We study the group of homotopy classes of self maps of compact Lie groups which induce the trivial homomorphism on homotopy groups. We completely determine the groups for SU(3) and Sp(2). We investigate these groups for simple Lie groups in the cases when Lie groups are p-regular or quasi p-regular. We apply our results to the groups of self homotopy equivalences. Introduction Let [X,Y ] be the...

this paper presents a new audio encryption algorithm based on permutation and residue number system. in the current approach, signal samples are combined with residue number system through permutation; therefore, a specific noise is generated. then, the audio signal is combined with the noise, generated by the algorithm, to produce a silence signal. for this purpose, the algorithm uses a predef...

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

Our goal in this paper is to advance the state of art topic uniqueness unconditional basis. To that end we establish general conditions on a pair (X,Y) formed by quasi-Banach space X and Banach Y which guarantee every basis their direct sum X⊕Y splits into bases each summand. As application our methods obtain that, among others, spaces Hp(Td)⊕T(2) Hp(Td)⊕ℓ2, for p∈(0,1) d∈N, have unique (up equ...

Let S be a subset of the positive integers, and let σ be a permutation of S. We say that σ is a k-avoiding permutation of S if σ does not contain any k-term AP as a subsequence. Similarly, the set S is said to be k-avoidable if there exists a k-avoiding permutation of S.

the recent years have witnessed an increasing attention to the methods of multiple attribute decision making in solving the problems of the real world due to their shorter time of calculation and easy application. one of these methods is the ‘permutation method’ which has a strong logic in connection with ranking issues, but when the number of alternatives increases, solving problems through th...

the group $2^6{{}^{cdot}} g_2(2)$ is a maximal subgroup of the rudvalis group $ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. in this paper, we construct the character table of the group $2^6{{}^{cdot}} g_2(2)$ by using the technique of fischer-clifford matrices.

in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...