Let w be an Abelian differential on compact Riemann surface of genus g ≥ 1. We obtain an explicit holomorphic factorization formula for ζ-regularized determinant of the Laplacian in flat conical metrics with trivial holonomy |w|2, generalizing the classical Ray-Singer result in g = 1.

this research was conducted to investigate the physico-mechanical characteris-tics of the ethylcellulose-based coating membranes plasticized with different weight percents of dibutyl sebacate. in this experiment, free thin polymer sheetings of the sample formulations, by incorporating incremental weight percents of the plasticizer, were prepared employing a revised casting method of delayed sol...

Let (R, m) and (S, n) be commutative Noetherian local rings, and let φ : R→ S be a flat local homomorphism such that mS = n and the induced map on residue fields R/m→ S/n is an isomorphism. Given a finitely generated R-module M , we show that M has an S-module structure compatible with the given R-module structure if and only if Ext R (S,M) = 0 for each i ≥ 1. We say that an S-module N is exten...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

LetW be a finite irreducible real reflection group, which is a Coxeter group. A primitive derivation D, introduced and studied by K. Saito (e.g., [4]), plays a crucial role in the theory of differential forms with logarithmic poles along the Coxeter arrangement. For example, we may describe the contact order filtration of the logarithmic derivation module using the primitive derivations ([10, 1...

The availability of large data centers with tens of thousands of servers has led to the popular adoption of massive parallelism for data analysis on large datasets. Several query languages exist for running queries on massively parallel architectures, some based on the MapReduce infrastructure, others using proprietary implementations. Motivated by this trend, this paper analyzes the parallel c...

Let g be a finite-dimensional simple Lie algebra over C of type An, and let U be the q-analogue of its universal enveloping algebra defined by Drinfel’d [4] and Jimbo [6]. According to [9, 3.5.6, 6.2.3 & 6.3.4], for each dominant weight λ in the weight lattice of g there is an irreducible, finite-dimensional highest weight U -module V (λ) with highest weight λ. Kashiwara [7] and Lusztig [8] hav...

We study the dynamical properties of the propagation of innovation on a two-dimensional lattice, random network, scale-free network, and Cayley tree. In order to investigate the diversity of technological level, we study the scaling property of width, W(N,t), which represents the root mean square of the technological level of agents. Here, N is the total number of agents. From the numerical sim...

We test if the latest Gold set of 182 SNIa in conjunction with the CMB shift parameter show a preference between the ΛCDM model, three wCDM models, and the DGP model of modified gravity as an explanation for the current accelerating phase of the universe's expansion. We consider flat wCDM models with an equation of state w(a) that is (i) constant with scale factor a, (ii) varies as w 0 + w a (1...

We test if the latest Gold set of 182 SNIa in conjunction with the CMB shift parameter show a preference between the ΛCDM model, three wCDM models, and the DGP model of modified gravity as an explanation for the current accelerating phase of the universe's expansion. We consider flat wCDM models with an equation of state w(a) that is (i) constant with scale factor a, (ii) varies as w 0 + w a (1...