In this paper we present the solution to a longstanding problem of differential geometry: Lie’s third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-mode...

The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms. These solutions are defined on a manifold of the form M = M0 × M1 × . . . × Mn , where all Mi with i ≥ 1 are fixed Einstein (e.g., Ricci-flat) spaces. We consider a warped product metric on M . Here, M0 is a base manifold, and all sc...

The symmetry properties of the bosonic string effective action under Poisson-Lie duality transformations are investigated. A convenient and simple formulation of these duality transformations is found, that allows the reduction of the string effective action in a Kaluza-Klein framework. It is shown that the action is invariant provided that the two Lie algebras, forming the Drinfeld double, hav...

Introduction: Bacteria have at least one sigma factor (σ-factor) that transcribes the genes required for cell viability. Usually, transcription of σ-factors occurs and changes in response to a variety of environmental stresses. Expression of σ-factors is one of the strategies which is used in response to different stress conditions. This study was aimed to evaluate the effects...

We formalize higher dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the “FDA”-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) ar...

Let k3(n) denote the minimal cardinality of a ternary code of length n and covering radius one. In this paper we show k3(7) ≥ 156 and k3(8) ≥ 402 improving on the best previously known bounds k3(7) ≥ 153 and k3(8) ≥ 398. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in k...

Abstract We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic {HA}$ . Using a generalized negative translation, we first provide structured proof the fact that is $\Pi _{k+2}$ -conservative over {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma axiom scheme law-of-excluded-middl...

In this paper we investigate Poisson-Lie transformation of dilaton and vector field J appearing in Generalized Supergravity Equations. While the formulas literature work well for isometric sigma models, present examples which Equations are not preserved. Therefore, suggest modification these formulas.

Classification theory guarantees the existence of an isomorphism between any two E8’s, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠ 2,3 an explicit isomorphism between the algebra obtained from J by Faulkner’s construction and the algebra obtained from the split ...

This paper describes the design and implementation of a single-bit FIR Filter with balanced ternary coefficients (i.e. -1/0/+1) aimed at general DSP applications. The fixed filter coefficients were computed using a sigma delta modulation technique. The filter is based on a hierarchical adder structure that can be pipelined for high performance that has been designed and simulated in VHDL. The f...