let $r$ be a commutative ring and let $m$ be an $r$-module. in this article, we introduce the concept of the zariski socles of submodules of $m$ and investigate their properties. also we study modules with noetherian second spectrum and obtain some related results.

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

Our first main result states that the spectral norm $$\gamma $$ on \mathrm {Ham}(M, \omega ) , introduced in works of Viterbo, Schwarz and Oh, is continuous with respect to $$C^0$$ topology, when M symplectically aspherical. This statement was previously proven only case closed surfaces. As a corollary, using recent Kislev-Shelukhin, we obtain continuity barcodes aspherical symplectic manifolds...

objective: colorectal cancer (crc) is one of the most common and aggressive cancers worldwide. the majority of crc cases are sporadic that caused by somatic mutations. the adenomatous polyposis coli (apc; omim 611731) is a tumor suppressor gene of wnt pathway and is frequently mutated in crc cases. this study was designed to investigate the spectrum of apc gene mutations in iranian patients wit...

Laser Raman spectroscopy has been used detect structural changes in troponin C induced by Ca2+ binding. Addition of Ca2+ - Mg2+ sites produces perturbations in the amide III region of the spectrum indicative of increased alpha-helical content, and in regions of the spectrum corresponding to carboxylate, thiol, and phenol side chains. However, Ca2+ binding to the low affinity Ca2+ - specific sit...