in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

This paper investigates a set of novel techniques that lead to modular, deployable surface arrays which could be either flat or curved in their deployed shape. The two components of the proposed concepts are thin shells with smooth folds and spatial mechanisms with rolling hinges. Kinematics of the mechanism and motion of the shell has been shown to be fully compatible with each other during fo...

We report the first experimental demonstration of Gaussian beam-shaping based on the Generalized Phase Contrast (GPC) approach. We show that, when using a dynamic spatial light modulator (SLM), this approach can rapidly generate arbitrarily shaped beams. Moreover, we demonstrate that low-cost binary-phase optics fabricated using photolithography and chemical etching techniques can replace the S...

In this paper‎, ‎we study the class of rings in which every $P$-flat‎ ‎ideal is flat and which will be called $PFF$-rings‎. ‎In particular‎, ‎Von Neumann regular rings‎, ‎hereditary rings‎, ‎semi-hereditary ring‎, ‎PID and arithmetical rings are examples of $PFF$-rings‎. ‎In the context domain‎, ‎this notion coincide with‎ ‎Pr"{u}fer domain‎. ‎We provide necessary and sufficient conditions for‎...

Let OK be a complete discrete valuation ring of residue characteristic p > 0, and G be a finite flat group scheme over OK of order a power of p. We prove in this paper that the Abbes-Saito filtration of G is bounded by a linear function of the degree of G. Assume OK has generic characteristic 0 and the residue field of OK is perfect. Fargues constructed the higher level canonical subgroups for ...

In this continuation of [L-Y1], [L-L-S-Y], [L-Y2], and [L-Y3] (arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], arXiv:0901.0342 [math.AG], arXiv:0907.0268 [math.AG]), we study D-branes in a target-space(-time) with a fixed B-field background (Y, αB) along the line of the Polchinski-Grothendieck Ansatz, explained in [L-Y1] and further extended in the current work. We focus first on the gaug...

Motivated from some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define ...

Natural language understanding (NLU) is a core component of a dialogue system. Recently recurrent neural networks (RNN) obtained strong results on NLU due to their superior ability of preserving sequential information over time. Traditionally, the NLU module ignores the contexts of utterances and tags semantic slots for utterances considering their flat structures, as the underlying RNN structu...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.

Origami-inspired foldable structures have seen much recent interest for applications in which transportability or rapid construction are primary design drivers, for example emergency shelters and temporary staging structures. This paper proposes a new type of a structural module that can be manually folded from flat steel sheet into a novel self-braced triangular structural section. Simple geom...