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On some properties of Hassani transforms 关于Hassani变换的一些性质
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.79-91
Y. Grushka
In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalizedHassani spatial-temporal transformations in real Hilbert space are introduced. The originaltransformations, introduced by M.E. Hassani, are the particular cases of the transformations,introduced in this paper. It is proven that the classes of generalized Hassani transforms donot form a group of operators in the general case. Further, using these generalized Hassanitransformations as well as the theory of changeable sets and universal kinematics, the mathematicallystrict models of Hassani kinematics are constructed and the performance of the relativityprinciple in these models is discussed.
本文以阿尔及利亚物理学家M.E.Hassani的思想为基础,介绍了实希尔伯特空间中广义的Hassani时空变换。M.E.Hassani介绍的原始变换是本文介绍的变换的特殊情况。证明了广义Hassani变换类在一般情况下不形成一组算子。此外,利用这些广义Hassanti变换以及变集理论和通用运动学,建立了Hassani运动学的数学约束模型,并讨论了这些模型中相对原理的性能。
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引用次数: 1
The least dimonoid congruences on relatively free trioids 相对自由三似体上最小二似体同余
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.23-31
A. Zhuchok
When Loday and Ronco studied ternary planar trees, they introduced types of algebras,called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associativeoperations satisfying additional eight axioms relating these operations, while a trialgebra is justa linear analog of a trioid. If all operations of a trioid (trialgebra) coincide, we obtain the notionof a semigroup (associative algebra), and if two concrete operations of a trioid (trialgebra)coincide, we obtain the notion of a dimonoid (dialgebra) and so, trioids (trialgebras) are ageneralization of semigroups (associative algebras) and dimonoids (dialgebras). Trioids andtrialgebras have close relationships with the Hopf algebras, the Leibniz 3-algebras, the Rota-Baxter operators, and the post-Jordan algebras. Originally, these structures arose in algebraictopology. One of the most useful concepts in algebra is the free object. Every variety containsfree algebras and free objects in any variety of algebras are important in the study of thatvariety. Loday and Ronco constructed the free trioid of rank 1 and the free trialgebra. Recently,the free trioid of an arbitrary rank, the free commutative trioid, the free n-nilpotent trioid, thefree rectangular triband, the free left n-trinilpotent trioid and the free abelian trioid wereconstructed and the least dimonoid congruences as well as the least semigroup congruence onthe first four free algebras were characterized. However, just mentioned congruences on freeleft (right) n-trinilpotent trioids and free abelian trioids were not considered. In this paper, wecharacterize the least dimonoid congruences and the least semigroup congruence on free left(right) n-trinilpotent trioids and free abelian trioids.
当Loday和Ronco研究三元平面树时,他们引入了代数的类型,称为三胚和三代数。三元代数是一个非空集,配备了三个二进制关联运算,满足与这些运算相关的另外八个公理,而三代数只是三元代数的线性模拟。如果一个trioid(trialgebra)的所有运算都重合,我们得到了半群(结合代数)的概念,如果一个trioid(trialgebra)的两个具体运算重合,我们就得到了二monoid(dialgebra)的概念。三元组和三代数与Hopf代数、Leibniz 3-代数、Rota-Baxter算子和后Jordan代数有着密切的关系。最初,这些结构出现在代数拓扑中。代数中最有用的概念之一是自由对象。每一个变种都包含自由代数,任何变种代数中的自由对象在该变种的研究中都是重要的。Loday和Ronco构造了秩为1的自由三胚和自由三代数。最近,我们构造了任意秩的自由三元体、自由交换三元体,自由n-幂零三元体和自由矩形三元带、自由左n-三元势三元体以及自由阿贝尔三元体。然而,刚才提到的自由左(右)n-三元势三元体和自由阿贝尔三元体上的同余没有被考虑。本文刻画了自由左(右)n-三次幂三元组和自由阿贝尔三元组上的最小二单调同余和最小半群同余。
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引用次数: 0
$mathscr{T}$-Commuting Generalized Derivations on Ideals and Semi-Prime Ideal-II $mathscr{T}$-理想和半素理想II上的交换广义导子
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.98-110
N. Rehman, Hafedh M. Alnoghashi
The study's primary purpose is to investigate the $mathscr{A}/mathscr{T}$ structure of a quotient ring, where $mathscr{A}$ is an arbitrary ring and $mathscr{T}$ is a semi-prime ideal of $mathscr{A}$. In more details, we look at the differential identities in a semi-prime ideal of an arbitrary ring using $mathscr{T}$-commuting generalized derivation. The article proves a number of statements. A characteristic representative of these assertions is, for example, the following Theorem 3: Let $mathscr{A}$ be a ring with $mathscr{T}$ a semi-prime ideal and $mathscr{I}$ an ideal of $mathscr{A}.$ If $(lambda, psi)$ is a non-zero generalized derivation of $mathscr{A}$ and the derivation satisfies any one of the conditions:1) $lambda([a, b])pm[a, psi(b)]in mathscr{T}$, 2) $lambda(acirc b)pm acirc psi(b)in mathscr{T}$,$forall$ $a, bin mathscr{I},$ then $psi$ is $mathscr{T}$-commuting on $mathscr{I}.$ Furthermore, examples are provided to demonstrate that the constraints placed on the hypothesis of the various theorems were not unnecessary.
本研究的主要目的是研究商环的$mathscr{A}/mathscr{T}$结构,其中$mathscr{A}$是任意环,$mathscr{T}$为$mathscr{A}$的半素数理想。更详细地,我们使用$mathscr{T}$-交换广义导数来研究任意环的半素理想中的微分恒等式。这篇文章证明了一些说法。例如,这些断言的一个特征代表是以下定理3:设$mathscr{A}$是一个环,其中$mathscr{T}$为半素数理想,$mathscr{I}$则为$mathscr{A}的理想。$如果$(lambda,psi)$是$mathscr{a}$的非零广义导数,并且该导数满足以下条件之一:1)$lambda([a,b]此外,还提供了一些例子来证明对各种定理的假设施加的约束并不是没有必要的。
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引用次数: 1
Stable range conditions for abelian and duo rings 阿贝尔环和二重环的稳定值域条件
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.92-97
A. Dmytruk, A. Gatalevych, M. Kuchma
The article deals with the following question: when does the classical ring of quotientsof a duo ring exist and idempotents in the classical ring of quotients $Q_{Cl} (R)$ are thereidempotents in $R$? In the article we introduce the concepts of a ring of (von Neumann) regularrange 1, a ring of semihereditary range 1, a ring of regular range 1. We find relationshipsbetween the introduced classes of rings and known ones for abelian and duo rings.We proved that semihereditary local duo ring is a ring of semihereditary range 1. Also it was proved that a regular local Bezout duo ring is a ring of stable range 2. In particular, the following Theorem 1 is proved: For an abelian ring $R$ the following conditions are equivalent:$1.$ $R$ is a ring of stable range 1; $2.$ $R$ is a ring of von Neumann regular range 1. The paper also introduces the concept of the Gelfand element and a ring of the Gelfand range 1 for the case of a duo ring. Weproved that the Hermite duo ring of the Gelfand range 1 is an elementary divisor ring (Theorem 3).
本文讨论了如下问题:对偶环的经典商环何时存在,商环$Q_{Cl}(R)$中的幂等元在$R$中是幂等元?在本文中,我们引入了(von Neumann)正则范围1的环、半遗传范围1的圈、正则范围1环的概念。我们发现了引入的环类与阿贝尔环和对偶环的已知环类之间的关系。证明了半遗传局部对偶环是半遗传范围为1的环。还证明了正则局部Bezout对偶环是一个稳定范围为2的环。特别地,证明了以下定理1:对于阿贝尔环$R$,以下条件是等价的:$1.$$R$是稳定范围为1的环$2.$$R$是冯-诺依曼正则范围1的一个环。本文还引入了Gelfand元素的概念以及对偶环的Gelfand范围为1的环。我们证明了Gelfand范围1的Hermite对偶环是初等除数环(定理3)。
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引用次数: 1
On certain subclass of Dirichlet series absolutely convergent in half-plane 在半平面上绝对收敛的狄利克雷级数的某一子类
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.32-44
M. Sheremeta
Denote by $mathfrak{D}_0$ a class of absolutely convergent in half-plane $Pi_0={scolon text{Re},s<0}$ Dirichlet series$F(s)=e^{sh}-sum_{k=1}^{infty}f_kexp{s(lambda_k+h)},, s=sigma+it$, where $h> 0$, $h0$.For $0lealphafrac{alpha}{h}$,and belongs to the class $mathfrak{DG}_h(l,alpha)$ if and only if$text{Re}{e^{-hs}((1-l)F'(s)+frac{l}{h}F''(s))}>alpha$ for all $sin Pi_0$. It is provedthat $Fin mathfrak{DF}_h(l,alpha)$ if and only if $ sum_{k=1}^{infty}(h+llambda_k)f_kle h-alpha$, and$Fin mathfrak{DG}_h(l,alpha)$ if and only if $sum_{k=1}^{infty}(h+llambda_k)(lambda_k+h)f_kle h(h-alpha)$. If $F_jin mathfrak{DF}_h(l_j,alpha_j)$, $j=1, 2$, where $l_jge0$ and $0le alpha_j0$ and $delta>0$ the neighborhood of the function $Fin mathfrak{D}_0$ is defined as follows$O_{j,delta}(F)={G(s)=e^{s}-sum_{k=1}^{infty}g_kexp{slambda_k}in mathfrak{D}_0colon sum_{k=1}^{infty}lambda^j_k|g_k-f_k|ledelta}$. It is described the neighborhoods of functions from classes $mathfrak{DF}_h(l,alpha)$ and $mathfrak{DG}_h(l,alpha)$. Conditions on real parameters $gamma_0,,gamma_1,,gamma_2,,a_1$ and $a_2$ of the differential equation $w''+(gamma_0e^{2hs}+gamma_1e^{hs}+gamma_2) w=a_1e^{hs}+a_2e^{2hs}$ are found, under which this equation has a solutioneither in $mathfrak{DF}_h(l,alpha)$ or in $mathfrak{DG}_h(l,alpha)$.
以$mathfrak表示{D}_0$在半平面上绝对收敛的一类$Pi_0={scolontext{Re},s0$,$h0$。对于$0lealphafrac{alpha}{h}$,属于类$mathfrak{DG}_h(l,alpha)$当且仅当$text{Re}{e^{-hs}((1-l)F'(s)+frac{l}{h}F''(s)}>alpha$用于所有sinPi_0$。证明$Finmathfrak{DF}_h(l,alpha)$当且仅当$sum_{k=1}^{infty}(h+llambda_k)f_kle h-alpha$和$finmathfrak{DG}_h(l,alpha)$当且仅当$sum_{k=1}^{infty}(h+llambda_k)(lambda_6k+h)f_kle h(h-alpha$)$。如果$F_jinmathfrak{DF}_h(l_j,alpha_j)$,$j=1,2$,其中$l_jge0$和$0lealpha_j0$和$delta>0$是函数$Finmathfrak的邻域{D}_0$定义如下$O_{j,delta}(F)={G(s)=e^{s}-sum_{k=1}^{infty}g_kexp{slambda}inmathfrak{D}_0冒号sum_{k=1}^{fty}lambda ^j_k|g_k-f_k|ledelta}$。它描述了类$mathfrak中函数的邻域{DF}_h(l,alpha)$和$mathfrak{DG}_h(l,alpha)$。求出了微分方程$w’’+(gamma_0e^{2hs}+gamma_1e^}hs}+gamma_2)w=a_1e^(hs})+a_2e^(2hs)$的实参数$gamma-0,,gamma_1,,a_1$和$a_2$的条件,在此条件下该方程在$mathfrak中有一个解{DF}_h(l,alpha)$或在$mathfrak中{DG}_h(l,alpha)$。
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引用次数: 1
Boundary value matrix problems and Drazin invertible operators 边值矩阵问题与Drazin可逆算子
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.16-22
K. Miloud Hocine
Let $A$ and $B$ be given linear operators on Banach spaces $X$ and $Y$, we denote by $M_C$ the operator defined on $X oplus Y$ by $M_{C}=begin{pmatrix}A & C 0 & B%end{pmatrix}.$In this paper, we study an abstract boundaryvalue matrix problems with a spectral parameter described by Drazin invertibile operators of the form $$begin{cases}U_L=lambda M_{C}w+F, & Gamma w=Phi, & end{cases}%$$where $U_L , M_C$ are upper triangular operators matrices $(2times 2)$ acting in Banach spaces, $Gamma$ is boundary operator, $F$ and $Phi $ are given vectors and $lambda $ is a complex spectral parameter.We introduce theconcept of initial boundary operators adapted to the Drazin invertibility andwe present a spectral approach for solving the problem. It can be shown thatthe considered boundary value problems are uniquely solvable and that theirsolutions are explicitly calculated. As an application we give an example to illustrate our results.
设$A$和$B$为巴拿赫空间$X$和$Y$上的线性算子,我们用$M_C$表示$X 0 + Y$上定义的算子:$M_{C}=begin{pmatrix}A & C 0 & B%end{pmatrix}。本文研究了一类谱参数由Drazin可逆算子描述的抽象边值矩阵问题,其形式为$$begin{cases}U_L=lambda M_{C}w+F, & Gamma w=Phi, & end{cases}%$$,其中$U_L, M_C$为作用于Banach空间的上三角算子矩阵$(2乘2)$,$Gamma$为边界算子,$F$和$Phi $为给定向量,$lambda $为复谱参数。我们引入了适应Drazin可逆性的初始边界算子的概念,并给出了求解该问题的谱方法。可以证明所考虑的边值问题是唯一可解的,并且它们的解是显式计算的。作为一个应用,我们给出了一个例子来说明我们的结果。
{"title":"Boundary value matrix problems and Drazin invertible operators","authors":"K. Miloud Hocine","doi":"10.30970/ms.57.1.16-22","DOIUrl":"https://doi.org/10.30970/ms.57.1.16-22","url":null,"abstract":"Let $A$ and $B$ be given linear operators on Banach spaces $X$ and $Y$, we denote by $M_C$ the operator defined on $X oplus Y$ by $M_{C}=begin{pmatrix}A & C 0 & B%end{pmatrix}.$In this paper, we study an abstract boundaryvalue matrix problems with a spectral parameter described by Drazin invertibile operators of the form $$begin{cases}U_L=lambda M_{C}w+F, & Gamma w=Phi, & end{cases}%$$where $U_L , M_C$ are upper triangular operators matrices $(2times 2)$ acting in Banach spaces, $Gamma$ is boundary operator, $F$ and $Phi $ are given vectors and $lambda $ is a complex spectral parameter.We introduce theconcept of initial boundary operators adapted to the Drazin invertibility andwe present a spectral approach for solving the problem. It can be shown thatthe considered boundary value problems are uniquely solvable and that theirsolutions are explicitly calculated. As an application we give an example to illustrate our results.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41708523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Universally prestarlike functions associated with shell like domain 类壳结构域的普遍类星前函数
Q3 Mathematics Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.53-61
K. Vijaya, G. Murugusundaramoorthy, S. Yalçın
In this paper, we introduce universally prestarlikegeneralized functions of order $vartheta $ with $vartheta leq 1$ associated with shell like domain, and we getcoefficient bounds and the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ forsuch functions.
在本文中,我们引入了与类壳域相关的$varthetaleq1$阶的泛前线性广义函数,得到了系数界和第二个Hankel行列式$|a_{2}a_{4}-a_{3} ^{2}|$用于这些函数。
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引用次数: 0
Well-posedness of the Cauchy problem for system of oscillators on 2D–lattice in weighted $l^2$-spaces 加权$ 1 ^2$-空间中二维格上振子系统Cauchy问题的适定性
Q3 Mathematics Pub Date : 2021-12-27 DOI: 10.30970/ms.56.2.176-184
S. Bak, G. Kovtonyuk
We consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two dimensional integer-valued lattice. It is assumed that each oscillator interacts linearly with its four nearest neighbors and the oscillators are at the rest at infinity. We study the initial value problem (the Cauchy problem) for such system. This system naturally can be considered as an operator-differential equation in the Hilbert, or even Banach, spaces of sequences. We note that $l^2$ is the simplest choice of such spaces. With this choice of the configuration space, the phase space is $l^2times l^2$, and the equation can be written in the Hamiltonian form with the Hamiltonian $H$. Recall that from a physical point of view the Hamiltonian represents the full energy of the system, i.e., the sum of kinetic and potential energy. Note that the Hamiltonian $H$ is a conserved quantity, i.e., for any solution of equation the Hamiltonian is constant. For this space, there are some results on the global solvability of the corresponding Cauchy problem. In the present paper, results on the $l^2$-well-posedness are extended to weighted $l^2$-spaces $l^2_Theta$. We suppose that the weight $Theta$ satisfies some regularity assumption. Under some assumptions for nonlinearity and coefficients of the equation, we prove that every solution of the Cauchy problem from $C^2left((-T, T); l^2)$ belongs to $C^2left((-T, T); l^2_Thetaright)$. And we obtain the results on existence of a unique global solutions of the Cauchy problem for system of oscillators on a two-dimensional lattice in a wide class of weighted $l^2$-spaces. These results can be applied to discrete sine-Gordon type equations and discrete Klein-Gordon type equations on a two-dimensional lattice. In particular, the Cauchy problems for these equations are globally well-posed in every weighted $l^2$-space with a regular weight.
我们考虑一个无限常微分方程组,它描述了二维整数值晶格上线性耦合非线性振荡器的无限系统的动力学。假设每个振荡器与其四个最近的邻居线性相互作用,并且振荡器在无穷大处处于其余位置。我们研究了这类系统的初值问题(柯西问题)。这个系统自然可以被认为是序列的Hilbert空间,甚至Banach空间中的算子微分方程。我们注意到$l^2$是此类空间中最简单的选择。通过这种配置空间的选择,相空间是$l^2 乘以l^2$,并且方程可以写成具有哈密顿量$H$的哈密顿形式。回想一下,从物理的角度来看,哈密顿量代表系统的全部能量,即动能和势能的总和。注意,哈密顿量$H$是一个守恒量,即,对于方程的任何解,哈密顿量都是常数。对于这个空间,给出了相应柯西问题的全局可解性的一些结果。本文将关于$l^2$适定性的结果推广到加权的$l^2*空间$l^2_Theta$。我们假设权重$Theta$满足一些正则性假设。在对方程的非线性和系数的一些假设下,我们证明了从$C^2开始的Cauchy问题的每一个解都是左((-T,T);l^2)$属于$C^2 left((-T,T);l^2_Thetaright)$。在广义加权$l^2$-空间中,我们得到了二维格上振子系统Cauchy问题唯一全局解的存在性的结果。这些结果可以应用于二维格上的离散正弦Gordon型方程和离散Klein-Gordon型方程式。特别地,这些方程的柯西问题在具有规则权重的每个加权$l^2$-空间中是全局适定的。
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引用次数: 0
A counterexample to Henry E. Dudeney’s star puzzle Henry E. Dudeney的星星谜题的反例
Q3 Mathematics Pub Date : 2021-12-27 DOI: 10.30970/ms.56.2.215-217
A. Ravsky
We found a solution of Henry E. Dudeney’s star puzzle (a path on a chessboard from c5 to d4 in 14 straight strokes) in 14 queen moves, which was claimed impossible by the puzzle author. Generalizing this result to other board sizes, we obtained bounds on minimal number of moves in a board filling queen path with given source and destination.
我们找到了亨利·E·杜德尼的星形拼图(棋盘上从c5到d4的路径,用14个直拍)的14个皇后招式的解决方案,拼图作者声称这是不可能的。将这一结果推广到其他棋盘尺寸,我们获得了在给定源和目的地的棋盘填充皇后路径中最小移动次数的界。
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引用次数: 0
Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes 连续节点集上埃尔米特型的插值有理积分分数
Q3 Mathematics Pub Date : 2021-12-27 DOI: 10.30970/ms.56.2.185-192
Y. Baranetskij, I. Demkiv, M. Kopach, A. Solomko
Some approaches to the construction of interpolation rational integral approximations with arbitrary multiplicity of nodes are analyzed. An integral rational Hermitian-type interpolant of the third order on a continual set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the second degree, is constructed and investigated. The resulting interpolant is one that holds any rational functional of the resulting form. Проаналізовано ряд підходів до побудови інтерполяційних раціональних інтегральних наближень з довільною кратністю вузлів. Будується та досліджується інтегральний раціональний інтерполянт типу Ерміта третього порядку на континуальній множині вузлів, який є відношенням функціонального полінома першого степеня до функціонального полінома другого степеня. Одержаний інтерполянт є таким, що зберігає будь який раціональний функціонал одержаного вигляду.
分析了构造具有任意多个节点的插值有理积分近似的一些方法。构造并研究了连续节点集上的三阶积分有理Hermitian型插值,它是一阶函数多项式与二阶函数多项式的比值。生成的中介元是一个保持生成形式的任何有理函数的中介元。在一组连续的节点上开发和研究了一种三阶Armit型积分有理界面,这是函数一次多项式与函数二次多项式的比值。保留插值存储保留视图的任何有理函数。
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引用次数: 0
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Matematychni Studii
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