Linear Differential Equation for the Radial Distribution Function of Quantum Mechanics

1971 ◽  
Vol 54 (6) ◽  
pp. 2739-2741 ◽  
Author(s):  
M. D. Kostin
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Quantum Mechanics ◽  
Linear Differential Equation ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Linear Differential

scholarly journals On Radial Distribution of Julia Sets of Solutions to Certain Second Order Complex Linear Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guowei Zhang ◽  
Jian Wang ◽  
Lianzhong Yang
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Radial Distribution ◽  
Julia Set ◽  
Second Order ◽  
Order Complex ◽  
Entire Solutions ◽  
Deficient Value ◽  
Complex Linear ◽  
Linear Differential

We mainly investigate the radial distribution of the Julia set of entire solutions to a special second order complex linear differential equation, one of the entire coefficients of which has a finite deficient value.

The Influence of Hydrogen atoms on the Performance of Radial Distribution Function Based Descriptors in the Chemoinformatic Studies of HIV-1 Prote-ase Complexes with Inhibitors.

2020 ◽  
Vol 17 ◽  
Author(s):  
Jurica Novak ◽  
Maria A. Grishina ◽  
Vladimir A. Potemkin
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Current Model ◽  
Direct Interaction ◽  
Hydroxyl Group ◽  
Linear Regression Method ◽  
Hydrogen Atoms ◽  
Protease Enzyme ◽  
Hiv 1

: In this letter the newly introduced approach based on the radial distribution function (RDF) weighted by the number of va-lence shell electrons is applied for a series of HIV-1 protease enzyme and its complexes with inhibitors to evaluate the influ-ence of hydrogen atoms on the performance of the model. The multiple linear regression method was used for the selection of the relevant descriptors. Two groups of residues having dominant contribution to the RDF descriptor are identified as relevant for the inhibition. In the first group are residues like Arg8, Asp25, Thr26, Gly27 and Asp29, which establish direct interaction with the inhibitor, while the second group consists of the amino acids at the interface of the two homodimer sub-units or with the solvent. The crucial motif pointed out by our approach as the most important for inhibition of the enzyme’s activity and present in all inhibitors is hydroxyl group that establish hydrogen bond with Asp25 side chain. Additionally, the comparison to the model without hydrogen showed that both models are of similar quality, but the downside of the current model is the need for the determination of residues’ protonation states.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

scholarly journals Steady Motion of Ice Sheets

1980 ◽  
Vol 25 (92) ◽  
pp. 229-246 ◽  
Author(s):  
L. W. Morland ◽  
I. R. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Power Law ◽  
Perturbation Expansion ◽  
Ice Sheet ◽  
Leading Order ◽  
Plane Flow ◽  
General Law ◽  
Non Linear ◽  
Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

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