Several specific types of generalized maps of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized maps of a generalized topological space is reported herein as a starting point for more generalized classes.

Several specific types of ordinary and generalized separation axioms of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized separation axioms of a generalized topological space is reported herein as a starting point for more generalized classes.

Several specific types of generalized compactness of generalized topological spaces have been defined, investigated and related to compactness in ordinary topological spaces from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized compactness in a generalized topological space is reported herein as a starting point for more generalized classes.

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

Several specific types of ordinary and generalized connectedness in a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new type of generalized connectedness in a generalized topological space is reported herein as a starting point for more generalized types.

In a generalized topological space Tg = (Ω, Tg), generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, are merely two of a number of generalized primitive operators which may be employed to topologize the underlying set Ω in the generalized sense. Generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, are other generalized primitive operators by means of which characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) can be given without even realizing generalized interior and generalized closure operations first in order to topologize Ω in the generalized sense. In a recent work, the present authors have defined novel types of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in Tg and studied their essential properties and commutativity. In this work, they propose to present novel definitions of generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, a set of consistent, independent axioms after studying their essential properties, and established further characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) in Tg.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

To define the optimistic multiple-granulation (OMG) supra interior operator and the OMG-supra closure operator associated with a set A in a multiple-granulation approximation space, we used the concepts of the OMG-lower set OL (A) and the OMG-upper set OU (A). These operators create an approximate topological space known as optimistic multiple-granulation supratopological spaces. OMG-supra-open and OMG-supra-closed approximation sets are also defined, followed by OMG-supra-continuous approximation and OMG-irresolute approximation.

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush--Kuhn--Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash's critical and equilibrium points coincide in the case of invex payoff functions.

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

Let G[F,Vk, Huv] be the graph with k pockets, where F is a simple graph of order n ≥ 1,Vk= {v1,v2,··· ,vk} is a subset of the vertex set of F and Hvis a simple graph of order m ≥ 2,v is a specified vertex of Hv. Also let G[F,Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek= {e1,e2,···ek} is a subset of the edge set of F and Huvis a simple graph of order m ≥ 3, uv is a specified edge of Huvsuch that Huv− u is isomorphic to Huv− v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk, Hv] and G[F,Ek, Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

A 58 year old female presented with abdominal pain, vomiting and constipation. Laboratory tests indicated elevated white blood cell count and C-reactive protein levels. Imaging via CT scan revealed a large cystic mass in the right ovary, abscesses and generalized small bowel distension, which initially led to a diagnosis of ovarian cancer with peritoneal carcinomatosis. Despite conservative management, the patient’s condition did not improve, prompting a laparotomy. Intraoperative findings included generalized peritonitis, significant small bowel dilation due to inflammatory adhesions and a perforated dermoid ovarian cyst. The cyst was resected and a prophylactic ileostomy was installed. Histopathological examination confirmed the diagnosis of a benign dermoid ovarian cyst. This case illustrates the rare presentation of a perforated dermoid cyst mimicking peritoneal carcinomatosis and emphasizes the importance of considering such complications in the differential diagnosis of bowel obstruction and peritoneal disease. Early recognition and appropriate surgical intervention are crucial for optimal outcomes.

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.

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.

The morphology and the activity of a submarine caldera, Avyssos, at the northern part of Nisyros volcano in the South Aegean Sea (Greece), has been studied by means of remotely operated underwater vehicle dives. The recorded time series of temperature and conductivity over the submarine volcano have been analyzed in terms of the Generalized Moments Method. The findings of the mathematical analysis shed light on the volcanic activity, but also on the morphology (shape) of the submarine volcano. The conductivity time series indicates the volcano is at rest in agreement with other types of observations. On the other hand, temperature fluctuations, which in general describe a multifractal process, show that the submarine caldera operates as an open system that interacts with its surroundings. This type of analysis can be used as an indicator for the state of activity and the morphological structure (closed or open system) of a submarine volcano.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

In the Euclidean form of the theory of gravity, where there is no dedicated time parameter, a generalized canonical form of the principle of least action is proposed. On its basis, the quantum principle of least action is formulated, in which the “dynamics” of the universe in the Origin is described by the eigenvector of the action operator - the wave functional on the space of 4D Riemannian geometries and configurations of matter fields in some compact region of 4D space. The corresponding eigenvalue of the action operator determines the initial state for the world history of the universe outside this region, where the metric signature is Lorentzian and thus the time parameter exists. The boundary of the Origin region is determined by the condition that the rate of change of the determinant of the 3D metric tensor is zero on it. A modification of quantum theory is proposed that eliminates the uncertainty of the sign of the Hilbert-Einstein action in the Euclidean region of the Origin. On this basis, we formulate a minimum principle for the eigenvalue of the action operator, similar to the principle of minimum energy for the ground state in quantum mechanics. It has been suggested that in the initial state the universe contains a certain distribution of its own mass, which is not directly related to the fields of matter.

Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of q-Statistics. Fast forward to Constantino Tsallis’ illustrious 80th birthday celebration in 2023, where Deniz Eroglu and Ugur Tirnakli delved into Constantino’s collaborative network, injecting renewed vitality into the project. With hearts brimming with appreciation for Tsallis’ enduring inspiration, Eroglu, Boghosian, Borges and Tirnakli proudly present this meticulously crafted manuscript as a token of their gratitude.

Maximum likelihood estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics but MLE cannot solve the problem of incomplete data or hidden data because it is impossible to maximize likelihood function from hidden data. Expectation maximum (EM) algorithm is a powerful mathematical tool for solving this problem if there is a relationship between hidden data and observed data. Such hinting relationship is specified by a mapping from hidden data to observed data or by a joint probability between hidden data and observed data. In other words, the relationship helps us know hidden data by surveying observed data. The essential ideology of EM is to maximize the expectation of likelihood function over observed data based on the hinting relationship instead of maximizing directly the likelihood function of hidden data. Pioneers in EM algorithm proved its convergence. As a result, EM algorithm produces parameter estimators as well as MLE does. This tutorial aims to provide explanations of EM algorithm in order to help researchers comprehend it. Moreover some improvements of EM algorithm are also proposed in the tutorial such as combination of EM and third-order convergence Newton-Raphson process, combination of EM and gradient descent method, and combination of EM and particle swarm optimization (PSO) algorithm.

Anxiety in older adults is a prevalent yet under-recognized condition associated with significant societal and individual burdens. This study used a machine learning approach to compare the relative importance of 57 risk and protective factors for anxiety symptoms in a population-representative sample of middle-aged and older European adults (N = 65,684; ages 45–103 years; 55.7% women; 15 countries represented). Results revealed loneliness and self-rated poor health as primary risk factors (Nagelkerke R2 = .272), with additional predictive contributions from country of residence, functional limitations, financial distress, and family care burden. Notably, follow-up analysis showed that none of 16 social network variables were associated with loneliness; rather, cohabitating with a partner/spouse was most strongly associated with reduced loneliness. Further research is needed to elucidate directional associations between loneliness and anxiety (both general and sub-types). These findings underscore the imperative of addressing loneliness for mitigating anxiety and related mental health conditions among aging populations.

Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasi probability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.

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

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.

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 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.

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.

This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustrate them with examples. We will see the minimum requirements under which critical points, solutions of Stampacchia and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we will show an economical application, using again solutions of the variational problems to identify with Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.

The main goal of this article is to demonstrate the impact of environmental data on the spreading of Covid-19. In this research, data has been collected from 70 cities/provinces that are affected by Covid-19. Here, environmental data refers to temperatures, humidity and population density in each of these cities/provinces. This data has been analyzed using statistical models such as Poisson, Quasi-Poisson and negative Binomial. It is found that a negative Binomial regression model is the best fit for our data. Our results reveal that average high temperature is the vital factor to slow down the spread of Covid-19. In addition, higher population density found to be an important factor for the quick spreading of Covid-19 where it is quite impossible to maintain the social distance and the virus can spread easily.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

Live fuel moisture content (LFMC) influences fire activity at landscape scale and fire behavior in laboratory experiments. However, field evidences linking LFMC to fire behavior are very limited despite numerous field experiments. In the present study, we reanalyze a shrubland fire dataset with a special focus on LFMC to explain this counterintuitive outcome. We found that this controversy might result from three reasons. First, the range of experimental LFMC data was too moist to reveal significant effect with the widespread exponential or power functions. Indeed, LFMC exhibited a strong effect below 100%, but marginal above this threshold, contrary to these functions. Second, we found that the LFMC significance was unlikely when the size of the dataset was smaller than 40. Finally, a complementary analysis suggested that 10 to 15% of random measurement error in variables could lead to an underestimation by 30 % of the LFMC effect. The effect of LFMC in field experiments is thus stronger than previously reported in the range prevailing during the actual French fire season and in accordance with observations at different scales. This highlights the need to improve our understanding of the relationship between LFMC and fire behavior to refine fire danger predictions.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

The main objective of this study is to analyze the impact of investment in Research & Development on the performance and value of companies, that is, to try to explain how R&D investment influences the companies’ performance. For this purpose, a dynamic panel data model was estimated using the Generalized Method of Moments, which made possible to measure the impact of R&D investment on performance through the Return on Operating Assets ratio for the Portuguese companies that invested the most between 2012 to 2019. The results show that the investment in R&D is not statistically significant in explaining the operating return on assets. However, the lagged financial performance in one period, the leverage, the asset turnover ratio and the accounts payable turnover show to have impact on the variable under study.

This article aims to determine the different factors that are associated with anxiety symptoms among Filipino farmers in Central Luzon. Eligible participants were screened for anxiety symptoms using the Generalized Anxiety Disorder-7 (GAD-7), while the Data Collection Tool for Factors Associated with Anxiety Symptoms (DCFAAS) was constructed and validated to determine the exposure of these factors. Among the 113 eligible farmers, only 19 (16.8%) experienced anxiety symptoms, with excessive worrying (39.8%) being the most frequent anxiety symptom. The mental health of Filipino farmers was significantly affected by the presence of physical illness (OR = 10.70 [1.367, 83.773]) and having relatives affecting work completion (OR = 6.45 [1.346, 30.896]). Therefore, policies must be focused on tackling these issues to address the mental health issues faced by farmers. The low prevalence of anxiety symptoms may stem from existing perceptions and barriers encountered in confiding psychological issues, and the Filipino’s religiosity and resiliency. Keywords: Farmers, Agriculture, Central Luzon, Generalized Anxiety Disorder, GAD-7

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.

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.

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.

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 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.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

The manuscript deals with a new two-parameter unit stochastic distribution, obtained by transforming the Gumbel distribution, using generalized logistic mapping, into a unit interval. The distribution thus obtained is called the Gumbel–Logistic Unit (abbr. GLU) distribution, and its key stochastic properties have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. Also, the procedure for estimating parameters based on quantiles, along with the asymptotic properties of the obtained estimators and the study of their numerical simulation, is presented. Finally, the application of the GLU distribution in modeling some real–world data related to telecommunications is considered.

In this study, the complex interactions between the well-known Mittag-Leffler functions with two, three, and four parameters are explored. We first study the integral forms of the Mittag-Leffler function $\mathsf{E}_{\alpha, \beta}^{\rho,\kappa}(z)$ with the goal of clarifying its mathematical behaviours and features. Moreover, we create relations between these functions and generalised hypergeometric functions and Fox-Wright functions, expanding the range of their use and comprehension. We explore a number of unique situations by in-depth examination, providing insight into the subtle characteristics of these functions. This investigation advances our theoretical knowledge and opens up possibilities for future applications in a number of scientific fields. As such, this study adds to the current conversation in mathematical analysis and is an important tool for both practitioners and researchers.

The fixed and random effects models are popular methods for identifying the causal effects of treatment. First, I introduce the two-way fixed effects model and show a class of the estimators for the random effects models. Misidentification may occur in these models due to the treatment effect heterogeneity. Then, I propose the differential error component models to address such problems while the models exclude the fixed effects of units and time periods and consider the random effects of units and time periods. Meanwhile, I present a simulation of a staggered design and revisit the application in (De Chaisemartin and D'Haultfoeuille, 2020). The results demonstrate that one additional newspaper increases the 0.31% average effect of the presidential turnout and the 1.05% average effect when the newspapers’ changes are non-negative, where the proposed estimators are robust and efficient.

This article aims to carry out experiments on water absorption by husked red rice, at constant temperatures of 28, 40 and 50 °C. The description of the absorption kinetics, as well as the analyses of water distribution and volumetric expansion of each grain, at a given instant, was done using a diffusion model. In order for the model to be as close as possible to the real physical situation, the mesh necessary to numerically solve the diffusion equation was generated from the photograph of a grain. Thus, the diffusion equation was written in Boundary-Fitted Coordinates (BFC). The solution of the diffusion equation written in generalized coordinates was then discretized in space and time, using the Finite Volume method, with a fully implicit formulation, considering variable volume and also variable mass diffusivity as a function of local moisture content. Optimizations based on Levenberg-Marquardt algorithm make it possible to determine the parameters of an exponential function relating mass diffusivity and the local moisture content for each temperature. Statistical indicators (chi-square, determination coefficient and Student’s t-test) allowed concluding that the model proposed was very satisfactory for all temperatures, making it possible to simulate water absorption, water distribution and volumetric expansion of the grain over time.

The e-commerce sector is in a constant state of growth and evolution, particularly within its subdomain of online food delivery. As such, ensuring customer satisfaction is critical for companies working in this field. One way to achieve this is by providing accurate delivery time estimation. While companies can track couriers via GPS, they often lack real-time data on traffic and road conditions, complicating delivery time predictions. To address this, a range of statistical and machine learning techniques are being employed, including neural networks and specialized expert systems, with different degree of success. One issue with neural networks and machine learning models is their heavy dependence on vast, high quality data. To mitigate this issue we propose two Bayesian generalized linear models to predict time of the delivery. Utilizing a linear combination of predictor variables, we generate practical range of outputs with Hamiltonian Monte Carlo sampling method. These models offer a balance of generality and adaptability, allowing for tuning with expert knowledge. They were compared with PSIS-LOO and WAIC criteria. Results show that both models accurately estimated delivery times from the dataset, while maintaining numerical stability. Model with more predictor variables proved to be more accurate.

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.

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.

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.

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.

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.

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.

Dietary patterns established during adolescence might play a role in adulthood disease. We examined the stability of dietary patterns (DPs) from childhood through adolescence and into young adulthood (from age 8 to 34 years). Data from 130 participants (53 females) of Saskatchewan Pediatric Bone Mineral Accrual Study (aged 8-15 years, at baseline) were included. Multiple 24-hour recalls were collected annually from 1991 to 1997, 2002 to 2005 and 2010 and 2011. Using principal component analysis, “Vegetarian-style”, “Western-like”, “High-fat, high-protein”, “Mixed” and “Snack” DPs were derived at baseline. Applied DP scores for all annual measurements were calculated using factor loading of baseline DPs and energy-adjusted food group intakes. We analyzed data using generalized estimating equations. The tracking coefficient represents correlation between baseline dietary pattern scores and all other follow-up dietary pattern scores. We found a moderate tracking for the “Vegetarian-style” (ß=0.44, P<0.001) and “High-fat, high-protein” (ß=0.39, P<0.001) DPs in females and “Vegetarian-style” DP (ß=0.30, P<0.001) in males. Remaining DPs showed a poor-to-fair tracking in both sexes. No tracking for “Western-like” DP in females was observed. Assessing overall change in DP scores from childhood to young adulthood showed an increasing trend in adherence to “Vegetarian-style” DP and decreasing trend in adherence to “High-fat, high-protein” DP by age in both sexes (P<0.001). While “Western-like” and “Mixed” DP scores increased only in males (P<0.001). These findings suggest that healthy dietary habits established during childhood and adolescence moderately continue into adulthood.

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.

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.

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.

(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.

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.

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.

This paper addresses a variant of the product for the Dirichlet $L$--functions. We propose a completely detailed proof for the truth of the generalized Riemann conjecture for the Dirichlet $L$--functions, which states that the real part of the nontrivial zeros is $1/2$. The Wang and Hardy--Littlewood theorems are also discussed with removing the need for it. The results are applicable to show the truth of the Goldbach's conjecture.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

Reliable access to electricity has become a necessity worldwide, and without it, no country can operate health systems and achieve sustainable development goals (SDGs). However, while developed countries have been successfully electrified for many decades, most developing countries have fallen short, contributing to significant impacts, particularly the health sector. The present study explores the relationship between electrification and health vulnerability in developing countries between 1990 and 2020 using the Feasible Generalized Least Square (FGLS) approach. The varied electrification across countries motivates the use of non-linear associations between electrification and health vulnerability. We demonstrate that electrification and health vulnerability have an inverted U-shaped association. Further analysis indicates that most developing countries have achieved a mature level of an inverted U-shaped curve, showing a reduction in health vulnerability with increasing electrification. There are few developing countries, mainly African countries, struggling to reach maturity. The results of this study indicate the need for increased access to electrification, in combination with a reduction in the use of biomass and fossil fuel feedstocks, to mitigate health vulnerability in developing countries.

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated "peaks" and "fat" tails is also discussed.

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.

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.

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.

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.

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.

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.

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.

Spike-and-wave discharge (SWD) pattern detection in electroencephalography (EEG) signals is a key signal processing problem. It is particularly important for overcoming time-consuming, difficult, and error-prone manual analysis of long-term EEG recordings. This paper presents a new SWD method with a low computational complexity that can be easily trained with data from standard medical protocols. Precisely, EEG signals are divided into time segments for which the Morlet 1-D decomposition is applied. The generalized Gaussian distribution (GGD) statistical model is fitted to the resulting wavelet coefficients. A k-nearest neighbors (k-NN) self-supervised classifier is trained using the GGD parameters to detect the spike-and-wave pattern. Experiments were conducted using 106 spike-and-wave signals and 106 non-spike-and-wave signals for training and another 96 annotated EEG segments from six human subjects for testing. The proposed SWD classification methodology achieved 95 % sensitivity (True positive rate), 87% specificity (True Negative Rate), and 92% accuracy. These results set the path to new research to study causes underlying the so-called absence epilepsy in long-term EEG recordings.

In this paper, we consider the generalized sextic functional equation \begin{align*} \sum_{i=0}^{7}{}_7 C_{i} (-1)^{7-i}f(x+iy) = 0. \end{align*} And by applying the fixed point theory in the sense of L. C\u adariu and V. Radu, we will discuss the stability of the solutions for this functional equation.

Land Surface Temperature (LST) is routinely retrieved from remote sensing instruments using semi-empirical relationships between top of atmosphere (TOA) radiances and LST, using ancillary data such as total column water vapor or emissivity. These algorithms are calibrated using a set of forward radiative transfer simulations that return the TOA radiances given the LST and the thermodynamic profiles. The simulations are done in order to cover a wide range of surface and atmospheric conditions and viewing geometries. This work analyses calibration strategies, considering some of the most critical factors that need to be taken into account when building a calibration dataset, covering the full dynamic range of relevant variables. A sensitivity analysis of split-windows and single channel algorithms revealed that selecting a set of atmospheric profiles that spans the full range of surface temperatures and total column water vapor combinations that are physically possible seems beneficial for the quality of the regression model. However, the calibration is extremely sensitive to the low-level structure of the atmosphere indicating that the presence of atmospheric boundary layer features such as temperature inversions or strong vertical gradients of thermodynamic properties may affect LST retrievals in a non-trivial way. This article describes the criteria established in the EUMETSAT Land Surface Analysis – Satellite Application Facility to calibrate its LST algorithms applied both for current and forthcoming sensors.

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.

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.

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.

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.

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.

Working capital management requires a careful attention by the corporate managers because it plays an important role in corporate stability. Social belongingness of managers induced them to learn from their society, colleagues and from overall industrial movement. They also learn from their peers which have more strategical efficiency. In line with these arguments, the objective of current study is to explores the peer influence on corporate working capital management practices. To making analysis, ten-years data (2009-2018) of non-financial publicly listed firms at PSX were collected and the cash conversion cycle (CCC) uses as a proxy variable of working capital management (WCM). To estimate the regression, an econometric technique named the Generalized Method of Moments (GMM) was used. The empirical findings suggest the significant impact of peer WCM on corporate WCM. It also suggests the significant impact of other variables that determine the WCM. This study recommends social learning policy to corporate managers. They can learn from their peers to manage the working capital. Most previous studies discuss the peer influence on investment decisions, corporate cash holding and financing policy, etc., but no study explores such a relationship specifically in the Pakistani non-financial sector data set.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are furthermore the inverses of one another. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions.

Pigeon paramyxovirus serotype 1 (PPMV-1), primarily originating from racing pigeons, has become a global panzootic, spreading to poultry and wild birds, thus posing a threat to the poultry industry. Egypt uses both inactivated pigeon paramyxovirus (PPMV-1) and conventional Newcastle disease virus (NDV) vaccines to protect pigeons. However, the impact of prevalent strains and the effectiveness of available vaccines in pigeons in Egypt are unclear. This study investigates the virulence of PPMV-1 isolated from vaccinated pigeons in Sharkia, Egypt (Pigeon/ Egypt/Sharkia-19/2015/KX580988). Ten-day-old specific-pathogen-free embryonated chicken eggs infected with this strain exhibited a mean death time (MDT) of 86.4±5.88 hours. The intracerebral pathogenicity index (ICPI) in day-old chicks was 0.8, while pigeons experienced an ICPI of 0.96 and an intravenous pathogenicity index (IVPI) of 2.11. These findings classify the strain as virulent and velogenic. Experimental infection with this PPMV-1 strain at 106 EID50/0.1 ml resulted in a 62.5% mortality rate in pigeons, displaying nervous and enteric distress. The virus caused extensive lesions in visceral organs, with strong immunohistochemistry signals in all examined organs, indicating the systemic spread of the virus concurrent to its neurotropic and viscerotropic tropism. Furthermore, vaccination using inactivated PPMV-1 and live NDV LaSota vaccine regimen protected 100% of pigeons against mortality, while a single NDV LaSota vaccine provided 62.5% protection. The PPMV alone or combined with NDV LaSota induced protective levels of hemagglutination inhibition antibody titers and reduced virus shedding from buccal and cloacal cavities. These findings suggest that using both inactivated PPMV-1 (G-VI) and live attenuated NDV (LaSota) vaccines is an effective prophylactic regimen for preventing and controlling PPMV-1 and NDV in pigeons, thereby reducing the risk of interspecies transmission.

This work offers a new log generalized odd log-logistic exponential regression model for analyzing weekly dengue fever cases in 2022 with a location-systematic component. To achieve this, a data set of 49 observations of dengue fever cases in the Federal District of Brazil is employed. A review of the mathematical properties of the generalized odd log-logistic exponential distribution is provided, the maximum likelihood method is used to estimate the parameters, and, through Monte Carlo simulations, the accuracy of the estimators is investigated. The model's fit is assessed using global influence metrics and residual analysis. For the time scenario studied, the proposed regression identified factors that have an impact on dengue fever cases, which may contribute to improve disease control. Finally, several interpretations are addressed, and a discussion presents results that aid in better understanding the data set and future research on different data.

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

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.

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.

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.

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 consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

This paper aims to quantify the effect of the deadly novel coronavirus (COVID-19) pandemic outbreak on Chinese stock market performance. Shanghai Stock Exchange Composite Index and its component sector indices are examined in this study. The pandemic is represented by a lockdown dummy, new COVID-19 cases and a dummy for 3 February 2020. First, descriptive analysis is performed on these indices to compare their performances before and during the lockdown period. Next, regression analysis with Exponential Generalized Autoregressive Conditional Heteroscedasticity specification is estimated to quantify the pandemic effect on the Chinese stock market. This paper finds that health care, information technology and telecommunication services sectors were relatively more pandemic-resistant, while other sectors were more severely hurt by the pandemic outbreak. The extent to which each sector was affected by pandemic and sentiments in other financial and commodity markets were reported in details in this paper. The findings of this paper are resourceful for investors to avoid huge loss amid pandemic outburst and the China Securities Regulatory Commission in handling future pandemic occurrence to cool down excessive market sentiments.

In financial time series modelling and forecasting, combining ARMA and GARCH models tend to produce superior and reliable models for volatility persistence, half-life volatility and backtesting (application of model in real life). In Nigeria, banking stocks are mostly traded because of its potential benefits to investors. This study modelled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 2^nd 2001 to May 8^th 2017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were used to analysed the collected data using student t and skewed student t distributions, and the analyses are carried out R environment using rugard and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models ranges from 5 days to 100 days but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. This study recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank stock returns has the ability to returns to its mean price return.

In this paper, we analyze the generalized Ulam-Hyers stability of affine type AQ Functional Equation in various Banach Spaces using Direct and Fixed Methods

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.

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.

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.