Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK, and typically each operation can be obtained in many alternative ways. Interestingly, identifying the fastest implementation—without executing it—is a challeng...

in this paper, we introduce the notion of multiplier in -algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and ( -derivations in -algebras. we introduce the concept of idempotent multipliers in bl-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. also, we introduce...

Working withing the framework of Hopf algebras, a random walk and the associated diffusion equation are constructed on a space that is algebraically described as the merging of the real line algebra with the anyonic line algebra. Technically this merged structure is a smash algebra, namely an algebra resulting by a braided tensoring of real with anyonic line algebras. The motivation of introduc...

A certain generalization of the algebra gl(N,R) of first-order differential operators acting on a space of inhomogeneous polynomials in R is constructed. The generators of this (non)Lie algebra depend on permutation operators. It is shown that the Hamiltonian of the N -body Calogero model can be represented as a second-order polynomial in the generators of this algebra. Given representation imp...

The quantum Cram\'er-Rao bound is a cornerstone of modern metrology, as it provides the ultimate precision in parameter estimation. In multiparameter scenario, this becomes matrix inequality, which can be cast to scalar form with properly chosen weight matrix. Multiparameter estimation thus elicits tradeoffs each estimated. We show that, if information encoded unitary transformation, we natural...

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...

Modern processing techniques for turkey involve rapid chilling to slow microbial growth and early deboning of the economically important breast meat. This paper shows that these 2 processes lead to significantly tougher meat with higher cooking losses. The toughening appears to be due to less extensive proteolysis and shortening of the sarcomeres. Calpains I and II and their inhibitor, calpasta...

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebr...

We show that the Bessel equation can be cast, by means of suitable transformations, into a system of two damped/amplified parametric oscillator equations. The relation with the group contraction mechanism is analyzed and the breakdown of loop-antiloop symmetry due to group contraction manifests itself as violation of time-reversal symmetry. A preliminary discussion of the relation between some ...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...