A bstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting study condensed matter systems with non-relativistic symmetry. Derivation an action principle for these generally proved challenging various reasons. In this technical note, we employ the formulation double field theory construct actions variety ...

Let ε>0 be a small parameter. We consider the domain Ωε:=Ω∖Dε, where Ω is an open in Rn, and Dε family of balls radius dε=o(ε) distributed periodically with period ε. Δε Laplace operator Ωε subject to Robin condition ∂u∂n+γεu=0 γε≥0 on boundary holes Dirichlet exterior boundary. Kaizu (1985, 1989) Brillard (1988) have shown that, under appropriate assumptions dε γε, converges strong resolvent s...

we investigate the stability of generalizedderivations on banach algebras with a bounded central approximateidentity. we show that every approximate generalized derivation inthe sense of rassias, is an exact generalized derivation. also thestability problem of generalized derivations on the faithful banachalgebras is investigated.

The author has published equations for predicting the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via (possibly resilient) line connections, but has never published the full derivation of these equations. The author also derived equations for the case when the connections are rigid point connections but has never u...

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

recently, the algebraic theory of mv -algebras is intensively studied. in this paper, we extend the concept of derivation of $mv$-algebras and we give someillustrative examples. moreover, as a generalization of derivations of $mv$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $mv$-algebras.also, we investigate some properties of them.

We consider the double field formulation of closed bosonic string theory, and calculate Poisson bracket algebra symmetry generators governing both general coordinate local gauge transformations. Parameters these symmetries depend on a coordinate, defined as direct sum initial T-dual coordinate. When no antisymmetric is present, $C$-bracket appears Lie generalization in theory. With introduction...