-
Construction of 4 x 4 symmetric stochastic matrices with given spectra Open Math. (IF 1.7) Pub Date : 2024-03-16 Jaewon Jung, Donggyun Kim
The symmetric stochastic inverse eigenvalue problem (SSIEP) asks which lists of real numbers occur as the spectra of symmetric stochastic matrices. When the cardinality of a list is 4, Kaddoura and Mourad provided a sufficient condition for SSIEP by a mapping and convexity technique. They also conjectured that the sufficient condition is the necessary condition. This study presents the same sufficient
-
Local and global solvability for the Boussinesq system in Besov spaces Open Math. (IF 1.7) Pub Date : 2024-03-14 Shuokai Yan, Lu Wang, Qinghua Zhang
This article focuses on local and global existence and uniqueness for the strong solution to the Boussinesq system in R n {{\mathbb{R}}}^{n} ( n ≥ 3 n\ge 3 ) with full viscosity in Besov spaces. Under the hypotheses 1 < p < ∞ 1\lt p\lt \infty and − min { n ∕ p , 2 − n ∕ p } < s ≤ n ∕ p -\min \left\{n/p,2-n/p\right\}\lt s\le n/p , and the initial condition ( θ 0 , u 0 ) ∈ B ˙ p , 1 s − 1 × B ˙ p , 1
-
Enhanced Young-type inequalities utilizing Kantorovich approach for semidefinite matrices Open Math. (IF 1.7) Pub Date : 2024-03-14 Feras Bani-Ahmad, Mohammad Hussein Mohammad Rashid
This article introduces new Young-type inequalities, leveraging the Kantorovich constant, by refining the original inequality. In addition, we present a range of norm-based inequalities applicable to positive semidefinite matrices, such as the Hilbert-Schmidt norm and the trace norm. The importance of these results lies in their dual significance: they hold inherent value on their own, and they also
-
Combined system of additive functional equations in Banach algebras Open Math. (IF 1.7) Pub Date : 2024-03-14 Siriluk Donganont, Choonkil Park
In this study, we solve the system of additive functional equations: h ( x + y ) = h ( x ) + h ( y ) , g ( x + y ) = f ( x ) + f ( y ) , 2 f x + y 2 = g ( x ) + g ( y ) , \left\{\begin{array}{l}h\left(x+y)=h\left(x)+h(y),\\ g\left(x+y)=f\left(x)+f(y),\\ 2f\left(\frac{x+y}{2}\right)=g\left(x)+g(y),\end{array}\right. and we investigate the stability of (homomorphism, derivation)-systems in Banach algebras
-
The product of a quartic and a sextic number cannot be octic Open Math. (IF 1.7) Pub Date : 2024-03-12 Artūras Dubickas, Lukas Maciulevičius
In this article, we prove that the product of two algebraic numbers of degrees 4 and 6 over Q {\mathbb{Q}} cannot be of degree 8. This completes the classification of so-called product-feasible triplets ( a , b , c ) ∈ N 3 \left(a,b,c)\in {{\mathbb{N}}}^{3} with a ≤ b ≤ c a\le b\le c and b ≤ 7 b\le 7 . The triplet ( a , b , c ) \left(a,b,c) is called product-feasible if there are algebraic numbers
-
Weighted Hermite-Hadamard-type inequalities without any symmetry condition on the weight function Open Math. (IF 1.7) Pub Date : 2024-03-12 Mohamed Jleli, Bessem Samet
We establish weighted Hermite-Hadamard-type inequalities for some classes of differentiable functions without assuming any symmetry property on the weight function. Next, we apply our obtained results to the approximation of some classes of weighted integrals.
-
On certain functional equation related to derivations Open Math. (IF 1.7) Pub Date : 2024-02-09 Benjamin Marcen, Joso Vukman
In this article, we prove the following result. Let n ≥ 3 n\ge 3 be some fixed integer and let R R be a prime ring with char ( R ) ≠ ( n + 1 ) ! 2 n − 2 {\rm{char}}\left(R)\ne \left(n+1)\!{2}^{n-2} . Suppose there exists an additive mapping D : R → R D:R\to R satisfying the relation 2 n − 2 D ( x n ) = ∑ i = 0 n − 2 n − 2 i x i D ( x 2 ) x n − 2 − i + ( 2 n − 2 − 1 ) ( D ( x ) x n − 1 + x n − 1 D (
-
On the maximum atom-bond sum-connectivity index of graphs Open Math. (IF 1.7) Pub Date : 2024-02-09 Tariq Alraqad, Hicham Saber, Akbar Ali, Abeer M. Albalahi
The atom-bond sum-connectivity (ABS) index of a graph G G with edges e 1 , … , e m {e}_{1},\ldots ,{e}_{m} is the sum of the numbers 1 − 2 ( d e i + 2 ) − 1 \sqrt{1-2{\left({d}_{{e}_{i}}+2)}^{-1}} over 1 ≤ i ≤ m 1\le i\le m , where d e i {d}_{{e}_{i}} is the number of edges adjacent to e i {e}_{i} . In this article, we study the maximum values of the ABS index over graphs with given parameters. More
-
An application of Hayashi's inequality in numerical integration Open Math. (IF 1.7) Pub Date : 2024-01-12 Ahmed Salem Heilat, Ahmad Qazza, Raed Hatamleh, Rania Saadeh, Mohammad W. Alomari
This study systematically develops error estimates tailored to a specific set of general quadrature rules that exclusively incorporate first derivatives. Moreover, it introduces refined versions of select generalized Ostrowski’s type inequalities, enhancing their applicability. Through the skillful application of Hayashi’s celebrated inequality to specific functions, the provided proofs underpin these
-
Uniqueness of exponential polynomials Open Math. (IF 1.7) Pub Date : 2024-01-10 Ge Wang, Zhiying He, Mingliang Fang
In this article, we study the uniqueness of exponential polynomials and mainly prove: Let n n be a positive integer, let p i ( z ) ( i = 1 , 2 , … , n ) {p}_{i}\left(z)\hspace{0.33em}\left(i=1,2,\ldots ,n) be nonzero polynomials, and let c i ≠ 0 ( i = 1 , 2 , … , n ) {c}_{i}\ne 0\hspace{0.33em}\left(i=1,2,\ldots ,n) be distinct finite complex numbers. Suppose that f ( z ) f\left(z) is an entire function
-
A quasi-boundary value regularization method for the spherically symmetric backward heat conduction problem Open Math. (IF 1.7) Pub Date : 2024-01-08 Wei Cheng, Yi-Liang Liu
In this article, we investigate a spherically symmetric backward heat conduction problem, starting from the final temperature. This problem is severely ill posed: the solution (if it exists) does not depend continuously on the final data. A conditional stability result of its solution is given. Further, we propose a quasi-boundary value regularization method to solve this ill-posed problem. Two Hölder
-
Average value of the divisor class numbers of real cubic function fields Open Math. (IF 1.7) Pub Date : 2024-01-08 Yoonjin Lee, Jungyun Lee, Jinjoo Yoo
We compute an asymptotic formula for the divisor class numbers of real cubic function fields K m = k ( m 3 ) {K}_{m}=k\left(\sqrt[3]{m}) , where F q {{\mathbb{F}}}_{q} is a finite field with q q elements, q ≡ 1 ( mod 3 ) q\equiv 1\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3) , k ≔ F q ( T ) k:= {{\mathbb{F}}}_{q}\left(T) is the rational function field, and m ∈ F q [ T ] m\in {{\mathbb{F}}}_{q}\left[T]
-
The structure fault tolerance of burnt pancake networks Open Math. (IF 1.7) Pub Date : 2024-01-08 Huifen Ge, Chengfu Ye, Shumin Zhang
One of the symbolic parameters to measure the fault tolerance of a network is its connectivity. The H H -structure connectivity and H H -substructure connectivity extend the classical connectivity and are more practical. For a graph G G and its connected subgraph H H , the H H -structure connectivity κ ( G ; H ) \kappa \left(G;\hspace{0.33em}H) (resp. H H -substructure connectivity κ s ( G ; H ) {\kappa
-
Some estimates for commutators of sharp maximal function on the p-adic Lebesgue spaces Open Math. (IF 1.7) Pub Date : 2024-01-08 Jianglong Wu, Yunpeng Chang
In this article, the main aim is to consider the boundedness of the nonlinear commutator of p p -adic sharp maximal operator ℳ p ♯ {{\mathcal{ {\mathcal M} }}}_{p}^{\sharp } with symbols belonging to the p p -adic Lipschitz spaces in the context of the p p -adic version of (variable) Lebesgue spaces, by which some new characterizations of the Lipschitz spaces are obtained in the p p -adic field context
-
A digital Jordan surface theorem with respect to a graph connectedness Open Math. (IF 1.7) Pub Date : 2024-01-06 Josef Šlapal
After introducing a graph connectedness induced by a given set of paths of the same length, we focus on the 2-adjacency graph on the digital line Z {\mathbb{Z}} with a certain set of paths of length n n for every positive integer n n . The connectedness in the strong product of three copies of the graph is used to define digital Jordan surfaces. These are obtained as polyhedral surfaces bounding the
-
A preconditioned iterative method for coupled fractional partial differential equation in European option pricing Open Math. (IF 1.7) Pub Date : 2024-01-03 Shuang Wu, Lot-Kei Chou, Xu Chen, Siu-Long Lei
Recently, regime-switching option pricing based on fractional diffusion models has been used, which explains many significant empirical facts about financial markets better. There are many methods to solve the problem, but to the best of our knowledge, effective preconditioners for the second-order schemes have not been proposed. Thus, in this article, an implicit numerical scheme is developed for
-
On a blow-up criterion for solution of 3D fractional Navier-Stokes-Coriolis equations in Lei-Lin-Gevrey spaces Open Math. (IF 1.7) Pub Date : 2024-01-02 Xiaochun Sun, Gaoting Xu, Yulian Wu
In this article, we researched the existence of the solution to the fractional Navier-Stokes equations with the Coriolis force under initial data, which belong to the Lei-Lin-Gevrey spaces. Moreover, we showed a blow-up criterion, i.e., when the maximal time of existence T * {T}^{* } is finite, we proved that the norm of this same solution, in a specific Lei-Lin-Gevrey space, goes to infinity, as time
-
Eigenfunctions in Finsler Gaussian solitons Open Math. (IF 1.7) Pub Date : 2024-01-02 Caiyun Liu, Songting Yin
Gaussian solitons are important examples in the theory of Riemannian measure space. In the first part, we explicitly characterize the first eigenfunctions of the drift Laplacian in a Gaussian shrinking soliton, which shows that apart from each coordinate function, other first eigenfunctions must involve exponential functions and the so-called error functions. Moreover, the second eigenfunctions are
-
New fractional integral inequalities via Euler's beta function Open Math. (IF 1.7) Pub Date : 2023-12-22 Ohud Bulayhan Almutairi
In this article, we present new fractional integral inequalities via Euler’s beta function in terms of s s -convex mappings. We develop some new generalizations of fractional trapezoid- and midpoint-type inequalities using the class of differentiable s s -convexity. The results obtained in this study extended other related results reported in the literature.
-
An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition Open Math. (IF 1.7) Pub Date : 2023-12-22 Shuimu Zou, Jun Zhang
In this article, we develop an efficient Legendre-Galerkin approximation based on a reduced-dimension scheme for the fourth-order equation with singular potential and simply supported plate (SSP) boundary conditions in a circular domain. First, we deduce the equivalent reduced-dimension scheme and essential pole condition associated with the original problem, based on which a class of weighted Sobolev
-
On pomonoid of partial transformations of a poset Open Math. (IF 1.7) Pub Date : 2023-12-16 Bana Al Subaiei
The main objective of this article is to study the ordered partial transformations PO ( X ) {\mathcal{PO}}\left(X) of a poset X X . The findings show that the set of all partial transformations of a poset with a pointwise order is not necessarily a pomonoid. Some conditions are implemented to guarantee that PO ( X ) {\mathcal{PO}}\left(X) is a pomonoid and this pomonoid is denoted by PO ↑ ( X ) {{
-
Global well-posedness of initial-boundary value problem of fifth-order KdV equation posed on finite interval Open Math. (IF 1.7) Pub Date : 2023-12-16 Xiangqing Zhao, Chengqiang Wang, Jifeng Bao
We have established the existence and uniqueness of the local solution for (0.1) ∂ t u + ∂ x 5 u − u ∂ x u = 0 , 0 < x < 1 , t > 0 , u ( x , 0 ) = φ ( x ) , 0 < x < 1 , u ( 0 , t ) = h 1 ( t ) , u ( 1 , t ) = h 2 ( t ) , ∂ x u ( 1 , t ) = h 3 ( t ) , ∂ x u ( 0 , t ) = h 4 ( t ) , ∂ x 2 u ( 1 , t ) = h 5 ( t ) , t > 0 , \left\{\begin{array}{ll}{\partial }_{t}u+{\partial }_{x}^{5}u-u{\partial }_{x}u=0
-
Approximate solvability method for nonlocal impulsive evolution equation Open Math. (IF 1.7) Pub Date : 2023-12-14 Weifeng Ma, Yongxiang Li
In this article, without assuming the compactness of semigroup, we deal with the existence and uniqueness of a mild solution for semilinear impulsive evolution equation with nonlocal condition in a reflexive Banach space by applying the approximate solvability method and Yosida approximations of the infinitesimal generator of C 0-semigroup.
-
Construction of a functional by a given second-order Ito stochastic equation Open Math. (IF 1.7) Pub Date : 2023-12-11 Marat Tleubergenov, Gulmira Vassilina, Shakhmira Ismailova
In this article, we consider the problem of extending Hamilton’s principle to the class of natural mechanical systems with random perturbing forces of white noise type. By the method of moment functions, we construct the functionals taking a stationary value on the solutions of a given stochastic equation of Lagrangian structure.
-
Stability result for Lord Shulman swelling porous thermo-elastic soils with distributed delay term Open Math. (IF 1.7) Pub Date : 2023-12-08 Abdelbaki Choucha, Salah Mahmoud Boulaaras, Rashid Jan
The Lord Shulman swelling porous thermo-elastic soil system with the presence of a distributed delay term is studied in this work. We will establish the well-posedness of the system and the exponential stability of the system is derived.
-
A series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine Open Math. (IF 1.7) Pub Date : 2023-12-08 Yan-Fang Li, Feng Qi
In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of specific determinants and prove a decreasing property of the ratio of two logarithmic expressions containing the cosine function.
-
The 𝔪-WG° inverse in the Minkowski space Open Math. (IF 1.7) Pub Date : 2023-12-08 Xiaoji Liu, Kaiyue Zhang, Hongwei Jin
In this article, we study the m {\mathfrak{m}} -WG ∘ {}^{\circ } inverse which presents a generalization of the m {\mathfrak{m}} -WG inverse in the Minkowski space. We first show the existence and the uniqueness of the generalized inverse. Then, we discuss several properties and characterizations of the m {\mathfrak{m}} -WG ∘ {}^{\circ } inverse by using the core-EP decomposition. Applying the generalized
-
Evolutoids and pedaloids of frontals on timelike surfaces Open Math. (IF 1.7) Pub Date : 2023-12-06 Yongqiao Wang, Lin Yang, Yuan Chang, Haiming Liu
In this article, we define evolutoids and pedaloids of frontals on timelike surfaces in Minkowski 3-space. The evolutoids of frontals on timelike surfaces are not only the generalization of evolutoids of curves in the Minkowski plane but also the generalization of caustics in Minkowski 3-space. As an application of the singularity theory, we classify the singularities of evolutoids and reveal the relationships
-
A double-phase eigenvalue problem with large exponents Open Math. (IF 1.7) Pub Date : 2023-12-06 Lujuan Yu
In the present article, we consider a double-phase eigenvalue problem with large exponents. Let λ ( p n , q n ) 1 {\lambda }_{\left({p}_{n},{q}_{n})}^{1} be the first eigenvalues and u n {u}_{n} be the first eigenfunctions, normalized by ‖ u n ‖ ℋ n = 1 \Vert {u}_{n}{\Vert }_{{{\mathcal{ {\mathcal H} }}}_{n}}=1 . Under some assumptions on the exponents p n {p}_{n} and q n {q}_{n} , we show that λ (
-
On the number of perfect matchings in random polygonal chains Open Math. (IF 1.7) Pub Date : 2023-12-06 Shouliu Wei, Yongde Feng, Xiaoling Ke, Jianwu Huang
Let G G be a graph. A perfect matching of G G is a regular spanning subgraph of degree one. Enumeration of perfect matchings of a (molecule) graph is interest in chemistry, physics, and mathematics. But the enumeration problem of perfect matchings for general graphs (even in bipartite graphs) is non-deterministic polynomial (NP)-hard. Xiao et al. [C. Xiao, H. Chen, L. Liu, Perfect matchings in random
-
On Bohr's inequality for special subclasses of stable starlike harmonic mappings Open Math. (IF 1.7) Pub Date : 2023-12-01 Wei Jin, Zhihong Liu, Qian Hu, Wenbo Zhang
The focus of this article is to explore the Bohr inequality for a specific subset of harmonic starlike mappings introduced by Ghosh and Vasudevarao (Some basic properties of certain subclass of harmonic univalent functions, Complex Var. Elliptic Equ. 63 (2018), no. 12, 1687–1703.). This set is denoted as ℬ H 0 ( M ) ≔ { f = h + g ¯ ∈ ℋ 0 : ∣ z h ″ ( z ) ∣ ≤ M − ∣ z g ″ ( z ) ∣ } {{\mathcal{ {\mathcal
-
Properties of meromorphic solutions of first-order differential-difference equations Open Math. (IF 1.7) Pub Date : 2023-12-01 Lihao Wu, Baoqin Chen, Sheng Li
For the first-order differential-difference equations of the form A ( z ) f ( z + 1 ) + B ( z ) f ′ ( z ) + C ( z ) f ( z ) = F ( z ) , A\left(z)f\left(z+1)+B\left(z)f^{\prime} \left(z)+C\left(z)f\left(z)=F\left(z), where A ( z ) , B ( z ) , C ( z ) A\left(z),B\left(z),C\left(z) , and F ( z ) F\left(z) are polynomials, the existence, growth, zeros, poles, and fixed points of their nonconstant meromorphic
-
Schur-power convexity of integral mean for convex functions on the coordinates Open Math. (IF 1.7) Pub Date : 2023-12-01 Huannan Shi, Jing Zhang
In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore, we introduce novel and fascinating inequalities for binary means as a practical application.
-
A characterization of a ∼ admissible congruence on a weakly type B semigroup Open Math. (IF 1.7) Pub Date : 2023-12-01 Chunhua Li, Jieying Fang, Lingxiang Meng, Huawei Huang
In this article, the notions of ∼ \sim admissible congruences and ∼ \sim normal congruences on a weakly type B semigroup are characterized and the relationship between ∼ \sim admissible congruences and ∼ \sim normal congruences is investigated. In particular, some properties of such congruences on a weakly type B semigroup are given using an approach of kernel-trace. Finally, we extend the congruence
-
Ricci ϕ-invariance on almost cosymplectic three-manifolds Open Math. (IF 1.7) Pub Date : 2023-11-28 Quanxiang Pan
Let M 3 {M}^{3} be a strictly almost cosymplectic three-manifold whose Ricci operator is weakly ϕ \phi -invariant. In this article, it is proved that Ricci curvatures of M 3 {M}^{3} are invariant along the Reeb flow if and only if M 3 {M}^{3} is locally isometric to the Lie group E ( 1 , 1 ) E\left(1,1) of rigid motions of the Minkowski 2-space equipped with a left-invariant almost cosymplectic structure
-
About a dubious proof of a correct result about closed Newton Cotes error formulas Open Math. (IF 1.7) Pub Date : 2023-11-24 David J. López, Jose A. Padilla, Juan Ruiz, Carlos Tapia, Juan C. Trillo
In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [ a , b ] . \left[a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least,
-
Properties of locally semi-compact Ir-topological groups Open Math. (IF 1.7) Pub Date : 2023-11-24 ZhongLi Wang, Wen Chean Teh
This study investigates some topological properties of locally semi-compact Ir-topological groups and establishes the relationship between Ir-topological groups and semi-compact spaces. The proved theorems generalize the corresponding results of Ir-topological group. Finally, we define a quotient topology on the Ir-topological group and study some topological properties of the space.
-
Ordering stability of Nash equilibria for a class of differential games Open Math. (IF 1.7) Pub Date : 2023-11-21 Keke Jia, Shihuang Hong, Jieqing Yue
This study is concerned with the stability of Nash equilibria for a class of n n -person noncooperative differential games. More precisely, due to a preorder induced by a convex cone on a real linear normed space, we define a new concept called ordering stability of equilibria against the perturbation of the right-hand side functions of state equations for the differential game. Moreover, using the
-
A new reverse half-discrete Hilbert-type inequality with one partial sum involving one derivative function of higher order Open Math. (IF 1.7) Pub Date : 2023-11-21 Jianquan Liao, Bicheng Yang
In this article, a new reverse half-discrete Hilbert-type inequality with one partial sum involving one derivative function of higher order is obtained, by using the weight functions, the mid-value theorem, and the techniques of real analysis. A few equivalent statements of the best possible constant factor related to several parameters are considered. As applications, the equivalent forms and some
-
Transcendental entire solutions of several complex product-type nonlinear partial differential equations in ℂ2 Open Math. (IF 1.7) Pub Date : 2023-11-20 Yi Hui Xu, Yan Fang Li, Xiao Lan Liu, Hong Yan Xu
Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) ( a 1 u + b 1 u z 1 + c 1 u z 2 ) ( a 2 u + b 2 u z 1 + c 2 u z 2 ) = 1 , \left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})\left({a}_{2}u+{b}_{2}{u}_{{z}_{1}}+{c}_{2}{u}_{{z}_{2}})=1, and ( a 1 u + b 1 u z 1 + c 1 u z 2 ) ( a 2 u + b 2 u z 1 + c 2 u z 2 ) = e g ,
-
Spin(8,C)-Higgs pairs over a compact Riemann surface Open Math. (IF 1.7) Pub Date : 2023-11-17 Álvaro Antón-Sancho
Let X X be a compact Riemann surface of genus g ≥ 2 g\ge 2 , G G be a semisimple complex Lie group and ρ : G → GL ( V ) \rho :G\to {\rm{GL}}\left(V) be a complex representation of G G . Given a principal G G -bundle E E over X X , a vector bundle E ( V ) E\left(V) whose typical fiber is a copy of V V is induced. A ( G , ρ ) \left(G,\rho ) -Higgs pair is a pair ( E , φ ) \left(E,\varphi ) , where E
-
Liouville theorems for Kirchhoff-type parabolic equations and system on the Heisenberg group Open Math. (IF 1.7) Pub Date : 2023-11-13 Wei Shi
In this article, the Liouville theorems for the Kirchhoff-type parabolic equations on the Heisenberg group were established. The main technique for proving the result relies on the method of test functions.
-
Construction of analytical solutions to systems of two stochastic differential equations Open Math. (IF 1.7) Pub Date : 2023-11-13 Zenonas Navickas, Inga Telksniene, Tadas Telksnys, Romas Marcinkevicius, Minvydas Ragulskis
A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a way that eliminating the stochastic component yields the original system of ODEs. One of the main benefits of this scheme is the ability to construct
-
Two-distance vertex-distinguishing index of sparse graphs Open Math. (IF 1.7) Pub Date : 2023-11-11 Zhengyue He, Li Liang, Wei Gao
The two-distance vertex-distinguishing index χ d 2 ′ ( G ) {\chi }_{d2}^{^{\prime} }\left(G) of graph G G is defined as the smallest integer k k , for which the edges of G G can be properly colored using k k colors. In this way, any pair of vertices at distance of two have distinct sets of colors. The two-distance vertex-distinguishing edge coloring of graphs can be used to solve some network problems
-
The θ-derivative as unifying framework of a class of derivatives Open Math. (IF 1.7) Pub Date : 2023-11-11 Muneerah AL Nuwairan
In this article, we develop a unified framework for studying some derivatives defined as limits. This framework, the θ \theta -derivative, is used to investigate the relationships between these derivatives and their relation to the ordinary derivative. It is shown that the existence of any of these derivatives is equivalent to the existence of the ordinary derivative. By using these results, we show
-
Regularity and abundance on semigroups of partial transformations with invariant set Open Math. (IF 1.7) Pub Date : 2023-11-11 Thapakorn Pantarak, Yanisa Chaiya
Let P ( X ) P\left(X) be a partial transformation semigroup on a non-empty set X X . For a fixed non-empty subset Y Y of X X , let P T ¯ ( X , Y ) = { α ∈ P ( X ) ∣ ( dom α ∩ Y ) α ⊆ Y } . \overline{PT}\left(X,Y)=\left\{\alpha \in P\left(X)| \left({\rm{dom}}\hspace{0.33em}\alpha \cap Y)\alpha \subseteq Y\right\}. Then, P T ¯ ( X , Y ) \overline{PT}\left(X,Y) consists of all the mapping in P ( X ) P\left(X)
-
A comprehensive review on fractional-order optimal control problem and its solution Open Math. (IF 1.7) Pub Date : 2023-11-01 Assmaa Abd-Elmonem, Ramashis Banerjee, Shabir Ahmad, Wasim Jamshed, Kottakkaran Sooppy Nisar, Mohamed R. Eid, Rabha W. Ibrahim, Sayed M. El Din
This article presents a comprehensive literature survey on fractional-order optimal control problems. Fractional-order differential equation is extensively used nowadays to model real-world systems accurately, which exhibit fractal dimensions, memory effects, as well as chaotic behaviour. These versatile features attract engineers to concentrate more on this, and it is widely used in the broad domain
-
Hilfer proportional nonlocal fractional integro-multipoint boundary value problems Open Math. (IF 1.7) Pub Date : 2023-10-27 Ayub Samadi, Sotiris K. Ntouyas, Asawathep Cuntavepanit, Jessada Tariboon
In this article, we introduce and study a boundary value problem for ( k , χ ¯ * ) \left(k,{\bar{\chi }}_{* }) -Hilfer generalized proportional fractional differential equation of order in an interval (1, 2], equipped with integro-multipoint nonlocal boundary conditions. In the scalar case setting, the existence results are proved via Leray-Schauder nonlinear alternative and Krasnosel’skiĭ’s fixed
-
Strong limit of processes constructed from a renewal process Open Math. (IF 1.7) Pub Date : 2023-10-27 Xavier Bardina, Carles Rovira
We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally, we compute the rate of convergence in a particular case.
-
On Graham partitions twisted by the Legendre symbol Open Math. (IF 1.7) Pub Date : 2023-10-26 Byungchan Kim, Ji Young Kim, Chong Gyu Lee, Sang June Lee, Poo-Sung Park, Yoon Kyung Park
We investigate when there is a partition of a positive integer n n , n = f ( λ 1 ) + f ( λ 2 ) + ⋯ + f ( λ ℓ ) , n=f\left({\lambda }_{1})+f\left({\lambda }_{2})+\cdots +f\left({\lambda }_{\ell }), satisfying that 1 = χ p ( λ 1 ) λ 1 + χ p ( λ 2 ) λ 2 + ⋯ + χ p ( λ ℓ ) λ ℓ , 1=\frac{{\chi }_{p}\left({\lambda }_{1})}{{\lambda }_{1}}+\frac{{\chi }_{p}\left({\lambda }_{2})}{{\lambda }_{2}}+\cdots +\frac{{\chi
-
Notes on pseudodifferential operators commutators and Lipschitz functions Open Math. (IF 1.7) Pub Date : 2023-10-25 Yu-long Deng
This article focuses on the boundedness of the commutators generated by pseudodifferential operators with Lipschitz functions and obtains a sufficient condition such that these operators are bounded from L p ( R n ) {L}^{p}\left({{\bf{R}}}^{n}) into the homogeneous Triebel-Lizorkin space F ˙ p γ , ∞ ( R n ) {\dot{F}}_{p}^{\gamma ,\infty }\left({{\bf{R}}}^{n}) and from L p ( R n ) {L}^{p}\left({{\bf{R}}}^{n})
-
Markov decision processes approximation with coupled dynamics via Markov deterministic control systems Open Math. (IF 1.7) Pub Date : 2023-10-24 Gustavo Portillo-Ramírez, Hugo Cruz-Suárez, Ruy López-Ríos, Rubén Blancas-Rivera
This article presents an approximation of discrete Markov decision processes with small noise on Borel spaces with an infinite horizon and an expected total discounted cost by the corresponding deterministic Markov process. In both cases, the dynamics evolve through a system consisting of two coupled difference equations. It is assumed that the difference equations of the system are perturbed by a
-
Minimal-time problems for linear control systems on homogeneous spaces of low-dimensional solvable nonnilpotent Lie groups Open Math. (IF 1.7) Pub Date : 2023-10-24 Adriano Da Silva, Maria Torreblanca, Edgar Apaza, Yaan Bedoya
In this article, we are concerned with minimal-time optimal problems for the class of controllable linear control system on low-dimensional nonnilpotent solvable Lie groups and their homogeneous spaces.
-
Analysis of solutions for the fractional differential equation with Hadamard-type Open Math. (IF 1.7) Pub Date : 2023-10-20 Huijuan Zhu, Yuanfang Ru, Fanglei Wang
We mainly consider the existence and stability results of the positive solutions for the fractional differential equation with Hadamard-type by applying fixed point theorems, if the nonlinearity may be continuous or singular. We also construct some examples to show the applicability of the results.
-
Generalized Lie n-derivations on arbitrary triangular algebras Open Math. (IF 1.7) Pub Date : 2023-10-19 He Yuan, Zhuo Liu
In this study, we consider generalized Lie n n -derivations of an arbitrary triangular algebra T T through the constructed triangular algebra T 0 {T}_{0} , where T 0 {T}_{0} is constructed using the notion of maximal left (right) ring of quotients.
-
Entire solutions of two certain Fermat-type ordinary differential equations Open Math. (IF 1.7) Pub Date : 2023-10-11 Binbin Hu, Liu Yang
In this article, we investigate the precise expression forms of entire solutions for two certain Fermat-type ordinary differential equations: ( a 0 f + a 1 f ′ ) 2 + ( a 0 f + a 2 f ′ ) 2 = p {\left({a}_{0}f+{a}_{1}{f}^{^{\prime} })}^{2}+{\left({a}_{0}f+{a}_{2}{f}^{^{\prime} })}^{2}=p and ( a 0 f + a 1 f ′ ) 2 + ( a 0 f + a 2 f ′ ) 2 = e g \hspace{0.39em}{\left({a}_{0}f+{a}_{1}{f}^{^{\prime} })}^{
-
On a class of stochastic differential equations driven by the generalized stochastic mixed variational inequalities Open Math. (IF 1.7) Pub Date : 2023-10-11 Qiaofeng Zeng, Chao Min, Feifei Fan
A new class of stochastic differential equations (SDEs) is introduced in this article, which is driven by the generalized stochastic mixed variational inequality (GS-MVI). First, the property of the solution sets of the GS-MVI is proved by Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem and Aumann’s measurable selection theorem. Next, we obtain the Carathéodory property of the solution set, with
-
Well-posedness and stability analysis for Timoshenko beam system with Coleman-Gurtin's and Gurtin-Pipkin's thermal laws Open Math. (IF 1.7) Pub Date : 2023-10-10 Soh Edwin Mukiawa
In this article, the effect of Coleman-Gurtin’s and Gurtin-Pipkin’s thermal laws on the displacement of a Timoshenko beam system with suspenders is studied. Using the existing semi-group theory and energy method, the existence and uniqueness of weak global solution, as well as a stability result without imposing any conditions on the coefficient parameters, are established.
-
Linear maps preserving equivalence or asymptotic equivalence on Banach space Open Math. (IF 1.7) Pub Date : 2023-10-10 Zijie Qin, Lin Chen
Let X X be a complex Banach space with dimension at least two and B ( X ) B\left(X) the algebra of all bounded linear operators on X X . We show that a bijective linear map Φ \Phi preserves asymptotic equivalence if and only if it preserves equivalence, and in turn, if and only if there exist invertible bounded linear operators T T and S S such that either Φ ( A ) = T A S \Phi \left(A)=TAS or Φ ( A
-
On some spaces via topological ideals Open Math. (IF 1.7) Pub Date : 2023-10-04 Chawalit Boonpok
Our main purpose is to introduce and investigate the concepts of some forms of spaces via topological ideals. Some characterizations of some forms of spaces via topological ideals are established. Moreover, several properties of ⋆ \star -monotonically normal ideal topological spaces are considered.