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Biconservative Lorentz Hypersurfaces with at Least Three Principal Curvatures 具有至少三个主曲率的双保守洛伦兹超曲面
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-11-14 DOI: 10.5556/j.tkjm.54.2023.4876
F. Pashaie
Biconservative submanifolds, with important role in mathematical physics and differential geometry, arise as the conservative stress-energy tensor associated to the variational problem of biharmonic submanifolds. Many examples of biconservative hypersurfaces have constant mean curvature. A famous conjecture of Bang-Yen Chen on Euclidean spaces says that everybiharmonic submanifold has null mean curvature. Inspired by Chen conjecture, we study biconservative Lorentz submanifolds of the Minkowski spaces. Although the conjecture has not been generally confirmed, it has been proven in many cases, and this has led to its spread to various types of submenifolds. As an extension, we consider a advanced version of the conjecture (namely, $L_1$-conjecture) on Lorentz hypersurfaces of the pseudo-Euclidean space $mathbb{M}^5 :=mathbb{E}^5_1$ (i.e. the Minkowski 5-space). We show every $L_1$-biconservative Lorentz hypersurface of $mathbb{M}^5$ with constant mean curvature and at least three principal curvatures has constant second mean curvature.
双守恒子流形作为与双调和子流形变分问题相关的保守应力-能量张量而出现,在数学物理和微分几何中具有重要的作用。许多双保守超曲面的例子都有恒定的平均曲率。陈邦彦在欧几里得空间上的一个著名猜想是:每一双调和子流形具有零平均曲率。在Chen猜想的启发下,我们研究了Minkowski空间的双保守Lorentz子流形。虽然这一猜想尚未得到普遍证实,但在许多情况下已被证明,这导致了它在各种类型的子折叠中的传播。作为扩展,我们考虑了伪欧几里德空间$mathbb{M}^5:=mathbb{E}^5_1$(即Minkowski 5-空间)的洛伦兹超曲面上的猜想的一个高级版本(即$L_1$-猜想)。我们证明了$mathbb{M}^5$具有恒定平均曲率和至少三个主曲率的$L_1$-双保守洛伦兹超曲面具有恒定的次平均曲率。
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引用次数: 0
Algorithm for Finite Family of Variational Inequality with Fixed Point of Two Non-expansive Mappings 两个非扩张映射的不动点变分不等式有限族的算法
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-10-20 DOI: 10.5556/j.tkjm.54.2023.4865
Monika Swami, S. Rathee
In the recent work, a new hybrid technique for computing the common solution of fixed point of a finite family of two non-expansive mapping and variational inequality problem for inverse strongly monotone mapping in a real Hilbert space is provided. We also demonstrate the convergence of the hybrid approach using an example.
本文给出了一种计算实Hilbert空间中强单调逆映射有限族不动点公解和变分不等式问题的新混合方法。我们还用一个例子证明了混合方法的收敛性。
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引用次数: 0
Adjoint Relations Between the Category of Poset Acts and Some Other Categories 后置行为范畴与其他范畴的伴随关系
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-10-15 DOI: 10.5556/j.tkjm.54.2023.4966
L. Shahbaz
In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors between this category and the categories Pos-S of all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study the existence of their left and right adjoints. It is shown that the category Pos-S is a full reflective and coreflective subcategory of PosAct-S.
在本文中,首先讨论了拟多项式S上所有偏序行为在postact -S范畴中的同余;在所有偏序集的po范畴中引入了一个s -行为,它们之间具有保持动作的单调映射。然后,我们研究了PosAct-S范畴中自由对象和共自由对象的存在性。更确切地说,我们考虑在这个范畴和所有s-偏集的po - s、所有偏集的po、所有s-偏集的Act-S和所有集合的Set范畴之间的所有遗忘函子,并研究它们的左右伴随的存在性。结果表明,post - s范畴是post - s的全反思性和共反思性子范畴。
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引用次数: 1
Fitted Operator Average Finite Difference Method for Singularly Perturbed Delay Parabolic Reaction Diffusion Problems with Non-Local Boundary Conditions 非局部边界条件下奇摄动时滞抛物型反应扩散问题的拟合算子平均有限差分法
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-10-14 DOI: 10.5556/j.tkjm.54.2023.4175
Wakjira Tolassa Gobena, G. Duressa
This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.
研究了具有非局部边界条件的空间变量上具有大时滞的奇摄动时滞抛物型反应扩散问题的数值解。该问题的解在空间域两侧有抛物线边界层,并建立了内层。在渐近解中引入拟合参数,应用平均有限差分逼近,提出了一种拟合算子有限差分法。采用辛普森规则处理非局部边界条件。并对其稳定性和一致收敛性进行了分析。为了验证该格式的适用性,给出了数值算例,并对不同的扰动参数$varepsilon$和网格尺寸进行了求解。数值结果以最大绝对误差和收敛速度的形式列示,结果表明,本文方法在两个方向上都是二阶均匀收敛的,并且改进了文献中已有方法的结果。
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引用次数: 5
Refinements of Some Numerical Radius Inequalities for Hilbert Space Operators 希尔伯特空间算子若干数值半径不等式的改进
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-10-14 DOI: 10.5556/j.tkjm.54.2023.4061
M. Rashid
Some power inequalities for the numerical radius based on the recent Dragomir extension of Furuta's inequality are established. Some particular cases are also provided. Moreover, we get an improvement of the H"older-McCarthy operator inequality in the case when $rgeq 1$ and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.
基于Furuta不等式的最近的Dragomir推广,建立了数值半径的一些幂不等式。还提供了一些具体案例。此外,在$rgeq 1$的情况下,我们得到了Hölder-McCarthy算子不等式的改进,并改进了Hilbert空间算子的和和积涉及数值半径幂的广义不等式。
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引用次数: 2
Solving Unconstrained Optimization Problems with Some Three-term Conjugate Gradient Methods 用三项共轭梯度法求解无约束优化问题
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-09-16 DOI: 10.5556/j.tkjm.54.2023.4185
Ladan Arman
In this paper, based on the efficient Conjugate Descent ({tt CD}) method, two generalized {tt CD}algorithms are proposed to solve the unconstrained optimization problems.These methods are three-term conjugate gradient methods which the generateddirections by using the conjugate gradient parameters and independent of the line searchsatisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search,the global convergence of the proposed methods are proved. Also, the preliminary numericalresults on the {tt CUTEst} collection are presented to show effectiveness of our methods.
本文在高效共轭下降法({tt CD})的基础上,提出了求解无约束优化问题的两种广义{tt CD}算法。这些方法是利用共轭梯度参数生成方向的三项共轭梯度方法,不依赖于直线搜索,满足充分下降条件。在强Wolfe线搜索条件下,证明了所提方法的全局收敛性。此外,还给出了{tt CUTEst}集合的初步数值结果,以显示我们的方法的有效性。
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引用次数: 0
Normalized null hypersurfaces in the Lorentz-Minkowski space satisfying $L_r x =U x +b$ Lorentz-Minkowski空间中满足L_r x =U x +b的归一化零超曲面
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-08-21 DOI: 10.5556/j.tkjm.54.2023.4851
Hans FOTSING TETSING, C. Atindogbe, Ferdinand Nkageu
In the present paper, we classify all normalized null hypersurfaces $x: (M,g,N)toR^{n+2}_1$ endowed with UCC-normalization with vanishing $1-$form $tau$, satisfying $L_r x =U x +b$ for some (field of) screen constant matrix $Uin R^{(n+2)times(n+2)}$ and vector$binR^{n+2}_{1}$, where $L_r$ is the linearized operator of the$(r+1)th-$mean curvature of the normalized null hypersurface for$r=0,...,n$. For $r=0$, $L_0=Delta^eta$ is nothing but the (pseudo-)Laplacian operator on $(M, g, N)$. We prove that the lightcone $Lambda_0^{n+1}$, lightcone cylinders $Lambda_0^{m+1}timesR^{n-m}$, $1leq mleq n-1$ and $(r+1)-$maximal Monge null hypersurfaces are the only UCC-normalized Monge null hypersurface with vanishing normalization $1-$form $tau$ satisfying the above equation. In case $U$ is the (field of) scalar matrix $ lambda I$, $lambdainR$ and hence is constant on the whole $M$, we show that the only normalized Monge null hypersurfaces $x: (M,g,N)toR^{n+2}_1$ satisfying $Delta^eta x =lambda x +b$, are open pieces of hyperplanes.
本文对具有ucc归一化的所有归一化空超曲面$x: (M,g,N)toR^{n+2}_1$进行了分类,其中$L_r$是$r=0,...,n$归一化空超曲面$(r+1)th-$的平均曲率的线性化算子,并将$1-$从$tau$中消失,满足$L_r x =U x +b$的屏幕常数矩阵$Uin R^{(n+2)times(n+2)}$和向量$binR^{n+2}_{1}$。对于$r=0$, $L_0=Delta^eta$只是$(M, g, N)$上的(伪)拉普拉斯运算符。我们证明了光锥$Lambda_0^{n+1}$、光锥柱面$Lambda_0^{m+1}timesR^{n-m}$、$1leq mleq n-1$和$(r+1)-$是满足上述方程的唯一具有消失归一化形式$1-$$tau$的ucc归一化的最大Monge零超曲面。如果$U$是标量矩阵$ lambda I$, $lambdainR$的(域),因此在整个$M$上是常数,我们证明了满足$Delta^eta x =lambda x +b$的唯一归一化的Monge零超曲面$x: (M,g,N)toR^{n+2}_1$是超平面的开放块。
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引用次数: 1
Suberesolving codes Suberesolving代码
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-07-29 DOI: 10.5556/j.tkjm.54.2023.4635
Somayyeh Jangjooye Shaldehi
‎We show that any right continuing factor code with retract  0  into an irreducible shift of finite type is right eresolving‎, ‎and we give some sufficient conditions for a right eresolving almost everywhere code being right eresolving everywhere‎. ‎Suberesolving codes as a generalization of ersolving codes have been introduced and we determine some shift spaces which preserved by suberesolving codes‎. ‎Also‎, ‎we show that any bi-eresolving (resp‎. ‎bi-suberesolving) code on an irreducible shift of finite type (resp‎. ‎a synchronized system) is open (resp‎. ‎semi-open) and any right suberesolving code on a synchronized system is right continuing almost everywhere‎.
证明了任何将0缩回为有限型不可约位移的右连因式码是右可解析的,并给出了右可解析几乎处处码是右可解析的一些充分条件。作为求解码的一种推广,引入了求解码,并确定了一些由求解码保留的移位空间。此外,我们还证明了任何双分辨(双分辨)的。有限型不可约移位上的双解析码。(一个同步的系统)是开放的(参见)。(半开放)并且同步系统上的任何右解析代码几乎在任何地方都是正确的。
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引用次数: 0
On the signed strong total Roman domination number of graphs 关于有符号的强总罗马统治数图
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-07-29 DOI: 10.5556/j.tkjm.54.2023.3907
A. Mahmoodi, M. Atapour, S. Norouzian
Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)rightarrow{-1, 1,2,ldots, lceilfrac{Delta}{2}rceil+1}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=sum_{uin N(v)}f(u)geq 1$, where$N(v)$ is the open neighborhood of $v$ and (ii) every vertex $v$ forwhich $f(v)=-1$ is adjacent to at least one vertex$w$ for which $f(w)geq 1+lceilfrac{1}{2}vert N(w)cap V_{-1}vertrceil$, where$V_{-1}={vin V: f(v)=-1}$.The minimum of thevalues $omega(f)=sum_{vin V}f(v)$, taken over all signed strongtotal Roman dominating functions $f$ of $G$, is called the signed strong totalRoman domination number of $G$ and is denoted by $gamma_{ssTR}(G)$.In this paper, we initiate signed strong total Roman domination number of a graph and giveseveral bounds for this parameter. Then, among other results, we determine the signed strong total Roman dominationnumber of special classes of graphs.
让 $G=(V,E)$ 是一个有限且简单的有序图 $n$ 最大化度 $Delta$. 图上有符号的强全罗马支配函数 $G$ 是一个函数 $f:V(G)rightarrow{-1, 1,2,ldots, lceilfrac{Delta}{2}rceil+1}$ 满足(i)每个顶点的条件 $v$ 的 $G$, $f(N(v))=sum_{uin N(v)}f(u)geq 1$,其中$N(v)$ 开放的社区是什么 $v$ (ii)每个顶点 $v$ 为了什么 $f(v)=-1$ 至少与一个顶点相邻$w$ 为了什么? $f(w)geq 1+lceilfrac{1}{2}vert N(w)cap V_{-1}vertrceil$,其中$V_{-1}={vin V: f(v)=-1}$值的最小值 $omega(f)=sum_{vin V}f(v)$接管了所有签署的罗马统治职能 $f$ 的 $G$的符号强总罗马统治数 $G$ 表示为 $gamma_{ssTR}(G)$本文提出了图的签名强总罗马支配数,并给出了该参数的若干界。然后,在其他结果中,我们确定了图的特殊类的符号强总罗马支配数。
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引用次数: 0
CR-submanifolds of SQ-Sasakian manifold sq - sasaki流形的cr -子流形
IF 0.6 Q2 MATHEMATICS Pub Date : 2022-07-29 DOI: 10.5556/j.tkjm.54.2023.4656
S. Yadav, S. Hui, Mohd Iqbal, Pradip Mandal, M. Aslam
In this paper we discussed CR-submanifold of SQ-Sasakian manifold. Next, we considered Chaki pseudo parallel as well as Deszcz pseudo parallel CR-submanifold of SQ-Sasakian manifold. Further we studied almost Ricci soliton and almost Yamabe soliton with torse forming vector field on CR-subamnifold of SQ-Sasakian manifold using semi-symmetric metric connection.
本文讨论了sq - sasaki流形的cr -子流形。其次,我们考虑了q - sasakian流形的Chaki伪并行和Deszcz伪并行cr -子流形。进一步利用半对称度量连接研究了SQ-Sasakian流形cr -亚折线上具有扭转形成向量场的几乎Ricci孤子和几乎Yamabe孤子。
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引用次数: 0
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Tamkang Journal of Mathematics
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