Some results on the cofiniteness and annihilators of local cohomology modules

Let (R,𝔪) be a Noetherian local ring. In this paper, we give a new characterization for the universal catenaricity of R and the Cohen–Macaulayness of all its formal fibers, and we study the cofiniteness and annihilators of local cohomology modules.     

Global Convergence Property of Scaled Two-Step BFGS Method

This paper is aimed to extend the scheme of self scaling, appropriate for the quasi-Newton methods, to the two-step quasi-Newton methods. The scaling scheme has been performed during the main approach of updating the current Hessian approximation and prior to the computation of the next quasi-Newton direction whenever necessary. Global convergence property of the new method is explored on uniformly convex functions with the standard Wolfe line search. Preliminary numerical testing has been performed showing that this technique improves the performance of the two-step method substantially.     

Inverse median location problems with variable coordinates

Given n points in \mathbbR^d{\mathbb{R}^d} with nonnegative weights, the inverse 1-median problem with variable coordinates consists in changing the coordinates of the given points at minimum cost such that a prespecified point in \mathbbR^d{\mathbb{R}^d} becomes the 1-median. The cost is proportional to the increase or decrease of the corresponding point coordinate. If the distances between points are measured by the rectilinear norm, the inverse 1-median problem is NP{\mathcal{NP}}-hard, but it can be solved in pseudo-polynomial time. Moreover, a fully polynomial time approximation scheme exists in this case. If the point weights are assumed to be equal, the corresponding inverse problem can be reduced to d continuous knapsack problems and is therefore solvable in O(nd) time. In case that the squared Euclidean norm is used, we derive another efficient combinatorial algorithm which solves the problem in O(nd) time. It is also shown that the inverse 1-median problem endowed with the Chebyshev norm in the plane is NP{\mathcal{NP}}-hard. Another pseudo-polynomial algorithm is developed for this case, but it is shown that no fully polynomial time approximation scheme does exist.     

Diastereoselective synthesis of cyclohexadienes via tandem cyclization strategies

Molecular Diversity - A new protocol has been developed for the diastereoselective synthesis of 1,3-cyclohexadienes using vinyl malononitriles, dibenzalacetones and NaH as reagents in THF. This...     

Does the onset of epileptic seizure start from a bifurcation point?

Detection of epileptic seizures is a major challenge of these days. There are lots of papers which pay their attention to this subject. Recently, some dynamical disease with attacks such as epilepsy are considered as a system in which critical slowing down can be seen before their attacks (seizure). Although there are not many researches on the prediction of seizures using this phenomenon. Recently [P. Milanowski, P. Suffczynski, Int. J. Neural Syst. 26, 1650053 (2016)] have investigated the application of critical slowing down indicators and surprisingly they found that only in 8% of nearby 300 epileptic patients have the evidence of critical slowing down before seizures. The main goal of this paper is finding the answer of the important question “can we trust that epileptic seizures are bifurcations in the neural system”. In order to find the answer, different studies on the prediction of seizure are investigated and we prove that features which are used in those papers are critical slowing down indicators although they are not aware of it. So we present some reasons for the occurrence of critical slowing down before the seizure. We hope that this study will be a motivation of future studies on the application of critical slowing down indicators for predicting epileptic seizures.     

Magnetic molecularly imprinted polymer for the efficient and selective preconcentration of diazinon before its determination by high‐performance liquid chromatography

A molecularly imprinted polymer was selectively applied for solid‐phase extraction and diazinon residues enrichment before high‐performance liquid chromatography. Diazinon was thermally copolymerized with Fe₃O₄@polyethyleneglycol nanoparticles, methacrylic acid (functional monomer), 2‐hydroxyethyl methacrylate (co‐monomer), and ethylene glycol dimethacrylate (cross‐linking monomer) in the presence of acetonitrile (porogen) and 2,2‐azobisisobutyronitrile (initiator). Then, the imprinted diazinon was reproducibly eluted with methanol/acetic acid (9:1, v/v). The sorbent particles were characterized by X‐ray diffraction, Fourier transform infrared spectroscopy, and scanning electron microscopy. The comprehensive study of variables through experimental design showed that the maximum performance was achieved under these conditions: pH 7, 10 mL sample volume, 15 mg sorbent, 10 min vortex time, 5 min ultrasonic time, 200 μL methanol/acetic acid (9:1, v/v) as eluent, and 5 min desorption time. Under optimized conditions, the molecularly imprinted polymer solid‐phase extraction method demonstrated a linear range (0.02–5 g/mL), a correlation coefficient of 0.997, and 0.005 g/mL detection limit.     

Synthesis of (E)-2-amino-N′-benzylidenehexahydroquinoline-3-carbohydrazide

Molecular Diversity - A one-pot, multi-component protocol for the synthesis of a new class of functionalized quinoline carbohydrazide derivatives via reaction of various anilines, dimedone,...     

Layered double hydroxides (LDHs): As efficient heterogeneous catalyst for the cyanosilylation of aromatic aldehydes

We report the first application of Layered Double Hydroxides (LDHs) as efficient and novel heterogeneous catalyst for the cyanosilylation of aldehydes with excellent yields and simple work up. The reaction between different aldehydes with electron-withdrawing and releasing groups and trimethylsilyl cyanide (TMSCN) proceeds in dry CH₂Cl₂ at room temperature in the presence of Mg-Al-Cu LDH. The catalyst recycled and reused for four times without loss of catalytic activity. The structures of all compounds were corroborated spectroscopically (¹H- and ¹³C-NMR, and elemental analysis). A plausible mechanism for this type of reaction is proposed.     

Facile synthesis of [1,2,4]triazino[4,3-b][1,2,4,5]tetrazepin derivatives by a one-pot reactions using 4-amino-3-hydrazinyl-6-methyl-1,2,4-triazin-5 (4H)-one

<正>4-Amino-3-mercapto-6-methyl-l,2,4-triazin-5(4H)-one 1 converted to 4-amino-6-methy-3-(methylthio)-1,2,4-triazin-5(4H)-one by methylation with methyl iodide.Controlled hydrazination of the resulting compound afforded 4-amino-3-hydrazinyl-6- methyl-l,2,4-triazin-5(4H)-one 2 as a building block,to the synthesis of some novel derivatives of[1,2,4]triazino- [4,3,b][1,2,4,5]tetrazepine 3-6,by the reaction with 3-chloropentane-2,4-dione,chloro acetonitrile,1,3-dichloroacetone,and methyl bromoacetate.This general synthetic procedure can be extended to the preparation of wide variety of tetrazepines using 1,2- bielectrophiles derivatives.