let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

We study the asymptotic behaviour, as ε goes to zero, of the entropy solution uε to a class of nonlinear elliptic problems whose prototype is −div ( (δε)p−1 |∇uε|p−2∇uε ) = f ε in Ωε , uε = 0 on ∂Ωε, where 1 < p < N , Ωε = Ω ∪ Σε, Ω ⊂ R is a bounded domain of class C1,1, surrounded along its boundary by a layer Σε of small thickness ε, δε = 1 in Ω, δε = ε in Σε, and f ε belongs to L1(Ωε). The s...

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

We consider a beam whose cross-section is a tubular neighborhood, with thickness scaling with a parameter δε, of a simple curve γ whose length scales with ε. To model a thin-walled beam we assume that δε goes to zero faster than ε, and we measure the rate of convergence by a slenderness parameter s which is the ratio between ε2 and δε. In this Part I of the work we focus on the case where the c...

We consider a beam whose cross-section is a tubular neighborhood of a simple closed curve γ. We assume that the wall thickness, i.e., the size of the neighborhood, scales with a parameter δε while the length of γ scales with ε. We characterize a thin-walled beam by assuming that δε goes to zero faster than ε. Starting from the three dimensional linear theory of elasticity, by letting ε go to ze...

Back Propagation and its variations are widely used as methods for training artificial neural networks. One such variation, Resilient Back Propagation (RPROP), has proven to be one of the best in terms of speed of convergence. Our SARPROP enhancement, based on Simulated Annealing, is described in this paper and is shown to increase the rate of convergence for some problems. The extension involv...