Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.     

Hydrogen-bonded and π-stacked nickel(II) thiosemicarbazone complexes: Synthesis,spectral and structural studies

Transition Metal Chemistry - Mixed ligand Ni(II) complexes were synthesized from triphenylphosphine and S-methyl- or S-ethyl-isothiosemicarbazone ligands derived from...     

Statistical equi-equal convergence of positive linear operators

Positivity - Many researchers have been interested in the concept of statistical convergence because of the fact that it is stronger than the classical convergence. Also, the concepts of...     

A novel amperometric hydrogen peroxide biosensor based on pyrrole-PAMAM dendrimer modified gold electrode

Horseradish peroxidase (HRP) was immobilized into an electrochemically prepared copolymer of pyrrole–PAMAM (PAMAM; polyamidoamine) dendrimers for the construction of amperometric hydrogen peroxide biosensor. First, second, and third generation amidoamine–pyrrole dendrons having branched amine periphery and focal pyrrole functionality were synthesized via divergent pathway. Pyrrole dendrimers were covalently attached onto the electrode surface and polymerized by electrochemical copolymerization with pyrrole monomer. The synthesized dendrimers and copolymers have been characterized by FTIR-ATR and NMR. These copolymers have been utilized as conducting films for amperometric hydrogen peroxide sensing. The HRP retains its bioactivity after immobilization into the dendronized pyrrole-copolymers. Amperometric response was measured as a function of concentration of hydrogen peroxide, at fixed potential of +0.35 V vs. Ag/AgCl in a phosphate buffered saline (pH 7.5). The effect of pH and temperature of the medium, storage, and reusability properties were investigated. The results indicate an efficient immobilization of enzyme onto the PAMAM type dendrimer modified surface containing pyrrole monomer, which leads to high enzyme loading, and increased lifetime stability of the electrode.     

NONLINEAR DYNAMIC ANALYSIS OF A LAMINATED HYBRID COMPOSITE PLATE SUBJECTED TO TIME-DEPENDENT EXTERNAL PULSES

Nonlinear dynamic responses of a laminated hybrid composite plate subjected to time-dependent pulses are investigated. Dynamic equations of the plate are derived by the use of the virtual work principle. The geometric nonlinearity effects are taken into account with the von Kármán large deflection theory of thin plates. Approximate solutions for a clamped plate are assumed for the space domain. The single term approximation functions are selected by considering the nonlinear static deformation of plate obtained using the finite element method. The Galerkin Method is used to obtain the nonlinear differential equations in the time domain and a MATLAB software code is written to solve nonlinear coupled equations by using the Newmark Method. The results of approximate-numerical analysis are obtained and compared with the finite element results. Transient loading conditions considered include blast, sine, rectangular, and triangular pulses. A parametric study is conducted considering the effects of peak pressure, aspect ratio, fiber orientation and thicknesses.     

Identification of radical structures on 1‐pentamethylbenzyl‐3‐ethylimidazoliumsilver(I)bromide and 1,3‐bis(pentamethylbenzyl)‐4,5‐dimethylbenzimidazoliumsilver(I)bromide exposed to gamma rays: an EPR study

1‐Pentamethylbenzyl‐3‐ethylimidazoliumsilver(I)bromide and 1,3‐bis(pentamethylbenzyl)‐4,5dimethylbenzimidazoliumsilver(I)bromide and their Ag⁺ complexes were synthesized and their polycrystal forms were produced by recrystallization in dichloromethane/Et₂O solvent system. Structural determinations were carried out by ¹H NMR and ¹³C NMR with a Varian 400 NMR system using tetramethylsilane as internal standard and CDCl₃ as solvent. The disappearance of acidic N‐heterocyclic carbene proton showed the formation of Ag(I) complexes. Also, elemental analyses were carried out. Electron paramagnetic resonance (EPR) measurements were performed to determine the formed radical structure on the samples irradiated at the room temperature for 72 h by using ⁶⁰Co‐source with dose rate of 0.680 kGy. The EPR measurements were carried out in the temperature range of 200 K–450 K. Identical radicals were determined on the irradiated compounds. It was observed that the shapes of the spectra of the samples were independent of the temperature but, the resonance line intensities changed linearly with the temperature. Also, it was detected that the free radical on the 1‐pentamethylbenzyl‐3‐ethylimidazoliumsilver(I)bromide is not stable compared to that on the 1,3‐bis(pentamethylbenzyl)‐4,5dimethylbenzimidazoliumsilver(I)bromide. Copyright © 2016 John Wiley & Sons, Ltd.     

A note on “A LP-based heuristic for a time-constrained routing problem”

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination.     

Explanation of Anomalous Gas-Chromatographic (Gc) Behaviour in a Homologous Series of 2-Chloroethyl Phosphonic Acid Dialkyl Esters

Abstract

The study of GC separation of 2-chloroethylphosphonic acid di-n-alkyl (1–5 C atoms) esters (synthesised by us) on silicone stationary phases (OV-1, OV-17, OV-225) revealed a deviation from the expected linear dependence of retention indexes (RI) versus the number of C atoms of the alkyl chain: the first member of the series presents stronger retention than one can expect. This anomalous behaviour was observed especially on polar stationary phase (OV-225, see Figure l), and was emphasised with the increase of the column temperature. In an attempt to rationalise the above mentioned facts, we tried to relate the RI values to a global polarity parameter: the dipole moment, μ. The μ values for ClC₂H₄P(O)(OR)₂ were calculated by a method described in [1] (tested by comparing the calculated μ values with experimental ones for alkyl phosphonic acid dialkylesters), using molecular mechanics (COSMIC package) in the search of the conformational space, AM1 method (MOPAC 6.0) for the μ values of the conformers, and Boltzmann distribution for the global value (see Table I). At low temperature, the μ values are not related to the Kovats indexes. Those calculated at 200°C (column temperature range) demonstrate that, indeed, only in the case of the methyl derivative, the temperature rising led to a higher μ (enhanced population of the more polar conformers: ac position for the C-Ethyl group - ac for the Cl, μ ≈ 27 D, or ±ap for one R, μ ≈ 3.8 ÷ 4.3 D). It can be concluded that dipole-dipole forces contribute to the separation process of the first members of the series.