On a new division algorithm

A method for digital division is described. In this method the reciprocal of the divisor is first determined approximately by a third order iterative equation. Each multiplication in this equation is then performed by the Quasi Serial Multiplier method. The reciprocal of the divisor, thus obtained is finally multiplied by the dividend, using the same method.     

Time-delayed feedback control optimization for quasi linear systems under random excitations

A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .     

Shock wave interaction with area changes in ducts

Whitham's approximation for handling shock wave propagation in area changes (reductions) in a duct was checked in comparison with a numerical solution. Also the Whitham approximation for shock wave propagation from a constant cross-sectional duct to a duct of a smaller cross-sectional area was studied and compared with a numerical solution. It was found that for modest incident shock Mach numbers and modest area reductions the Whitham approximation provided a fair solution for the shock Mach number and for the post-shock pressure. For higher shock Mach numbers and/or area reductions, large discrepancies exit between the approximate and exact solutions. A wider range of applicability of the Whitham approximation is found for the monotonical area reduction case; it is quite narrow for the passage of a shock wave from a wider to a narrower duct case. In addition, the effect of the extent of the area change region on the time required for reaching a quasi-steady flow was studied. It was shown that the longer the area change segment is, the longer it takes to reach a quasi-steady flow.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Differentiability of type-2 fuzzy number-valued functions

In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability of the type-2 fuzzy number-valued functions is derived. In addition, a parametric closed form of the perfect triangular quasi type-2 fuzzy numbers is introduced, and finally, the applicability and an approach to solving type-2 fuzzy differential equations are illustrated using some examples and cases.     

一类拟线性抛物方程组非负entropy解的不存在性

本文在有界正则域内研究了一类加权拟线性抛物方程组.由单个抛物方程相关的已知结论得到此类方程组的非负entropy解的正下界,然后利用一般的Picone恒等式并构造适当的检验函数,证明此类方程组的非负entropy解不存在.     

Rudin性质与拟Z-连续Domain

对一般子集系统 Z,引入了 Rudin性质,给出了它的映射式刻划,作为拟连续偏序集和Z-连续偏序集的公共推广,引入了拟Z-连续Domain的概念,讨论了拟Z-连续Domain的基本性质,特别地,给出了 Rudin性质及其映射式刻划在拟 Z-连续Domain方面的若干应用,将关于拟连续偏序集的主要结果推广至了拟 Z-连续 Domain情形。     

L-拟序集上的广义Alexandroff拓扑

在一类特殊的 L -拟序集上定义广义 Alexandroff拓扑 ,限制到通常的拟序集上就是 Alexandroff拓扑 ,并且该拓扑可以由其上的一族 Alexandroff拓扑取并得到。还证明任意一个拓扑空间的拓扑都可以表示为某个 L-拟序集上的广义 Alexandroff拓扑。     

"Quasi flexible" automatic docking processing for studying stereoselective recognition mechanisms, part 2: Prediction of DeltaDeltaG of complexation and 1H-NMR NOE correlation

The purpose of this work is to apply the global molecular interaction evaluation ("Glob-MolInE") computational protocol to the study of two molecular complexes characterized by a chiral selector and a couple of enantiomeric selectands experimentally known to give large difference in the free energy of complexation much higher than the experimental error normally associated to the molecular mechanic calculations. We have considered the well known diastereomeric complexes between the selector (S)-N-(3,5-dinitrobenzoyl)-leucine-n-propylamide (S)-1 and the selectands (R) or (S)-N-(2-naphthyl)-alanine methyl ester 2, widely studied by enantioselective HPLC, NMR and X-ray. The experimental difference of free energy of complexation between [(S)-1*(R)-2] and [(S)-1*(S)-2] (-1.34 kcal/mol) was reproduced by the new computational protocol with an excellent confidence error. Detailed results about the conformational search, the "quasi-flexible" docking and the thermodynamic estimation are presented in this work. A remarkable correlation between the theoretical results and experimental data (NOE measurements, X-ray crystallographic structure of the [(S)-1*(S)-2] complex and the free energy of complexation) supports the validity of the computational approach and underline the importance of the conformational multiplicity in the definition of the macroscopic properties of the complex in solution.     

Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

The finite analytic numerical method for 3D quasi‐Laplace equation with conductivity in full tensor form is constructed in this article. For cubic grid system, the gradient of the potential variable will diverge when tending to the common edge joining the four grids with different conductivities. However, the potential gradient along the tangential direction is of limited value. As a consequence, the 3D quasi‐Laplace equations will behave as a quasi‐2D one. An approximate analytical solution of the 3D quasi‐Laplace equation can be found around the common edge, which is expressed as a combination of a power‐law function and a linear function. With the help of this approximate analytical solution, a 3D finite analytical numerical scheme is then constructed. Numerical examples show that the proposed numerical scheme can provide rather accurate solutions only with or subdivisions. More important, the convergent speed of the numerical scheme is independent of the conductivity heterogeneity. In contrast, when using the traditional numerical schemes, typically such as the MPFA method, the refinement ratio for the grid cell needs to increase dramatically to get an accurate result for the strong heterogeneous case.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1475–1492, 2017     

A Novel Approach to Monitoring of the Diffusion Junction Potential in Speciation Studies by Polarography under very Acidic Conditions. Part II: The Quasi‐Reversible Cu(II)‐Picolinic Acid System

The use of polarography to accurately determine stability constants of complexes formed under very acidic conditions (below pH 2) is demonstrated. The diffusion junction potentials, which must be accounted for below pH 2, were evaluated by applying protocols developed where Tl(I) is used as an internal reference. The Cu(II)‐picolinic acid (2‐pyridinecarboxylic acid) system studied was chosen since the CuL⁺ species only exists in solution below pH 2 under the conditions used and literature data exists to confirm the accuracy of procedure. Additionally, the reduction of Cu(II) was quasi‐reversible and procedures to determine the reversible half‐wave potentials were investigated. Average log β values of 7.75±0.09 for CuL⁺ and 14.8±0.1 for CuL₂ were obtained, which compared well to literature data.