In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We als...

Mixed solutions of konjac glucomannan supplemented with xanthan and alginate were studied using the technique of sedimentation velocity in the analytical ultracentrifuge. Interactions – as manifested by changes in the sedimentation coefficient distributions compared to unmixed controls – were observed for ternary mixtures in the presence of alginate. The complexes observed also appeared sensiti...

we introduce center-like subsets z*(r,f), z**(r,f) and z1(r,f), where r is a ring and f is a map from r to r. for f a derivation or a non-identity epimorphism and r a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of r.

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

In this paper we present a method of separating musical instrument sound sources from their monaural mixture, where we take the harmonic structure of music into account and use the sparseness and the overlapping NMF to select representative spectral basis vectors which are used to reconstruct unmixed sound. A method of spectral basis selection is illustrated and experimental results with monaur...

If C is a clutter with n vertices and q edges whose clutter matrix has column vectorsA = {v1, . . . , vq}, we call C an Ehrhart clutter if {(v1, 1), . . . , (vq, 1)} ⊂ {0, 1} n+1 is a Hilbert basis. Letting A(P ) be the Ehrhart ring of P = conv(A), we are able to show that if C is a uniform unmixed MFMC clutter, then C is an Ehrhart clutter and in this case we provide sharp upper bounds on the ...