Let σ n be the sum of all divisors id="M2"> and let id="M3"> open="[" close="]" t integral part id="M4"> . In this paper, we shall prove that id="M5"> ∑ ≤ x</m...

We study the problem of finding zero-sum blocks in bounded-sum sequences, which was introduced by Caro, Hansberg, and Montejano. Caro et al. determine minimum $\{-1,1\}$-sequence length for when there exist $k$ consecutive terms that sum to zero. corresponding sequence set $\{-1,1\}$ is replaced $\{-r,s\}$ arbitrary positive integers $r$ $s.$ This confirms a conjecture theirs. also construct $\...

We assessed the Gradient Phonemicity Hypothesis by testing whether a duration-based derived contrast in Scottish English can be seen phonemic just as a contrast based on vowel quality. We examined the electrophysiological correlates of the perception of such contrasts in native Scottish and French speakers. Results revealed differences between the two groups, mostly in the perception of duratio...

Let Fq be the finite field of q elements. Let H ⊆ Fq be a multiplicative subgroup. For a positive integer k and element b ∈ Fq, we give a sharp estimate for the number of k-element subsets of H which sum to b.

Between 1952 and 1954 Amitsur and Kurosh initiated the general theory of radicals in various contexts. In the case of all groups some interesting results concerning radicals were obtained by Kurosh, Shchukin, Ryabukhin, Gardner and others. In this paper we are going to examine radical theory in the class of all finite groups. This strong restriction gives chance to obtain stronger results, then...

In this paper, we obtain an explicit formula for the number of zero-sum k-element subsets in any finite abelian group.

Multimodal medical image fusion is a fundamental, but challenging, problem in the fields of brain science research and disease diagnosis, as it challenging for sparse representation (SR)-based to characterize activity levels with single measurement not lose effective information. In this study, Kronecker-criterion-based SR framework was applied patch-based level, integrating salient features mu...