Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.

In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{\beta,\alpha}$, $0

Generalized zero-shot learning (GZSL) aims to simultaneously recognize both seen classes and unseen classes by training only on seen class samples and auxiliary semantic descriptions. Recent state-of-the-art methods infer unseen classes based on semantic information or synthesize unseen classes using generative models based on semantic information, all of which rely on the correct alignment of visual-semantic features. However, they often overlook the inconsistency between original visual features and semantic attributes. Additionally, due to the existence of cross-modal dataset biases, the visual features extracted and synthesized by the model may also mismatch with some semantic features, which could hinder the model from properly aligning visual-semantic features. To address this issue, this paper proposes a GZSL framework that enhances the consistency of visual-semantic features using self-distillation and disentanglement network (SDDN). The aim is to utilize self-distillation and disentanglement network to obtain semantically consistent refined visual features and non-redundant semantic features to enhance the consistency of visual-semantic features. Firstly, SDDN utilizes self-distillation technology to refine the extracted and synthesized visual features of the model. Subsequently, the visual-semantic features are then disentangled and aligned using a disentanglement network to enhance the consistency of the visual-semantic features. Finally, the consistent visual-semantic features are fused to jointly train a GZSL classifier. Extensive experiments demonstrate that the proposed method achieves more competitive results on four challenging benchmark datasets (AWA2, CUB, FLO, and SUN).

The fractal dimension of is identified in this paper. More importantly, the undertaken research has shown how affects the Koch snowflake . The study has demonstrated the existence of negative values of (Koch snowflake), which connects to a considerable number of extremely intriguing mathematical and physical research areas. The information-theoretic impact on the Sierpiniski Gasket dimension , which corresponds to , was treated in a more fundamental way. Notably, the credibility of this current study adds to the existing kThe fractal dimension of is identified in this paper. More importantly, the undertaken research has shown how affects the Koch snowflake . The study has demonstrated the existence of negative values of (Koch snowflake), which connects to a considerable number of extremely intriguing mathematical and physical research areas. The information-theoretic impact on the Sierpiniski Gasket dimension , which corresponds to , was treated in a more fundamental way. Notably, the credibility of this current study adds to the existing knowledge for the information- theoretic fractal dimensions. On another applicative note, this paper offers some potential applications of fractal dimension to smart cities. The investigation of the threshold theorems for and in terms of the triad is part of the next study phase. Additionally, investigating the newly obtained 's corresponding arbitrary Sierpinski Gasket for the first time.applicative note, this paper offers some potential applications of fractal dimension to smart cities. The investigation of the threshold theorems for and in terms of the triad is part of the next study phase. Additionally, investigating the newly obtained 's corresponding arbitrary Sierpinski Gasket for the first time.

The present study aims to show on the one hand how easily one can get confused when doing research on the internet. Different platforms, fora and homepages supply the visitor with different - and sometimes contradictory - information. On the other hand, we show how to overcome these contradictions and produce valuable research based on almost all sources. For our study, we use the example of the Feit-Thompson conjecture, which is - in opposite to the well-known Feit-Thompson theorem - not widely known. We try to clarify the scientific literature on this topic and we embed our own result into the present state of art. We prove that pq−1p−1 does not divide qp−1q−1 if p and q are twin primes, i.e. p=q+2. Thus we prove that the Feit-Thompson conjecture is true for twin prime numbers.

Objective: To evaluate the variables influencing the length of stay (LoS) for COVID-19 ICU patients at Tygerberg Hospital (Cape Town) and to identify the covariates that significantly influenced it and any potential risk factors associated with LoS. Methods and Results: Poisson, negative binomial (NB), Hurdle–Poisson, and Hurdle–NB regression models were used to model the LoS in this prospective cohort study. The fitted models were compared using the Akaike information criterion (AIC), Vuong’s test criteria, and Rootograms. Based on the chosen performance criteria, the NB model provided the best fit outperforming other candidate models. The baseline LoS count was 8 days. On average, antibiotics reduced LoS by 0.74-fold (95% CI 0.62-0.89) compared to not taking antibiotics. The second wave had a significant effect on the average LoS, which decreased by 0.36-fold (95% CI 0.14-0.93) compared to the first wave. Average LoS increased by 1.01-fold (95% CI 1.01-1.02) for every one-year increase in the age of the patient and by 1.02-fold (95% CI 1.01-1.03) for every 1 unit increase in neutrophils. A 1 ng/L increase in log (TropT) levels decreased the average LoS by 0.87-fold (95% CI 0.81-0.93) similarly, a unit increase in the PF ratio decreased the average LoS by 0.998-fold (95% CI 0.997-0.999) respectively. Conclusion: The study identified common clinical characteristics associated with length of stay in ICU for COVID-19 patients, including age at admission, PF ratio, neutrophils, TropT, Wave, and antibiotic use. These results can aid in identifying risk factors for increased length of stay, assist in healthcare systems planning, and aid in evaluating different models for analysing this type of data.

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.

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.

The aim of this paper is to investigate whether multifractal analysis can be applied to study choroidal blood vessels and help ophthalmologists for the early diagnosis of retinitis pigmentosa (RP). In a case study, we use Spectral Domain Optical Coherence Tomography (SDOCT), which is a non-invasive and highly sensitive imaging technique of the retina and choroid. The image of a choroidal branching pattern can be regarded as a multifractal. Therefore, we calculate generalized Renyi point-centered dimensions, which is considered a measure of inhomogeneity of data, to prove that it increases in the patients with RP with respect to the control group.

In descriptive statistics, U -statistics arise naturally in producing minimum-variance unbiased estimators. In 1984, Serfling considered the distribution formed by evaluating the kernel of the U -statistics and proposed generalized L-statistics which includes Hodges-Lehamnn estimator and Bickel-Lehmann spread as special cases. However, the structures of the kernel distributions remain unclear. In 1954, Hodges and Lehmann demonstrated that if X and Y are independently sampled from the same unimodal distribution, X − Y will exhibit symmetrical unimodality with its peak centered at zero. Building upon this foundational work, the current study delves into the structure of the kernel distribution. It is shown that the kth central moment kernel distributions (k > 2) derived from a unimodal distribution exhibit location invariance and is also nearly unimodal with the mode and median close to zero. This article provides an approach to study the general structure of kernel distributions.

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.

This study examines the moderating effect of trained human capital on the associations of accounting information systems, generalized auditing software, and technology adoption with the performance of external auditors among Saudi listed companies. This study used a survey-based methodology. The final sample consisted of 136 responses with an 8% response rate. Using Smart-PL4 analysis, the results showed that there is a positive correlation between accounting information systems and external auditors. Conversely, a negative relationship between generalized auditing software and external auditors has been documented. In addition, this study reported a negative association between technology adoption and external auditors. However, the results highlight the positive relationship between trained human capital and external auditors. Overall, this study provides valuable insights for accounting and auditing policymakers on how external auditors’ performance is influenced by several factors in the Saudi audit market.

The current letter complements my info-geometric discoveries, especially those provided from two papers of mine. Fundamentally, the statistical relativization of the Generalized Brownian Motion Manifold. Following this innovative and unprecedented track of research will open a plethora of numerous info-geometric investigations to many unexplored related phenomena in the hope to uncover more new interpretations for the Generalized Brownian Motion Manifold from an info-geometric perspective.

This paper provides a first-time ever unification of information theory, semi-group theory with the theory of uncertain reasoning, through functional perspective. Fundamentally, the threshold theorems for the inference functional were devised. Furthermore, numerical experiments are illustrated. The complex proofs in our paper are original results which emphasizes the credibility of the class of Rényi Generalized Entropies as measures of information, and that the field is open to extend an enhanced methodology regarding queuing networks with heavy tails.

In the current work, the stable queueuing system's Generalised Z-Entropy (GZE) of Rényian formalism is examined in its fractal dimension. Notably, fractal dimension’s resulting behaviour that corresponds to the GZE parameters is examined through numerical tests. This research makes a substantial generalization in the literature by fusing fractal geometry and information theory to shed light on how entropy and complexity interact. More fundamentally, the significant role of fractal dimension to advance Big Data Analytics(BDAs) is highlighted. Closing remarks combined with open problems and the next phase of research are provided.

Dynamic behavior of coaxial axisymmetric planar cracks in the transversely isotropic magneto-electro-elastic (MEE) material in transient in-plane magneto-electro-mechanical loading is studied. Magneto-electrically impermeable as well as permeable cracks are assumed for crack surface. In the first step, considering prismatic and radial dynamic dislocations, electric and magnetic jumps are obtained through Laplace and Hankel transforms. These solutions are utilized to derive singular integral equations in the Laplace domain for the axisymmetric penny-shaped and annular cracks. Derived Cauchy singular type integral equations are solved to obtain the density of dislocation on the crack surfaces. Dislocation densities are utilized in computation of the dynamic stress intensity factors, electric displacement and magnetic induction in the vicinity tips of crack tips. Finally, some numerical case studies of a single and multiple cracks are presented. The effect of system parameters on the results is then discussed.

Information geometry (IG) is a fascinating combination of differential geometry and statistics where a Riemannian manifold's structure is applied to a statistical model. It may find numerous fascinating uses in the domains of theoretical neurology, machine learning, complexity, and (quantum) information theory, among others. (IG) aims to provide a differential-geometric perspective on statistical geodesic models' structure. In this case, IG, KD, and J-divergence (JD) are used to define the manifold of the Generalised Brownian Motion (GBM). Consequently, the geodesic equations (GEs) are devised, and GB information matrix exponential (IME) is presented. Moreover, for first time ever, the necessary and sufficient mathematical requirement that characterizes the developability of Generalized Brownian Motion(GBM) manifold is devised. Also, a novel sufficient and necessary conditions which characterizes the regions where the surface describing GBM is minimal is determined. Also, it is shown that GBM has a non-zero 0-Gaussian and Ricci curvatures. Consequently, this advances the establishment of a unified GBM- Relativistic Info-Geometric based analysis.

Modelling diameter distribution is an integral part of forest management. It requires the use of a suitable probability density function or cumulative distribution function with the appropriate fitting method. In this study, we compared the suitability of eight probability density functions fitted by derivative and optimization methods used for diameter distribution estimation of forest stands. The derivation and optimization were used on A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (2 and 3-parameter). We used data from 167 permanent sample plots from Atlantic forest (Quercus robur) and 59 temporary sample plots from tropical forests (Tectona grandis). The quality of the fits was evaluated with different indices such as Kolmogorov–Smirnov, Cramer-von Mises, mean absolute error, bias and mean squared error. The results showed Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, 3-parameter Weibull and generalized beta had consistent performance regardless of the fitting methods. The quality of fits produced by gamma, Gumbel and 2-parameter Weibull was poor.

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

In this paper, a positive answer to the open question of Fabino et al. is given, and the concept of I\c sik type set valued contractions is introduced and fixed point theorem for such contractions is established. Examples to support main theorems are given, and an application to integral inclusion is given.

Uchino first initiated the study of generalized Reynolds operators on associative algebras. Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to find the sums over inverse powers of zeroes for the incomplete Gamma- and Riemann zeta- functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeroes of the Hurwitz zeta-function , including the sum over the inverse first power of its appropriately defined non-trivial zeroes. We also study some related properties of the Hurwitz zeta-function zeroes. In particular, we show that for any natural N and small real epsilon, when z tends to n=0, -1, -2… we can find at least N zeroes of zeta in the - vicinity of 0 for sufficiently small epsilon, as well as one simple zero tending to 1, etc.

Sums of M consecutive squared integers (a+i)^2 equaling squared integers (for a<=1, 0<= i<= M-1) yield remarkable regular linear features when plotting values of M in function of a. These features correspond to groupings of pairs of a values for successive same values of M around straight lines of equation mu*M = 2a and are characterized in this paper for rational values of mu.

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy force in the model equations depend on concentration. We develop mathematical apparatus of studying inhomogeneous boundary value problems under consideration. It is based on using of a weak solution of the boundary value problem and construction of liftings of the inhomogeneous boundary data. They remove the inhomogeneity of the data and reduce original problems to equivalent homogeneous boundary value problems. Based on this apparatus we will prove the theorem of the global existence of a weak solution to boundary value problem under study and establish important properties of the solution. In particular, we will prove the validity of the maximum principle for the substance’s concentration. We will also establish sufficient conditions for the problem data, ensuring the local uniqueness of weak solutions.

A proposed interpretation of the characteristics and causes of the variation in science dynamics for technological evolution is described. The theoretical approach focuses on variability in research topics that guide scientific and technological evolution. Statistical method verifies the proposed approach by applying entropy, measures of dispersion and variance decomposition. The statistical evidence, using data of four main research fields in quantum technologies, suggests the following empirical properties: a) the growth of heterogeneity in research topics is inversely proportional to the age of research fields: recent research fields have a higher variability between topics with uncertainty in evolutionary dynamics, whereas older research fields have a lower variability and more concentration in specific research topics with stable evolution towards clear directions; b) the nature of research fields has a systematic effects in variability guiding the evolution of technologies. The theoretical approach and findings clarify main characteristics and causes of the evolution of science and technologies considering the underlying homogeneity or heterogeneity in research topics, providing main implications to improve the scientific and technological forecasting that may support appropriate R&amp;D investments towards promising research fields and technologies

Empirical equations representing, interpolating and smoothing groups of measurement results by regression methods are in widespread use in metrology and other fields of science and engineering. Standard equations for the propagation of measurement uncertainties to values computed from such equations are available but suffer from a lack of general acceptance and are only infrequently applied in practice. One reason for the slow uptake is the lack of clear methods to account for systematic error. In this paper, uncertainty propagation equations in terms of covariance matrices are generalized to allow for systematic errors in least-squares regression, and effects of the resulting uncertainties are investigated analytically. A stochastic ensemble model of systematic error is proposed for the computation of the non-diagonal elements of the weight matrix of the Generalized Least-Squares method (GLS) from the measurement uncertainty. A GLS projector formalism is described which separates the effects of measurement scatter on values calculated by the equation from those on the related “residuals”, i.e., the residual errors in the fitted data. The same projectors act similarly on the associated uncertainties and covariance matrices and permit the effects of systematic errors on the simulation covariance to be quantified. It is demonstrated that, in order to include systematic errors in the uncertainty estimates of GLS, covariance matrices may be substituted by novel, specifically defined dispersion matrices that are not specified yet by the GUM[1]. Systematic measurement errors may be estimated from various sources; a particularly easy way suggested here involves analyzing the structure in the regression residuals. It is demonstrated that GLS projectors exhibit inherent features of “error blindness” also with respect to systematic errors. [1] GUM: Guide to the Expression of Uncertainty in Measurement, http://www.bipm.org/en/publications/guides

We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.

The Power Theory of Exchange and Money (PTEM) refines the economic neoclassical two-equation model of exchange. PTEM replaces the statistical average condition of exchange, which represents the equality of supply and demand for all transactions in the market, with a more specific equation of the equality of the generalized power of the parties in relation to their objects of exchange. The purpose of the article is to show the application of PTEM for the study of various social phenomena. Along with a brief summary of the main statements of this theory, its integration into the existing corpus of theories and ideas in economics and sociology is considered. The conclusions of power theory are then applied to consider the following topics: the objective motivation of exchange by the desire to increase power, the power nature of market equilibrium, the power nature of money, the accumulation of power through profit, the creation of money as a power act, the role of the state in the creation of money, the measure of power as a possible tool for social and political research.

Abstract: Extensive research shows nurses’ work environment to be particularly stressful. This study develops, explores, and psychometrically tests a new profession specific ques-tionnaire identifying generalized and specific resistance resources, that make it possible to measure resources to manage work-related stress. An exploratory study design was em-ployed. The questionnaire was developed inspired by the MEASURE approach and the salutogenic theory of health. Building on the results from a literature review of nursing re-search and salutogenesis, supplemented by twelve interviews with hospital nurses, an item pool was generated. A first version was pilot tested in a group of nurses who were studying to become specialist nurses. A second version of the questionnaire was psycho-metrically tested on nurses in close patient care (n = 475), analysed using Principal Com-ponent Analysis as the extracting technique to identify the underlying structure of the questionnaire. The Principal Component Analysis revealed a four-component model of 19 items. “Manageability as a resource for handling the workload” was the strongest compo-nent, accounting for 21 % of the explained variance. “Contacts with patients as resources for nurses’ job satisfaction” (17.8 %). “Professional attitudes are labelled as resources to nursing” (15 %). “Colleagues are important resources for remaining in the nursing profes-sion” (11 %). The structure of the questionnaire indicates its usefulness in clinical practice for measuring resistance resources.

In the research we consider a structure-fluid interaction of oscillating piezodevice and acoustic liquid. Such problem requires finding resonance or anti-resonance frequencies of the solid structure to use them in the latter frequency-response analyses step. After finite element discretization of the issue, we need to solve a generalized eigenvalue problem (GEP). The most efficient numerical method for solving the partial GEP is the shift-and-invert Lanczos method. Each step of this algorithm requires solving a large scale system of linear algebraic equations (SLAEs) with special properties. Various ways of ordering grid nodes lead to coefficient matrices with different structure. Several methods are compared in terms of efficiency. The results of the numerical experiments are presented.

Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply "expectation," traditionally the probability-weighted outcome, regarded since the seventeenth century as the mathematical definition of "expectation." However, when considering the "expectation" of an individual confronted with a finite sequence of outcomes, particularly existential outcomes (e.g., a trader with a limited time to perform or lose his position in a trading operation), we find this individual "expects" the median terminal outcome over those finite trials, with the classical seventeenth-century definition being the asymptotic limit as trials increase to this. Since such finite-sequence "expectations" often differ in values from the classic one, so do the optimal allocations (e.g., growth-optimal). We examine these for fat-tailed distributions. The focus is on implementation, and the techniques described can be applied to all distributional forms.

Background: Patients’ effective hand hygiene helps to reduce healthcare-associated infections, prevents the spread of nosocomial infections and communicable diseases, such as COVID-19. This study aimed to describe effective hand hygiene decisions based on the Health Action Process Ap-proach (HAPA) and whether this pattern is invariant for mental health. Methods: Data were collected cross-sectionally from patients who had previously been admitted to a hospital (N=279; study 1) and longitudinally from psychosomatic rehabilitation patients (N=1,073; study 2). The fit of the HAPA framework and changes in hand hygiene decisions regarding com-pliance, as well as social-cognitive variables of the HAPA, and mental health status were examined. Results: The trimmed HAPA framework fitted the data well (χ2=27.1, df=12, p<.01, CMIN/df=2.26, CFI=.97, RMSEA=.08). According to multi-group structural equation modeling, the HAPA model with hand hygiene behavior were found to be invariant with regard to mental health. Conclusion: The trimmed HAPA framework revealed to be a generic framework in explaining so-cial-cognitive processes relating to hand hygiene decisions. Helping individuals to perform hand hygiene recommendation requires intention formation and bridging the intention-behavior gap. This can be done by promoting planning and self-efficacy. All processes appear generic to partic-ipants with and without mental health challenges.

Study of differential equation theory has come a long way with applications in the various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives on metric Lr which proved to be better in applications than approximate derivatives. But most of the studies involved are on fuzzy set theory, so it seems likely that intuitionistic fuzzy Lr - norm - based derivatives deserve study. In the study, the fuzzy derivative is extended to intuitionistic fuzzy derivatives with respect.to Lr - norm - based derivatives using intuitionistic fuzzy number valued functions. The efficacy of the proposed method is established by proving the associated theorems along with numerical examples. Further, the Cauchy problem is also studied with respect to intuitionistic fuzzy setting.

We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The strength of our method is that no additional information is required about the given original identity. The method readily extends to a generalized Fibonacci sequence.

Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.

One of the challenges in the healthcare sector is making accurate forecasts across insurance years for claims reserve. The state-of-the-art envisages various methods for estimating the claims reserve but without being applied to systems that do not present huge variability and heterogeneity, such as the healthcare sector. The methodology is based on generalized linear models using the Overdispersed Poisson distribution as shown in the state-of-the-art. In this context, we developed a method to estimate the parameters of the quasi-likelihood function using a Gauss-Newton algorithm optimized through a genetic algorithm. The genetic algorithm plays a crucial role in glimpsing the position of the global minimum to ensure a correct convergence of the Gauss-Newton method, where the choice of the initial guess is fundamental. The proposed methodology has been entirely developed using MATLAB and has been applied to estimate the claims reserve in the healthcare system of the Tuscany Region in Italy, as case study. The results obtained were validated by comparing them with the state-of-the-art by measuring the confidence intervals of the Overdispersed Poisson distribution parameters. Therefore local healthcare authorities could use the proposed and improved methodology to allocate the resources dedicated to healthcare and global management.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

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 main aim of this study is to predict whether the type of breast cancer is “benign” or “malignant” by classical generalized linear model (GLM) approach and an extended family of GLM called generalized linear mixed model (GLMM) approach for binomially distributed response variable with binary link functions. In this study, an advanced statistical modeling approach based on the GLMM to the traditional statistical modeling approach based on the GLM for binomially distributed response variable with various binary link functions is proposed to investigate the relationships between the “malignant or benign diagnosis of the BC in patients” and “nine attributes” of 699 BC diagnosed patients. This study also focuses on the statistical significance of the accurate classification of the BC diagnosed patients in cancer studies in medicine in “benign” or “malignant” type based on the WBC dataset. In this study, the superiority of the GLMM approach over the GLM approach for the binary response variable especially belonging to the WBC dataset is emphasized in the field of cancer diagnosis in medicine. Also the importance and the power of the IC and performance metrics as the goodness-of-fit test statistics are strongly emphasized for accurate statistical inferences from the “best” fitted model. In this study, from the main findings, the best fitted model among the GLM and GLMM approaches for the binary response variable is determined as the GLMM under “logit” link function with “id” random effect with the most statistically significant odds of the occurance of the BC being “malignant” as 7.9104, 5.6888, 5.6643, 4.9842, 4.1212, 2.0679, 1.8755, and 1.3970 times more than being “benign” for every one-unit increase in the quantities of “clump thickness”, “bland chromatin”, “mitoses”, “bare nuclei”, “cell shape”, “marginal adhesion”, “epithelial cell size”, and “cell size”, respectively.

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.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

In this work, a generalized analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit a general symmetry. The generalized spin projection operators are derived and the electrodynamics for hypothetical fermions are explored using the proposed spin matrices. The fermionic quantum Heisenberg model is constructed using the proposed spin matrices and comparative studies against simulation results using the Pauli spin matrices are conducted. Further analysis on key findings as well as discussions on extending the proposed spin matrix framework to describe hypothetical bosonic systems (spin-1) are provided.

The involvement of the prefrontal cortical dopaminergic system in psychopathology of epilepsies and comorbid conditions such as autism spectrum disorder (ASD) still needs to be explored. We used autoradiography to study the D1-like (D1DR) and D2-like (D2DR) receptor binding density in the prefrontal cortex of normal Wistar rats and Wistar-derived strains with generalized convulsive and/or nonconvulsive epilepsies. WAG/Rij rats served as a model for non-convulsive absence epilepsy, WAG/Rij-AGS as a model of mixed convulsive/non-convulsive forms, and KM strain was a model for convulsive epilepsy comorbiding with ASD-like behavioral phenotype. Prefrontal cortex of rats with any of epileptic pathology studied, demonstrated profound decreases in binding densities to both D1DR, D2DR; the effects were localized in the primary and secondary anterior cingulate cortexi, and adjacent regions. The local decreased D1DR and D2DR binding densities were independent (not correlated) from each other. The particular group of epileptic rats with ASD-like phenotype (KM strain), displayed changes in the lateral prefrontal cortex and adjacent regions: D1DR were lowered, but those to D2DR elevated, in anterior dysgranular insular cortex and adjacent regions. Thus, epilepsy-related changes in the dopaminergic system of rat archeocortex were localized in the medial regions, whereas ASD-related candidates were seen in the lateral aspects. The findings point to putative local dopaminergic dysfunctions, associated with generalized epilepsies and/or ASD.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

In this paper, new types of M-fractional wave solutions of mathematical physics model named as truncated M-fractional (1+1)-dimensional non-linear simplified Modified Camassa-Holm model are achieved by applying the modified simplest equation (MSE), Sardar sub-equation and generalized Kudryashov techniques. The gained solutions containing dark, bright, periodic and mixed wave solitons. Effect of fractional order derivative is also discussed. Achieved wave solitons are verified by Mathematica tool. Few of the gained wave solitons are also described through 2-dimensional, 3-dimensional and contour graphs through Mathematica tool. The gained solutions are helpful for the further development of concerned model. Finally, these techniques are simple, fruitful and effective to deal with non-linear FPDEs.

To avoid loss of information and incorrect ranking, this paper proposes a method for ranking generalized fuzzy numbers, which guarantees both horizontal and vertical values are important parameters affecting the final ranking score. In this method, the normalized height coefficient is introduced to evaluate the influence of the height of fuzzy numbers on the final ranking score. The higher the normalized height coefficient of a fuzzy number is, the higher its ranking. The left area and the right area are presented to calculate the impact of vertical value on the final ranking score. The left area is considered the benefit area. The right area is considered the cost area. The fuzzy number is preferred if the benefit area is larger and the cost area is smaller. The proposed method can be employed to rank both normal and non-normal fuzzy numbers without normalization or height minimization. Numerical examples and comparison with other methods highlight the feasibility and robustness of the proposed method, which can overcome the shortcomings of some existing methods and can support decision-makers to select the best alternative.

Unidirectional flow of a fluid with pressure-dependent viscosity through a porous structure is considered when the viscosity-pressure relationship is an exponential function of a pressure power function in order to investigate effects of the viscosity-pressure relation on the flow characteristics. The flow is governed by the generalized Brinkman’s equation with constant permeability, and a model flow domain of flow down an inclined porous channel is chosen for the sake of studying flow behaviour. Although the current work considers flow in a constant permeability porous structure, it does represent a first step in studying the more general, flow through a variable permeability porous channel. The arising governing equations are solved numerically using MATLAB and the flow is simulated to illustrate the effects of fluid properties as well as flow and medium parameters on the velocity profiles and shear stress.

We address weighted composition operators ψCφ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators.

The paper examines rational Darboux-Crum transforms (RDCTs) of the Jacobi-reference (JRef) potential on the line, with an emphasis on the transformations using only normalizable seed solutions. The Cooper-Ginocchio-Khare (CGK) potential constitutes the simplest example of this rich family of exactly solvable one-dimensional (1D) potentials. It was explicitly confirmed that that an arbitrary Darboux-Crum transformation (DCT) of the given Sturm-Liouville equation (SLE) can be represented as a chain of sequential Darboux deformations of the associated Liouville potentials. If the rational SLE (RSLE) under consideration is exactly solvable and the transformation function (TF) used at each step is nodeless then each RSLE constructed in such a way was proven being exactly solvable itself. The exact solvability of RDCTs of the JRef canonical SLE (CSLE) was also confirmed for the DCTs using pairs of juxtaposed eigenfunctions (an extension of the renowned Adler theorem to the RCSLEs of our interest). By re-expressing the reference polynomial fraction (RefPF) of the transformed CSLE in terms of the Krein determinant (KD), instead of Crum Wronskian (CW), it was shown that the eigenfunctions under consideration are expressible in terms of polynomial solutions of a generalized Heun equation with positions of the most poles dependent on the exponent parameters. The outlined technique was extended to two isospectral SUSY partners of the JRef potential (as well as to its third sibling with the inserted new lowest-energy level) which, by analogy with the CGK potential, are quantized by polynomial solutions of the 2-Heun equation with all four poles at some fixed positions on the real axis.

Throughout this paper, we will establish a comprehensive theoretical foundation and rigorously develop the methodology to investigate the structure of quotient ring S/P under the influence of symmetric generalized n-derivations, where S represents an arbitrary ring, and P signifies a prime ideal of S satisfying certain algebraic identities acting on prime ideal P without relying on the assumption of primeness or semi-primeness of the ring.

Generalized Bayes is a Bayesian approach based on the learning rate parameter η. In this study, we examine the effect of parameter η on the estimation results considering joint type-I and type-II hybrid censored samples from k exponential populations. In addition to the learning rate parameter, we consider two loss functions, the Linex and general entropy loss functions in the Bayesian approach. Monte Carlo simulations are performed to compare the performances of the estimation results under losses and different values of η. An illustrative example is performed to study the effect of the learning rate parameter and the different losses with different parameters.

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

The purpose of this systematic review is to examine the various articles published in the field of neuropsychology of anxiety research in terms of publication type and volume, methodology, and subject matter. The significance of this topic derives from the clinical and functional consequences of cognitive symptoms. Generalized anxiety disorder refers to the cluster of clinical symptoms characterized by predominant anxious anticipation and difficulty controlling worry. In order for the review to be systematic and reproducible, a search of the PsycINFO, Scopus, PubMed, Elsevier databases and an analysis using the PRISMA method are suggested. After analyzing the research data, empirical studies evaluating the clinical neuropsychology of generalized anxiety disorder are discussed.

This study investigates the transition from surface to underground mining at the Sepon Gold mine. The stability of surface slopes is assessed prior to commencing underground operations. Stope mining is adopted based on ore body characteristics and geological features. Finite element numerical analysis, employing the Generalized Hoek-Brown criterion, evaluates slope stability for surface slopes and opening stopes. The pit design comprises a 70° slope angle, 20 m height, and 10-15 m safety berm, meeting stability requirements with a factor of safety of 2.46. Underground mining design includes a 62° ore body dip, 50 m thick crown pillar to prevent surface subsidence, and 5 m wide, 5 m high stopes. Sill pillars are left for support after each level excavation. Rock bolts are employed in specific stope areas where is necessary, with continuous monitoring for surface deformation. The study analyzes the influence of stope sizes on pit wall and pit bottom stability, identifying slope failures near the hanging wall close to the pit bottom during underground mining. A slight increase in the displacement zone is observed on the upper crest of the top footwall. Overall, the findings demonstrate successful stability in the transition from surface to underground mining at Sepon Gold mine.

(1) Background. Cognitive impairment in people with Multiple Sclerosis (MS) has been studied in relation to some clinical variables (e.g., motor disability and disease duration) and lifestyle fac-tors such as Cognitive Reserve (CR). However, only very few studies have considered the interac-tion of clinical variables and cognitive reserve in preserving the integrity of the neuropsychologi-cal profile. In this paper, we hypothesised that a higher level of CR might predict good cognitive efficiency by modulating the clinical outcome of the disease. (2) Methods. A sample of 100 partic-ipants with MS (age range 30-74), was recruited and assessed remotely with a questionnaire to measure CR and a cognitive screening test. Data were analysed through Generalized Additive Models. (3) Results. We found that the model analysing the interaction between CR and disease duration, and between CR and motor disability was able to explain a significant percentage of cognitive performance. In particular, higher levels of CR predicted better cognitive performance despite long disease duration, unless the motor disability was severe. (4) Conclusion. This study highlights the crucial role of CR in modulating cognitive efficiency in people with MS.

Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about cen-tral areas with relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas with more active growth. However, effectively utilizing mul-tifractal spectrums to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator, and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time. While during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectrums alone. By integrating this index with multifractal spectrums, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

In this paper, the problem of predicting future failure times based on a jointly type-II censored sample from k exponential populations is considered. The Bayesian prediction intervals and point predictors were then obtained. Generalized Bayes is a Bayesian study based on a learning-rate parameter. This study investigated the effects of the learning rate parameters on the prediction results. The loss functions of squared error, Linex, and general entropy were used as point predictors. Monte Carlo simulations were performed to show the effectiveness of the learning rate parameter in improving the results of prediction intervals and point predictors.

This paper applied the space-time generalized finite difference scheme for solving the nonlinear dispersive shallow water waves as the modified Camassa−Holm equation, modified Degasperis-Procesi equation, Fornberg-Whitham equation, and its modified form. The proposed meshless numerical scheme was composed of the space-time generalized finite difference method, the two-step Newton-Raphson method, and the time-marching method. The space-time approach can treat the temporal derivative as one of the spatial derivatives. This numerical technique enables all the partial derivatives in the governing equation can be discretized by a spatial discretization method, and the mixed derivative can efficiently deal with using the proposed meshless numerical scheme. The space-time generalized finite difference method is advanced from the Taylor series expansion and the moving-least square method. The numerical discretization process is only related to functional data and weighting coefficients on the central node and its nearby nodes. Thus, the matrix system composed of nonlinear algebraic equations will be a sparse matrix and can be efficiently solved by the two-step Newton-Raphson method. Furthermore, the time-marching method was utilized to proceed with the space-time domain along the time axis. In this paper, several numerical examples were tested to verify the capability of the proposed space-time generalized finite difference scheme.

As a manifestation of technological innovation achievements, patents reflect the frontier of technological development in the field. This paper constructs a multi-entity patent collaboration network and analyzes its evolution patterns to provide a reference for innovation organizations to grasp the general direction of innovation development and select partners. Based on the data of collaboration patents of two and three organizations in China's new energy vehicles (NEV) industry from 2008 to 2021, this paper constructs higher-order interaction collaboration innovation networks in different periods to analyze the spatial evolution of networks and patent cooperation activities. The results show that the generalized degree distribution of nodes and edges conforms to the power-law distribution. The two-dimensional simplex networks gradually form triangle groups centered on the core nodes, and the importance of key edges is beginning to emerge. Key organizations and partners, including State Grid Corporation of China, Tsinghua University, and China Electric Power Research Institute, will largely determine the direction for the future development of cooperation innovation. The study also reveals that Beijing, Jiangsu, Zhejiang, Guangzhou, and Shanghai are in central positions in the cooperative innovation network, based on their cooperation breadth and depth measures. Additionally, key links formed by Beijing as hubs are not only the center of information exchange but also function as bridges that connect to other regions.

The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.

Let {ξ1, ξ2. . . .} be a sequence of independent possibly differently distributed random variables defined on a probability space (Ω, F, P) with distribution functions {F_ξ1., F_ξ2 , . . .}. Let η be a counting random variable independent of sequence {ξ1, ξ2. . . .}. In this paper, we find conditions under which distribution function of randomly stopped sum Sη = ξ1 + ξ2 + . . . + ξη belongs to the class of generalized subexponential distributions.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with second law of thermodynamics is explored by applying a generalized Coleman-Noll procedure. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or trough equilibrium states. We characterize several different types of perturbations, depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well.

In this article we investigate the generalized Kawahara-KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions. The arguments are based upon recent theoretical results.

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black holes under the generalized Brans-Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius~$r_+$~is small, the effect of the entropy correction term on the entropy is very obvious, while for larger values~$r_+$~, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of the geodesic motion of particles in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyzes the dependence of the innermost stable circular orbit on model parameters. Also, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, the specific energy and angular momentum of the particles which move in circular orbits.

W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order two, GQ(2,2), whose representation has been dubbed “the doily” by Stan Payne in 1973. In this paper we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order two.

This article develops applications of the generalized method of lines to numerical solutions of the time-independent, incompressible Navier-Stokes system in fluid mechanics. We recall that for such a method, the domain of the partial differential equation in question is discretized in lines (or more generally in curves), and the concerning solutions are written on these lines as functions of the boundary conditions and the domain boundary shape.

This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality principle is developed as an application to a Ginzburg-Landau type system in superconductivity in the absence of a magnetic field. In the first sections, we develop new general dual convex variational formulations, more specifically, dual formulations with a large region of convexity around the critical points which are suitable for the non-convex optimization for a large class of models in physics and engineering. Finally, in the last section we present some numerical results concerning the generalized method of lines applied to a Ginzburg-Landau type equation.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron-electron interactions and one-loop quantum electrodynamics effects. Here we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac-Coulomb and Dirac-Coulomb-Gaunt Hamiltonians.

In recent times, there has been a growing interest in the use of control charts as a feedback process monitoring technique. Particularly, CUSUM schemes have been proven to be efficient for monitoring processes where the magnitude of the sustained mean shifts is small or moderate. However, because of the constant control limits, the detection ability of CUSUM schemes becomes slow at the initial set-up of the process. The fast initial response FIR feature has often been used to enhance it at the process startup. Meanwhile, the dynamism of real-life problems has always encouraged a more sensitive CUSUM scheme capable of detecting process shifts more rapidly. In this paper, an improved CUSUM scheme for monitoring process mean is proposed. This scheme will be substantial for monitoring processes whose observations are obtained at a distant time interval for example hourly, daily or weekly and where the sustained shifts are assumed to be small or moderate. To demonstrate the practical applications of the proposed scheme, we present its real-life application using datasets from a bottling company and petroleum refinery laboratory.

It appears that up to 80% of females with autistic spectrum disorder (ASD) have not been diagnosed by 18 years of age. This translates to a prevalence of about 5-6%, and if true has serious implications for female mental health. One way of finding the true value is to use Bayes’ Theorem with a comorbid condition as a more easily recognizable flag. An obvious choice is anorexia nervosa (AN), but it transpires that the proportion of women with ASD who develop AN is unknown. This study uses published data in novel ways to provide two methods of estimating a range for this variable, and gives a median value of 8.3% for AN in ASD and with four other methods a median prevalence of 6% for female ASD. The clinical implications for diagnosis and management of ASD and comorbidities are discussed and a solution is provided for the rate of ASD in generalized joint hypermobility.

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schr\"odinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

Fire regimes in mountain landscapes of southern Europe have been shifting from their baselines due to the accumulation of fuel fostered by long-standing rural abandonment and fire exclusion policies. Understanding the role of fire on biodiversity is paramount to implement adequate management to mitigate the impacts of altered fire regimes and land abandonment on biodiversity. Here, we explored to what extent the spatiotemporal variation in burn severity has affected bird abundance of a mountain abandoned landscape located in the Atlantic-Mediterranean transition (NW Iberia). We took advantage of: (1) satellite images of Sentinel 2 and Landsat missions to compute burn severity indicators from 2010 to 2020, and (2) standardized bird surveys carried out over 206 point-counts along the breeding season of 2021. Bird abundance models were built from burn severity metrics together with well-known fire regime attributes (% of burnt area and time since fire). Our results showed that the spatiotemporal variation of burn severity significantly correlated with the abundance of the 39% of the modeled species, supporting the role of pyro-diversity in driving bird populations in our region. The burnt area also explained abundance patterns for 28% of species. Time since fire only correlated with the abundance of 3 species. Our findings confirm the importance of incorporating burn severity indicators into the toolkit of decision makers to anticipate the response of birds to fire management.

One of the possible mechanisms causing significant emissions of methane into the atmosphere within the Arctic shelf may be the decomposition of gas hydrates. Their accumulations within the Arctic shelf formed during Ice Age almost simultaneously with the formation of permafrost, which contributed to the emergence of a zone of stable existence of gas hydrates. The subsequent flooding of the Arctic shelf led to the degradation of the permafrost and the violation of the conditions for the existence of hydrates. To assess the state of the stability zone, methods of mathematical numerical modeling are used. Standard seismic methods are widely used to localize gas hydrates, but monitoring their physical state requires the development of fundamentally new approaches based on solving multiparameter inverse seismic problems. In particular, the degree of attenuation of seismic energy is one of the objective parameters for assessing the consolidation of gas hydrates: the closer they are to the beginning of decomposition, the higher the attenuation, and hence the lower the quality factor. Thus, the methods of seismic monitoring of the state of gas hydrates in order to predict the possibility of developing dangerous scenarios should be based on solving a multi-parameter inverse seismic problem. This publication is devoted to the presentation of this approach.

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

In this work, we explore the extreme searching of multidimensional functions by natural gradient descent based on Dirichlet and generalized Dirichlet distributions. The natural gradient is based on describing multidimensional surface with probability distributions, which allows us to reduce changing the accuracy of gradient and step-size. In this article, we propose an algorithm of natural gradient descent based on Dirichlet and generalized Dirichlet distributions. We demonstrate that the natural gradient descent with step-size adaptation with Dirichlet and generalized Dirichlet distributions has higher accuracy and does not take a large number of iterations for minimizing test functions than gradient descent and Adam.

– Every physical theory involving quantum fields does require a model of the quantum vacuum. The vacuum associated to quantum gravity must incorporate the prescriptions from both the theory of relativity and quantum physics. In this work, starting from the hypothesis of nucleation of sub-Planckian bubbles from a de Sitter vacuum, we study the necessary conditions to obtain baby universes, black holes and particles. The de Sitter-Planck background is described by an “infinite” Quantum Boltzmann statistics that generates fermions and bosons, and manifests itself as a deformation of the geometry that leads to a generalized uncertainty principle and a unified expression for the generalized Compton wavelength and event horizon size, drawing a connection between quantum black holes and elementary particles, the latter seen as a collective organization of the bubbles of the vacuum described by the generalized Compton wavelength. The quantum thermodynamics of black holes is then outlined and the physical history of each bubble is found to depend on the cosmological constant described in terms of thermodynamic pressure. Finally, a suggestive treatment of the Casimir effect is provided in the de Sitter-Planck background with Quantum-Boltzmann statistics and wormholes are explored as bubble coalescence processes.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

The application of transformations of the state equations of continuous linear and bilinear systems to the canonical form of controllability allows one to simplify the computation of Gramians of these systems. In the paper we developed the method and obtain algorithms for computation of the controllability and observability Gramians of continuous linear and bilinear stationary systems with many inputs and one output, based on the method of spectral expansion of the Gramians and the iterative method for computing the bilinear systems Gramians. An important feature of the concept is the idea of separability of the Gramians expansion: sep333arate computation of the scalar and matrix parts of the spectral Gramian expansion reduces the sub-Gramian matrices computation to calculation of numerical sequences of their elements. For the continuous linear systems with one output the method and the algorithm of the spectral decomposition of the controllability Gramian are developed in the form of Xiao matrices. Analytical expressions for the diagonal elements of the Gramian matrices are obtained, making use of which the rest elements can be calculated. For continuous linear systems with many outputs the spectral decompositions of the Gramians in the form of generalized Xiao matrices are obtained, which allows to significantly reduce the number of calculations. The obtained results are generalized for continuous bilinear systems with one output. Iterative spectral algorithms for computation of elements of Gramians of these systems are proposed. Examples are given that illustrate theoretical results.

For solving the fractional differential equations in computational fluid dynamics (CFD), it’s complicated and difficult by the Laplace and Fourier transforms. Based on the Caputo fractional derivative, the analytical solutions for unsteady unidirectional flows of a generalized Oldroyd-B fluid are deduced by the separation of variables method. Results show that the analytical solutions are given easily, and have good university. For some specific parameter values, the well-known analytical solutions for the generalized second grade fluid, the generalized Upper-Convected Maxwell (UCM) fluid as well as the ordinary Oldroyd-B fluid can be obtained.

Two extensions of the generalized double Lomax distribution are introduced - the spliced-scale generalized double Lomax distribution and the exponentiated generalized double Lomax distribution. Their properties are studied. Usefulness of the new distributions is shown by fitting them to stock returns datasets.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers of types I, II and III. Analogous results for numbers with $k$-prime factors will also be considered.

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.

Background: Residents of a large area of North-Eastern Italy were exposed for decades to high concentrations of perfluoroalkyl and polyfluoroalkyl substances (PFAS) via drinking water. Despite the large amount of evidence in adults of a positive association between serum PFAS and metabolic outcomes, studies focusing on children and adolescents are limited. We evaluated the associations between serum PFAS concentrations and lipid profile, blood pressure and body mass index (BMI) in highly exposed adolescents and children. Methods: A cross-sectional analysis was conducted in 6669 adolescents (14-19 years) and 2693 children (8-11 years) enrolled in the health surveillance program of the Veneto Region. Non-fasting blood samples were obtained and analyzed for perfluorooctanoic acid (PFOA) perfluorooctane sulfonate (PFOS), perfluorohexanesulfonic acid (PFHxS), perfluorononanoic acid (PFNA), total cholesterol (TC) high-density lipoprotein cholesterol (HDL-C) and triglycerides. Low-density lipoprotein cholesterol (LDL-C) was calculated. Systolic and diastolic blood pressure (BP) were measured and BMI z-score accounting for age and sex was estimated. The associations between ln-transformed PFAS (and categorized into quartiles) and continuous outcomes were assessed using generalized additive models. Analyses were stratified by gender and adjusted for potential confounders. Results: Among adolescents, significant associations were detected between all investigated PFAS and TC, LDL-C, and to a fewer extent HDL-C. Among children, PFOS and PFNA had significant associations with TC, LDL-C and HDL-C, while PFOA and PFHxS had significant associations with HDL-C only. Increased serum concentrations of PFAS, particularly PFOS, were associated with decreased BMI z-score. No statistically significant associations were observed between PFAS concentrations and BP. Conclusions: Our study supports a consistent association between PFAS concentration and serum lipids, stronger for PFOS and PFNA and with a greater magnitude among children compared to adolescents, and a negative association of PFAS with BMI.

The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3-D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport corrected interface and boundary conditions in NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to eliminate the error introduced by pin-wise homogenization. Moreover, several color set models with varying size and configuration are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or only zero order/moment DFs. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size color set models show better prediction in the whole-core calculations. By coupling different color set models DFs can offer the best accuracy at both eigenvalues and power distributions.

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

This paper provides attempts to formalize Hayek’s theory of knowledge. It has been theoretically shown that exponential income distribution is a spontaneous order of the well-functioning market economy. We show that this theoretical result is supported by the empirical evidence from the United Kingdom and China. In particular, we empirically show how the income structure of China evolved towards an exponential distribution after the market-oriented economic reformation. Furthermore, we strictly prove that, if the income structure of an economy obeys an exponential distribution, the income summation over all households leads to an aggregate production function with Hicks-neutral-like technical progress, in which the technology factor is exactly equal to society’s information stock that is a result of combining all of decentralized decisions.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is found that the expansion provides accurate approximations to solutions - including the liquid-vapor phase diagram - in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

The article presents a modified finite element (FE) based algorithm for nonlinear analysis of 2D beam structures, which takes into account the influence of the shear forces. The method proposed enables using complex materials with nonlinearities without the need of implementing advanced constitutive models in FE routines. It can be directly integrated with commonly available FE software for linear analysis of beam structures, so its functionality can be easily extended also with material nonlinearities. The presented approach adopts the generalized constitutive law algorithm to iteratively modify the stiffness of beam element. To address an influence of a shear stiffness, a Timoshenko beam element was used. The methodology was implemented and its performance was verified on several numerical examples. For validation, the displacements and the ultimate loads were compared with the values from a commercial FE software. The results shown a good correlation between the reference model and the method proposed.

In the paper, a modified nonlinear finite element method for analysis of trapezoidal plates geometrically reduced to shallow-shell Reissner-Mindlin formulation is presented. Due to the method proposed the complex plate cross-section and nonlinear materials may be modelled and no implementation of advanced constitutive law via user subroutines is needed. The generalized nonlinear constitutive law is used to update the stiffness of the plate element. The method enables modeling of complicated cross-sections, such as steel trapezoidal sheets, metal facing sandwich panels or reinforced concrete. Additionally, for those geometrically complex sections an advanced nonlinear material may be adopted. To verify the proposed method, a selected trapezoidal sheets were modeled in a commercial software as full 3D shell structures. By comparing displacements and forces, it was shown that both models behave almost identically, however, the simplified model has about 300-400 times less degrees of freedom, thus it is much more efficient.

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties such as heavy tails and skewness. Thanks to its flexibility, the Skewed Exponential Power Distribution (also called Skewed Generalized Error Distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing $k$-means approach. The usefulness of the proposal is showed by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.

This paper proposes a novel efficient multistage algorithm to extract source speech signals from a noisy convolutive mixture. The proposed approach comprises of two stages named Blind Source Separation (BSS) and De-noising. A hybrid source prior model separates the source signals from the noisy reverberant mixture in the BSS stage. Moreover, we model the low and high-energy components by generalized multivariate Gaussian and super-Gaussian models, respectively. We use Minimum Mean Square Error (MMSE) to reduce noise in the noisy convolutive mixture signal in the de-noising stage. Furthermore, two proposed models investigate the performance gain. In the first model, the speech signal is separated from the observed noisy convolutive mixture in the BSS stage, followed by suppression of noise in the estimated source signals in the de-noising module. In the second approach, the noise is reduced using the MMSE filtering technique in the received noisy convolutive mixture at the de-noising stage, followed by separation of source signals from the de-noised reverberant mixture at the BSS stage. We evaluate the performance of the proposed scheme in terms of signal-to-distortion ratio (SDR) with respect to other well-known multistage BSS methods. The results show the superior performance of the proposed algorithm over the other state-of-the-art methods.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.