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This paper offers an in‐depth investigation into pure ideals within the Hurwitz series ring. Specifically, by focusing on the Hurwitz series ring, denoted as HR over a ring R, we present a comprehensive characterization of differential ideals. In this paper, we prove that these differential ideals can be expressed in the form HI, where I represents an ideal in the underlying ring R. Through this analysis, a comprehensive understanding of the structure and properties of pure ideals within the Hurwitz series ring is achieved. [ABSTRACT FROM AUTHOR]

In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation. Some examples are given to show that our theorems' assumptions cannot be relaxed. The invariance problem of the center of the ring is also investigated. [ABSTRACT FROM AUTHOR]

Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine‐generated family is used to create a new bounded lifetime distribution, known as Sine‐Marshall–Olkin Topp–Leone distribution, for modeling data defined on the unit interval. Some statistical properties of the new bounded distribution, including quantile function, ordinary moments, incomplete moments, moment‐generating functions, inequality measures, Rényi entropy, and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramér–von Mises estimators are used to estimate the parameters of the new distribution. The behavior of the estimators obtained from the estimation methods are investigated using Monte Carlo simulation studies. The results show that the estimation methods are asymptotically efficient and consistent. The flexibility of the new bounded distribution is examined via data fitting using two proportional datasets. The results of the fittings show that the new bounded distribution performs significantly better than the competing bounded lifetime distributions. Finally, Sine‐Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and Kumaraswamy regression models. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a reflected backward stochastic differential equation (RBSDE) with jumps, focusing on cases where the mean reflection is nonlinear. Unlike traditional RBSDEs, this particular type of RBSDE imposes a constraint defined by the mean of a loss function that does not follow the continuous condition. We start by deriving an a priori estimate of the solution, followed by establishing the uniqueness and existence of the solution. Theoretical results are illustrated by way of an example of the application of super‐hedging to the reinsurance and investment problem under a risk constraint. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a novel variation of almost Hardy–Rogers (ψ, ϕ)‐type multivalued contraction and ϑ‐type contraction mappings. The main focus is on proving new fixed point (FP) results in M℘‐metric space (M℘‐MS). Additionally, several consequences are derived from our main findings. To elucidate the recency of our outcomes, various examples are provided. Finally, we utilize the obtained results to scrutinize the existence of solutions for nonlinear fourth‐order differential equations (NFODEs). [ABSTRACT FROM AUTHOR]

This research paper introduces the novel subclass ϒΣϑ,β,μq˜ of bi‐univalent functions that are connected to Fibonacci numbers. Our main contributions in this study involve establishing constraints on the absolute values of the second coefficient |a2| and the third coefficient |a3| for functions within this specific subclass. In addition, we provide solutions to Fekete–Szegö functional problems. Furthermore, our investigation reveals intriguing outcomes resulting from the specific parameter values used in our main findings. [ABSTRACT FROM AUTHOR]

In this paper, the impact of viral illnesses on the predator-prey relationship with an optimal control analysis is studied. An ecoepidemiological model of four compartments, namely, susceptible prey, susceptible predator, infected prey, and infected predator populations, in the interaction of the prey-predator system is formulated. The fundamental tenet of our ecoepidemiology model is that sick predators do not engage in predation. It is confirmed that the system's solution exists, is positive, and is bounded. The system's equilibrium points are determined and computed. Lyapunov functions and a linearizing form are used for local and global stability analysis, respectively. The next generation matrix approach is used to calculate the threshold value for diseased predators and prey at the disease-free equilibrium point. Optimal treatment options for vulnerable and infected populations are established by applying optimal control theory to the ecoepidemiology model of a prey-predator system. MATLAB software is utilized to obtain numerical simulations that validate the analytical outcomes. The optimal control problem simulations demonstrate that the number of infected populations in a given prey-predator system can be decreased by implementing control measures. [ABSTRACT FROM AUTHOR]

In literature, several types of join operations of two graphs based on subdivision graph, Q -graph, R -graph, and total graph have been introduced, and their spectral properties have been studied. In this paper, we introduce a new double join operation based on H 1 , H 2 -merged subdivision graph. We compute the spectrum of a special block matrix and then use it to describe the distance spectra of some double join operations of graphs. At last, we give several families of distance equienergetic graphs of diameter 3. [ABSTRACT FROM AUTHOR]

For non-negative integers d 1 and d 2 , if V 1 and V 2 are two partitions of a graph G 's vertex set V G , such that V 1 and V 2 induce two subgraphs of G , called G V 1 with maximum degree at most d 1 and G V 2 with maximum degree at most d 2 , respectively, then the graph G is said to be improper d 1 , d 2 -colorable, as well as d 1 , d 2 -colorable. A class of planar graphs without C 3 , C 4 , and C 6 is denoted by C. In 2019, Dross and Ochem proved that G is 0 , 6 -colorable, for each graph G in C. Given that d 1 + d 2 ≥ 6 , this inspires us to investigate whether G is d 1 , d 2 -colorable, for each graph G in C. In this paper, we provide a partial solution by showing that G is (3, 3)-colorable, for each graph G in C. [ABSTRACT FROM AUTHOR]

This paper explores the concept of almost positively closed models in the framework of positive logic. To accomplish this, we initially define various forms of the positive amalgamation property, such as h-amalgamation and symmetric and asymmetric amalgamation properties. Subsequently, we introduce certain structures that enjoy these properties. Following this, we introduce the concepts of Δ -almost positively closed and Δ -weekly almost positively closed. The classes of these structures contain and exhibit properties that closely resemble those of positive existentially closed models. In order to investigate the relationship between positive almost closed and positive strong amalgamation properties, we first introduce the sets of positive algebraic formulas E T and Alg T and the properties of positive strong amalgamation. We then show that if a model A of a theory T is a E T + A -weekly almost positively closed, then A is a positive strong amalgamation basis of T , and if A is a positive strong amalgamation basis of T , then A is A l T + A -weekly almost positively closed. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to analyse investment returns using a stochastic model and inform investors about the best stock market to invest in. To this effect, a Markov chain random walk model was successfully developed and implemented on 450 monthly market returns data spanning from January 1976 to December 2020 for Canada, India, Mexico, South Africa, and Switzerland obtained from the Federal Reserves of the Bank of St. Louis. The limiting state probabilities and six-month moving crush probabilities were estimated for each country, and these were used to assess the performance of the markets. The Mexican market was observed to have the least probabilities for all the negative states, while the Indian market recorded the largest limiting probabilities. In the case of positive states, the Mexican market recorded the highest limiting probabilities, while the Indian market recorded the lowest limiting probabilities. The results showed that the Mexican market performed better than the others over the study period, whilst India performed poorly. These findings provide crucial information for market regulators and investors in setting regulations and decision-making in investment. [ABSTRACT FROM AUTHOR]

In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis. [ABSTRACT FROM AUTHOR]

Decisions regarding competing risks are usually based on a continuous-valued marker toward predicting a cause-specific outcome. The classification power of a marker can be summarized using the time-dependent receiver operating characteristic curve and the corresponding area under the curve (AUC). This paper proposes a Gaussian copula-based model to represent the joint distribution of the continuous-valued marker, the overall survival time, and the cause-specific outcome. Then, it is used to characterize the time-varying ROC curve in the context of competing risks. Covariate effects are incorporated by linking linear components to the skewed normal distribution for the margin of the marker, a parametric proportional hazards model for the survival time, and a logit model for the cause of failure. Estimation is carried out using maximum likelihood, and a bootstrap technique is implemented to obtain confidence intervals for the AUC. Information-criteria strategies are employed to find a parsimonious model. The performance of the proposed model is evaluated in simulation studies, considering different sample sizes and censoring distributions. The methods are illustrated with the reanalysis of a prostate cancer clinical trial. The joint regression strategy produces a straightforward and flexible model of the time-dependent ROC curve in the presence of competing risks, enhancing the understanding of how covariates may affect the discrimination of a marker. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a class of biunivalent functions, denoted by H n , r , α , that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients a 2 and a 3 . Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class. [ABSTRACT FROM AUTHOR]

Hom–Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom–Lie algebras are studied further. In the theory of groups, investigations of the properties of the solvable and nilpotent groups are well-developed. We establish a theory of the solvable and nilpotent Hom–Lie algebras analogous to that of the solvable and nilpotent groups. We also provide examples to illustrate our results and discuss possible directions for further research. Dedicated to Al Farouk School & Kinder garten-Irbid-Jordan [ABSTRACT FROM AUTHOR]

In epidemiology, the rule of association is used to determine the factors at the origin of diseases; implicative statistical analysis is thus a necessary tool in epidemiology too. Epidemiologists have more often chosen the so-called odds ratio measure in their studies of the quantification of the implicit link between an exposure and disease. In order to obtain good results, we need to be sure that the odds ratio measure is really the most relevant measure available. Therefore, it is necessary to study the mathematical properties of the odds ratio. This paper proposes a comparative study of the behaviour and mathematical properties of the odds ratio measure, the measure of Guillaume–Khenchaff (MGK), and the normalised odd-ratio measure. We have chosen the MGK measure because the literature considers it to be a good measure for extracting implicit association rules according to its mathematical properties. The result in this paper concerns only the study of probabilistic data. [ABSTRACT FROM AUTHOR]

Linear and quadratic discriminant analysis are two fundamental classification methods used in statistical learning. Moments (MM), maximum likelihood (ML), minimum volume ellipsoids (MVE), and t-distribution methods are used to estimate the parameter of independent variables on the multivariate normal distribution in order to classify binary dependent variables. The MM and ML methods are popular and effective methods that approximate the distribution parameter and use observed data. However, the MVE and t-distribution methods focus on the resampling algorithm, a reliable tool for high resistance. This paper starts by explaining the concepts of linear and quadratic discriminant analysis and then presents the four other methods used to create the decision boundary. Our simulation study generated the independent variables by setting the coefficient correlation via multivariate normal distribution or multicollinearity, often through basic logistic regression used to construct the binary dependent variable. For application to Pima Indian diabetic dataset, we expressed the classification of diabetes as the dependent variable and used a dataset of eight independent variables. This paper aimed to determine the highest average percentage of accuracy. Our results showed that the MM and ML methods successfully used large independent variables for linear discriminant analysis (LDA). However, the t-distribution method of quadratic discriminant analysis (QDA) performed better when using small independent variables. [ABSTRACT FROM AUTHOR]

In this paper, we establish some inequalities involving the modulus of the derivative of rational functions with prescribed poles and restricted zeros. The obtained results generalize some known inequalities for rational functions. Moreover, our results also contain certain known polynomial inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a well known class studied by Ramesha in 1995 and later by Janteng in 2006, and we then extend the class to a wider class of functions f denoted by n α β , γ which are normalized and univalent, in the unit disk D = z ∈ ℂ : z < 1 satisfying the condition Re α z 2 f ′ ′ z / g z + z f ′ z / g z > β , 0 ≤ α < 1,0 ≤ β < 1 , where g is analytic function in D , such that g z ≠ 0 , with a new condition that is introduced. The main purpose of this paper is to give an estimate for the same a 3 − μ a 2 2 when f belongs to the class n α β , γ . [ABSTRACT FROM AUTHOR]

There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in n-dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs. [ABSTRACT FROM AUTHOR]

Topological index (TI) is a mapping that associates a real number to the under study (molecular) graph which predicts its various physical and chemical properties. The generalized degree distance index is the latest developed TI having compatible significance among the list of distance-based TIs. In this paper, the minimum generalized degree distance of unicyclic, bicyclic, and four cyclic graphs is determined. Mainly, the associated extremal (minimal) graphs are also identified among all the aforesaid classes of graphs. [ABSTRACT FROM AUTHOR]

The study of topological indices in graph theory is one of the more important topics, as the scientific development that occurred in the previous century had an important impact by linking it to many chemical and physical properties such as boiling point and melting point. So, our interest in this paper is to study many of the topological indices "generalized indices' network" for some graphs that have somewhat strange structure, so it is called the cog-graphs of special graphs "molecular network", by finding their polynomials based on vertex − edge degree then deriving them with respect to x , y , and x y , respectively, after substitution x = y = 1 of these special graphs are cog-path, cog-cycle, cog-star, cog-wheel, cog-fan, and cog-hand fan graphs; the importance of some types of these graphs is the fact that some vertices have degree four, which corresponds to the stability of some chemical compounds. These topological indices are first and second Zagreb, reduced first and second Zagreb, hyper Zagreb, forgotten, Albertson, and sigma indices. [ABSTRACT FROM AUTHOR]

In analytic geometry, Bézout's theorem stated the number of intersection points of two algebraic curves and Fulton introduced the intersection multiplicity of two curves at some point in local case. It is meaningful to give the exact expression of the intersection multiplicity of two curves at some point. In this paper, we mainly express the intersection multiplicity of two curves at some point in R 2 and A K 2 under fold point, where char K = 0. First, we give a sufficient and necessary condition for the coincidence of the intersection multiplicity of two curves at some point and the smallest degree of the terms of these two curves in R 2 . Furthermore, we show that two different definitions of intersection multiplicity of two curves at a point in A K 2 are equivalent and then give the exact expression of the intersection multiplicity of two curves at some point in A K 2 under fold point. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3-variables quadratic functional equation in the setting of 2-Banach space. Also, we obtain some hyperstability results for the 3-variables quadratic functional equation. The results obtained in this paper extend several known results of the literature to the setting of 2-Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the characteristic of a minimal ideal and a minimal generalized ideal, which is meant to be one of minimal left ideal, minimal right ideal, bi-ideal, quasi-ideal, and m , n -ideal in a ring, is either zero or a prime number p. When the characteristic is zero, then the minimal ideal (minimal generalized ideal) as additive group is torsion-free, and when the characteristic is p , then every element of its additive group has order p. Furthermore, we give some properties for minimal ideals and for generalized ideals which depend on their characteristics. [ABSTRACT FROM AUTHOR]

Let a be a real number satisfying 03 by successive Morse surgeries. On the other hand, when n is even, we show that Mna is obtained from Pn by successive Morse surgeries. Here, Pn denotes the configuration space of equilateral n-gons in ℝ2, which has singular points when n is even. [ABSTRACT FROM AUTHOR]

In this paper, two new versions of the Schur algorithm for computing the matrix exponential of an n × n complex matrix A are presented. Instead of the Schur form, these algorithms use the Jordan–Schur form of A. The Jordan–Schur form is found by less computation and it is determined more reliable than the reduction to Jordan form since it is obtained using only unitary similarity transformations. In contrast to the known methods, the diagonal blocks of the matrix exponential are obtained by using finite Taylor series. This improves the accuracy and avoids the decisions made about the termination of the series expansion. The off-diagonal blocks of the exponential are determined by modifications of the Schur–Parlett or Schur–Fréchet method, which takes advantage of the Jordan–Schur form of the matrix. The numerical features of the new algorithms are discussed, revealing their advantages and disadvantages in comparison with the other methods for computing the matrix exponential. Computational experiments show that using the new algorithms, the matrix exponential is determined in certain cases with higher accuracy than some widely used methods, however, at the price of an increase in the computational cost which is of order n 4 . It is shown that the Jordan–Schur algorithms for computing the matrix exponential are appropriate for matrices with multiple eigenvalues and are especially efficient in cases of large Weyr characteristics. [ABSTRACT FROM AUTHOR]

Given an matrix A , considered as a linear map A : ℝ n ⟶ ℝ n , then A induces a topological space structure on ℝ n which differs quite a lot from the usual one (induced by the Euclidean metric). This new topological structure on ℝ n has very interesting properties with a nice special geometric flavor, and it is a particular case of the so called "primal space," In particular, some algebraic information can be shown in a topological fashion and the other way around. If X is a non-empty set and f : X ⟶ X is a map, there exists a topology τ f induced on X by f , defined by τ f = U ⊂ X : f − 1 U ⊂ U . The pair X , τ f is called the primal space induced by f. In this paper, we investigate some characteristics of primal space structure induced on the vector space ℝ n by matrices; in particular, we describe geometrical properties of the respective spaces for the case. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of weak solutions to a Dirichlet problem for a semilinear elliptic equation involving the difference of two main nonlinearities functions that depends on a real parameter λ. According to the values of λ , we give both nonexistence and multiplicity results by using variational methods. In particular, we first exhibit a critical positive value such that the problem admits at least a nontrivial non-negative weak solution if and only if λ is greater than or equal to this critical value. Furthermore, for λ greater than a second critical positive value, we show the existence of two independent nontrivial non-negative weak solutions to the problem. [ABSTRACT FROM AUTHOR]

Let C and Q be closed convex subsets of real Hilbert spaces H1 and H2, respectively, and let g:C→R be a strictly real-valued convex function such that the gradient ∇g is an 1/L-ism with a constant L>0. In this paper, we introduce an iterative scheme using the gradient projection method, based on Mann’s type approximation scheme for solving the constrained convex minimization problem (CCMP), that is, to find a minimizer q∈C of the function g over set C. As an application, it has been shown that the problem (CCMP) reduces to the split feasibility problem (SFP) which is to find q∈C such that Aq∈Q where A:H1→H2 is a linear bounded operator. We suggest and analyze this iterative scheme under some appropriate conditions imposed on the parameters such that another strong convergence theorems for the CCMP and the SFP are obtained. The results presented in this paper improve and extend the main results of Tian and Zhang (2017) and many others. The data availability for the proposed SFP is shown and the example of this problem is also shown through numerical results. [ABSTRACT FROM AUTHOR]

The permanent is important invariants of a graph with some applications in physics. If G is a graph with adjacency matrix A = a i j , then the permanent of A is defined as perm A = ∑ σ ∈ S n ∏ i = 1 n a i σ i , where S n denotes the symmetric group on n symbols. In this paper, the general form of the adjacency matrices of hexagonal and armchair chains will be computed. As a consequence of our work, it is proved that if G k and H k denote the hexagonal and armchair chains, respectively, then perm A G 1 = 4 , perm A G k = k + 1 2 , k ≥ 2 , and perm A H k = 4 k with k ≥ 1. One question about the permanent of a hexagonal zig-zag chain is also presented. [ABSTRACT FROM AUTHOR]

In the current research, the numerical solutions for heat transfer in an Eyring–Powell fluid that conducts electricity past an exponentially growing sheet with chemical reactions are examined. As the sheet is stretched in the x direction, the flow occupies the region y > 0. MHD, radiation, joule heating effects, and thermal relaxation time are all used to represent the flow scenario. The emergent problem is represented using PDEs, which are then converted to ODEs using appropriate similarity transformations. The converted problem is solved numerically using the SLM method. The main goal of this paper is to compare the results of solving the velocity and temperature equations in the presence of K changes through SLM, introducing it as a precise and appropriate method for solving nonlinear differential equations. Tables with the numerical results are created for comparison. This contrast is important because it shows how precisely the successive linearization method can resolve a set of nonlinear differential equations. Following that, the generated solution is studied and explained in relation to a variety of engineering parameters. Additionally, the thermal relaxation period is inversely proportional to the thickness of the thermal boundary layer and the temperature, but the Eckert number E c is the opposite. As E c grows, the temperature within the channel increases. [ABSTRACT FROM AUTHOR]

Let X and Y be Banach spaces and Ω ⊆ X. Let f : Ω ⟶ Y be a single valued function which is nonsmooth. Suppose that F : X⇉ 2 Y is a set-valued mapping which has closed graph. In the present paper, we study the extended Newton-type method for solving the nonsmooth generalized equation 0 ∈ f x + F x and analyze its semilocal and local convergence under the conditions that f + F − 1 is Lipschitz-like and f admits a certain type of approximation which generalizes the concept of point-based approximation so-called n , α -point-based approximation. Applications of n , α -point-based approximation are provided for smooth functions in the cases n = 1 and n = 2 as well as for normal maps. In particular, when 0 < α < 1 and the derivative of f , denoted ∇ f , is ℓ , α -Hölder continuous, we have shown that f admits 1 , α -point-based approximation for n = 1 while f admits 2 , α -point-based approximation for n = 2 , when 0 < α < 1 and the second derivative of f , denoted ∇ 2 f , is K , α -Hölder. Moreover, we have constructed an n , α -point-based approximation for the normal maps f C + F when f has an n , α -point-based approximation. Finally, a numerical experiment is provided to validate the theoretical result of this study. [ABSTRACT FROM AUTHOR]

The paper aims to introduce and investigate a new class of generalized Fubini-type polynomials. The generating functions, special cases, and properties are introduced. Using the generating functions, various interesting identities, and relations are derived. Also, special polynomials are obtained from the general class of polynomials. Finally, probabilistic applications and some probabilistic properties are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we focus on a collocation approach based on Daubechies wavelet scaling functions for approximating the solution of Volterra's model of population growth of a species with a closed system. We present that the integral and derivative terms, which appear in Volterra's model of the population, will be computed exactly in dyadic points. Utilizing this collocation technique, Volterra's population model reduces into a system of nonlinear algebraic equations. In addition, an error bound for our method will be explored. The numerical results demonstrate the applicability and accuracy of our method. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on building the ℒ -fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of ℒ -fuzzy filter and ℒ -fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the concept of prime ℒ -fuzzy filter and propose some illustrative examples. Then, we bring out their properties and show how they are related to the concept of ℒ -fuzzy prime filter. Thirdly, we characterize ℒ -fuzzy maximal filter and maximal ℒ -fuzzy filter by atoms and coatoms. In the case where ℒ is a distributive lattice, we prove that maximal ℒ -fuzzy filters are prime. Finally, we are interested in ℒ -fuzzy cosets of an ℒ -fuzzy filter, and we prove that the set of all ℒ -fuzzy cosets of any ℒ -fuzzy filter of a residuated multilattice is a residuated multilattice. [ABSTRACT FROM AUTHOR]

In this paper, we study the mathematical analysis of a nonlinear age-dependent predator–prey system with diffusion in a bounded domain with a non-standard functional response. Using the fixed point theorem, we first show a global existence result for the problem with spatial variable. Other results of existence concerning the spatial homogeneous problem and the stationary system are discussed. At last, numerical simulations are performed by using finite difference method to validate the results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in the human organism with a deficient immune system, during consecutive intakes of contaminated food. This process quantifies the exposure to toxins of subjects living with comorbidity (children not breastfed, the elderly, and pregnant women) to food-borne diseases. The Adomian Decomposition Method and the fractional integration of Riemann Liouville are used in the modeling processes. [ABSTRACT FROM AUTHOR]

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation y t − ∑ j = 1 k p j t y r j t ′ + q t G y g t − u t H y h t = f t , where p j and r j for each j and q , u , G , H , g , h , and f are all continuous functions and q ≥ 0 , u ≥ 0 , h t < t , g t < t , and r j t < t for each j. Further, each r j t , g t , and h t ⟶ ∞ as t ⟶ ∞. This paper improves and generalizes some known results. [ABSTRACT FROM AUTHOR]

In this paper, we design and investigate a higher order ε -uniformly convergent method to solve singularly perturbed parabolic reaction-diffusion problems with a large time delay. We use the Crank–Nicolson method for the time derivative, while the spatial derivative is discretized using a nonstandard finite difference approach on a uniform mesh. Furthermore, to improve the order of convergence, we used the Richardson extrapolation technique. The designed scheme converges independent of the perturbation parameter (ε -uniformly convergent) and also achieves fourth-order convergent in both time and spatial variables. Two model examples are considered to demonstrate the applicability of the suggested method. The proposed method produces better accuracy and a higher rate of convergence than some methods that appear in the literature. [ABSTRACT FROM AUTHOR]

The key purpose of this paper is to work on the boundedness of generalized Bessel–Riesz operators defined with doubling measures in Lebesgue spaces with different measures. Relating Bessel decaying the kernel of the operators is satisfying some elementary properties. Doubling measure, Young's inequality, and Minköwski's inequality will be used in proofs of boundedness of integral operators. In addition, we also explore the relation between the parameters of the kernel and generalized integral operators and see the norm of these generalized operators which will also be bounded by the norm of their kernel with different measures. [ABSTRACT FROM AUTHOR]

Biomathematics is an interdisciplinary subject consisting of mathematics and biology, which is widely applicable for the analysis of biological problems. In this paper, we provide a mathematical model of two-phase hepatic blood flow in a jaundice patient's artery. The blood flow is thought to be a two-phased process. The clinical data of a jaundice patient (blood pressure and hemoglobin) is gathered. To begin, hemoglobin is transformed into hematocrit, and blood pressure is turned to a decline in blood pressure. For the examination of hepatic arteries in Newtonian and non-Newtonian movements, a mathematical model is constructed. The relationship between two-phase blood flow flux and blood pressure reduction in the hepatic artery is established. For various hematocrit levels, the blood pressure decrease is determined. The patient's states are defined by the slope of the linear relationship between computed blood pressure decrease and hematocrit. [ABSTRACT FROM AUTHOR]

In this paper, we employ the logistic map and the cubic map to locate the relaxation and the convergence to the periodic fixed point of a system, specifically, the period—1 fixed point. The study has shown that the period—1 fixed point of a logistic map as a recurrence has its convergence at a transcritical bifurcation having its power-law fit with exponent β = − 1 when α = 1 and μ = 0. The cubic map shows its convergence to the fixed point at a pitchfork bifurcation decaying at a power law with exponent β = − 1 / 2 α = 1 and μ = 0. However, the system shows their relaxation time at the same power law with exponents and z = − 1. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for estimating trends in extreme spatiotemporal processes using both information from marginal distributions and dependence structure. We combine two statistical approaches of an extreme value theory: the temporal and spatial nonstationarities are handled via a tail trend function in the marginal distributions. The spatial dependence structure is modeled by a latent spatial process using generalized ℓ -Pareto processes. This methodology for trend analysis of extreme events is applied to precipitation data from Burkina Faso. We show that a significant increasing trend for the 50 and 100 year return levels in some parts of the country. We also show that extreme precipitation is spatially correlated with distance for a radius of approximately 200 km. [ABSTRACT FROM AUTHOR]