On Topological Structure of the First Non-abelian Cohomology of Topological Groups

Let $G$, $R$ and $A$ be topological groups. Suppose that $G$ and $R$ act continuously on $A$, and $G$ acts continuously on $R$. In this paper, we define a partially crossed topological $G-R$-bimodule $(A,\mu)$, where $\mu:A\rightarrow R$ is a continuous homomorphism. Let $Der_{c}(G,(A,\mu))$ be the set of all $(\alpha,r)$ such that $\alpha:G\rightarrow A$ is a continuous crossed homomorphism and $\mu\alpha(g)=r^{g}r^{-1}$. We introduce a topology on $Der_{c}(G,(A,\mu))$. We show that $Der_{c}(G,(A,\mu))$ is a topological group, wherever $G$ and $R$ are locally compact. We define the first cohomology, $H^{1}(G,(A,\mu))$, of $G$ with coefficients in $(A,\mu)$ as a quotient space of $Der_{c}(G,(A,\mu))$. Also, we state conditions under which $H^{1}(G,(A,\mu))$ is a topological group. Finally, we show that under what conditions $H^{1}(G,(A,\mu))$ is one of the following: $k$-space, discrete, locally compact and compact.Comment: 15 page

Standard Projective Simplicial Kernels and the Second Abelian Cohomology of Topological Groups

Let $A$ be an abelian topological $G$-module. We give an interpretion for the second cohomology, $H^{2}(G,A)$, of $G$ with coefficients in $A$. As a result we show that if $P$ is a projective topological group, then $H^{2}(P,A)=0$ for every abelian topological $P$-module $A$.Comment: 12 page

First Non-abelian Cohomology of Topological Groups II

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-abelian cohomology of a topological group by the notion of a principle homogeneous space.Comment: 18 page

SUT System Description for NIST SRE 2016

This paper describes the submission to fixed condition of NIST SRE 2016 by Sharif University of Technology (SUT) team. We provide a full description of the systems that were included in our submission. We start with an overview of the datasets that were used for training and development. It is followed by describing front-ends which contain different VAD and feature types. UBM and i-vector extractor training are the next details in this paper. As one of the important steps in system preparation, preconditioning the i-vectors are explained in more details. Then, we describe the classifier and score normalization methods. And finally, some results on SRE16 evaluation dataset are reported and analyzed.Comment: Presented in NIST SRE 2016 Evaluation Worksho

On Dynamics of Brans--Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans-Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogenous cosmological models. Then, we show that formulation of the Brans-Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann-Robertson-Walker cosmological models.Comment: 15 page

New Methods for Solving Large Scale Linear Programming Problems in the Windows and Linux computer operating systems

In this study, calculations necessary to solve the large scale linear programming problems in two operating systems, Linux and Windows 7 (Win), are compared using two different methods. Relying on the interior-point methods, linear-programming interior point solvers (LIPSOL) software was used for the first method and relying on an augmented Lagrangian method-based algorithm, the second method used the generalized derivative. The performed calculations for various problems show the produced random in the Linux operating system (OS) and Win OS indicate the efficiency of the performed calculations in the Linux OS in terms of the accuracy and using of the optimum memory.Comment: 8 pages; This paper will be published in Appl. Math. Inf. Sci. Vol. 7 No. 1 (2013

Big Handlebody Distance Implies Finite Mapping Class Group

We show that if $M$ is a closed three manifold with a Heegaard splitting with sufficiently big "handlebody distance" then the subgroup of the mapping class group of the Heegaard surface, which extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of $M$ is finite.Comment: 9 page

Modular-type functions attached to mirror quintic Calabi-Yau varieties

In this article we study a differential algebra of modular-type functions attached to the periods of a one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of quintic threefolds. Such an algebra is generated by seven functions satisfying functional and differential equations in parallel to the modular functional equations of classical Eisenstein series and the Ramanujan differential equation. Our result is the first example of automorphic-type functions attached to varieties whose period domain is not Hermitian symmetric. It is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures

Primitive ideal space of Higher-rank graph C∗C^*-algebras and decomposability

In this paper, we describe primitive ideal space of the $C^*$-algebra $C^*(\Lambda)$ associated to any locally convex row-finite $k$-graph $\Lambda$. To do this, we will apply the Farthing's desourcifying method on a recent result of Carlsen, Kang, Shotwell, and Sims. We also characterize certain maximal ideals of $C^*(\Lambda)$. Furthermore, we study the decomposability of $C^*(\Lambda)$. We apply the description of primitive ideals to show that if $I$ is a direct summand of $C^*(\Lambda)$, then it is gauge-invariant and isomorphic to a certain $k$-graph $C^*$-algebra. So, we may characterize decomposable higher-rank $C^*$-algebras by giving necessary and sufficient conditions for the underlying $k$-graphs. Moreover, we determine all such $C^*$-algebras which can be decomposed into a direct sum of finitely many indecomposable $C^*$-algebras.Comment: The last versio

Spoken Pass-Phrase Verification in the i-vector Space

The task of spoken pass-phrase verification is to decide whether a test utterance contains the same phrase as given enrollment utterances. Beside other applications, pass-phrase verification can complement an independent speaker verification subsystem in text-dependent speaker verification. It can also be used for liveness detection by verifying that the user is able to correctly respond to a randomly prompted phrase. In this paper, we build on our previous work on i-vector based text-dependent speaker verification, where we have shown that i-vectors extracted using phrase specific Hidden Markov Models (HMMs) or using Deep Neural Network (DNN) based bottle-neck (BN) features help to reject utterances with wrong pass-phrases. We apply the same i-vector extraction techniques to the stand-alone task of speaker-independent spoken pass-phrase classification and verification. The experiments on RSR2015 and RedDots databases show that very simple scoring techniques (e.g. cosine distance scoring) applied to such i-vectors can provide results superior to those previously published on the same data