modeling. Spatial analysis revealed that the majority of gold ore bodies are situated near the main fault, with gold mineralization primarily occurring within a spatial range of approximately -80 meters to 20 meters from the main fault plane. This spatial distribution predominantly aligns in a SW-NE direction. Spatial characteristic extraction of fault slope indicators suggests that the slope angles are conducive to the migration and accumulation of ore-forming hydrothermal fluids, with ore body metal content rapidly increasing within an angle range of approximately 20° to 60°. The shape analysis of the mainfault indicates that the principal spaces of mineralization enrichment are within -10m to 20m of the fault plane undulations, where gold resources are concentrated in a relatively flat area. However, the degree of mineralization is more pronounced in the protruding sections than in the depressed areas. The areas with significant dip changes in faults display higher variations in orebody attitudes, with mineralization noticeably weaker in areas where the fault steepness changes markedly. Ore-bearing units exhibit significantly higher grades within the -17° to 3° interval of fault steepness transition. This interval also sees a rapid accumulation of gold resources. The Nibao gold mine's mineralization is derived from deep, ore-bearing hydrothermal fluids ascending along major fractures, precipitating, and accumulating in favorable ore-hosting spaces (faults, anticline cores) and lithological combinations (sedimentary tuffs, tuffs). Three deep potential gold targets were identified, highlighting the deep western edge of the F1 fault and the deep southeast-trending lower plate as prospective areas for future exploration. This study underscores the effectiveness of 3D prospective modeling as an indispensable tool for elucidating the spatial distribution of fault-controlled Carlin-type gold deposits and their tectonic determinants.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Background and Objectives Neurofibromatosis 1 (NF1 MIM # 162200), also known as von Recklinghausen disease, is among the most common autosomal dominantly transmitted disorders characterized mainly by neurocutaneous manifestations such as café au lait spots, intertriginous freckling, various types of neurofibromas (cutaneous neurofibromas or plexiform tumors), neurological manifestations, and bone abnormalities. It occurs with an incidence of 1:3000–1:4000 cases. Cone-rod dystrophies belong to the large group of retinal dystrophies, a highly heterogeneous group of disorders clinically manifested mainly by damage to cone and rod cells and have a broad spectrum of clinical manifestations. Many genes are involved in their etiology, with more than 100 currently identified, including the CRX gene responsible for the autosomal dominant form of cone-rod dystrophy (ad CORD). Materials and Methods: The authors present an intriguing case of a patient diagnosed with Neurofibromatosis type 1 (NF1) as an infant and ocular involvement (myopia and astigmatism onset at age 15), which yielded a surprising molecular testing result. Results: Molecular DNA analysis identified a rare occurrence of two mutational variants, including a pathogenic variant in the NF1 gene, c.3871-2A, and a likely pathogenic variant in the CRX gene c.119G>A. Conclusions: The authors present this case to highlight the surprises offered by molecular testing in a condition where the diagnosis is usually based on clinical criteria, thus providing patients with competent genetic advice.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted the Lorentz group of symmetry which is maintained also in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxy Clusters are huge physical systems having dimensions of many hundreds of millions of light years. Thus any change at the cluster center will be noticed at the rim only hundreds of millions of years later. Those retardation effects are neglected in present day cluster modelling and in particular are neglected in virial calculations used to relate mass and velocities on the cluster. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the velocities in a galactic cluster without postulating dark matter. It should be stressed that the current approach does not require that velocities, $v$ are high, in fact the vast majority of cluster bodies are substantially subluminal. In other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are less than ~1000 km/s, which makes this ratio $0.01$ or smaller. However, one should consider the fact that every gravitational system even if it is made of subluminal bodies has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system such as stars and galaxies and even galactic clusters exchange mass with its environment. For example, the sun losses mass through the solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative, how large is the retardation distance? The change of mass of the sun is quite small and thus the retardation distance of the solar system is quite large allowing us to neglect retardation effects within the solar system. However, for galaxies and galaxy clusters the retardation distance is within the system itself and cannot be neglected.

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in $T$ $$\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.$$

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.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

Bell's theorem can be refuted by presenting a counterexample which predicts correctly the expectation values of QM. As Bell has only ruled out noncontextual models a contextual model with hidden variables would refute his theorem. Such a model is presented able to explain the spin measurement results with entangled photons or electrons. It is not ruled out by the Kochen-Specker Theorem. Consequences for the feasibility of quantum computers are discussed.

In this short paper we study some properties of the lines associated with van Aubel’s theorem in the special case when squares are replaced with equilateral triangles constructed on the sides of an arbitrary quadrilateral.

To assess the community health workers’ (CHWs) knowledge, attitude, and practices (KAP) in type-2 diabetes (T2D) and hypertension (HTN) management. We thus also sought to assess the potential health system barriers for incorporating CHWs in T2D and HTN management. Mixed-method study comprised (1) a survey among 153 active CHWs to assess their KAP of T2D and HTN, and (2) semi-structured interviews with key informants to understand challenges of the health system and proposed solutions in incorporating CHWs in T2D and HTN management. The majority of CHWs correctly answered general knowledge questions on NCDs, risk factors, and prevention; however, only one-quarter correctly answered questions on smoking, family history, or tobacco use as risk factors. Most respondents appeared to have positive attitudes and have been practicing some activities related to T2D and HTN. Both financial and non-financial resource constraints were cited as challenges of the health system; therefore, re-structuring the role definition of CHWs and task of responsibilities, and assessment the need and workload have been proposed as ways forwards to effectively incorporate CHWs in T2D and HTN care. CHWs in Cambodia have shown their potential in T2D and HTN management; however, a well-designed strategy including technical training, clearly defined roles and responsibilities, and strong supporting structure are important to maximize their potential in the health system.

The three-pronged sliding universal coupling is a new kind of three-pronged coupling. To study its kinematic and dynamic characteristics, directional cosine matrices are utilized as tools to analyze the coordinate systems by establishing simplified geometric models and corresponding motions. Through the analysis of the motions of the input and output shafts and employing the method of single-force element, a set of equilibrium equations for the forces acting on the output shaft and the input shaft are formulated for solution analysis. The research indicates that during the rotation process, there exists a small angular difference between the input shaft and the intermediate shaft, demonstrating the quasi-constant angular velocity characteristics of the new tripod sliding universal coupling. The curves of the forces and torques acting on each component of the coupling approximate sinusoidal curves. The optimal operating angle range for the new tripod universal coupling is at angle , during which the system exhibits good transmission and mechanical performance.

Protein tyrosine phosphatase receptor type E (PTPRE) is a member of the “classical” protein tyrosine phosphatase subfamily and regulates a variety of cellular processes in a tissue-specific manner by antagonizing the function of protein tyrosine kinases. PTPRE plays a tumorigenic role in different human cancer cells, but its role in retinoblastoma (RB), the most common malignant eye cancer in children, remains to be elucidated. Etoposide resistant RB cell lines and RB patients display significant higher PTPRE expression levels compared to chemosensitive counterparts and the healthy human retina, respectively. PTPRE promotor methylation analyses revealed that PTPRE expression in RB is not regulated via this mechanism. Lentiviral PTPRE knockdown (KD) induced a significant decrease in growth kinetics, cell viability, and anchorage independent growth of etoposide resistant Y79 and WERI RB cells. Caspase-dependent apoptosis rates were significantly increased and a re-sensitization for etoposide could be observed after PTPRE depletion. In vivo chicken chorioallantoic membrane (CAM) assays revealed decreased tumor formation capacity as well as reduced tumor size and weight following PTPRE KD. Expression levels of miR631 were significantly downregulated in etoposide resistant RB cells and patients. Transient miR631 overexpression resulted in significantly decreased PTPRE levels and concomitantly decreased proliferation and increased apoptosis levels in etoposide resistant RB cells, impacts mirroring PTPRE KD effects and indicating PTPRE regulation via this miR. Additionally, PTPRE KD led to altered phosphorylation of protein kinase SGK3 and - dependent on the cell line - also AKT and ERK1/2, suggesting potential PTPRE downstream signaling pathways. In summary, these results indicate an oncogenic role of PTPRE in chemoresistant retinoblastoma.

For a set of closed curved surfaces that resemble a Langmuir monolayer an energy is defined that depends only on the curvature of the surfaces interacting with the dimensions normal to the surfaces, that is, the thickness of these surfaces. The thickness, or depth, of the surfaces originates because of surface-particles with chains, that move freely on the inside of the surfaces at a certain depth. This is a purely geometrical description that does not depend on the introduction of ad hoc constants like the elastic constant. With a statistical mechanical model the equations of state are calculated for a gas of non-connected sphere-like surfaces in a volume. There are two states of which the lower temperature state is depending mostly on the interaction energy and surface properties, and the higher temperature state is depending mostly on sphere kinetic and volume properties. This results in aggregation of the sphere-like surfaces from many small ones to few large ones when lowering temperature and vice versa. The model allows for the calculation of the partition function and, when the emergence of the curvature - depth interaction is described as a phase-transformation, for the application of Noether’s theorem. Because of these properties the model is interesting in its own right apart from being an addition to existing elastic descriptions of surfaces.

Background and Objectives: In this current state, Type 2 Diabetes Mellitus (T2DM) is more prevalent in the population, and metformin is used as a first-line medication for treating it. There was up surge in the utilization of alternative therapies in the management of diabetes. Especially in diabetes, Herbal medicines are considered safe and reliable by majority of the population. Aim: The purpose of this research is aimed to estimate the safety and efficacy of Polyherbal Metabolite Compounds (PHMC) capsules in adults with T2DM. Materials and Methods: In this study, 60 T2DM patients aged 18-60 years were randomly assigned to Groups A (30) receiving Metformin 500 mg twice a day after food and Group B (30) receiving PHMC capsule 500 mg twice a day after food in a prospective, randomized and open-label clinical study. The in-silico simulation study was performed to selected plants major compounds on target protein Insulin-like Growth Factor-1 (1K3A). Result: The PHMC is found to be safe and effective in the management of T2DM. The FBS, PPBS and HbA1c were significantly lowered (p

Background and Objectives: Cancer as the second leading cause of death in the United States poses a huge healthcare burden. Barriers to access to advanced therapies influence the outcome of cancer treatment. In this study, we examined whether insurance types affect the quality of cancer clinical care regarding access to an important monoclonal antibody, ramucirumab. Materials and Methods: Data for 13,340 cancer patients with Purchased or Medicaid insurance from the All of Us Database were collected for this study. The Chi-square test of proportions was employed to determine the significance of patient cohort characteristics and ramucirumab usage between Purchased and Medicaid insurance groups. The independent t-test was utilized to assess the influences of other determinants on insurance types. Results: Cancer patients who are African American, with lower socioeconomic status, or with lower educational attainment are more likely to be insured by Medicaid. Analysis of survey questions demonstrated the relationship between income and education level with insurance type as Medicaid cancer patients were less likely to receive primary care and specialist physician access and more likely to request lower cost medications. In addition, those with Medicaid insurance were identified to have poorer access to expensive therapeutics like ramucirumab compared to those with Purchased insurance.  Conclusions: The inequities of the US healthcare system are observed for cancer patient care; access to physicians and therapeutics are highly varied and dependent on insurance types. Socioeconomic status determines insurance type, which unfortunately generates a significant impact on cancer treatment and disease outcome.

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.

There are no theorems (proven theories) in the biological sciences. We propose that the 3 31 nt minihelix tRNA evolution theorem be universally accepted as one. The 3 31 nt minihelix theorem completely describes evolution of type I and type II tRNAs from ordered precursors (RNA repeats and inverted repeats). Despite diversification of tRNAome sequences, statistical tests overwhelmingly support the theorem. Furthermore, the theorem relates the dominant pathway for the origin of life on Earth, specifically, how tRNAomes and the genetic code may have coevolved. Alternate models for tRNA evolution (i.e., 2 minihelix, convergent and accretion models) are falsified. In the context of the pre-life world, tRNA was a molecule that via mutation could modify anticodon sequences and teach itself to code. We relate the clearest history to date of the chemical evolution of life on Earth. From analysis of tRNA evolution, ribozyme-mediated RNA ligation was a primary driving force in evolution of complexity during the pre-life to life transition on Earth.

The process of sexual reproduction in eukaryotes starts when gametes from two different sexes encounter each other. Paramecium, a unicellular eukaryote, undergoes conjugation and uses a gametic nucleus to enter the sexual reproductive process. The molecules responsible for recognizing mating partners, hypothetically called mating-type substances, are still unclear. We have identified an O3-type mating substance polypeptide and its gene sequence using protein chemistry, molecular genetics, immunofluorescence, RNA inter-ference, and microinjection. The O3-type substance is a polypeptide found in the ciliary membranes, located from the head to the ventral side of cells. The O3-type substance has a kinase-like domain in its N-terminal part located outside the cell and four EF-hand motifs that bind calcium ions in its C-terminal part located inside the cell. RNA interference and immunofluorescence revealed that this polypeptide positively correlated with the expression of mating reactivity. Microinjection of an expression vector incorporating the O3Pc-MSP gene induced additional O3 mating type in the recipient clones of different mating types or syngen. Phylogenetic analysis indicates this gene is widely present in eukaryotes and exhibits high homology among closely related species. The O3Pc-MSP gene had nine silent mutations compared to the complementary mating type of the E3 homologue gene.

(1) Background: Among the chronic complications of type 2 diabetes mellitus, cancer became the leading cause of death in several countries. Our objective was the determination of whether prevalent type 2 diabetes mellitus is associated with a higher incidence of cancer. (2) Methods: This study is a nationwide analysis performed in Hungary. Study population was divided into a group with type 2 diabetes mellitus and into a non-diabetic group. The primary outcome was the risk related to overall cancer incidence. A key secondary outcome was the overall incidence of cancer in distinct study years. Further outcomes were the annual percent changes. (3) Results: The odds ratio related to the overall incidence of cancer was 2.50 (95% confidence interval: 2.46-2.55, P<0.0001) in patients with diabetes as related to controls. The odds ratio was higher in males than in females. The highest risk was found in the 18-39-year-old subgroup. The annual cancer incidence rate declined in controls, but not in patients with diabetes. Several types of cancer showed a decreasing tendency in non-diabetic controls.; (4) Conclusions: type 2 diabetes is associated with a higher risk of cancer. High risk in young patients with type 2 diabetes suggests that these young individuals should be considered as a risk group.

(1) Background: Patients with type 2 diabetes mellitus (T2DM) are at higher risk of cancer but how these two diseases associate is still debated. The goal was the assessment of the overall incidence of cancer among patients with newly diagnosed T2DM in Hungary. Summarizing, incident T2DM is associated with a significantly higher overall risk of incident cancer, with a reverse correlation of age. Newly registered T2DM patients were suggested to be screened for cancer within 6 months. (2) Methods: A nationwide, retrospective, longitudinal study was performed using a Hungarian database. The incident T2DM and diabetes free Hungarian population were included in the study. The primary endpoints were the overall and site-specific incidence and annual percentage change of the incidence of cancer in both populations. (3) Results: The overall incidence of cancer in patients amounted to 29.4/1000 and 6.6/1000 with or without T2DM, respectively, and the OR (95%CI) of cancer of the T2DM group was 4.32 (4.14-4.53), p<0.0001. The risk of having cancer was age-dependent, having the highest odd in the age group 18-39. The incidence of cancer was declining in the non-diabetic but was unchanged in T2DM population. The average lag time of diagnosing a cancer after the detection of T2DM was 3.86 months.; (4) Conclusions: Iincident T2DM is associated with a significantly higher overall risk of incident cancer, with a reverse correlation of age. Newly registered T2DM patients were suggested to be screened for cancer within 6 months.

Diabetes mellitus (DM) poses a significant challenge to global health, with its prevalence projected to rise dramatically by 2045. This narrative review explores the bidirectional relationship between periodontitis (PD) and type 1 diabetes mellitus (T1DM), focusing on cellular and molecular mechanisms derived by the interplay between oral microbiota and the host immune response. A comprehensive search of literature published between 2008 and 2023 was conducted to elucidate the association between these two diseases. Preclinical and clinical evidence suggests a bidirectional relationship, with individuals with T1DM exhibiting heightened susceptibility to periodontitis, and vice versa. The review includes recent findings from human clinical studies, revealing variations in oral microbiota composition in T1DM patients, including increases in certain pathogenic species such as Porphyromonas gingivalis, Prevotella intermedia, and Aggregatibacter actinomycetemcomitans, along with shifts in microbial diversity and abundance. Molecular mechanisms underlying this association involve oxidative stress and dysregulated host immune responses, mediated by inflammatory cytokines such as IL-6, IL-8, and MMPs. Furthermore, disruptions in bone turnover markers, such as RANKL and OPG, contribute to periodontal complications in T1DM patients. While preventive measures to manage periodontal complications in T1DM patients may improve overall health outcomes, further research is needed to understand the intricate interactions between oral microbiota, host response, periodontal disease, and systemic health in this population.

The vomeronasal system serves as a pivotal element in mammalian sensory biology, allowing the perception of chemical signals essential for social communication via the activation of two main receptor families, V1R and V2R. The expression of V1Rs and V2Rs is linked with that of the G-protein alpha-subunits, Gαi2 and Gαo, respectively. The exploration of the evolutionary pathways of V1Rs and V2Rs across all mammalian species remains a main challenge, juxtaposing available genomic data against emerging immunohistochemical evidence. However, recent investigations, in contrast to what is predicted by the currently annotated genomic sequences, have revealed the expression of Gαo in the vomeronasal neuroepithelium of wild canids, including wolves and foxes. In the present study, the employment of a specific antibody raised against the mouse V2R2, member of the C-family of vomeronasal receptors, V2Rs, has confirmed the expression of this receptor in the fox and wolf, but it has revealed the lack of expression in the dog. This may reflect the impact of domestication on the regression of the VNS in this species, in contrast to their wild counterparts, and underscores the effects of artificial selection on sensory functions. Thus, these findings suggest a more refined chemical detection capability in wild species.

The theoretical limit of link prediction is a fundamental problem in this field. Taking the network structure as object to research this problem is the mainstream method. This paper proposes a new viewpoint that link prediction methods can be divided into single or combination methods, based on the way they derive the similarity matrix, and investigates whether there a theoretical limit exists for combination methods. We propose and prove necessary and sufficient conditions for the combination method to reach the theoretical limit. The limit theorem reveals the essence of combination method that is to estimate probability density functions of existing links and nonexistent links. Based on limit theorem, a new combination method, theoretical limit fusion (TLF) method, is proposed. Simulations and experiments on real networks demonstrated that TLF method can achieve higher prediction accuracy.

In this paper, we calculate the deflection angle of photon by Casimir wormhole in the weak field limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on the Gaussian optical metric. Then we find the deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. Second, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

The typically qualitative treatment of evidence underlying different causal hypotheses that attempt to explain singular historic events is criticized. Instead of using ad hoc qualitative arguments, it is here advocated to use Bayes theorem to assess how well evidence either support or weaken a specific causal hypothesis. It is argued that such a practice will enable scientists who study singular historic events to discuss, compare and aggregate different beliefs in a meaningful way.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

The paper proves a theorem about the structure of the distribution function on which the extremum of fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters, hence the problem is greatly simplified since it is reduced to the search for an extremum of some function.

Considering the current needs of industry 4.0, especially in the condition of systems linked to artificial intelligence, this multidisciplinary concept work and difficult to execute, proposes the main idea of recognizing patterns using mathematical concepts of simple access and logical resolution of great potential. The objective of this work is to demonstrate a process for pattern recognition by applying the Fibonacci concept to vibration signals of hybrid dynamical systems. For this to be possible, it was necessary to use the concepts of preprocessing in a vector for pattern recognition, together with the concepts of the golden rule of Fibonacci, finally, all applied in the theorem of Jeffcott Rotors. The general result, from a technical point of view, demonstrates positivity and relationship of patterns, because, considering the aspect of the location between the values of the experimental and numerical result, both signs have similarities.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons-Werner method to the optical geometry of Horndeski black hole and implement the Gauss-Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and non-plasma medium is examined.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

PHA synthases (PhaC) are grouped into four classes based on the kinetics and mechanisms of reaction. The grouping of PhaC enzymes into four classes is dependent on substrate specificity, according to the preference in forming short chain length (scl) or medium chain length (mcl) polymers: class I, class III, and class IV produce scl-PHAs depending on propionate, butyrate, valerate and hexanoate precursors, while class II phaC synthesize mcl-PHAs based on the alkane (C6 to C14) precursors. PHA synthases of class I, in particular PhaC_Cs from Chromobacterium USM2 and PhaC_Cn/RePhaC1 from Cupriavidus necator/R. eutropha, have been analysed and the crystal structures of the C-domains have been determined. PhaC_Cn/RePhaC1 was also studied by small angle X-ray scattering (SAXS) analysis. Models have been proposed for dimerization, catalysis mechanism, substrate recognition and affinity, product formation and product egress route. The assays based on amino acid substitution by mutagenesis have been useful to validate the hypothesis on the role of amino acids in catalysis and in accommodation of bulky substrates, for the synthesis of PHB co-polymers and medium chain length-PHA polymers with optimized chemical properties.

The paper presents a new type of hydraulic clutch operating with magnetorheological (MR) fluids and the results achieved from both theoretical analysis and experimental measurement. The hy-draulic clutch system of its own design with MR working fluid and a rotating magnetic field lo-cated is designed. The principle of this clutch is to use a rotating magnetic field created by an al-ternating current electromagnet to set the MR fluid in motion. In the tests of the hydraulic clutch with a rotating magnetic field, MR fluid produced on their own, consisting of solid iron particles of various diameters mixed with a silicone oil, are used as working fluids. The rheological properties of MR fluids are assessed on the basis of tests carried out with a Brookfield DV2T rheometer equipped with a magnetic device for generating the magnetic field of its own design. The char-acteristics of the hydraulic clutch with MR working fluid and the rotating magnetic field are tested on a specially built test stand. As a result of the research, it has been found that the torque transmitted by the clutch is the greater, the higher the rotational speed of the magnetic field and the lower the rotational speed of the beaker in which the working fluid is placed, and that the greatest torque occurs for the working fluid with the highest iron content. Based on the analysis of the structure and characteristics of the clutch in which the magnetic field is used, it has been shown that the design of the developed clutch is similar to that of an induction clutch, and its characteristics correspond to the characteristics of the eddy current clutch. Therefore, the proposed new clutch working with MR fluid and the rotating magnetic field can be applied to stationary power transmission system similarly to an eddy current clutch.

The kinetics and efficacy profiles of photoinitiated polymerization are theoretically presented. For the same dose, lower light intensity achieves a higher steady-state-efficacy (SSE) in type-I; in contrast, type-II has an equal SSE. Higher light intensity has a faster rising efficacy, due to faster depletion of photoinitiator (PS) concentration. However, type-II process is also affected by the available oxygen. Higher light intensity produces more efficient singlet oxygen, resulting a higher transient efficacy, in which all intensities reach the same SSE when oxygen is completely depleted. With external oxygen, type-II efficacy increases with time, otherwise, it is governed only by the light dose, i.e., same dose achieves same efficacy. Moreover, type-II has an efficacy follows Bunsen Roscoe law (BRL), whereas type-I follows non-BRL. The measured type-I efficacy and gelation profile are analyzed by our analytic formulas. Schematics of the photocrosslinking stage defined by the availability of oxygen is developed, where both type-I and –II coexist until the oxygen is depleted. The overall efficacy may be enhanced by resupply of PS or oxygen during the light exposure. The roles of light dose and PS concentration on the efficacy of photoinitiated polymerization should be are governed a new concept of a volume efficacy (Ve), defined by the product of the crosslink (or gelation) depth (CD) and local [efficacy].

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

Among the many Lysosomal Storage Disorders (LSDs) that would benefit from the establish-ment of novel cell models, either patient-derived or genetically engineered, is Mucopolysaccha-ridosis type II (MPS II). In fact, even though a specific therapeutic approach does exist for this disorder (Enzyme Replacement Therapy, ERT, with recombinant human IDS) and haematopoiet-ic stem cell transplantation (HSCT) may also hold promise whenever the disorder is diagnosed soon enough, both approaches have their own drawbacks. Here we present our results on the establishment and characterization of two MPS II pa-tient-derived stem cell line(s) from deciduous baby teeth. To the best of our knowledge, this is the first time a stem cell population is isolated from LSD patient samples obtained from the oral cavity. Taking into account our results on the molecular and biochemical characterization of those cells and our first insights on their subcellular MPS phenotype, we consider these cells will be a valuable tool for both pathophysiological assessments and drugs screenings. Ultimately, we believe patient-derived dental pulp stem cells (DPSC) may represent a feasible alternative to induced pluripotent stem cells (iPSC) in many labs with standard cell culture con-ditions and limited (human and economic) resources.

In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

In this article the possible impact on the present state of particle physics theory is discussed of two unrecognized theoretical elements. These elements are the awareness that (a) the quark is a Dirac particle with a polarisable dipole moment in a scalar field and that (b) Dirac’s wave equation for fermions, if derived from Einstein’s geodesic equation, reveals a scaling theorem for quarks. It is shown that recognition of these elements proves by theory quite some relationships that are up to now only empirically assessed, such as for instance, the mass relationships between the elementary quarks, the relationship between the bare mass and the constituent mass of quarks, the mass spectrum of hadrons and the mass values of the Z boson and the Higgs boson.

This study aimed to elucidate the similarities and differences between amyloid-forming corpora amylacea (CA) in the prostate and lung, examine the nature of CAs in cystic tumors of the atrioventricular node (CTAVN), and clarify the distinctions between amyloid-forming CA and spheroid-type amyloid deposition. We conducted proteomics analyses using liquid chromatography–tandem mass spectrometry with laser microdissection and immunohistochemistry to validate the characteristics of CAs in the lung and prostate. Our findings revealed that CAs in these organs primarily consist of common proteins (β2-microglobulin and lysozyme) and locally produced proteins. Moreover, we observed a discrepancy between the histopathological and proteomic analysis results in CTAVN-associated CAs. In addition, while the histopathological appearance of amyloid-forming CAs and spheroid-type amyloid deposits were nearly identical, the latter deposition lacked β2-microglobulin and lysozyme, and exhibited evident destruction of surrounding tissue. A literature review further supported these findings. These results suggest that amyloid-forming CAs in the lung and prostate are formed through a shared mechanism, serving as waste containers (wasteosomes) and/or storage for excess proteins (functional amyloids). In contrast, we hypothesize that while amyloid-forming CA and spheroid-type amyloid deposits are formed, in part, through common mechanisms, the latter are pathological.

Background Homologous recombination deficiency (HRD) evolved into a major diagnostic marker in high grade ovarian cancer (HGOC) predicting the response to poly (Adenosine diphosphate-ribose) polymerase inhibitors (PARPi) and also platinum-based therapy. In addition to HRD, the type of peritoneal tumor spread influences treatment response and patient survival; miliary type tumor spread has poorer predicted outcome than non-miliary type tumor spread. Methods Known methods for HRD assessment were adapted for our technical requirements and the Predictive-value Integrated Genomic Instability Score (PIGIS) for HRD assessment evolved as an outcome. PIGIS was validated in HGOC samples from 122 patients. We used PIGIS to analyze whether the type of tumor spread correlated with HRD status and whether this had an impact on survival. Results We demonstrated that PIGIS can discriminate HRD positive from HRD negative samples. Tumors with miliary tumor spread are HRD negative and have a very bad prognosis with a progression free survival (PFS) of 15.6 months and an overall survival (OS) of 3.9 years. However, HRD negative non-miliary spreading tumors in our cohort had a much better prognosis (PFS 35.4 months, OS 8.9 years), similar to HRD positive tumors (PFS 34.7 months, OS 8.9 years). Conclusions Our results indicate that in a predominantly PARPi naïve cohort the type of tumor spread might be a better predictor of response to platinum sensitivity than HRD. It remains to be determined, whether this also applies for sensitivity to PARPi.

Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s Theorem from analytic Euclidean geometry into the Poincar´e ball model of analytic hyperbolic geometry, which is based on M¨obius addition. The translation of Ptolemy’s Theorem from Euclidean geometry into hyperbolic geometry is achieved by means of the hyperbolic trigonometry, called gyrotrigonometry, to which the Poincar´e ball model gives rise, and by means of the duality of trigonometry and gyrotrigonometry.

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs' approach in the thermodynamic description of heterogeneous systems and assuming that the basic assumptions of classical nucleation theory commonly employed in application to crystallization hold, a general form of the nucleation theorem can be formulated valid not only for one-component but generally for multi-component systems. This result is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, recently developed by us expressions for the curvature dependence of the surface tension, respectively, the dependence of the surface tension on pressure and/or temperature are employed. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)] holds also for multi-component systems as far as mentioned above assumptions are fulfilled. In the application of classical nucleation theory to crystallization processes it is assumed as one of its basic ingredients that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. This assumption is, however, in general, it is not true. This limitation of the theoretical description can be overcome by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem as derived based on classical nucleation theory holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

Orthohepadnavirus causes chronic hepatitis in a broad range of mammals, including primates, cats, woodchucks, and bats. Hepatitis B virus (HBV) X protein inhibits type-I interferon (IFN) signaling, promoting HBV escape from the innate immune system to establish persistent infection. However, whether X proteins of Orthohepadnavirus viruses in the other species have similar inhibitory activity remains unknown. Here, we investigated the anti-IFN activity of 17 Orthohepadnavirus X proteins derived from various hosts. We observed conserved activity of Orthohepadnavirus X proteins in inhibiting TIR-domain-containing adaptor protein inducing IFN-β (TRIF)-mediated IFN-β signaling pathway through TRIF degradation. X proteins from domestic cat hepadnavirus (DCH), a novel member of Orthohepadnavirus, inhibited mitochondrial antiviral signaling protein (MAVS)-mediated IFNβ signaling pathway comparable with HBV X. These results indicate that inhibition of IFN signaling is conserved in Orthohepadnavirus X proteins.

Hepatocellular carcinoma (HCC) is a heterogeneous malignancy with complex carcinogenesis. Although there has been significant progress in the treatment of HCC over the past decades, drug resistance to chemotherapy remains a major obstacle in its successful management. In this study we were able to reduce chemoresistance in cisplatin-resistant HepG2 cells by either silencing the expression of transglutaminase type 2 (TG2) using siRNA or by pre-treatment of cells with the TG2 enzyme inhibitor cystamine. Further analysis revealed that, whereas the full-length TG2 isoform (TG2-L) was almost completely cytoplasmic in its distribution, the majority of the short TG2 isoform (TG2-S) was membrane-associated in both parental and chemoresistant HepG2 cells. Following induction of cisplatin toxicity in non-chemoresistant parental cells, TG2-S together with cisplatin quickly relocated to the cytosolic fraction. Conversely, no cytosolic relocalisation of TG2-S or nuclear accumulation cisplatin was observed following identical treatment of chemoresistant cells, where TG2-S remained predominantly membrane-associated. This suggests that deficient subcellular relocalisation of TG2-S from membranous structures into the cytoplasm may limit the apoptic response to cisplatin toxicity in chemoresistant cells. Structural analysis of TG2 revealed the presence of binding motifs for interaction of TG-S with the membrane scaffold protein LC3/LC3 homologue that could contribute to a novel mechanism of chemotherapeutic resistance in HepG2 cells.

This paper introduces a rigorous and comprehensive approach for the assessment of marine shafting systems through the utilization of an advanced Pi-Theorem based scaling methodology. Integrating journal bearing similarity assessment and shaft-line scaling methodology with advanced dimensional analysis, the study aims to provide a methodology foundation for systematic replication and analysis of marine shafting systems through scaled models. The proposed scaling methodology ensures geometric and mechanical similarity in terms of shaft-line deflection, considering key scaling parameters such as shaft length, diameter, weight, loads, rotational speed, material properties, bearing locations, and offsets. The advanced dimensional analysis computes specific non-dimensional ratios to guarantee a close resemblance between a real-size system and a scaled lab model, enabling meaningful experimentation. The methodology is analytically derived and validated with numerical simulations for a case study, conducting comparative analysis, evaluating discrepancies, and utilizing the integrated framework for experimentation.

Exercising surds to represent figures is a common practice in scientific and Engineering fields, especially in scripts where calculators are banned or unapproachable. Peter Chew Theorem make result becomes simple when dealing with converting Quadratic Surds. The substance of the Peter Chew Theorem lies in enabling the forthcoming generation to simple break problems related to Quadratic Surds more effectively, easing a direct comparison with contemporary results. By employing the Peter Chew Theorem, one can streamline the tutoring and literacy of math, particularly concerning second- order direct equations with constant portions. This theorem's objective aligns with Albert Einstein's famed quotation Everything should be made as simple as possible, but not simpler.

In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikove-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium.

Evolutionary, sequence and structural analyses of tRNA variable (V) loops provides a new understanding. Type I tRNA V loops have a primordial length of 5 nt, and type II tRNA V loops have a primordial length of 14 nt. Sequence-based alignments of type I and type II V loops gave deceptive results. Type II V loops are characterized by the trajectory of the V arm, the size and sequence of the loop and the first and last V loop nucleotides and their known contacts. Depending on the V arm trajectory, type II V stems and loops can be interaction sites for aminoacyl-tRNA synthetases. So, type II V arms for tRNALeu, tRNASer and tRNATyr (found in Bacteria) were coevolved and selected to distinguish determinants to support cognate tRNA charging. The alignment of type I and type II V loops was adjusted based on tRNA evolution. Results are consistent with Archaea being an older and simpler life form than Bacteria. TRNAome sequences were derived from radiation of an ordered tRNAPri (Pri for primordial) sequence comprised of known RNA repeats and inverted repeats. V loop and tRNA sequences, therefore, convey a history of the primary successful pathway in the origin of life.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

D-type cyclins encode G1/S cell cycle checkpoint proteins, that play a crucial role in defining cell cycle exit and progression. Precise control of cell cycle exit is vital during embryonic development, with defects in the pathways regulating intracellular D-type cyclins resulting in abnormal initiation of stem cell differentiation in a variety of different organ systems. Furthermore, stabilisation of D-type cyclins is observed in a wide range of disorders characterised by cellular over-proliferation, including cancers and overgrowth disorders. In this review, we will summarise and compare the roles played by each D-type cyclin during development and provide examples of how their intracellular dysregulation can be an underlying cause of disease.

Lacunary polyoxometalates (POMs) are negatively charged metal−oxo clusters, formally obtained from plenary topologies via fragment removal. Owing to the fragment removal, the lacunary POMs archetypes are rich in nucleophilic terminal oxo ligands, making them suitable for post-synthetic coordination with various heterometals. Trilacunary heteropolytungstates (het-ero-POTs) based on bowl-shaped {W9O30} framework incorporating a central lone-pair containing {XO3} hetergroup (X = AsIII, SbIII, and BiIII) function as all-inorganic scaffolds that in the presence of d-block metal cations typically construct sandwich-like dimers of Hervé and/or Krebs. Herein we review the preparative approaches, compositional and magnetic versatility of the constructing Hervé and Krebs type dimers and discuss prospective use as POMtronics.

(1) Background Diabetic Retinopathy (DR) is the primary cause of poor vision in young adults. Screening for DR is important but many patients do not attend; (2) Methods: We validated an algorithm for predicting DR and its progression by conducting a retrospective study of 11 children in a population of 120,389 T2DM (3) Results: By applying the algorithm to the population showed an AUC of 0.93 (95% CI, 0.92–0.94) for any-DR and 0.90 (95% CI, 0.89–0.91) for referable-DR(4) Conclusions: The algorithm is useful for predicting patients who could develop referable forms of DR and also for any-DR. This would allow a personalized screening plan to be drawn up for each patient.

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing relevant mathematical laws and all physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical pictures and physics for (in)finite freedom systems are discovered. This paper gives both general variational principle and general Noether theorem as well as their classical and quantum new physics, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

This article introduces an innovative design method for public lighting systems that surpasses the limitations of conventional approaches, which rely on predefined lamp characteristics and spatial arrangement. By employing a multi-criteria decision algorithm, our study proposes an optimal design methodology considering several key aspects, including the distance between lamps, their type, power, and light distribution. The goal is to achieve optimal illumination that enhances visibility on public roads for drivers and pedestrians while simultaneously minimizing glare, installation costs and maximizing energy efficiency. The proposed methodology is implemented through an algorithm developed in Matlab, with results validated through simulations in Dialux. This information is used to construct a decision matrix, assessed using the CRITIC method across 180 different scenarios within a specific case study. The findings demonstrate the effectiveness of multi-criteria decision-making as a tool for significantly improving the planning and design of lighting in public illumination systems, allowing for selecting the optimal combination of parameters that ensure the best lighting conditions.

Background Apolipoprotein E (APOE) gene polymorphism has been implicated in the pathogenesis of various metabolic disorders, including type 2 diabetes mellitus (T2DM). Type 2 diabetes mellitus (T2DM) is a major public health concern worldwide, including in Pakistan. Cardiovascular problems linked with T2DM have a significant impact on people and society. The study's goal is to investigate the relationship between Apolipoprotein E (ApoE) genotypes, lipid profiles, and cardiovascular complications such as ischemic heart disease (IHD) and stroke. Methods: This study was carried out on 260 subjects, divided into control D1: Diabetics without cardiovascular issues. D2: Diabetics with heart disease. D3: Diabetics with stroke. D4: Diabetics with both heart disease and stroke. Anthropometric parameters (age, BMI) and risk factors (smoking, diabetes duration, hypertension) were assessed in all groups. Serum levels of TC, TG, LDL, HDL, VLDL, creatinine, BSF, and HbA1c were measured. Apolipoprotein E gene polymorphism was determined using PCR-RFLP. Results: Hypertension, BMI, and dyslipidemia, defined as elevated levels of total cholesterol, triglycerides, LDL, HDL, and VLDL, as well as uncontrolled hyperglycemia (elevated fasting blood sugar and glycated hemoglobin) in T2DM, were linked to vascular complications such as IHD and stroke. Hypertension was prevalent in 75.4% of the population, with greater rates among the elderly. Stage 2 hypertension was more prevalent in all age groups. Apolipoprotein E gene polymorphism was discovered, with genotypes 3/3, 4/4, 2/3, and 3/4 being the most prevalent. Genotype 3/4 was more common in diabetics who had IHD/stroke or both problems, whereas genotype 2/3 was linked to DM and stroke. Conclusion: It is concluded that BMI, hypertension, hyperglycemia, atherosclerosis, and dyslipidemia are linked with cardiovascular complications of type 2 diabetes. Apolipoprotein E gene polymorphism is associated with cardiovascular disease in diabetic patients by affecting the lipid profile.

This paper presents an approach to the elastic analysis of beams subjected to Saint-Venant torsion using Green’s theorem and the finite difference method (FDM). The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. A solution to this torsion problem consists of finding a stress function that satisfies the governing equation and the boundary conditions. The FDM is an approximate method for solving problems described with differential equations; it does not involve solving differential equations, equations are formulated with values at selected nodes of the structure. In this paper, the beam’s cross-section was discretized using a two-dimensional grid and additional nodes were introduced on the boundaries. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary conditions. Beams with solid sections as well as multiply connected cross-sections were analyzed using this model; shear stresses and localized stresses at reentrant corners, torsion constant, and warping displacements were determined. Furthermore, beams with thin-walled closed sections, single-cell or multiple-cell, were analyzed using the Prandtl stress function whereby a linear distribution of the shear stresses over the thickness was considered; closed-form solutions for shear stresses and torsion constant were derived. The results obtained in this study showed good agreement with the exact results for rectangular cross-sections, and the accuracy was increased through a grid refinement. For thin-walled closed sections, the shear stresses obtained at the centerline using the closed-form solutions were in agreement with the values using Bredt’s analysis but the maximal values in the cross-section, which did not necessarily occur at the position with the smallest thickness, were higher; in addition, the results using the closed-form solutions were in good agreement with those using FDM.

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and applying the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma as well as non-plasma medium.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

Fluctuation theorems are a class of equalities each of which links a thermodynamic path functional such as heat and work to a state function such as entropy and free energy. Jinwoo and Tanaka [L. Jinwoo and H. Tanaka, Sci. Rep. 5, 7832 (2015)] have shown that each microstate of a fluctuating system can be regarded as an ensemble (or a 'macrostate') if we consider trajectories that reach each microstate. They have revealed that local forms of entropy and free energy are true thermodynamic potentials of each microstate, encoding heat, and work, respectively, within an ensemble of paths that reach each state. Here we show that information that is characterized by the local form of mutual information between two subsystems in a heat bath is also a true thermodynamic potential of each coupled state and encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange [T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)] by showing that the fluctuation theorem holds even within an ensemble of paths that reach a coupled state during dynamic co-evolution of two subsystems.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A energy processes such as the classical heat engines, apparently well follow the second law of thermodynamics; Type B energy processes, such as the newly discovered thermotrophic function that isothermally utilizes environmental heat energy to do useful work in driving ATP synthesis, which follows the first law of thermodynamics (conservation of mass and energy) but does not have to be constrained by the second law, owing to their special asymmetric functions. Several Type-B energy processes such as asymmetric-function-gated isothermal electricity and epicatalysis have been created through human efforts. The innovative efforts on Type-B processes to enable isothermally utilizing endless environmental heat energy could help to liberate all peoples from their dependence on fossil fuel energy, thus helping to reduce greenhouse gas CO2 emissions and control climate change towards a sustainable future for the humanity on Earth.

We have investigated the interfacial dislocations in InxGa1–xN/GaN (0 ≤ x ≤ 0.20) heterostructures using diffraction contrast analysis in a transmission electron microscopy. The analysis indicate that the structural properties of the interface dislocations depend on the indium composition. For lower indium composition up to x = 0.09, we observed that the screw-type dislocations and dislocation half loops occurred at the interface even though the former do not contributes toward elastic relaxation of the misfit strain in the InGaN layer. With the increase of indium composition (0.13 ≤ x ≤ 0.17), in addition to the network of screw-type dislocations, edge-type misfit dislocations were found generated with their density gradually increasing. For higher indium composition (0.18 ≤ x ≤ 0.20), all the interfacial dislocations are transformed into a network of straight misfit dislocations along the <10-10> directions leading to partially relaxation of the InGaN epilayer. The presence of dislocation half loops may be explained by slip on the basal plane, the formation of misfit dislocations are attributed to punch-out mechanism.

Diabetes mellitus (DM) is a metabolic disease characterized by chronic hyperglycemia associated with impaired carbohydrate, lipid and protein metabolism, with concomitant absence of insulin secretion or reduced sensitivity to its metabolic effects. Patients with diabetes mellitus have 30% more risk of developing heart failure and cardiovascular disease with respect to healthy people. Heart and cardiovascular problems are the first cause of death worldwide and the main complications which lead to high healthcare costs. Such complications can be delayed or avoided by taking prescribed medications in conjunction with a healthy lifestyle (i.e. diet and physical activity). The American College of Sports Medicine and the American Diabetes Association recommend that diabetic people reduce total sedentary time by incorporating physical activity in their weekly routine. This narrative literature review has the aim to summarize and present the main guidelines, pre-exercise cardiovascular screening recommendations, and considerations for patients with diabetes and comorbidities who are planning to participate in regular exercise regimens.

In applied mathematics, statistics, operation research, physics, and engineering mathematics, confluent representations of hypergeometric functions in one and two variables are known to exist, and their occurrence in a variety of applications is also well recognised. In this article, we intend to present a new derivation of the extended Watson summation theorem for the Kim et al. given series 4F3. We assessed four attractive integrals involving generalized hypergeometric function as an application. With a few particular cases, this note will come to an end. In the results given above, symmetry appears on its own.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

Maxwell's fish eye has been known to be a perfect lens in optics. In this letter, using the Gibbons-Werner method, namely Gauss-Bonnet theorem on optical geometry of black hole, we extend the calculation of the weak gravitational lensing within the Maxwell's fisheye as a perfect lensing in medium composed of an isotropic refractive index that near-field information can be obtained from far-field distances. Moreover, these results provide an excellent tool to observe compact massive object by weak gravitational lensing within the dark matter medium and to understand the nature of the dark matter that may effect the gravitational waves. Moreover, we show that Gauss-Bonnet theorem is a global effect and this method can be used as a new tool on any optical geometry of compact objects in dark matter medium.

In this note, we demonstrate the quantum no-hiding theorem of Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)] using the IBM 5Q quantum processor. We also analyze the circuit using the ZX calculus of Coecke and Duncan [New J Phys. 13(4), 043016 (2011)], which provides a pictorial/category-theoretic demonstration of the no-hiding theorem.

Starting from the fact that in sensorless control systems of Permanent Magnet Synchronous Motor (PMSM) the load torque can have short and significant variations, this paper presents the sensorless control of a PMSM based on a Linear Adaptive Disturbance Rejection Controller (LADRC) type controller. Essentially, the successful operation of the LADRC controller to achieve PMSM rotor speed control performance depends on a good estimation of the disturbances acting on the system. Traditionally, an Extended State Observer (ESO) is used to make such an estimate. In this paper, it is proposed to use a Disturbance Observer (DO) to estimate the external disturbances, and after their rejection, the LADRC controller ensures an equivalent global behavior of the control system with an ideal double integrator, and thus increased ease in achieving the desired control performance. Control structures and Matlab/Simulink implementation of the sensorless PMSM control system based on LADRC controller with ESO/DO type observer are presented, as well as its use in tandem with a Reinforcement Learning Twin-Delayed Deep Deterministic Policy Gradient (RL-TD3) specially trained agent that provides correction signals for more accurate estimation of external disturbances and hence improved control performance. Qualitatively superior performance is achieved by using LADRC with the RL-TD3 agent control structure in terms of parametric robustness, response time, and steady-state error. Also, by calculating the fractal dimension (DF) of the controlled signal and the PMSM rotor speed, it is found that the higher the DF, the better the performance of the control system. The validation of the superiority of the proposed control structures is carried out by means of numerical simulations in the Matlab/Simulink environment.

Chagas disease is a Neglected Tropical Disease with limited and ineffective therapy. In a search for new antitrypanosomal compounds, we investigated the potential of metabolites from bacteria living in corals and sediments of the Southeastern Brazilian coast. Three corals Tubastraea coccinea, Mussismilia hispida, Madracis decactis and sediments yielded 11 bacterial strains, that were fully identified by MALDI-ToF/MS or gene sequencing, resulting in six genera - Vibrio, Shewanella, Mesoflavibacter, Halomonas, Bacillus and Alteromonas. To conduct this study, EtOAc extracts were prepared and tested against Trypanosoma cruzi. Crude extracts showed IC50 values ranging from 15 to 51 μg/mL against trypomastigotes. The bacterium Mesoflavibacter zeaxanthinifaciens was selected for fractionation, resulting in an active fraction (FII) with IC50 values of 17.7 μg/mL and 23.8 μg/mL against the trypomastigotes and amastigotes, respectively, with neither mammalian cytotoxicity nor hemolytic activity. Using NMR and ESI-HRMS analysis, FII revealed the presence of unsaturated iso-type fatty acids. Its lethal action was investigated, leading to a protein spectral profile of the parasite altered after treatment. FII also induced a rapid permeabilization of the plasma membrane of the parasite, leading to cell death. These findings demonstrate these unsaturated iso-type fatty acids as possible new hits against T. cruzi.

Neurofibromatosis type 2 (NF2) is a genetic syndrome characterized by the growth of benign tumors in the nervous system, particularly bilateral vestibular schwannomas, meningiomas, and ependymomas. This review consolidates the current knowledge on NF2 syndrome, emphasizing the molecular pathology associated with the mutations in the gene of the same name, the NF2 gene, and the subsequent dysfunction of its product, the Merlin protein. Merlin, a tumor suppressor, integrates multiple signaling pathways that regulate cell contact, proliferation, and motility, thereby influencing tumor growth. The loss of Merlin disrupts these pathways, leading to tumorigenesis. We discuss the roles of another two proteins potentially associated with NF2-deficiency as well as Merlin: Yes-associated protein 1 (YAP), which may promote tumor growth, and Raf kinase inhibitory protein (RKIP), which appears to suppress tumor development. Additionally, this review discusses the efficacy of various treatments, such as molecular therapies that target specific pathways or inhibit neomorphic protein-protein interaction caused by NF2-deficiency. This overview not only expands on the fundamental understanding of NF2 pathophysiology but also explores the potential of novel therapeutic targets that affect the clinical approach to NF2 syndrome.

Type two diabetes mellitus (T2DM) represents a chronic condition with increasing prevalence worldwide among the older population. T2DM condition increases the risk of micro and macro-vascular complications as well as the risk of geriatric syndromes as falls, fractures and cognitive impairment. The management of T2DM in the older population represents a challenge for the cli-nician, and a Comprehensive Geriatric Assessment should always be prioritized, in order to tailor the glycate haemoglobin target according to functional and cognitive status comorbidities, life ex-pectancy and type of therapy. According to the most recent guidelines, older adults with T2DM should be cathegorized in three groups: healthy patients with good functional status, patients with complications and reduced functionality and patients at the end of life; for each group the target for the glycemic control is different, also according to the type of treatment drug. The therapeutic ap-proach should always begin with lifestyle changes; after that, several lines of therapies are available, with different mechanism of action and potential effect other than glucose level reduction. Partic-ular interest is growing around sodium-glucose cotransporter-2 inhibitors, due to their effect on the cardiovascular system. In this review we evaluate the therapeutic options available for the treat-ment of older diabetic patients, to ensure a correct treatment approach

In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas sedenions called q-Fibonacci and q-Lucas sedenions. We present some fundamental properties of these type of sedenions such as Binet formulas, exponential generating fuctions, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity.

In this paper, we identify issues and possible solutions in the key area of large-scale antenna systems, also know as Massive Multiple Input Multiple Output (MIMO) systems. Additionally, we propose the use of Massive MIMO technology as a means to tackle the uplink mixed-service communication problem. Under the assumption of an available physical narrowband shared channel (PNSCH), the capacity of the MTC network and, in turn, that of the whole system, can be increased by grouping Machine-Type Communication (MTC) devices into clusters and letting each cluster share the same time-frequency physical resource blocks. We study the feasibility of applying sub-optimal linear detection to the problem of detecting a large number of MTC devices sharing the same time-frequency resources at the uplink of a base station (BS) equipped with a large number of antennas, M. In our study, we derive the achievable lower-bound rates for the studied sub-optimal linear detectors and show that the transmitted power of each MTC device can be reduced as M increases, which is a very important result for powerconstrained MTC devices running on batteries. Our simulation results suggest that, as M is made progressively larger, the performance of sub-optimal linear detection methods approach the matched filter bound, also known as perfect interference-cancellation bound.