We give a classification of Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians
${\rm SU}_{2,m}/S(U_2{\cdot}U_m)$ with commuting conditions between the restricted normal Jacobi operator $\overline{R}_N\phi$ and the shape operator $A$ (or the Ricci tensor $S$)., Doo Hyun Hwang, Eunmi Pak, Changhwa Woo., and Obsahuje bibliografii
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains., Michal Hrbek, Pavel Růžička., and Seznam literatury
Let $C[0,t]$ denote a generalized Wiener space, the space of real-valued continuous functions on the interval $[0,t]$, and define a random vector $Z_n C[0,t]\to\mathbb R^{n+1}$ by Z_n(x)=\biggl(x(0)+a(0), \int_0^{t_1}h(s) {\rm d} x(s)+x(0)+a(t_1), \cdots,\int_0^{t_n}h(s) {\rm d} x(s)+x(0)+a(t_n)\biggr), where $a\in C[0,t]$, $h\in L_2[0,t]$, and $0<t_1 < \cdots< t_n\le t$ is a partition of $[0,t]$. Using simple formulas for generalized conditional Wiener integrals, given $Z_n$ we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions $F$ in a Banach algebra which corresponds to Cameron-Storvick's Banach algebra $\mathcal S$. Finally, we express the generalized analytic conditional Feynman integral of $F$ as a limit of the non-conditional generalized Wiener integral of a polygonal function using a change of scale transformation for which a normal density is the kernel. This result extends the existing change of scale formulas on the classical Wiener space, abstract Wiener space and the analogue of the Wiener space $C[0,t]$., Byoung Soo Kim, Dong Hyun Cho., and Obsahuje bibliografické odkazy
Let R be a commutative Noetherian ring and let C be a semidualizing R-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every Gc-injective module G, the character module G+ is Gc-flat, then the class GIc(R) Ac(R) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class GIc(R) Ac(R) is covering., Elham Tavasoli, Maryam Salimi., and Obsahuje bibliografii
A graph is called distance integral (or D-integral) if all eigenvalues of its distance matrix are integers. In their study of D-integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on D-integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs {K_{{p_1},{p_2},{p_3}}} with p1 < p2 < p3, and {K_{{p_1},{p_2},{p_3},{p_4}}} with p1 < p2 < p3 < p4, as well as the infinite classes of distance integral complete multipartite graphs {K_{{a_1}{p_1},{a_2}{p_2},...,{a_s}{p_s}}} with s = 5, 6., Pavel Híc, Milan Pokorný., and Obsahuje seznam literatury
This paper is about some geometric properties of the gluing of order k in the category of Sikorski differential spaces, where k is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour of kth order tangent spaces, their dimensions, and other geometric properties, are described in the context of the process of gluing differential spaces. At the end some examples are given. The paper is self-consistent, i.e., a short review of the differential spaces theory is presented at the beginning., Krzysztof Drachal., and Obsahuje seznam literatury