Abstract : We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin \cite{P1}. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism $f$ of a compact smooth manifold $M$ has the robustly pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (ii) For a $C^1$ generic diffeomorphism $f$ of a compact smooth manifold $M$, if $f$ has the pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (iii) If a diffeomorphism $f$ has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. Finally, (iv) for $C^1$ generically, if a diffeomorphism $f$ has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. In addition, we investigate cases of volume preserving diffeomorphisms.
Abstract : In this paper, we study new classes of operators $k$-quasi $(m, n)$-paranormal operator, $k$-quasi $(m, n)^*$-paranormal operator, $k$-qu\-asi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q^{*}}$ operator which are the generalization of $(m, n)$-paranormal and $(m, n)^*$-paranormal operators. We give matrix characterizations for $k$-quasi $(m, n)$-paranormal and $k$-quasi $(m, n)^*$-paranormal operators. Also we study some properties of $k$-quasi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q}^*$ operators. Moreover, these classes of composition operators on $L^2$ spaces are characterized.
Abstract : The main object of the present paper is to study conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection satisfying the condition $\overset{\star}{C}(\xi,U)\cdot\overset{\star}{S}=0$. Finally we characterized concircular curvature tensor on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection.
Abstract : Magnetic curves are the trajectories of charged particals \linebreak which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between $\beta $-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for $\gamma $-magnetic curves. Finally, we give an evaluation of what we did.
Abstract : We introduce the study of generic lightlike submanifolds of a semi-Riemannian product manifold. We establish a characterization theorem for the induced connection on a generic lightlike submanifold to be a metric connection. We also find some conditions for the integrability of the distributions associated with generic lightlike submanifolds and discuss the geometry of foliations. Then we search for some results enabling a generic lightlike submanifold of a semi-Riemannian product manifold to be a generic lightlike product manifold. Finally, we examine minimal generic lightlike submanifolds of a semi-Riemannian product manifold.
Abstract : This paper is concerned with the following Schr\"{o}dinger-\linebreak Poisson system$$\left\{\begin{array}{ll} -{\Delta}u+V(x)u+K(x){\phi}u=a(x)|u|^{p-2}u &\mbox{in}\ \mathbb{R}^3, \\[0.1cm] -{\Delta}{\phi}=K(x)u^{2}&\mbox{in}\ \mathbb{R}^3, \\[0.1cm]\end{array}\right.$$where $4<p<6$. For the case that $K$ is nonnegative, $V$ and $a$ are indefinite, we prove the above problem possesses one ground state sign-changing solutionwith exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions islarger than that of the ground state solutions. The novelty of this paper is that the potential $a$ is indefinite and allowed to vanish at infinity. In this sense, we complementthe existing results obtained by Batista and Furtado \cite{BF18}.
Abstract : Let $f:X\rightarrow Y$ be a map between simply connected CW-complexes of finite type with $X$ finite. In this paper, we prove that the rational cohomology of mapping spaces map$(X,Y;f)$ contains a polynomial algebra over a generator of degree $N$, where $ N= $ max$ \lbrace i, \pi_{i }(Y)\otimes \mathbb{Q}\neq 0 \rbrace$ is an even number. Moreover, we are interested in determining the rational homotopy type of map$\left( \mathbb{S}^{n}, \mathbb{C} P^{m};f\right) $ and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.
Abstract : Let $R$ be a commutative graded ring with nonzero identity and $n$ a positive integer. Our principal aim in this paper is to introduce and study the notions of graded $n$-irreducible and strongly graded $n$-irreducible ideals which are generalizations of $n$-irreducible and strongly $n$-irreducible ideals to the context of graded rings, respectively. A proper graded ideal $I$ of $R$ is called graded $n$-irreducible (respectively, strongly graded $n$-irreducible) if for each graded ideals $I_{1}, \ldots,I_{n+1}$ of $R$, $I=I_{1} \cap \cdots \cap I_{n+1}$ (respectively, $I_{1} \cap \cdots \cap I_{n+1} \subseteq I$ ) implies that there are $n$ of the $I_{i}$ 's whose intersection is $I$ (respectively, whose intersection is in $I$). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded $n$-irreducible ideal which is not an $n$-irreducible ideal and an example of a graded ideal which is graded $n$-irreducible, but not graded $(n-1)$-irreducible.
Abstract : Let $S$ be a semigroup. We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\ x,y\in S,\] where $\sigma:S\rightarrow S$ is an automorphism, and $\mu :S\rightarrow \mathbb{C}$ is a multiplicative function such that $\mu (x\sigma (x))=1$ for all $x\in S$.
Abstract : In this paper, for the bounded solution of the non-densely defined non-autonomous evolution equation, we present the condition for asymptotic periodicity by using the circular spectral theory of functions on the half line and the extrapolation theory of non-densely defined evolution equation.
Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie
Commun. Korean Math. Soc. 2023; 38(3): 807-819
https://doi.org/10.4134/CKMS.c220217
Ejaz Sabir Lone, Pankaj Pandey
Commun. Korean Math. Soc. 2023; 38(1): 223-234
https://doi.org/10.4134/CKMS.c220011
MOHAMED CHHITI, SALAH EDDINE MAHDOU
Commun. Korean Math. Soc. 2023; 38(3): 705-714
https://doi.org/10.4134/CKMS.c220260
Guodong Hua
Commun. Korean Math. Soc. 2023; 38(2): 319-330
https://doi.org/10.4134/CKMS.c210366
Uday Chand De, Dipankar Hazra
Commun. Korean Math. Soc. 2024; 39(1): 201-210
https://doi.org/10.4134/CKMS.c230105
Asuman Guven Aksoy, Daniel Akech Thiong
Commun. Korean Math. Soc. 2023; 38(4): 1127-1139
https://doi.org/10.4134/CKMS.c230003
Anass Assarrar, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 1001-1017
https://doi.org/10.4134/CKMS.c230004
Md. Adud, BIKASH CHAKRABORTY
Commun. Korean Math. Soc. 2024; 39(1): 117-125
https://doi.org/10.4134/CKMS.c230016
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