in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

We consider a family of four-dimensional non-linear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterised by two distinct topological charges, the Chern-Pontryagin charge of the gauge field and the degree of the map, i.e. the winding number, of the S4 field. The one...

T he building sector is the largest energy consumer in the world. Therefore, it is economically, socially, and environmentally signifi cant to reduce the energy consumption of buildings. Achieving substantial energy reduction in buildings may require rethinking the whole processes of design, construction , and operation of a building. This article focuses on the specifi c

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.

We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number 〈N〉 is a thermal expectation value, and we compute the finite temperature fluctuations, (∆N) = 〈N〉 − 〈N〉. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopologica...

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...

background: sigma factors are proteins that regulate transcription in bacteria. sigma factors can be activated in response to different environmental conditions. the rpos (rna polymerase, sigma s) gene encodes sigma-38 (σ38, or rpos), a 37.8 kda protein in pseudomonas aeruginosa (p. aeruginosa) strains. rpos is a central regulator of the general stress response and operates in both retroactive ...

investigations are carried out to evaluate the performance of a low heat rejection (lhr) diesel engine consisting of air gap insulated piston with 3-mm air gap, with superni (an alloy of nickel) crown and air gap insulated liner with superni insert with different operating conditions of crude jatropha oil with varied injection timing and injection pressure.  performance parameters of brake ther...

We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. W...