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Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a "o" instead of "o" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new. [ABSTRACT FROM AUTHOR]

Thomas L. Saaty, a world-renowned scholar and our beloved Advisory Editor, passed away on August 14, 2017 at the age of 91. He has made many fundamental contributions to operations research, analytics, business and mathematics. Despite his heavy illness for 14 months, as passionate about science, he has also enthusiastically published his research. We review his final works published in 2017 and 2018. We are also honored to reveal and publish his final statements on neural firing and synthesis in making comparisons & life satisfaction, respectively, in his final two papers; the previous one submitted by him just before his passing and the other one submitted by his co-authors after his death to European Journal of Pure and Applied Mathematics (EJPAM). We just would like to remember and honor Saaty's memory by publishing his final papers at EJPAM and this humble remarks dedicated to the memory of Thomas L. Saaty on the occasion of the first anniversary of his passing, August 14, 2018. [ABSTRACT FROM AUTHOR]

This paper introduces a pioneering advancement in rough set theory by presenting a new class of rough sets termed h-rough sets. Central to this novel approach are the concepts of h-lower and h-upper approximations, intricately tied to the notion of h-open sets. We delve into the fundamental properties of h-rough sets and establish the framework of h-approximation spaces, offering a comprehensive understanding of their theoretical underpinnings. Moreover, we introduce and rigorously analyze the concepts of h-rough equality and h-rough inclusion, providing formal definitions and insightful examinations of their implications in data approximation tasks. Through detailed examples and thorough exploration, this paper showcases how h-rough sets extend rough set theory, offering more flexible and precise techniques for data approximation. This study not only contributes to the theoretical development of rough set theory but also opens up exciting possibilities for practical applications across various domains. [ABSTRACT FROM AUTHOR]

Let G be a nontrivial connected graph with vertex set V (G) and the edge set E(G). A set S ⊆ V (G) is a geodetic hop dominating set of G if the following two conditions hold for each x ∈ V (G)\S: (1) x lies in some u-v geodesic in G with u, v ∈ S, and (2) x is of distance 2 from a vertex in S. The minimum cardinality γhg(G) of a geodetic hop dominating set of G is the geodetic hop domination number of G. A geodetic hop dominating set S is a minimal geodetic hop dominating set if S does not contain a proper subset that is itself a geodetic hop dominating set. The maximum cardinality of a minimal geodetic hop dominating set in G is the upper geodetic hop domination number of G, and is denoted by γ + hg(G). This paper initiates the study of the minimal geodetic hop dominating set and the corresponding upper geodetic hop domination number of nontrivial connected graphs. Interestingly, every pair of positive integers a and b with 2 ≤ a ≤ b is realizable as the geodetic domination number and the upper geodetic hop domination number, respectively, of some graph. Furthermore, this paper investigates the concept in the join, corona and lexicographic product of graphs. [ABSTRACT FROM AUTHOR]

Although Selberg-type single positive definite symmetric matrices gamma and beta integrals have been evaluated by several authors, see e.g., Askey and Richards [1], Gupta and Kabe [2, 4], Mathai [8], and elsewhere in the vast multivariate statistical analysis literature. However, several other types of Selberg-type integrals appear to have been neglected in the literature. Thus e.g., Selberg-type integrals associated with inverse Wishart densities, inverse multivariate beta densities, their noncentral counterparts, etc, have not been explored as yet. The present paper records Selberg-type generalized quadratic forms gamma and beta integrals. Our methodology is based on hypercomplex (HC) multivariate normal distribution theory, Kabe [6]. [ABSTRACT FROM AUTHOR]

The nervous system uses its own kind of mathematical function patterns for both external and internal realities. The conscious part of the nervous system is there to respond to what happens outside by regulating externally received information signals from the senses and the skin and muscles of the body itself. To do that, it needs to communicate with its subconscious using the familiar language of neural firing. In this paper, we show that because reciprocal pairwise comparisons are performed at the neural level, the division algebra of the octonions, in which commutativity and associativity are not satisfied, provides the structure needed to represent mental processes and that these processes could be represented in G2-manifolds. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of the direct product of sets that involve Fermatean neutrosophic (FN) elements in structures called INK-algebras. It defines terms like the direct product of Fermatean neutrosophic INK-ideals (FNINK-Is) in INK-algebras and Fermatean neutrosophic sets (FNSs), FNINK-Is, and Fermatean neutrosophic closed INK-ideals (FNCINK-Is). The proof of theorems illustrating the relationships between these ideas is included in the paper. It also defines the INK-subalgebra embedded in an INK-algebra and gives a theorem elucidating the connection between the direct product of FNINK-Is and the images of these subalgebras. In essence, the paper investigates and establishes connections between different mathematical ideas concerning INK-algebras and FNSs. [ABSTRACT FROM AUTHOR]

In this paper, we address several scientific and technological challenges with a novel He's non-perturbative approach (NPA), it simplifying processing time compared to traditional methods. The proposed approach transforms nonlinear ordinary differential equations (ODEs) into linear ones, analogous to simple harmonic motion, and producing a new frequency. Studying the periodic solutions leads to enhanced design, performance, reliability, and efficiency across these fields. This new approach is based mainly on the He's frequency formulation (HFF). This method yields highly accurate outcomes, surpassing well-known approximate methodologies, as validated through numerical comparisons in the Mathematical Software (MS). The congruence between numerical solution tests and theoretical predictions further supports our findings. While classical perturbation methods rely on Taylor expansions to simplify restoring forces, the NPA also enables stability analysis. Consequently, for analyzing approximations of highly non-linear oscillators in MS, the NPA serves as a more reliable tool. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new method motivated by current advancements in general inertial algorithms. Specifically, we incorporate double inertial extrapolation terms into an iterative sequence, derived from Krasnosel'skii-Mann techniques. The weak convergence theorem for fixed points of nonexpansive mappings in real Hilbert spaces is established. The theoretical developments are rigorously proven, extending existing methods in literature. We also utilize our convergence analysis to solve real-world problems, such as convex minimization problems and zero finding for sums of monotone operators. [ABSTRACT FROM AUTHOR]

A Pythagorean triple is a triple of positive integers (a, b, c) such that a² + b² = c². If a, b are coprime, then it is called a primitive Pythagorean triple. It is known that every primitive Pythagorean triple can be generated from the triple (3, 4, 5) using multiplication by unique number and order of three specific 3 × 3 matrices, which yields a ternary tree of triplets. Two such trees were described by Berggren and Price, respectively. A different approach is to view the primitive Pythagorean triples as points in the three-dimensional Euclidean space. In this paper, we prove that the triple of descendants of any primitive Pythagorean triple in Berggren's or Price's tree forms a triangle (and therefore defines a plane), and we present our results related to these triangles (and these planes). [ABSTRACT FROM AUTHOR]

This paper deals with the notions of upper and lower slightly α(τ1, τ2)-continuous multifunctions. Furthermore, several characterizations of upper and lower slightly α(τ1, τ2)-continuous multifunctions are discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the concepts of upper and lower c-(τ1, τ2)-continuous multifunctions. Moreover, several characterizations of upper and lower c-(τ1, τ2)-continuous multifunctions are investigated. [ABSTRACT FROM AUTHOR]

Let G be a connected graph and uv ∈ E(G). We say, the vertex v even sum dominates u (u even sum dominates v) if deg(v)+deg(u) is an even number. A set S is an even sum dominating set (ESDS) if every vertex v ∈ V is either in S or even sum dominated by a vertex in S. An even sum dominating set S is a mimimal even sum dominating set if no proper subset S'⊂ S is an even sum dominating set. The even sum domination number γes(G) of a graph G is the minimum cardinality of an even sum dominating set of G. In this paper, we discuss some properties and bounds for this concept. We also derive even sum domination number for some standard graphs. [ABSTRACT FROM AUTHOR]

The concept of entropy, emerged from thermodynamics and statistical mechanics is of fundamental importance in some scientific and technological areas such as communication theory, physics, probability and statistics. Fuzzy entropy is much looked upon concept for measuring fuzzy information. The concept of fuzzy entropy was firstly mentioned by Zadeh way back in 1965 as a measure of fuzziness. In this paper, we introduce Mathai - Haubold fuzzy entropy with the proof of its validity. In addition, the elegant properties are studied of the proposed fuzzy entropy measure. [ABSTRACT FROM AUTHOR]

Let H be a complex Hilbert space and let T represent a bounded linear operator on H. In this paper we introduce, a new class of non normal operators, the (M, k)-quasi paranormal operator. An operator T is said to be a (M,k)-quasi paranormal operator, for a non negative integer k and a real positive number M if it satisfies ||Tk+1x||2 < M||Tk+2x|| ||Tkx||, for all x ∈ H. This new class of operators is generalization of some of the non normal operators, such as, the k-quasi paranormal and M-paranormal operators. We prove the basic properties, the structural and spectral properties and also the matrix representation of this new class of operators. [ABSTRACT FROM AUTHOR]

n recent years, some applications of Lah numbers were discovered in the real world problem of telecommunications and optics. The aim of this paper is to study the λ-analogues of Lah numbers and Lah-Bell polynomials which are λ-analogues of the Lah numbers and and LahBell polynomials. Here we note that λ-analogues appear when we replace the falling factorials by the generalized falling factorials in the defining equations. By using generating function method, we study some properties, explicit expressions, generating functions and Dobinski-like formulas for those numbers and polynomials. We also treat the more general λ-analogues of r-Lah numbers and r-extended λ-Lah-Bell polynomials. In addition, we show that the expectations of two random variables, both associated with the Poisson random variable with parameter α/λ, are equal to the λ-analogue of the Lah-Bell polynomial evaluated at α for one and the r-extended λ-Lah-Bell polynomial evaluated at α for the other. [ABSTRACT FROM AUTHOR]

In this paper a new generalized norm is defined and Riesz type inequalities for harmonic functions on the unit disk are discussed by applying it. Also sharp constants are obtained for certain special values considered in the reverse case of the standard Riesz inequality. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the Riesz theorem for harmonic quasiregular mappings for a special case (when p = 2) in the unit disc. Our results improve similar results in this field and are proved with milder conditions. Moreover, we prove another variant forms of Riesz inequality for harmonic quasiregular functions. [ABSTRACT FROM AUTHOR]

In this paper, we present several characterization theorems on approach groups, and ultra approach groups. In so doing, we first give necessary and sufficient conditions for an approach structure to be compatible with group structure. We show that every ultra approach group is ultrauniformizable. Secondly, starting with an approach space, and its natural neighborhood system on a group, we characterize the resulting neighborhood approach group. Finally, we show that the category of ultra approach-Cauchy group is a topological category, and more importantly, we show that the category of ultra approach-Cauchy groups and the category of strongly normal ultra approach-limit groups are isomorphic. [ABSTRACT FROM AUTHOR]

This paper intends to investigate the causal relationship between teachers’ self-efficacy and teacher teaching practices in Saudi Arabia using Structural Equation Modeling (SEM) based on the public database of the Teaching and Learning International Survey (TALIS 2018). In this study, 2744 teachers responded to the survey, representing lower secondary in mainstream public and private schools in Saudi Arabia. Based on the literature review and the exploratory factor analysis presented in the TALIS 2018 technical report, three constructs represent teacher teaching practices including (clarity of instructional, cognitive activation, and classroom management practices). Teacher self-efficacy includes two constructs (classroom management efficacy and instruction efficacy). After applying structural equation modeling, the main finding indicates a positive influence of teacher self-efficacy on the clarity of instructional practices, cognitive activation practices, and classroom management practices. [ABSTRACT FROM AUTHOR]

Let G = (V (G), E(G)) be a graph with degree sequence ⟨d1, d2, · · ·, dn⟩, where d1 ≥ d2 ≥ · · · ≥ dn. The polynomial representation of G is given by fG(x) = Σn i=1 x di = ∆( X G) k=1 akx k, where ak is the number of vertices of G having degree k for each i = 1, 2, · · · n = ∆(G). In this paper, we give the polynomial representation of the complement and line graph of a graph, the shadow graph, complementary prism, edge corona, strong product, symmetric product, and disjunction of two graphs. [ABSTRACT FROM AUTHOR]

In this paper, we study relations between inner products derived from the standard n-inner product defined on an inner product space. In particular, we are interested in knowing when orthogonality with respect to the original inner product is preserved by the derived inner product. [ABSTRACT FROM AUTHOR]

Let G is a cyclic group. Then H(G) is a trivial group and if G = G1∗ . . . ∗ Gn is the free product of the groups G1, . . ., Gn, then H(G) = H(G1 ∗ . . . ∗ G∗) ≊ H(G1) × . . . × H(Gn). Furthermore, if the groups G1, G2, . . ., Gnare cyclic groups, then H(G) is a trivial group. In this paper we show that for every group G there exists a group denoted H(G) and is called the associated group of G satisfying some important properties that as application we show that if F is a quasi-free group and G is any group, then H(F)is trivial and H(F ∗ G) ≊ H(G), where a group is termed a quasi-free group if it is a free product of cyclic groups of any order. [ABSTRACT FROM AUTHOR]

A great deal of inventory costs are typically unpredictable because of the unpredictability of a competitive market. The fluctating demand from customer’s and the unpredictability of the market economy make it difficult for researchers and operation research practitioners to appropriately replicate an inventory problem. In order to prevail this type of unpredictability circumstances, in this paper, we have represented the inventory parameters as interval. Using this concept, we progressed a two-warehouse inventory model for deteriorating items with a fixed Shelf life, partially backlogging shortages and interval-valued deterioration rate. In addition to this the parameters like ordering cost, purchase cost, shortage cost, deterioration cost for both the rented and owned warehouse except the backlogging parameter have been considered as interval-valued. The uncertainty in the inventory parameters motivated us to view them as interval-valued in the present research. Based on the assumptions, the cost function of this problem is a highly nonlinear constraint optimization problem. Mathematica is used to tackle this nonlinear optimization problem. A numerical example has been presented to demonstrate the computational result. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy. [ABSTRACT FROM AUTHOR]

A study of s...-open sets in generalized topological spaces started in 2011 by Min [4]. In this paper, we introduce the concepts of s ...-open sets, s...-closed sets, s...-continuous functions and s...-irresolute functions on generalized topological spaces. We also study some basic properties of such sets and functions. 2020 Mathematics Subject Classifications: 54A05 [ABSTRACT FROM AUTHOR]

This paper presents the notions of bipolar fuzzy commutative ideals of a BCK-algebra. We also study various properties regarding this concept. We prove various characterisations for bipolar fuzzy commutative ideals. Moreover, a relationship between bipolar fuzzy commutative ideals and bipolar fuzzy positive implicative ideals is presented. In addition, we present the notation of bipolar fuzzy characteristic commutative ideal. Then a relationship between a bipolar fuzzy characteristic commutative ideal and its level-cut commutative ideals is provided. [ABSTRACT FROM AUTHOR]

This paper focuses on finding the upper bounds of the second Hankel and Toeplitz determinants, whose entries are logarithmic coefficients of inverse functions for a new subclass of starlike functions with respect to symmetric conjugate points associated with the exponential function defined by subordination. Results on initial Taylor coefficients and logarithmic coefficients of inverse functions for a new subclass are also presented. This study may inspire others to focus further to the coefficient functional problems associated with the inverse functions of various classes of univalent functions. [ABSTRACT FROM AUTHOR]

In this paper, a delay - induced pest control model is proposed. We have introduced a time delay in healthy trees and whitefly population in the infected tree density of the proposed system of equations to reduce the probability of healthy trees becoming infected, as well as the level of infection. We have analyzed the impact of time delay on the stability of the equilibrium and establish requirements to verify its asymptotic stability over all delays. The solutions of this system of non-linear ordinary differential equations(ODEs) and delay differential equations(DDEs) are presented by using homotopy perturbation method(HPM). Numerical simulation is also obtained for the same model of both ODE and DDE by using MATLAB software. The proposed method works very well and is easy to use, as shown by these findings. Our aim is to control the spread of whitefly such that harvest is not affected. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to find the inversion formula for the covariant transform Wρk φ0. This formula is equivalent to the decomposition of the unitary representation ρk into irreducible components. We consider an eigenvalue 1+s² of the Casimir operator: dρk(C) = −4v2 (∂²u + ∂²v), where k = 0. To find the inversion formula, first we study the representations of SL2(R), ρk and ρτ, induced from the complex characters of K and N respectively. Then, we find the induced covariant transform Wρk φ0 with N-eigenvector to obtain a transform in the space L2 (SL2(R)/N). Thereafter, we compute the contravariant transform with K-eigenvector Mρτ ϕ0 : L2 (SL2(R)/K) → L2 (SL2(R)/K). [ABSTRACT FROM AUTHOR]

This paper is concerned with the concepts of upper and lower weakly (T1, T2)-continuous multifunctions. Moreover, some characterizations of upper and lower weakly (T1, T2)-continuous multifunctions are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce hierarchy elements in an almost distributive lattice with respect to a non-empty set and obtain some of their algebraic properties. We characterize initial segments, ideals, and maximal sets in almost distributive lattices in terms of hierarchy sets and prove that the class of hierarchy sets forms a distributive lattice, which is not an induced sublattice. Also, we characterize hierarchy sets using compatible sets in an almost distributive lattice. [ABSTRACT FROM AUTHOR]

Through concepts from non-commutative algebra and homology, this paper resolves the conjecture that lets the first bifunctor extension to be zero when the projective dimension is finite, for a simple module S of an Artinian ring whose cube of its Jacobson radical is zero and under the condition that any simple module over this ring of finite projective dimension has a radical square zero of the cover projective of its first syzygy. For that, we use a property of the simple module which realizes the minimum of the finite projective dimensions of simple modules. Our main result is presented in the form of a corollary in the case of an Artinian ring with radical cubed zero such that the projective cover of its radical is of Loewy length two and its supremum being finite. In the part of discussions, we succeed to show the no loop conjecture through two examples. The first one is about its weak version by taking a quiver algebra A verifying J³ = 0 and without considering that rad² (P(Ω(S))) = 0 for every simple module, while the second one shows that if the extension quiver has a loop in a simple module then its projective dimension is infinite for every nilpotence index of the Jacobson radical. More importantly, we finally provide a practical third example for our special case. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some types of separation axioms via F-open sets, namely F Ti(i = 0, 1, 2, 3, 4), F-regular and F-normal spaces, and investigate their properties, relationships and characterizations. We show that every F Tispace is a Tispace for i = 0, 1, 2, 3, 4. However, the converse is true whenever X is finite. [ABSTRACT FROM AUTHOR]

Let G = (V (G), E(G)) be a simple and undirected graph. A dominating set S ⊆ V (G) is called a differentiating odd dominating set if for every vertex v ∈ V (G), |N[v] ∩ S| ≡ 1(mod 2) and NG[u] ∩ S≠ NG[v] ∩ S for every two distinct vertices u and v in V (G). The minimum cardinality of a differentiating odd dominating set of G, denoted by γo D(G), is called the differentiating odd domination number. In this paper, we discuss differentiating odd dominating sets and give bounds or exact values of the differentiating odd domination numbers of some graphs. We give necessary and sufficient conditions for some graphs to admit a differentiating odd dominating set. Moreover, we characterize the differentiating odd dominating sets in graphs resulting from join, corona, and lexicographic product of some graphs and determine the differentiating odd domination numbers of these graphs. [ABSTRACT FROM AUTHOR]

In this paper, we unveil a novel category of Frobenius-Genocchi polynomials, grounded in the Bell numbers and Apostol-type functions. Our exploration delves into a comprehensive examination of these polynomials, elucidating various properties. Employing diverse analytical methods and leveraging generating functions for Bell-based Apostol-Frobenius-Type poly-Genocchi polynomials of higher order, we derive explicit and implicit summation formulas, complemented by their symmetric identities. [ABSTRACT FROM AUTHOR]

Let G be a connected graph. A set S ⊆ V (G) is convex 2-dominating if S is both convex and 2-dominating. The minimum cardinality among all convex 2-dominating sets in G, denoted by γ2con(G), is called the convex 2-domination number of G. In this paper, we initiate the study of convex 2- domination in graphs. We show that any two positive integers a and b with 6 ≤ a ≤ b are, respectively, realizable as the convex domination number and convex 2-domination number of some connected graph. Furthermore, we characterize the convex 2-dominating sets in the join, corona, lexicographic product, and Cartesian product of two graphs and determine the corresponding convex 2-domination number of each of these graphs. [ABSTRACT FROM AUTHOR]

A bacterial disease called leptospirosis is very typical in both tropical and subtropical regions. It is a well-known animal-borne illness that is brought on by spiral-shaped bacteria (Leptospira spp.). Both directly and indirectly, the disease can spread to humans through the urine of sick animals or polluted water, soil, or food. Two phases might appear in leptospirosis symptoms. The patient will have mild symptoms during the first phase, which is known as the Septicemic phase. In the meantime, the Immune phase, the second, is more severe. This study aimed to create a mathematical model of leptospirosis disease using free-living bacteria. In the model, interactions occur between people, free-living Leptospira, animal hosts, and animal vectors. The population’s characteristics are used to build the model, and the actual issue is used to identify the disease’s transmission paths. While the endemic equilibrium is investigated numerically through ODE45 solver, the disease-free equilibrium is analyzed theoretically. The paper demonstrates that for the established mathematical model with an epidemic threshold R0, analytical and numerical solutions produced the same outcome. [ABSTRACT FROM AUTHOR]

A defensive alliance in a graph G is a nonempty set of vertices S ⊆ V (G) such that for every vertex v ∈ S, |N[v] ∩ S| ≥ |N(v) ∩ (V (G) ∖ S)|. A defensive alliance S is called global if every vertex in V (G) ∖ S is adjacent to at least one member of the alliance S. In this paper, the concept of restrained global defensive alliance in graphs was introduced. In particular, a global defensive alliance S is a restrained global defensive alliance if the induced subgraph of V ∖ S has no isolated vertex. Here, some properties of this alliance were identified, and its bounds were also determined. In addition, the restrained global defensive alliance number was also formulated, along with characterizations of some special classes of graphs, specifically complete, complete bipartite, and path graphs. [ABSTRACT FROM AUTHOR]

This paper deals on the valuation of European call option price in a stochastic environment by employing three factors which are the stochastic model of the asset value, the stochastic interest rate and the transaction cost. We specify that our underlying asset and the stochastic interest rate, particularly Hull-White model, follows a fractional Brownian Motion governed by Hurst parameter H. We used the hedging and replicating technique to established the zero-coupon bond on the European option. Finally, we give a closed-form formula of the European call option price. [ABSTRACT FROM AUTHOR]

The influx of researches on hyperstructure theory has encouraged many researchers to introduce new algebras. Notable among these is the work of Indangan and Petalcorin who introduced hyper GR-algebra and that of Macodi and Petalcorin who studied fuzzification of hyper GR-algebra. Macodi extended the fuzzification of hyper GR-algebra into intuitionistic fuzzification and introduced the concept of an intuitionistic fuzzy hyper GR-ideal. Following the works of Macodi and Petalcorin, this paper established an intuitionistic fuzzy implicative hyper GR-ideal and obtained its characterization using level subsets. Moreover, some properties of intuitionistic fuzzy implicative hyper GR-ideals are presented. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method for solving the fractional order Fredholm integrodifferential equations via the Caputo-Liouville derivative is presented. The method uses the wellknown shifted Chebyshev expansion and a truncated series to represent the unknown function. It also incorporates numerical integration techniques like the Trapezoidal, Simpson's 1/3, and Simpson's 8/3 methods. The paper also provides an approximation for the derivative of an integer. The procedure converts the provided problem into a system of algebraic equations using shifted Chebyshev coefficients and collocation points. The coefficients are found by solving this system using well-known techniques like Newton's method. Numerical results are presented graphycally to illustrate the applicability, efficacy, and accuracy of the approach presented in this work. All calculations in this study were performed using the MATHEMATICA software program. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph of order n. In this paper, we introduce a new distance matrix called the universal distance matrix of G, denoted as UD (G) and it is defined as UD (G) = αTr (G) + βD(G) + γJ + δI, where Tr (G) is the diagonal matrix whose elements are the vertex transmissions, and D(G) is the distance matrix of G. Here J is the all-ones matrix, and I is the identity matrix and α, β, γ, δ ∈ R and β ̸= 0. This unified definition enables us to derive the spectra of different matrices associated with the distance matrix of graphs. The set of eigenvalues of the universal distance matrix namely, {ρ1, ρ2,.. ., ρn} is known as the universal distance spectrum of G. As a consequence, by taking appropriate values for α, β, γ, δ ∈ R and β ̸= 0, we obtain the eigenvalues of distance matrix, distance Laplacian matrix, distance signless Laplacian matrix, generalized distance matrix, distance Seidal matrix and distance matrices of graph complements. In this paper, we obtain the universal distance spectra of regular graph, join of two regular graphs, joined union of three regular graphs, generalized joined union of n disjoint graphs with one arbitrary graph H using the Schur complement of a block matrix. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of a B-filter in a B-algebra (X, ∗, 0) and presents characteristics of its properties: for any a ∈ X, the set ⟨a⟩B = {ak: k ∈ Z} forms a B-ideal and B-filter of X. Moreover, this paper showns some properties of exponents on B-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we consider various Stirling numbers of both kinds, including the unsigned degenerate Stirling numbers of the first kind, the degenerate Stirling numbers of the second kind, the unsigned degenerate r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind. The aim of this paper is by using generating functions to further study explicit expressions, some identities and equivalent relations for those Stirling numbers. [ABSTRACT FROM AUTHOR]

This paper explores the solutions of certain fractional partial differential equations using two methods; the first method involves separation of variables, which is a common technique for solving partial differential equations. However, since many equations cannot be separated in this way, the tensor product of Banach spaces method is applied to find the atomic solutions. To solve the resulting ordinary differential equations, the reproducing Kernel Hilbert space method is used to find numerical solutions, which are then used to find the numerical solution of the partial differential equation. The residual errors indicate that this method is effective and powerful. In summary, this paper presents a study on the solutions of certain fractional partial differential equations using two methods and demonstrates the effectiveness of these methods in finding numerical solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a novel trigonometric B-spline collocation method for solving a specific class of second-order boundary value problems. The study showcases the method’s practicality and effectiveness through various numerical examples. Furthermore, it evaluates the technique’s performance by calculating maximum errors for different step sizes in the spatial domain. The paper also conducts a comparative analysis with alternative methods, demonstrating the superior accuracy of the trigonometric B-spline approach. [ABSTRACT FROM AUTHOR]

This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called j-edge intersection graph of cycle graph, denoted by EC(n,j) . The vertex set of EC(n,j) is the set of spanning subgraphs of cycle graph with j edges where n ≥ 3 and j is a nonnegative integer such that 1 ≤ j ≤ n. Two distinct vertices are adjacent if they have exactly one edge in common. EC(n,j) is considered as a simple graph. Furthermore, EC(n,j) is characterized by the value of j that is when j = 1 or ⌈ n/2 ⌉ < j ≤ n and 2 ≤ j ≤ ⌈ n/2 ⌉. When j = 1 or ⌈ n/2 ⌉ < j ≤ n, the new graph only produced an empty graph. Hence, the proponents only considered the value when/2 ≤ j ≤ ⌈ n/2 ⌉ in determining the order and size of EC(n,j) . Moreover, this paper discusses necessary and sufficient conditions where the j-edge intersection graph of Cn is isomorphic to the cycle graph. Furthermore, the researchers determined a lower bound for the independence number, and an upper bound for the domination number of EC(n,j) when j = 2. [ABSTRACT FROM AUTHOR]

This paper is motivated by the work of Taekyun Kim and Dae San Kim on the degenerate Laplace transform and degenerate gamma function, as published in the Russian Journal of Mathematical Physics. We introduce the degenerate Laplace-type integral transform and delve into its properties and interrelations. This paper focuses on the degenerate Laplace-type integral transforms of several fundamental functions, including the degenerate sine, degenerate cosine, degenerate hyperbolic sine, and degenerate hyperbolic cosine functions. Furthermore, we establish crucial connections between the degenerate Laplace-type integral transform and existing degenerate integral transforms. Specifically, we explore its relationships with the degenerate Laplace transform, the degenerate Elzaki transform, and the degenerate Sumudu transforms. [ABSTRACT FROM AUTHOR]

This paper establishes the linear algebra of the (r, β)-Stirling matrix. Along the way, this paper derives various identities, such as its factorization and relationship to the Pascal matrix and the Stirling matrix of the second kind. Additionally, this paper develops a natural extension of the Vandermonde matrix, which can be used to study and evaluate successive power sums of arithmetic progressions. [ABSTRACT FROM AUTHOR]

Let G be a graph. Then Q ⊆ V (G) is called a certified vertex cover of G if Q is a vertex cover of G and every x ∈ Q, x has either zero or at least two neighbors in V (G) \ Q. The certified vertex cover number of G, denoted by βcer(G), is the minimum cardinality of a certified vertex cover of G. In this paper, we investigate this newly defined concept on some special graphs and on the join of two graphs. We characterize certified vertex cover in these graphs and subsequently derive the simplified formulas for calculating the certified vertex cover number. Moreover, we present some bounds and properties of certified vertex cover. [ABSTRACT FROM AUTHOR]