In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their "space of evolution" associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (eg, Galileo's group in classical physics). Souriau Lie Group Thermodynamics was also addressed 30 years after Souriau by R. F. Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. Souriau method could then be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory. We will illustrate this method for homogeneous Siegel domains and more especially for Poincaré unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map. For this case, the coadjoint action on moment map is equivariant. For non-null cohomology, we give the case of Lie group SE(2). Finally, we will propose a new geometric definition of Entropy that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Entropy by Legendre transform, as a generalized Casimir invariant function in adjoint representation, where Souriau cocycle is a measure of the lack of equivariance of the moment mapping.

Plant cells' ability to withstand abiotic stress is strongly linked to modifications in their mechanical characteristics. Nevertheless, the lack of a workable method for consistently tracking plant cell mechanical properties severely restricts our comprehension of the mechanical alterations in plant cells under stress. With Polyethylene Glycol (PEG6000), we created a drought-like environment, and we used the Double Resonator Piezoelectric Cytometry (DRPC) method to dynamically and non-invasively track changes in the stress (ΔS) created and viscoelasticity (storage modulus G' and loss modulus G") of protoplasts and suspension cells of rice during drought stress. The findings demonstrate that, rice suspension cells and protoplasts react mechanically differently to 5%–15% PEG6000 stress, implying distinct resistance mechanisms. However, neither of them can withstand 25% PEG6000 stress, they respond mechanically similarly to 25% PEG6000 stress. The results of DRPC are further corroborated by the morphological alterations of rice cells and protoplasts observed under an optical microscope. To sum up, the DRPC technique functions as a precise cellular mechanical sensor and offers novel research tools for the evaluation of plant cell adversity and differentiating between the mechanical reactions of cells and protoplasts under abiotic stress.

The existences of the N→C dative bonds in the complexes between N-containing molecules and fullerenes have been verified both theoretically and experimentally. However, finding stable N→C dative bonds is still a highly challenging task. In this work, we investigated computationally the N→C dative bonds in the complexes formed by fullerene C60 with 1,2,5-chalcogenadiazoles, 2,1,3-benzochalcogenadiazoles and 1,2,4,5-chalcogenatriazoles, respectively. It was found that the N→C dative bonds are formed along with the formation of the N–Ch···C (Ch = S, Se, Te) chalcogen bonds. In the gas phase, from S-containing complexes through Se-containing complexes to Te-containing complexes, the intrinsic interaction energies become more and more negative, which indicates that the N–Ch···C chalcogen bonds can facilitate the formation of the N→C dative bonds. The intrinsic interaction energies are compensated by the large deformation energy of fullerene C60. The total interaction energies of Te-containing complexes are negative, while both of the total interaction energies of S-containing complexes and Se-containing complexes are positive. This means that the N→C dative bonds in the Te-containing complexes are more easily observed in experiments in comparison with those in the S-containing complexes and Se-containing complexes. This study provides a new theoretical perspective on the experimental observation of the N→C dative bonds in the complexes involving fullerenes. Further, the formation of stable N→C dative bonds in the complexes involving fullerenes can significantly change the properties of fullerenes, which will greatly simulate and expand the application range of fullerenes.

Proposed fundamental laws of biology and a model of health and disease underscore the importance of the lymphatic system. The lymphatics are responsible for two of the laws of biology and the fulcrum of health and disease balancing proliferation with regeneration through the immune system. It is responsible for protection from the environment and repair of senile and damaged tissue. Life is constantly bombarded by forces that increase entropy. Lymphatics provide negative entropy to maintain health. Lymphatics help maintain cellular homeostasis removing products of metabolism. Using these principles, the role of lymphatics is investigated in salt sensitivity hypertension, cardiorenal system, the new pillar of heart failure and kidney disease - Sodium-Glucose Transport Protein 2 (SGLT2) Inhibitors, and brain diseases. The realization of organ lymphatics in maintenance of health and disease opens the avenue to new therapeutics. This is the unrealized potential of lymphatic study.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

This study provides a comprehensive analysis of the conformational dynamics of pseudo-endocannabinoid receptors (p-CBRs) CB₁ and CB₂ in response to ligand binding. The ligands studied include N-arachidonoyl dopamine (NADA), Cannabidiol (CBD), known agonists (FUB-MDMB and E3R), and inverse agonists (Taranabant and AM630). Using homology models based on crystal structures (PDB ID: 5U09 for CB₁ and 5ZTY for CB₂), molecular docking, and molecular dynamics (MD) simulations, the research validates the structural integrity and dynamic behaviours of these pseudo-receptors. Induced-fit docking revealed NADA as having the highest binding affinity for both receptors, with docking scores of −13.92 kcal/mol for CB₁ and −13.32 kcal/mol for CB₂, facilitated by key hydrogen bond interactions. MD simulations over 250 ns at ~298 K showed successful equilibration, indicating the most stable interaction for NADA, thereby further validating the models. CB₁ and CB₂ exhibited distinct conformational responses to ligands, with Cα RMSD and Cα RMSF analyses suggesting a more rigid binding pocket for CB₁ and a flexible binding pocket for CB₂. These findings highlight the significance of receptor behaviour and dynamics in the development of cannabinoid-based therapeutics, supporting the potential of CBD and NADA as modulators for CB₁ and CB₂, respectively.

Due to the success of artificial intelligence (AI) applications in the medical field over the past decade, concerns about the explainability of these systems have increased. The reliability requirements of black-box led algorithms for making decisions affecting patients pose a challenge even beyond their accuracy. Recent advances in AI increasingly underscore the need to incorporate explainability into these systems. While most traditional AI methods and expert systems are inherently interpretable, recent literature has focused primarily on explainability techniques for more complex models such as deep learning. This scoping review analyzes the existing literature on explainability and interpretability of AI methods in the medical and clinical field, providing an overview of past and current research trends, and limitations that might impede the development of Explainable Artificial Intelligence (XAI) in medicine, challenges, and possible research directions. In addition, this review discusses possible alternatives for leveraging medical knowledge to improve interpretability in clinical settings, while taking into account the needs of users.

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

In this work, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and response, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and prove the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020 and scalar predictors are GDP and number of beds in hospitals.

The prim objective of commenced article is to determine q-sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analogue of fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-sumudu transform of general class of q-polynomials and q-sumudu transforms of the basic analogues of Fox’s H-function and I-functions.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

Keywords: Linear differential arrays; beam steering; frequency-invariant beamforming.

It is familiar that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with $\varepsilon\mu=1$, a so-called isorefractive or diaphanous ball. Here we re-examine that example, and attempt to extend it to an electromagnetic $\delta$-function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented.

1) Background: Several studies have shown the benefit of drawing when learning anatomy. Virtual Reality (VR) also appears to be useful to increase the understanding of the location of anatomical structures. This study aims to describe how students in an Operating Room Nursing (OR nursing) master study program perceive the benefit of active learning methods, including drawing and the use of VR. 2) Methods: We combined these two methods in a class of 29 students. 38 half-finished drawings of anatomical structures were made. The students were to complete these during lectures with guidance from the teacher. The students also attended a two-hour VR session where they were to find various anatomical structures. A paper questionnaire was applied to evaluate the teaching program. Data were analyzed statistically. 3) Results: The students highly appreciated these learning methods. They reported that drawing made them work more actively during lectures and increased their learning outcome. They also perceived that the use of VR technology increased their understanding of the location of anatomical structures. 4) Conclusion: The combination of drawing and VR technology may be of benefit to OR Nursing students when learning anatomy by both increasing student activity and learning outcomes.

We investigate the influence of the Abrikosov vortex lattice on the Casimir force in a setup constituted by high-temperature superconductors subject to an external magnetic field. The Abrikosov lattice is a property of type II superconductors in which normal and superconducting carriers coexist and these latter define a periodic pattern with squared symmetry. We find that the optical properties determined by spatial redistribution of the superconducting order parameter induce Casimir forces with a periodic structure whose minimal strengths coincide with the vortex cores.

We present a new family of Bessel solutions of the paraxial equation. Such solutions keep their form during propagation due to a quadratic phase factor that makes them scaled propagation invariant fields. The Bessel beams we introduce have the particularity that the topological phase is twice the order of the Bessel function and the argument varies quadratically with the radius

The paper considers the physical consequences of bimetric geodesically (pro jectively) invariant equations of gravitation. The correct expression for the energy- impulse tensor of the gravitational field is obtained and with its help the key role of the gravitational defect of mass-energy for the energy of the newborn universe is shown..

In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes a simple two-step iteration. This approach significantly improves the convergence and requires no surd numbers in computation of the arctangent function.

In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.

The formula of the Generalized Ambiguity Function (GAF) of passive bistatic SAR system using the non-cooperative illuminators which transmit PSK modulating signals is derived to analyze the spatial resolution of the system. The average GAF is introduced to remove the effect of particular sequence of symbols on resolution because the particular sequence of symbols is usually unpredictable before being received. The influence of the waveform parameters of the PSK modulating signals, such as length of the symbol sequence and roll-off factor, on spatial resolution is investigated by numerical simulation. It is confirmed that the influence of the length of the symbol sequence and roll-off factor is very slight but still exists.

Quadruped robots possess significant mobility in complex and uneven terrains due to their outstanding stability and flexibility, making them highly suitable in rescue missions, environmental monitoring, and smart agriculture. With the increasing use of quadruped robots in more demanding scenarios, ensuring accurate and stable state estimation in complex environments has become particularly important. Existing state estimation algorithms relying on multi-sensor fusion, such as those using IMU, LiDAR, and visual data, often face challenges on non-stationary terrains due to issues like foot-end slippage or unstable contact, leading to significant state drift. To tackle this problem, this paper introduces a state estimation algorithm that integrates an Invariant Extended Kalman Filter (InEKF) with a disturbance observer, aiming at estimating the motion state of quadruped robots on non-stationary terrains. Firstly, foot-end slippage is modeled as a deviation in body velocity and explicitly included in the state equations, allowing for a more precise representation of how slippage affects the state. Secondly, the state update process integrates both foot-end velocity and position observations to improve the overall accuracy and comprehensiveness of the estimation. Lastly, a foot-end contact probability model, coupled with an adaptive covariance adjustment strategy, is employed to dynamically modulate the influence of the observations. These enhancements significantly improve the filter's robustness and the accuracy of state estimation in non-stationary terrain scenarios. Experiments conducted with the Jueying Mini quadruped robot on various non-stationary terrains show that the enhanced InEKF method offers notable advantages over traditional filters in compensating for foot-end slippage and adapting to different terrains.

Alzheimer’s disease (AD) and the therapies of AD with anti-amyloid1-42 (Aβ) monoclonal antibodies are associated with the vascular complications of brain edema, hemorrhage, and cerebral amyloid angiopathy (CAA) termed amyloid-related imaging abnormalities (ARIAs). The neuropathology of normal and AD brains demonstrates that monocyte/macrophages (MMs) are critical in successful brain clearance in healthy brain by up-loading, transporting, and degrading Aβ but fail degradation and clearance in AD patients by releasing Aβ into vessels at the blood-brain barrier, causing vasculitis and ARIAs. The naturally-formed epoxides (EpFAs) of polyunsaturated fatty acids (PUFA’s), including arachidonic, docosahexaenoic, and eicosapentaenoic fatty acids, may repair degradation of Aβ by regulating Aβ-degrading enzymes, inflammatory cytokines, and unfolded protein response (UPR) to endoplasmic reticulum stress in a homeostatic fashion. EpFAs are, however, degraded by the soluble epoxide hydrolase enzyme (sEH) but are protected by the sEH inhibitor (sEHI) TPPU. In the cultures of AD patients’ macrophages, TPPU with the epoxide EEQ, and the cGAS/STING inhibitor H-151 increased uptake of Aβ at 2 hours and degradation of Aβ at 24 hours. In conclusion, the soluble epoxide hydrolase inhibitor TPPU with omega-3 fatty acids and the cGAS/STING inhibitor H-151 increase Aβ uptake and degradation in macrophages of AD patients, and potentially enhancing Aβ clearance in the AD brain.

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

The Casimir effect can either work over very short distances or at very low temperatures. At the cosmic scale, we naturally deal with long distances, but at the same time, we encounter extraordinarily low temperatures, namely the CMB (Cosmic Microwave Background) tem- perature. Recently, there has been increased interest in the Casimir effect and its implications in cosmology. Here, we briefly demonstrate that the luminosity and radiation pressure of the CMB is mathematical identical to a theoretical Casimir effect within the Hubble sphere, or actually our solution seems to be valid for any Schwarzschild black hole. The Casimir effect forevery Schwarzschild black hole is identical. This also include the Hubble sphere if we treat it as a Schwarzschild black hole that is related to increased interest in black hole cosmology.

Drowsiness is a main factor for various costly defects, even fatal accidents in areas such as construction, transportation, industry and medicine, due to the lack of monitoring vigilance in the mentioned areas. The implementation of a drowsiness detection system can greatly help to reduce the defects and accident rates by alerting individuals when they enter a drowsy state. This research proposes an Electroencephalography (EEG) based approach for detecting drowsiness. EEG signals are passed through a preprocessing chain composed of artifact removal and segmentation to ensure accurate detection followed by different feature extraction methods to extract the different features related to drowsiness. This work explores the use of various machine learning algorithms such as Support Vector Machine (SVM) the K Nearest Neighbor (KNN) the Naive Bayes (NB) the Decision Tree (DT) and the Multilayer Perceptron (MLP) to analyze EEG signals sourced from the DROZY database, carefully labeled into two distinct states of alertness (awake, and drowsy). Segmentation into 10-second intervals ensures precise detection, while a relevant feature selection layer enhances accuracy and generalizability. The proposed approach achieves high accuracy rates of 99.84% and 96.4% for intra (subject by subject) and inter (cross-subject) modes, respectively. SVM emerges as the most effective model for drowsiness detection in the intra mode, while MLP demonstrates superior accuracy in the inter mode. This research offers a promising avenue for implementing proactive drowsiness detection systems to enhance occupational safety across various industries.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

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.

A new generalized definition of Mersenne numbers is proposed of the form (a^n - (a-1)^n), called Global Generalized Mersenne numbers, or simply Generalized Mersenne numbers and noted GM_{a,n} where a is the base and n is the exponent, both being positive integers. The properties are investigated for prime exponents n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. In particular, it is found that, for any base a, Generalized Mersenne numbers are in general such that (GM_{a,n} - 1) are even and divisible by n, a and (a-1) for any odd prime exponent n and by (a(a-1)+1) for any prime exponent n > 5. The remaining factor is a function of triangular numbers of (a-1), specific to each prime exponent n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, allowing to show first, that (GM_{a,n} - 1) are divisible by 6, and more precisely GM_{a,n} are congruent to 1(mod 12) or 7(mod 12) depending on the congruence of the base a(mod 4); second, that (GM_{a,n} - 1) are divisible by 10 if n == 1(mod 4) and, if n == 3(mod 4), GM_{a,n} == 1(mod 10), or 7(mod 10) or 9(mod 10) depending on the congruence of the base a(mod 5); third, that all factors c_{i} of GM_{a,n} are of the form (2nf_{i}+1) with f_{i} natural integers such that c_{i} is prime itself or the product of primes of the form (2nj+1) with j natural integer; fourth, that for odd prime exponents n, all GM_{a,n} are periodically congruent to either +/-1\(mod 8) or +/-3(mod 8) depending on the congruence of the base a(mod 8); and fifth, that the factors of a composite GM_{a,n} is of the form (2nf_{i}+1) with f_{i} == u(mod 4) and u being either 0, 1, 2 or 3 depending on the congruence of the exponent n(mod 4) and on the congruence of the base a(mod 8). The potential use of Generalized Mersenne primes in cryptography is shortly addressed.

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve their fit. In this paper, we explore a further extension of the quasi-Lindley model. Maximum likelihood, least square error, Anderson-Darling algorithm, and expectation-maximization algorithm are four techniques for estimating the parameters under study. All techniques provide accurate and reliable estimates of the parameters. However, the mean square error of the expectation maximization approach was lower. The usefulness of the proposed model was demonstrated by analyzing a dynamical systems data set, and the analysis shows that it outperforms the other models in all statistical models considered.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm as related to the Weyl Integrable Geometry. After a brief review of the mathematical framework, we will highlight the main results related to inflation within the SIV [9], the growth of the density fluctuations [8], and the application of the SIV to scale-invariant dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals [7]. The connection of the weak-field SIV results to the un-proper time parametrization within the reparametrization paradigm is also discussed [14].

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

The Casimir–Lifshitz friction force and the heating rates of two metal plates with a narrow vacuum gap between them during nonrelativistic motion of one of them are calculated analytically and numerically within the framework of fluctuation electrodynamics. Changes in material properties are taken into account using the Bloch-Grüneisen and modified Bloch-Grüneisen (with finite residual resistance) resistivity models within the Drude approximation. It is shown that identical plates with the same initial temperature have the same heating rate, determined by the power of the friction force, and the possibility of measuring the friction force from the heating kinetics of nonmagnetic metal plates with temperatures of 1–10 K is substantiated.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

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

In this review, we outline our current understanding of the mechanisms involved in the absorption, storage, and transport of dietary vitamin A to the eye, the trafficking of rod opsin protein to the photoreceptor outer segments, which encompasses the logistical backbone required for visual function. Two key mechanisms of this process are emphasized in this manuscript: Ocular and systemic vitamin A membrane transporters, and rhodopsin transporters. Understanding the complementary mechanisms responsible for the generation and proper transport of the retinylidene opsin to the photoreceptor outer segment will eventually shed light on the importance of genes encoded by these proteins, and their relationship on normal visual function and in the pathophysiology of retinal degenerative diseases.

Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a class of estimators, consistent simultanously for both a semiparametric distribution and a distinct parametric distribution, is proposed. These efficient estimators are robust to both gross errors and departures from parametric assumptions, making them ideal for estimating the mean and central moments of common unimodal distributions. This article also illuminates the understanding of the common nature of probability distributions and the measures of them.

In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace-Runge-Lenz vector, the Redmond vector in the presence of an electric field, the Landau-Avron-Sivardière vector when the system is subject to a magnetic field, and the supergeneralized Runge-Lenz vector for the two-center problem. Application to Stark and Zeeman effects are outlined. The existence of constants of motion in the charge-dyon system is also briefly mentioned.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

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.

Hyperspectral image and LiDAR image fusion plays a crucial role in remote sensing by capturing spatial relationships and modeling semantic information for accurate classification and recognition. However, existing methods, like Graph Convolutional Networks (GCNs), face challenges in constructing effective graph structures due to variations in local semantic information and limited receptiveness to large-scale contextual structures. To overcome these limitations, we proposed a invariant attribute-driven binary bi-branch classification (IABC) method which is a unified network that combines binary Convolutional Neural Network (CNN) and GCN with invariant attributes. Our approach utilizes a joint detection framework that can simultaneously learn features from small-scale regular regions and large-scale irregular regions, resulting in an enhanced structured representation of HSI and LiDAR images in the spectral-spatial domain. This approach not only improves the accuracy of classification and recognition but also reduces storage requirements and enables real-time decision-making, which is crucial for effectively processing large-scale remote sensing data. Extensive experiments demonstrates the superior performance of our proposed method in hyperspectral image analysis tasks. The combination of CNNs and GCNs allows for accurate modeling of spatial relationships and effective construction of graph structures. Furthermore, the integration of binary quantization enhances computational efficiency, enabling real-time processing of large-scale data. Therefore, our approach presents a promising opportunity for advancing remote sensing applications using deep learning techniques.

We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet-Liouvillian by applying the Floquet method and Brillouin-Wigner-Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy-dependent self-energy. The obtained effective Floquet-Liouvillian exhibits the two competing instabilities, i.e., parametric and resonance instabilities, which determine the stationary mode as a result of the balance between them in the dissipative DCE. Solving the complex eigenvalue problem of the Floquet-Liouvillian, we have determined the stationary mode with vanishing values of the imaginary parts of the eigenvalues. We find a new non-local multimode DCE represented by a multimode Bogoliubov transformation of the cavity mode and the photon band. We show the practical advantage for the observation of DCE in that we can largely reduce the pump frequency when the cavity system is embedded in a narrow band photonic crystal with a bandgap.

This paper, based on the "Unified Theory of Forces," rigorously proves the formula of de Broglie's wave function. This helps us better understand the following important issues: 1) Theoretically prove and understand the essence of de Broglie's wave function; 2) Prove that when the particle's momentum P is determined, the greater the mass of the particle, the more concentrated its wave function distribution, and the weaker the interference effect; 3) Correct the spatial distribution of the wave function of free particles, proving that the wave function of free particles is strictly constrained within a finite spatial range, which is consistent with the facts we observe.

In this work, an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically is introduced. The goal is to optimally partition the sensor characteristic, i.e. to select the vertices of the approximating polyline (approximant) along with their positions on, the sensor characteristics so that the distance (i.e. the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative non-linear optimization problems are solved, whose essential difference is in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by numerical minimization of the L^1--metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by minimizing numerically the L^2-metric (area-, or energy-based separation measure) for the same set of optimization variables –the locations, and the number of polyline vertices.

Real-time tracking is one of the most challenging problems in computer vision. Most Transformer-based trackers usually require expensive computational and storage power, which leads to the inability of these robust trackers to achieve real-time performance in resource-constrained devices. In this work, we propose a lightweight tracker, AnteaTrack. To localize the target more precisely, we develop a scaling-invariant max-filtering operator employing a sliding window combined with local max-pooling, which filters out the suspected target from the feature and performs an augmented representation while suppressing the background. For a more tight bounding box, we employ Pixel-Shuffle to increase the resolution of the feature map and get a more fine-grained representation of the target. In addition, AnteaTrack can run in real-time at 47 frames per second(FPS) on the CPU. We tested AnteaTrack on 5 datasets, and a large number of experiments have shown that AnteaTrack provides the most efficient solution compared to the same type of CPU real-time trackers. The code will be available at https://github.com/cnchange/AnteaTrack.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm based on the Weyl Integrable Geometry (WIG) as an extension to the standard Einstein General Relativity (EGR). After a brief review of the mathematical framework, where we also highlight the connection between the weak-field SIV equations and the notion of un-proper time parametrization within the reparametrization paradigm, we continue with the main results related to early Universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. In the late time Universe the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth-Moon system.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

Sepsis is a serious disease that can lead to mortality. The etiology of the disease is connected to how the body as a host reacts toward microbes such as bacteria, viruses, and fungi invasion. Current research shows that during sepsis, the reaction toward microbe attacks takes two main phases. The first is known as a cytokine storm, while the second is a vicious cycle of pro-inflammatory responses followed by a strict anti-inflammatory response led by CD4+ Tregs. Various immunomodulatory therapies have been proposed to break the cycle of pro- and anti-inflammatory reactions to sepsis. However, clinical trials did not show promising results, indicating further research into the mechanism that Treg uses to inhibit proinflammatory reactions. We used next-generation sequencing (NGS) analysis of bulk RNA-seq and single-cell RNA-seq data to examine the exact molecular pathways used by Treg to inhibit the immune response in sepsis. Our approach identified ACOD1 (Aconitate Decarboxylase 1) as a primary mediator of Treg suppression of immune cells. We identified and validated CD36 as a downstream target of ACOD1. CD36 is a known metabolite regulator in Tregs. Taken together, our results indicate that targeting ACOD1 could prove valuable in regulating Treg function during sepsis.

Background: Anxiety disorders can be both an independent risk factor of many somatic conditions and the cause of complications of various organic disorders leading to poor prognosis. Objectives: The purpose of this study is to compare the heart rate variability (HRV) recorded both during the day and at night in patients with anxiety disorders and healthy individuals. Methods: The study was conducted on fifty consecutive outpatients with anxiety disorders who participated in intensive group psychotherapy. The diagnosis was made according to DSM-IV-TR criteria using the PSE-10 questionnaire. Out of 50 patients under study, 17 were diagnosed with panic disorder (PD) and 21 with generalized anxiety disorder (GAD). The control group consisted of 40 healthy people. The resulting three groups were compared in terms of circadian HRV using the Oxford Medilog Suprima Holter System. Results: The HRV analysis showed the nocturnal falls in the time and frequency parameters related to parasympathetic activity (rMSSD, pNN50, HF). The most unfavourable alterations were observed in the PD group, which comprised the disappearance of day vs. night amplitude of the majority of HRV parameters. Hence, the PD group was particularly susceptible to the arrhythmic events. It was noticeable that nocturnal vagotonia in the PD group was significantly lower as compared with the GAD and control group. Conclusions: The innovative aspect of the present study was to find a distinct profile of HRV with regard to the types of anxiety disorders because of the existing considerable differences between the nature of PD and GAD.

This paper attempts to address the phenomenon of normal vibrations, (referred to as dynamic vibrations) occurring on a surface which is already in vibrational motion due to other kinematic phenomena. Such a surface will have a metric tensor, normal, and ambient velocity which diverges from the surface’s original various dynamic tensorial descriptors. This paper formulates the wave equation defined in a coordinate space, and extends the equation to observe vibrations on a surface with the use of the Laplace-Beltrami operator in a tensorial fashion drawing on conventions from the newly established Calculus of Moving Surfaces (CMS). The Paper then identifies the way which these normal vibrations will manifest within ambient space. Finally, a counter-intuitive relation between the magnitude of such dynamic vibrations and dynamic surface’s time-dependent mean curvature presents itself, for which dynamic vibrations superimposed on original dynamic motion will eliminate the other, and the surface remains static under an arbitrary initial motion. From this condition, resubstitution within the wave equation yields a novel coupled PDE system which within contains the time-evolution of the surface’s mean curvature and its dynamic vibrations. This analysis can have application for algorithms designed for mechanical stabilization during seismic activity, as well as analyzing stabilization algorithms for other various applications and can also have application with respect to biotechnological innovations for analyzing properties defined on the surface of cell-Like biological entities such as metabolism, lipid content, and actin dynamics.

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail.The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality.

Background: Vestibular Neuritis (VN) induces Acute Vestibular Syndrome (AVS). This study aimed to identify predictive factors of VN recovery by healing and/or compensation. Methods: In this longitudinal and prospective study, 40 patients were included. The first assessment (T0) included medical history taking (general and specific), for cardiovascular risk factors (CVRFs), a battery of diagnostic tests, bithermal caloric test (BCT), video Head Impulse Test (VHIT) and skull vibration induced nystagmus (SVIN). All patients also completed a Dizziness Handicap Inventory (DHI). All assessments were repeated 90±15 days (T3) later. Subjective criteria compensation were based on DHI total score and objective criteria compensation on the instrumental test results. Four groups of patients (A, B, C, D) were delineated by combining patients with normal vs abnormal vestibular tests and patients with normal vs abnormal DH. Results: CVRFs were associated with a poorer recovery of symptoms but not the age or BMI. Vestibular tests mainly BCT (canal paresis %), VHIT (lateral semicircular canal gain) and SVINT (nystagmus slow phase velocity) recovered within normal values in 20%, 20%, 26% of cases respectively at T3 for the 40-patient group. Conclusions: Vascular risk factors (hypercholesterolemia) are correlated with patients who do not recover their symptoms either by healing or compensation. The evolution did not show any significant difference between high or low frequency vestibular tests in patients recovering from their symptoms. However, some patients with objective recovery may continue to show persisting subjective symptoms.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

Proteomics research has become one of the most important topics in the fields of life science and natural science. At present, research on protein–protein interaction networks (PPINs) mainly focuses on detecting protein complexes or function modules. However, existing approaches are either ineffective or incomplete. In this paper, we investigate function module detection mechanisms in PPIN, including open databases, existing detection algorithms and recent solutions. After that, we describe the proposed solution based on simplified swarm optimization (SSO) algorithm and gene ontology knowledge. The proposed solution implements SSO algorithm for clustering proteins with similar function, and imports biological gene ontology knowledge for further identifying function complexes and improving detection accuracy. Furthermore, we use four different categories of species dataset for experiment: Fruitfly, Mouse, Scere, and Human. The testing and analysis result show that the proposed solution is feasible, efficient and could achieve a higher accuracy of prediction than existing approaches.

The invariant mass of free particles is used to derive a bound-state equation for several particle atomic systems at rest. This relativistic-kinematic bound-state equation is applied to the hydrogen and helium atoms. The derived equation has the well-known solutions for the single-electron bound states of the hydrogen atom, and the two-electron states of the helium atom. For the hydrogen atom, existence of the two-particle bound states, for which the electron and the proton kinetic energies are of the same order of magnitude, is predicted. The three-particle bound states with the same feature of the kinetic energies can exist in the helium atom. Radiative operators for processes involving the hydrogen two-particle bound states, are obtained. It is discussed that these new two- and three-particle bound states should be optically inactive.

This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest only is considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.

All the arguments of a wavefunction are defined at the same instant implying a notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts are in contradiction with special relativity. We propose to define the wavefunction with respect to the invariant proper time of special relativity instead of standard time. Moreover, we shall adopt the original idea of Schrodinger suggesting that the wavefunction represents an ontological cloud-like object that we shall call ‘individual fabric’ that has a finite density amplitude vanishing at infinity. Consequently, measurement can be assimilated to a confining potential that triggers an inherent non-local mechanism within the individual fabric. It is formalised by multiplying the wavefunction with a localising gaussian as in the GRW theory but in a deterministic manner.

Eddy current testing can be used to interrogate steels but it is hampered by the lift-off distance of the sensor. Previously, the lift-off point of intersection (LOI) feature has been found for the pulsed eddy current (PEC) testing. In this paper, a lift-off invariant inductance (LII) feature is proposed for the multi-frequency eddy current (MEC) testing, which merely targets the ferromagnetic steels. That is, at a certain working frequency, the measured inductance signal is found nearly immune to the lift-off distance of the sensor. Such working frequency and inductance are termed as the lift-off invariant frequency (LIF) and LII. Through simulations and experimental measurements of different steels under the multi-frequency manner, the LII has been verified to be merely related to the sensor parameters and independent of different steels. By referring to the LIF of the test piece and using an iterative inverse solver, one of the steel properties (either the electrical conductivity or magnetic permeability) can be reconstructed with a high accuracy.

In this article, the geometry of pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci-generalized pseudoparallel invariant submanifolds of an almost $\alpha$-cosymplectic $(\kappa,\mu,\nu)$ space has been searched under the some conditions. We also give some characterizations for such submanifolds. I think that obtained new results contribute to differential geometry.

Hematological malignancies refer to a heterogeneous group of neoplastic conditions of lymphoid and hematopoietic tissues classified in leukemias, Hodgkin and non-Hodgkin lymphomas and multiple myeloma, according to their presumed cell of origin, genetic abnormalities, and clinical features. Metabolic adaptation and immune escape, which influence various cellular functions including proliferation and survival of hematological malignant tumor cells, are major aspects of these malignancies that lead to therapeutic drug resistance. Targeting specific metabolic pathways is emerging as novel therapeutic strategy in hematopoietic neoplasms, particularly in acute myeloid leukemia and multiple myeloma. In this context, CD147, also known as Extracellular Matrix Metalloproteinase Inducer (EMMPRIN) or Basigin, is one target-candidate involved in reprogramming metabolism in different cancer cells, including hematological malignant tumor cells. CD147 overexpression significantly contributes to the metabolic transformation of these cancer cells, by mediating signaling pathway, growth, metastasis and metabolic reprogramming, through its interaction, direct or not, with various membrane proteins related to metabolic, regulation including monocarboxylated transporters, integrins, P-glycoprotein and Glucose Transporter 1. This review explores the metabolic functions of CD147 and its impact on the tumor microenvironment, influencing the progression and neoplastic transformation in leukemias, myeloma and lymphomas. Furthermore, we highlight new opportunities for the development of targeted therapies against CD147, potentially improving the treatment of hematologic malignancies.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

Mutations in KRT1 (keratin 1) or KRT10 (keratin 10) underlie a spectrum of diseases known as keratinopathic ichthyoses. Epidermolytic ichthyosis (EI) is caused by heterozygous missense mutations in the genes KRT1 or KRT10, mutations in the gene KRT2 (keratin 2) lead to superficial epidermolytic ichthyosis, and congenital reticular ichthyosiform erythroderma is caused by frameshift mutations in the genes KRT10 or KRT1, which lead to the phenomenon of revertant mosaicism. Epidermolytic ichthyosis is also present in a mosaic pattern known as epidermolytic (acantholytic) nevus, isolated or diffuse. In the latter case, gonadic involvement is possible, leading to a rare pedigree in which a parent with diffuse epidermolytic nevus (linear EI) gives birth to a child affected by EI. We present here an update on the phenotypic presentations of keratinopathic ichthyoses and their molecular mechanisms.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

In this paper, we introduce the generalized Tetranacci quaternions and present some properties of these quaternions.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

Objectives: Stress urinary incontinence (SUI) negatively affects the quality of life and sexual function in women. This study aimed to evaluate the efficacy of radiofrequency (RF) therapy in reducing SUI symptoms and its impact on sexual function. Methods: Thirty-four women with SUI were enrolled and underwent a single RF treatment session using the Viveve® System (Viveve Medical Inc., USA) with parameters of 90 J/cm² and 220 pulses per hour. Assessments at baseline and 6 months post-treatment included perineal ultrasound and personal interviews to evaluate lower urinary tract symptoms and sexual function. Urodynamic studies, voiding diaries, and questionnaires such as the Female Sexual Function Index (FSFI), Overactive Bladder Symp-tom Score (OABSS), Urogenital Distress Inventory-6 (UDI-6), Incontinence Impact Question-naire-7 (IIQ-7), and International Consultation on Incontinence Questionnaire-Short Form (ICIQ-SF) measured outcomes. Results: RF therapy significantly improved sexual function, with higher FSFI scores in all domains except pain at 6 months. SUI symptoms were significantly re-duced, as indicated by improved scores on OABSS, UDI-6, IIQ-7, and ICIQ-SF, alongside better voiding diary results. Anatomical changes included reduced bladder neck mobility, decreased vaginal width, and a reduced rotation angle of the proximal urethra. Conclusions: RF therapy is effective and safe for treating mild to moderate SUI and enhances sexual function, potentially due to changes in vaginal topography. These results suggest RF therapy as a viable non-surgical op-tion for managing SUI and improving sexual health.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

This paper investigates generalized Bayesian (GB) inference in the context of a one-parameter Pareto distribution. The study focuses on the derivation of generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the Pareto distribution using type II censored data. In addition, the study investigates a one-sample prediction approach to examine generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP). To evaluate the performance of these estimation and prediction methods, Monte Carlo simulations were performed comparing GBE with GEBE and GBP with GEBP for different parameter values and learning rate parameters (LRP).

Background: Molecular genetic events are among the numerous factors affecting the clinical course of papillary thyroid carcinoma (PTC). Recent studies have demonstrated that aberrant expression of miRNA, as well as different thyroid-related genes, correlate with the aggressive clinical course of PTC and unfavorable treatment outcome, which opens up new avenues for using them in personalization of the treatment strategy for patients with PTC. In the present work, our goal was to assess the applicability of molecular markers in preoperative diagnosis of aggressive variants of papillary thyroid cancer. Methods: The molecular genetic profile (expression levels of 34 different markers and BRAF mutation) was studied for 108 cytology specimens collected by fine-needle aspiration biopsy in patients with PTC having different clinical manifestations. Results: Statistically significant differences with adjustment for multiple comparisons (p &lt; 0.0015) for clinically aggressive variants of PTC were obtained for four markers: miRNA-146b, miRNA-221, FN1, and CDKN2A. Weak statistical correlation (0.0015&lt; р&lt;0.05) was observed for miRNA-31, -375, -551b, -148b, -125b, mtDNA, CITED1, TPO, HMGA2, CLU, NIS, SERPINA1, TFF3, and TMPRSS4. Conclusions: The recurrence risk of papillary thyroid carcinoma can be preoperatively predicted using miRNA-221, the fibronectin and cyclin-dependent kinase inhibitor 2A genes.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

Observer-based control is the most commonly used method in the control of electro-hydraulic servo system (EHSS) with uncertainties, but it suffers from the drawback of low accuracy under the influence of large external load forces and disturbances. To address this problem, this paper proposes a novel compensation function observer-based backstepping sliding mode control (BSMC) approach to achieve high-accuracy tracking control. In particular, the model uncertainties, including nonlinearities, parameter perturbations and external disturbances are analyzed and treated together as a lumped disturbance. Then, a fourth-order compensation function observer (CFO) is constructed, which fully utilizes the system state information to accurately estimate the lumped disturbance. On this basis, the estimate of the lumped disturbance is incorporated into the design of an backstepping sliding mode controller, allowing the control system to compensate for the disturbance effect. The stability of the closed-loop control system under the CFO and BSMC is rigorously proven through the use of Lyapunov theory, which guarantees that all the tracking error signals converge exponentially to the origin. Comparative simulations are carried out to show the effectiveness and efficiency of the proposed approach, i.e., compared with PID and ESO-based BSMC methods, the tracking accuracy is improved by 99.93% and 99.76%, respectively.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

LCK, a member of the Scr kinase family, is a non-receptor tyrosine kinase involved in immune cell activation, antigen recognition, tumor growth, and cytotoxic response. The enzyme has usually been linked to T lymphocyte activation upon antigen recognition. Lck activation is central to CD4, CD8, and NK activation. However, recently, it has become clearer that activating the enzyme in CD8 cells can be independent of antigen presentation and enhance cytotoxic response. The role of Lck in NK cytotoxic function has been controversial in a similar fashion as the role of the enzyme in CAR T cells. Inhibition of Lck has been mainly to treat hematologic malignancies with a high rate of success. They may be useful in treating other tumor types, and they may be useful to prevent cell exhaustion. New, more selective inhibitors have been documented, and they have shown inter-esting activities not only in tumor growth but in the treatment of autoimmune diseases, asthma, and graft vs host disease. Drug repurposing and bioinformatics can aid in solving several unsolved is-sues on the role of Lck in cancer. In summary, the role of Lck in immune response and tumor growth is not a simple event and requires more research.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

Lung involvement in rheumatic diseases is a major determinant of patient morbidity and mortality; however, its diagnosis depends on the detection methods used. We compared the incidence of pulmonary involvement in newly diagnosed treatment-naive patients with rheumatic diseases, as assessed by pulmonary function tests (PFTs) and chest high-resolution computed tomography (HRCT). This retrospective study reviewed the symptoms, spirometry results, and HRCT scans of 22 newly diagnosed, treatment-naïve patients and age-matched controls from the University General Hospital “Attikon”, Athens, Greece, between January 2021 and December 2023. Correlations between clinical findings and spirometry parameters were tested. HRCT scans revealed lung abnormalities in all patients, including peribronchial wall thickening (61.5%), ground glass opacities (59.1%), parenchymal bands (54.5%), air-trapping (50%), reticular patterns (45.5%), bronchiectatic changes (40.9%), and parenchymal opacities (31.8%). PFTs, performed in 17/22 (77.3%) patients, revealed definite pathology in 5 patients (restrictive: N=4; obstructive: N=1). No association was found between spirometric indices and clinical parameters. The results indicate a higher prevalence of abnormal chest CT than of PFT abnormalities, suggesting that HRCT is more sensitive in detecting early lung involvement in pediatric patients with rheumatic disease and should be considered in the routine evaluation of these patients.

This review summarizes studies dedicated to the assessment of microvascular function based on microcirculatory oscillations monitored by the FMSF technique. Two approaches are presented. The first approach uses oscillatory parameters measured under normoxia conditions, expressed as flowmotion (FM), vasomotion (VM), and the normoxia oscillatory index (NOI). These parameters have been used for identification of impaired microcirculatory oscillations associated with intense physical exercise, post-COVID syndrome, psychological stress, and erectile dysfunction. The second approach involves characterization of the microcirculatory response to hypoxia based on the measurement of hypoxia sensitivity (HS). The HS parameter is used to characterize microvascular complications in diabetes, such as diabetic kidney disease and diabetic foot ulcers. Based on research conducted by the authors of this review, the FMSF parameter ranges characterizing microvascular function are presented. The diagnostic approach to assessing microvascular function based on flowmotion monitored by the FMSF technique has a wide range of applications and potential to be integrated into widespread medical practice.

To advance probiotic research, a comprehensive understanding of bacterial interactions with human physiology at the molecular and cellular levels is fundamental. Lacticaseibacillus rhamnosus LGG® is a bacterial strain that has long been recognized for its beneficial effects on human health. Probiotic effector molecules derived from LGG®, including secreted proteins, surface-anchored proteins, polysaccharides, and lipoteichoic acids, that interact with host physiological processes have been identified. In vitro and animal studies have revealed that specific LGG® effector molecules stimulate epithelial cell survival, preserve intestinal barrier integrity, reduce oxidative stress, mitigate excessive mucosal inflammation, enhance IgA secretion, and provide long-term protection through epigenetic imprinting. Pili on the cell surface of LGG® promote adhesion to the intestinal mucosa and ensure close contact to host cells. Extracellular vesicles produced by LGG® recapitulate many of these effects through their cargo of effector molecules. Collectively, the effector molecules of LGG® exert a significant influence on both the gut mucosa and immune system, that promotes intestinal homeostasis and immune tolerance.

We propose a neural-network-based watermarking method that introduces the quantized activation function that approximates the quantization of JPEG compression. Many neural-network-based watermarking methods have been proposed. Conventional methods have acquired robustness against various attacks by introducing an attack simulation layer between the embedding network and the extraction network. The quantization process of JPEG compression was replaced by the noise addition process in the attack layer of the conventional methods. In this paper, we propose a quantized activation function that can simulate the JPEG quantization standard as it is in order to improve the robustness against the JPEG compression. Our quantized activation function consists of several hyperbolic tangent functions and is applied as an activation function for neural networks. Our network was introduced in the attack layer of ReDMark proposed by Ahmadi et al. to compare it with their method. That is, the embedding and extraction networks had the same structure. We compared the usual JPEG compressed images and the images applying the quantized activation function. The results showed that a network with quantized activation functions can approximate JPEG compression with high accuracy. We also compared the bit error rate (BER) of estimated watermarks generated by our network with those generated by ReDMark. We found that our network was able to produce estimated watermarks with lower BERs than those of ReDMark. Therefore, our network outperformed the conventional method with respect to image quality and BER.

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.

Generalized Bayesian (GB) is a Bayesian approach based on the learning rate parameter (LRP) () as a fraction of the power of the likelihood function. In this paper, we consider the GB method to perform inference studies for a class of exponential distributions. Generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the considered distributions were obtained based on the censored type II samples. In addition, generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP) were considered using a one-sample prediction scheme. Monte Carlo simulations were performed to compare the performance of the GBE and GEBE estimation results and the GBP and GEBP prediction results for different values of the LRP.

Chronic kidney disease patients treated by hemodialysis present a high cardio-vascular morbidity and mortality. There is an imperative need for novel biomarkers in identifying and to offer possible therapeutically intervention in these patients. We performed a prospective observational cohort study on 77 patients in the period October 2021 – October 2023. We measured serum plasma levels of Interleukin 1-Beta, Galectin 3, human suppression of tumorigenicity factor 2, bone morphogenetic protein 2 and fibroblastic growth factor 23 at the inclusion. We evaluated the correlations of these biomarkers with cardiac function and structure evaluated by echocardiography. Mean age was 61.02 (±11.81) years, 45 (56.2%) males and with a dialysis vintage of 4.95 (2.4-7.8) years. Median ejection fraction was 51 (43-54 %) and more than two thirds of the patients presented valvular calcifications. Overall mortality was 22%. Interleukin 1-Beta correlated positively with ejection fraction and global longitudinal strain and negatively with left atrium diameter and left ventricle tele systolic diameter. Galectin 3 values negatively correlated with aortic valve fibrosis and mitral valve calcifications and human suppression tumorigenity factor 2 negatively correlated with mitral valve calcifications. Some of these novel biomarkers could be used to better asses the cardio-vascular disease in patients on maintenance hemodialysis.

Let an odd integer \(\mathcal{X}\) be expressed as $\left\{\sum\limits_{M > m} b_M 2^M\right\} + 2^m - 1,$ where $b_M \in \{0, 1\}$ and $2^m - 1$ is referred to as the Governor. In Collatz-type functions, a high index Governor is eventually reduced to $2^1 - 1$. For the $3\mathcal{Z} + 1$ sequence, the Governor occurring in the Trivial cycle is $2^1 - 1$, while for the $5\mathcal{Z} + 1$ sequence, the Trivial Governors are $2^2 - 1$ and $2^1 - 1$. Therefore, in these specific sequences, the Collatz function reduces the Governor $2^m - 1$ to the Trivial Governor $2^{\mathcal{T}} - 1$. Once this Trivial Governor is reached, it can evolve to a higher index Governor through interactions with other terms. This feature allows $\mathcal{X}$ to reappear in a Collatz-type sequence, since $2^m - 1 = 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1).$ Thus, if $\mathcal{X}$ reappears, at least one odd ancestor of $\left\{\sum\limits_{M > m} b_M 2^M\right\} + 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1)$ must have the Governor $2^m - 1$. Ancestor mapping shows that all odd ancestors of $\mathcal{X}$ have the Trivial Governor for the respective Collatz sequence. This implies that odd integers that repeat in the $3\mathcal{Z} + 1$ sequence have the Governor $2^1 - 1$, while those forming a repeating cycle in the $5\mathcal{Z} + 1$ sequence have either $2^2 - 1$ or $2^1 - 1$ as the Governor. Successor mapping for the $3\mathcal{Z} + 1$ sequence further indicates that there are no auxiliary cycles, as the Trivial Governor is always transformed into a different index Governor. Similarly, successor mapping for the $5\mathcal{Z} + 1$ sequence reveals that the smallest odd integers forming an auxiliary cycle are smaller than $2^5$. Finally, attempts to identify integers that diverge for the $3\mathcal{Z} + 1$ sequence suggest that no such integers exist.

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle (MGRP). Within this framework new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: {\bf(i)} We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and the tensor to scalar ratio $r$. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. {\bf(ii)} The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. {\bf(iii)} For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a {\it new non-diagonal} coherent state representation complementary to the known Sudarshan diagonal one. {\bf(iv)} Mean value generators of $Mp(2)$ are related to the adiabatic invariant and topological charge of the spacetime (matrix element of the transition $-\infty < t < \infty$). {\bf(v)} The basic {\it even} and {\it odd} $n$-sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (in particular continuum for $n \rightarrow \infty$), they do not require any extrinsic generation process as the standard Schrodinger cat states, and are {\it entangled}. {\bf(vi)} The gravity or cosmological domains in one side and another of the Planck scale are {\it entangled}. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity reqion and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. {\bf(vii)} The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

Background: Periodontitis is a disease that leads to serious functional and aesthetic dysfunctions resulting in impairment of life quality; it exists in different forms and its etiology is related with multiple component causes. Angiogenesis, together with inflammatory infiltrate, are two key processes in the evolution of inflammatory processes involving gingival tissues. The aim of this study was to evaluate their alterations in relation to some important periodontal diseases-associated factors (i.e. smoke, sex, age, plaque, pus, probing pocket depth) in patients with diagnosis of Generalized Aggressive Periodontitis (GAP). Methods: Eighteen subjects with GAP were enrolled for this study. Percentage of inflammatory cells and vascular area were measured and evaluated in relation with each periodontal diseases-associated factor. Results: The results showed a significant decrease of the percentage of vascular area in association with almost all the periodontal diseases-related factors (smoke, age, PPD, plaque) and not significant differences in the percentage of inflammatory cells. Conclusions: Data suggest that, even if these factors are often commonly related to worsening of periodontal status, they did not affect inflammatory and vascular pattern, as we can assume. For the future, additional studies, aimed to evaluated each singular factor in a wider sample size, should be planned.

In recent experimental studies, we reported the aggravating effects of Asian sand dust (ASD) on male reproductive function in mice. However, the effects of fetal ASD exposure on male reproductive function have not been investigated. The present study investigated the effects of fetal ASD exposure on reproductive function in male offspring. Using pregnant CD-1 mice, ASD was administered intratracheally on days 7 and 14 of gestation, and the reproductive function of male offspring was determined at 5, 10, and 15 weeks after birth. The secondary sex ratio was significantly lower in the fetal ASD-exposed mice than in the controls. Histologic examination showed partial vacuolation of seminiferous tubules in immature mice. Moreover, daily sperm production (DSP) was significantly less in the fetal ASD-exposed mice than in the controls. DSP in the fetal ASD-exposed mice was approximately 10% less than the controls at both 5 and 10 weeks. However, both the histologic changes and the DSP decrease were reversed as the mice matured. These findings suggest that ASD exposure affects both the fetal development and the reproductive function of male offspring. In the future, it will be necessary to clarify the onset mechanisms of ASD-induced male fetus death and male reproductive disorders.

Selecting the optimal activation function for training deep neural networks has always been challenging because it significantly impacts the neural network’s performance and training speed. At this point, researchers are more likely to employ RELU than other well-known activation functions. After RELU, researchers have proposed many activation functions to improve RELU. None of them was capable of surpassing RELU as their most significant rival. SWISH outperformed RELU in several challenging experiments like classification, object detection, and tracking. Replacing RELU units with SWISH, which improves performance in many tasks. This paper proposed a new activation function surpassing Google’s brain’s SWISH function, Which we named AIF. Experiments indicate that our proposed activation function outperforms SWISH in various tasks.

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e. its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called "quantum potential" in this context is briefly discussed.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.