Pub Date : 2022-09-16DOI: 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.
{"title":"Solving Unconstrained Optimization Problems with Some Three-term Conjugate Gradient Methods","authors":"Ladan Arman","doi":"10.5556/j.tkjm.54.2023.4185","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4185","url":null,"abstract":"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.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74440709","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}
Pub Date : 2022-08-21DOI: 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。
{"title":"Normalized null hypersurfaces in the Lorentz-Minkowski space satisfying $L_r x =U x +b$","authors":"Hans FOTSING TETSING, C. Atindogbe, Ferdinand Nkageu","doi":"10.5556/j.tkjm.54.2023.4851","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4851","url":null,"abstract":"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.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87209023","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}
Pub Date : 2022-07-29DOI: 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.
{"title":"Suberesolving codes","authors":"Somayyeh Jangjooye Shaldehi","doi":"10.5556/j.tkjm.54.2023.4635","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4635","url":null,"abstract":"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.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77250418","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}
Pub Date : 2022-07-29DOI: 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.
{"title":"On the signed strong total Roman domination number of graphs","authors":"A. Mahmoodi, M. Atapour, S. Norouzian","doi":"10.5556/j.tkjm.54.2023.3907","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3907","url":null,"abstract":"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.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73035392","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}
Pub Date : 2022-07-29DOI: 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.
{"title":"CR-submanifolds of SQ-Sasakian manifold","authors":"S. Yadav, S. Hui, Mohd Iqbal, Pradip Mandal, M. Aslam","doi":"10.5556/j.tkjm.54.2023.4656","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4656","url":null,"abstract":"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.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72467106","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}
Pub Date : 2021-12-06DOI: 10.5556/j.tkjm.53.2022.3494
Maryam Salehnejad, M. Azhini
Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces.
{"title":"Vector Variational Inequalities In G-Convex Spaces","authors":"Maryam Salehnejad, M. Azhini","doi":"10.5556/j.tkjm.53.2022.3494","DOIUrl":"https://doi.org/10.5556/j.tkjm.53.2022.3494","url":null,"abstract":"\u0000\u0000\u0000Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73045487","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}
Pub Date : 2021-11-20DOI: 10.5556/j.tkjm.54.2023.3830
Bhawna Kohli
In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived.
{"title":"Optimality Conditions Using Convexifactors for a Multiobjective Fractional Bilevel Programming Problem","authors":"Bhawna Kohli","doi":"10.5556/j.tkjm.54.2023.3830","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3830","url":null,"abstract":"In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91251127","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}
Pub Date : 2021-11-14DOI: 10.5556/j.tkjm.53.2022.3644
A. Zivari-kazempour, M. Valaei
In this paper, we prove that if $varphi:mathcal{R}longrightarrowmathcal{R}'$ is an $n$-Jordan homomorphism, where $mathcal{R}$ has a unit $e$, then the map $alongmapsto varphi(e)^{n-2}varphi(a)$ is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.
{"title":"Characterization of $n$-Jordan Homomorphisms on Rings","authors":"A. Zivari-kazempour, M. Valaei","doi":"10.5556/j.tkjm.53.2022.3644","DOIUrl":"https://doi.org/10.5556/j.tkjm.53.2022.3644","url":null,"abstract":"In this paper, we prove that if $varphi:mathcal{R}longrightarrowmathcal{R}'$ is an $n$-Jordan homomorphism, where $mathcal{R}$ has a unit $e$, then the map $alongmapsto varphi(e)^{n-2}varphi(a)$ is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80884219","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}
Pub Date : 2021-11-13DOI: 10.5556/j.tkjm.54.2023.3971
A. Montes
In this paper, via a variational approach, we show the existence of periodic traveling waves for a Kadomtsev-Petviashvili Boussinesq type system that describes the propagation of long waves in wide channels. We show that those periodic solutions are characterized as critical points of some functional, for which the existence of critical points follows as a consequence of the Mountain Pass Theorem and Arzela-Ascoli Theorem.
{"title":"Existence of Periodic Traveling Wave Solutions for a K-P-Boussinesq Type System","authors":"A. Montes","doi":"10.5556/j.tkjm.54.2023.3971","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3971","url":null,"abstract":"In this paper, via a variational approach, we show the existence of periodic traveling waves for a Kadomtsev-Petviashvili Boussinesq type system that describes the propagation of long waves in wide channels. We show that those periodic solutions are characterized as critical points of some functional, for which the existence of critical points follows as a consequence of the Mountain Pass Theorem and Arzela-Ascoli Theorem.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87506313","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}
Pub Date : 2021-11-10DOI: 10.5556/j.tkjm.54.2023.3943
Abdulhamit Ekinci, S. Temir
In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. cite{Thakur}, Ullahand Arschad cite{UA}.
{"title":"Convergence Theorems for Suzuki Generalized Nonexpansive Mapping in Banach Spaces","authors":"Abdulhamit Ekinci, S. Temir","doi":"10.5556/j.tkjm.54.2023.3943","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3943","url":null,"abstract":"In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. cite{Thakur}, Ullahand Arschad cite{UA}.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72453545","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}
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