On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

Crystal structure of [RuCl2[N-(2,4,6-trimethyl-benzyl)N-(n-butyl)]-imidazolidin-2-ylidene] and [RuCl2[N-(2,4,6-trimethyl-benzyl)-N-(2-methoxyethyl)]-imidazolidin-2-ylidene]

Two imidazolidin ruthenium complexes, [RuCl₂{[N-(2,4,6-trimethyl-benzyl)-N-(n-butyl)]-imidazolidin-2-ylidene}], 1, and [RuCl₂{[N-(2,4,6-trimethyl-benzyl)-N-(2-methoxyethyl)]-imidazolidin-2-ylidene}], 2, have been synthesised and their crystal structures have been determined from single crystal X-ray diffraction data. Compound 1 is monoclinic, of space group C2/c with a = 18.466(4) Å, b = 14.816(3) Å, c = 15.413(3) Å, β = 118.067(2)^∘, and V = 3720.9(12) ų with Z = 8 for d_calc = 1.536 g/cm³. Compound 2 is monoclinic, of space group P2₁/c with a = 8.1800(5) Å, b = 14.344(8) Å, c = 14.809(9), β = 91.604(10)^∘, and V = 1736.7(18) ų with Z = 4 for d_calc = 1.653 g/cm³. In each complex the ligand functions as an arene and carbene, occupying four coordination sites. The two chlorines in each compound complete a distorted octahedron.     

Novel metallophthalocyanines bearing 3-(p-chlorophenyl)-5-p-tolyl-4H-1,2,4-triazole bulky substituents by microwave irradiation

The synthesis of metallophthalocyanines [6–9; M = Ni(II), Zn(II), Co(II) and Cu(II)] with four 1,2,4-triazole units obtained from 4-{(4-chloro-2-fluorobenzyl)[3-(4-chlorophenyl)-5-(4-methylphenyl)-4H-1,2,4-triazol-4-yl]amino}phthalonitrile (5) in the presence of dimethylaminoethanol and the corresponding anhydrous metal salts is described. The thermal stabilities of the Pc compounds were determined by thermogravimetric analysis. The new compounds were characterized by a combination of IR, ¹H NMR, ¹³C NMR, UV–Vis, elemental analysis.     

Regular expression constrained sequence alignment

We introduce regular expression constrained sequence alignment as the problem of finding the maximum alignment score between given strings $S_1$ and $S_2$ over all alignments such that in these alignments there exists a segment where some substring $s_1$ of $S_1$ is aligned to some substring $s_2$ of $S_2$, and both $s_1$ and $s_2$ match a given regular expression R, i.e. $s_1,s_2\in L(R)$ where $L(R)$ is the regular language described by R. For complexity results we assume, without loss of generality, that $n=|S_1|⩾|m|=|S_2|$. A motivation for the problem is that protein sequences can be aligned in a way that known motifs guide the alignments. We present an $\mathrm{O}(nmr)$ time algorithm for the regular expression constrained sequence alignment problem where $r=\mathrm{O}(t^4)$, and t is the number of states of a nondeterministic finite automaton N that accepts $L(R)$. We use in our algorithm a nondeterministic weighted finite automaton M that we construct from N. M has $\mathrm{O}(t^2)$ states where the transition-weights are obtained from the given costs of edit operations, and state-weights correspond to optimum alignment scores we compute using the underlying dynamic programming solution for sequence alignment. If we are given a deterministic finite automaton D accepting $L(R)$ with $t_d$ states then our construction creates a deterministic finite automaton $M_d$ with $t_d^2$ states. In this case, our algorithm takes $\mathrm{O}(t_d^{2}nm)$ time. Using $M_d$ results in faster computation than using M when $t_d<t^2$. If we only want to compute the optimum score, the space required by our algorithm is $\mathrm{O}(t^{2}n)$ ($\mathrm{O}(t_d^{2}m)$ if we use a given $M_d$). If we also want to compute an optimal alignment then our algorithm uses $\mathrm{O}(t^{2}m+t^2|s_1||s_2|)$ space ($\mathrm{O}(t_d^{2}m+t_d^2|s_1||s_2|)$ space if we use a given $M_d$) where $s_1$ and $s_2$ are substrings of $S_1$ and $S_2$, respectively, $s_1,s_2\in L(R)$, and $s_1$ and $s_2$ are aligned together in the optimal alignment that we construct. We also show that our method generalizes for the case of the problem with affine gap penalties, and for finding optimal regular expression constrained local sequence alignments.     

TRANSIENT SIMULATION OF INTERNAL SEPARATED FLOWS USING AN INTELLIGENT HIGHER-ORDER SPATIAL DISCRETIZATION SCHEME

This paper summarizes the method-of-lines (MOL) solution of the Navier–Stokes equations for an impulsively started incompressible laminar flow in a circular pipe with a sudden expansion. An intelligent higher-order spatial discretization scheme, which chooses upwind or downwind discretization in a zone-of-dependence manner when flow reversal occurs, was developed for separated flows. Stability characteristics of a linear advective–diffusive equation were examined to depict the necessity of such a scheme in the case of flow reversals. The proposed code was applied to predict the time development of an impulsively started flow in a pipe with a sudden expansion. Predictions were found to show the expected trends for both unsteady and steady states. This paper demonstrates the ease with which the Navier–Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs). Solutions of the Navier–Stokes equations in primitive variables formulation by using the MOL and intelligent higher-order spatial discretization scheme are not available to date. © 1997 by John Wiley & Sons, Ltd.     

Analytical stress analysis of partially plastic graded curved bars subjected to pure bending

An analytical model is developed to analyze stresses in functionally graded (FGM) curved bars under pure bending. Both elastic and partially plastic stress states are considered. The modulus of elasticity of the bar material is allowed to vary. While the model is outlined, important findings are mentioned. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient heating of a rotating elastic-plastic solid shaft

Based on Tresca's yield criterion and the flow rule associated with it, the transient plasticization in a rotating elastic–plastic solid shaft with temperature dependent yield stress subject to a temperature cycle is studied. Special attention is paid to the residual stresses. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of transition to turbulent flow and heat transfer inside a horizontal smooth rectangular duct under uniform bottom surface temperature

In this study, steady-state turbulent forced flow and heat transfer in a horizontal smooth rectangular duct both experimentally and numerically investigated. The study was carried out in the transition to turbulence region where Reynolds numbers range from 2,323 to 9,899. Flow is hydrodynamically and thermally developing (simultaneously developing flow) under uniform bottom surface temperature condition. A commercial CFD program Ansys Fluent 12.1 with different turbulent models was used to carry out the numerical study. Based on the present experimental data and three-dimensional numerical solutions, new engineering correlations were presented for the heat transfer and friction coefficients in the form of $ {\text{Nu}} = {\text{C}}_{2} {\text{Re}}^{{{\text{n}}_{ 1} }} $ and $ {\text{f}} = {\text{C}}_{3} {\text{Re}}^{{{\text{n}}_{3} }} $ , respectively. The results have shown that as the Reynolds number increases heat transfer coefficient increases but Darcy friction factor decreases. It is seen that there is a good agreement between the present experimental and numerical results. Examination of heat and mass transfer in rectangular cross-sectioned duct for different duct aspect ratio (α) was also carried out in this study. Average Nusselt number and average Darcy friction factor were expressed with graphics and correlations for different duct aspect ratios.     

Comparison of simulation methods for electronic structure calculations with experimental electron energy-loss spectra

The electronic structure of hexagonal GaN is studied using two simulation techniques in order to develop a method to interpret the fine-structure of an experimental nitrogen K-edge electron energy loss spectrum obtained using a scanning transmission electron microscope. The application of these simulation methods to the bulk spectrum is a necessary first step in developing a fundamental understanding of the effect of changes in the electronic structure on the properties of defects. It is found here that both of the techniques used, multiple scattering (MS) and density functional theory (DFT), produce excellent agreement with the experimental bulk spectrum. The MS method is limited in accuracy but efficient in time, while the DFT method is more accurate but time consuming. Through the combination of these methods, experimental energy loss spectra can be readily understood, and a means to unravel the complexities of the electronic structure can be determined.