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Let δ be a (d-1)-dimensional simplicial complex and let h(δ)=(h0,h1,...,hd) be its h-vector. A recent result of Murai and Terai guarantees that if δ satisfies Serre's condition (Sr), then (h0,h1,...,hr) is an M-vector and hr+hr+1+...+hd is nonnegative. In this article, we extend the result of Murai and Terai by giving r extra necessary conditions. More precisely, we prove that if δ satisfies Serre's condition (Sr), then iihr+i+1ihr+1+...+i+d-rihd, 0≤i≤r≤d, are all nonnegative  

Let I be a monomial ideal in the polynomial ring S=K [x1,... xn]. We study the Stanley depth of the integral closure Ī of I. We prove that for every integer k ≥ 1, the inequalities (S/Ik) ≤ sdepth (S/Ī) and sdepth(Ik) ≤ sdepth(Ī) hold. We also prove that for every monomial ideal I⊂ S there exist integers k1,k2≥ 1, such that for every s≥ 1, the inequalities sdepth (S/Isk1) ≤ sdepth(S/Ī) and sdepth (Isk2) ≤ sdepth (Ī) hold. In particular, mink{sdepth(S/Ik)} ≤ sdepth(S/Ī) and min̄k {sdepth (Ik)}≤ sdepth(Ī). We conjecture that for every integrally closed monomial ideal I, the inequalities sdepth(S/I)≥ n-l (I) and sdepth (I)≥ n-l (I)+1 hold, where l (I) is the analytic spread of I. Assuming the... 

Let F be a field, char (F) ≠ 2, and S ⊆ GLn (F), where n is a positive integer. In this paper we show that if for every distinct elements x, y ∈ S, x + y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring. © 2009 Elsevier Inc. All rights reserved  

Let K{double-struck} be a field, and let R = K{double-struck}[x1,.., xn] be the polynomial ring over K{double-struck} in n indeterminates x1,.., xn. Let G be a graph with vertex-set {x1,.., xn}, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J(k) and J[k], respectively. In this paper, we give necessary and sufficient conditions for R/Jk, R/J (k), and R/J [k] to be Cohen-Macaulay. We also study the limit behavior of the depths of these rings  

A very well-covered graph is a well-covered graph without isolated vertices such that the height of its edge ideal is half of the number of vertices. In this survey article, we gather together most of the old and new results on the edge and cover ideals of these graphs. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG  

Let G be a simple graph of order n and size m which is not a tree. If ℓ; ≤ 3 is a natural number and the length of every cycle of G is divisible by ℓ, then m ≤l/l-2 (n -2), and the equality holds if and only if the following hold: (i) ℓ is odd and G is a cycle of order ℓ or (ii) ℓ is even and G is a generalized 6>-graph with paths of length |l/2 It is shown that for a (0 mod ℓ)-cycle graph, m/n < l/l-1 if ℓ is odd, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n > l/l-2 - e. Also m/n > l/l-2 if ℓ is even, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n l/l-2-e  

Let K be a field and S = K[x1,...,xn] be the polynomial ring in n variables over the field K. Let G be a forest with p connected components G1,...,Gp and let I = I(G) be its edge ideal in S. Suppose that di is the diameter of Gi, 1 ≤ i ≤ p, and consider d = max{di I 1 ≤ i ≤ p}. Morey has shown that for every t ≥ 1, the quantity max is a lower bound for depth(S/It). In this paper, we show that for every t ≥ 1, the mentioned quantity is also a lower bound for sdepth(S/It). By combining this inequality with Burch's inequality, we show that any sufficiently large powers of edge ideals of forests are Stanley. Finally, we state and prove a generalization of our main theorem  

Let K be a field and S = K[x1,...,xn] be the polynomial ring in n variables over the field K. In this paper, it is shown that Stanley's conjecture holds for I and S/I if I is a product of monomial prime ideals or I is a high enough power of a polymatroidal or a stable ideal generated in a single degree  

Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (Sr) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen-Macaulay and satisfying Serre's condition (Sr). Let Δ be a (d-1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (hi,j(Δ))0≤j≤i≤d be the h-triangle of Δ and (hi,j(Γ(Δ)))0≤j≤i≤d be the h-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially (Sr) and for every i and j with 0≤j≤i≤r-1, the equality hi,j(Δ)=hi,j(Γ(Δ)) holds true  

Let Δ be a simplicial complex and χ be an s-coloring of Δ. Biermann and Van Tuyl have introduced the simplicial complex Δχ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of Δχ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of Δχ over a field is set-theoretic complete intersection. This also generalizes a result of Macchia  

The problem of finding a characterization of Cohen-Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen-Macaulay simplicial complexes  

Preparation, characterization and evaluation of new generation of micro-filters based on polyacrylonitrile electrospun nanofiberous membrane (ENM) were thoroughly investigated. First, quantitative relationships between average diameter, bead area density of nano-fibers and certain electrospinning parameters, i.e., concentration, voltage, spinning distance, and feed rate, were established by empirical modeling based on a central composite design. The analysis revealed that concentration, voltage and distance are the significant parameters. Also, adequacy checking indicated the appropriateness of fit for the models. Afterwards, bead-free ENMs with diameter of 100-500 nm were prepared and... 

Preparation, characterization and evaluation of new generation of micro-filters based on polyacrylonitrile electrospun nanofiberous membrane (ENM) were thoroughly investigated. First, quantitative relationships between average diameter, bead area density of nano-fibers and certain electrospinning parameters, i.e., concentration, voltage, spinning distance, and feed rate, were established by empirical modeling based on a central composite design. The analysis revealed that concentration, voltage and distance are the significant parameters. Also, adequacy checking indicated the appropriateness of fit for the models. Afterwards, bead-free ENMs with diameter of 100-500 nm were prepared and... 

The consolidation behavior of composite powders during pressure cycling at room temperature in uniaxial compaction experiments was studied and compared with monotonic compaction. Aluminum and various amounts of SiC powders (up to 50 vol%) were used to investigate the effect of hard reinforcement particle on the densification of soft aluminum matrix. The cyclic compaction was carried out at various pressure amplitudes, ranges from 90 to 360 MPa, at the frequency of 1 Hz. The pressure cycling was continued up to 5000 cycle, in which, the rate of consolidation was found to be fairly low. The consolidation of the composite powders under different loading modes was analyzed through... 

In this paper, the metric theory of Diophantine approximation associated with mixed type small linear forms is investigated. We prove Khintchine–Groshev type theorems for both the real and complex number systems. The motivation for these metrical results comes from their applications in signal processing. One such application is discussed explicitly. © Springer Nature Switzerland AG 2020  

Gradual chemical (displacement) reaction between CuO and Al powders during high-energy attrition milling under a high purity argon atmosphere was studied. Differential thermal analysis (DTA), X-ray diffraction (XRD) and transmission electron microscopy (TEM) techniques were employed to study the solid-state reaction. It was shown that the solid-state reaction occurred during mechanical alloying (MA) and resulted in the dissolution of copper into the aluminum lattice and formation of nanometric alumina particles. The reinforcement particles were mostly distributed at the grain boundaries of Al matrix with an average crystallite size of about 50 nm. In DTA curve of the milled powders, a small...