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...

There exist many good books on linear systems. I wish to mention here only some of them: L. Among these volumes the book by P.J. Antsaklis and A.M. Michel occupies a special place. It is an interesting and original introduction to modern control systems theory. It contains also many interesting problems from advanced systems theory. According to the authors the primary aim of the book is the fo...

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...

Let K be a closed subgroup of U(n) acting on the (2n+ 1)dimensional Heisenberg group Hn by automorphisms. One calls (K,Hn) a Gelfand pair when the integrable K-invariant functions on Hn form a commutative algebra under convolution. We prove that this is the case if and only if the coadjoint orbits for G := K n Hn which meet the annihilator k⊥ of the Lie algebra k of K do so in single K-orbits. ...

We consider the group $(\mathcal{G},*)$ of unitized multiplicative functions in incidence algebra non-crossing partitions, where ``$*$'' denotes convolution operation. introduce a larger $(\widetilde{\mathcal{G}},*)$ from same algebra, which satisfy weaker condition being ``semi-multiplicative''. The natural action $\widetilde{\mathcal{G}}$ on sequences multilinear functionals non-commutative p...

Abstract We address the efficient realization of matrix multiplication ( gemm ), with application in convolution operator for machine learning, RISC-V core present GreenWaves GAP8 processor. Our approach leverages BLIS (Basic Linear Algebra Instantiation Software) to develop an implementation that (1) re-organizes algorithm adapting its micro-kernel exploit hardware-supported dot product kernel...

Let G be a locally compact group. Consider the Banach algebra L1(G) ∗∗, equipped with the first Arens multiplication, as well as the algebra LUC(G)∗, the dual of the space of bounded left uniformly continuous functions on G, whose product extends the convolution in the measure algebra M(G). We present (for the most interesting case of a non-compact group) completely different – in particular, d...

introduction radiotherapy with small fields is used widely in newly developed techniques. additionally, dose calculation accuracy of treatment planning systems in small fields plays a crucial role in treatment outcome. in the present study, dose calculation accuracy of two commercial treatment planning systems was evaluated against monte carlo method. materials and methods siemens once or linea...