This paper investigates the proper class of all metric spaces considered up to isometry, equipped with the Gromov-Hausdorff distance. There constructed a pair of complete metric spaces, X and Y such that they have no metric spaces at zero distance, no optimal correspondence between X and Y, and therefore no linear geodesics joining them, but there exists a geodesic between them of a different type. There also described everywhere dense subclass of the Gromov-Hausdorff class such that any two points at finite distance within this subclass can be connected by a linear geodesic.
Let R be a commutative local ring and let C be a semidualizing R-module. In [E. Tavasoli, M. Salimi, Relative Matlis duality with respect to a semidualizing module, Bull. Math. Soc. Sci. Math. Roum., Nouv. Ser., 66(114), 4 (2023), 433-444], the notion of relative Matlis duality with respect to C, and C-Matlis reflexive modules are introduced, which generalized the notions of Matlis duality and Matlis reflexive modules. In this paper, we investigate conditions under which the R-modules Exti >= 0R (M, N) and TorRi >= 0(M, N) become C-Matlis reflexive, where M and N are R-modules. In addition, we deal with the isomorphic modules to the relative Matlis duality of R-modules Exti >= 0R (M, N), and TorRi >= 0(M, N) in the case that M and N are Matlis reflexive modules over the complete ring R.
In this paper, for solving a variational inequality problem governed by a boundedly Lipschitzian and strongly monotone mapping over the set of common fixed points of a sufficiently large finite family of nonexpansive mappings on Hilbert spaces, we propose strong convergence of any sequence, generated by this scheme, is proved under weaker conditions on iterative parameters without any additional assumption on the family of fixed point sets as well as the dimension of the spaces. An application to networked systems and a convex optimization problem over the intersection of a finite family of closed convex subsets with numerical experiments are given for illustration.
In this paper, we show the convergence of matrix series and the conditions for their convergence by finding an upper bound for some specific matrix inequalities. Finally, we introduce a new form of arithmetic-geometric matrix series and analyze their convergence.
LetF2 lambda be the space of tensor densities of degree lambda is an element of C on the supercircle S1|2. We consider the space D2,k lambda,& micro; of k-th order linear differential operators fromF2 lambda to F2 & micro; as a module over the superalgebra K(2) of contact vector fields on S1|2 and we compute the superalgebra K2,k lambda,& micro; of endomorphisms on D2,k lambda,& micro; commuting with the K(2)-action. We prove that this algebra is trivial except for lambda = 0.
In this paper we study with statistical convergence in the sense of the power series method which is not comparable with statistical convergence. Using this notion, we introduce the concepts of Pp-statistical exhaustiveness and weak Pp-statistical exhaustiveness. Also, we study several types of convergence of sequences of functions between two metric spaces and we obtain more general results from the concepts of exhaustiveness and the strong uniform convergence on a bornology.
The primary objective of this paper is to investigate the commutativity of sigma-prime rings with the second kind involution, involving pairs of derivations that satisfy specific differential identities. Finally, we present examples to illustrate that the conditions assumed in our results are essential and cannot be omitted.
Notions of ZK-limit points and ZK-cluster points of functions are studied in topological spaces. In the first countable space, all ZK-cluster points of a function f : S-* X belong to the closure of each member of the filter base Bf(ZK). Frechet compactness is studied in the light of ideals Z and /C of subsets of S and showed that in an Z-sequential Hausdorff space, Frechet compactness and Z-Frechet compactness are equivalent. Using the FDS-property introduced by D. Shakmatov, M. Tkachenko, R. Wilson in Houston J. Math., it is seen that ZK-Frechet compactness, Frechet compactness and Z-Frechet compactness are equivalent for a particular class of ideals on S.
In this paper, we consider a pseudo parabolic equation with weak-visco elastic term, where the exponent in the source term is variable. Using a differential inequality technique, we prove that the solution with positive initial energy become unbounded at a finite time, and find an upper bound for this time. A lower grow-up rate of solution is also obtained.
A central issue of the present paper is to consider the Korovkin-type approximation properties of the Lupa,s-Jain operators using A-statistical convergence and Abel convergence, which are well-known summability methods. We provide an instance of a sequence of positive linear operators to which the weighted Korovkin-type theorem does not apply, but the A-statistical approximation theorem does. Our results are one-way more substantial than some approximation results given in [Ba,scanbaz-Tunca et al., On Lupa,s-Jain Operators, Stud. Univ. Babe,s-Bolyai Math., 63(4) (2018), 525-537].
In this paper, we begin by introducing the exponential change of m-th root Finsler metrics, referred to as exponentially transformed m-th root Finsler metric. For this metric, we derive the fundamental metric tensors along with their inverses. Additionally, we determine the spray coefficients and establish the conditions under which the transformed metric is projectively related to an m-th root metric. Furthermore, we investigate the conditions for the transformed Finsler space to exhibit locally duality flatness and projective flatness. We also identify the conditions under which the transformed metrics to be the Berwald metric, weakly Berwald metric, Landsb erg metric, and weakly Landsb erg metric. Lastly, we show that every exponential change of m-th root Finsler metrics with almost vanishing H-curvature has vanishing H-curvature.
In this paper, we introduce SCR-warped product lightlike submanifold of golden semi-Riemannian manifold. We obtain characterization theorem of SCR-warped product lightlike submanifold of the type MT x lambda M perpendicular to of golden semi-Riemannian manifold. Further, we show that for a proper SCR-warped product lightlike submanifold of golden semi-Riemannian manifold, induced connection del is not a metric connection. Finally, we find necessary and sufficient conditions for SCR lightlike submanifold of golden semi-Riemannian manifold to be a SCR-warped product lightlike submanifold in terms of the canonical structures P and F. Moreover, we give two non-trivial examples of SCR-warped product lightlike submanifold of golden semi-Riemannian manifold.
In this paper, we have proposed a new extension of the Chris- Jerry distribution called as Weighted Chris- Jerry Distribution which depends on two parameters. The statistical properties of this distribution such as moments, survival functions and hazard rate, reverse hazard rate, order statistics, entropies and likelihood ratio test are derived. The two parameters are estimated using maximum likelihood estimator. To illustrate this distribution, real life data set is considered. This data set is analyzed through this distribution, to show how the proposed model worked in it.
In this paper we take a look at compactly generated weak Hausdorff spaces equipped with an action of a compact Lie group G together with their colimits and homotopy colimits. In particular, we investigate relations between (homotopy) colimits and mapping spaces, and consequently, homotopy groups.
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence, hence equivalent to the category of semilattice epimorphisms. Guided by the above example, we recall an “internal” characterization of surjective homomorphisms between general relational systems.
Here we unify two results of Steinhaus and their corresponding category analogues by extending them in the settings of category bases. We further show that in any perfect translation base, every abundant Baire set contains a full subset for which our second theorem fails.
We get some results about the factorization of $\phi_p(M) \in {\mathbb{F}}_2[x]$, where $p$ is a prime number, $\phi_p$ is the corresponding cyclotomic polynomial and $M$ is a Mersenne prime (polynomial). By the way, we better understand the factorization of the sum of the divisors of $M^{2h}$, for a positive integer $h$.
