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Rajendra Bhatia has made remarkable contributions to Mathematics research and teaching, and to growth of Mathematics in India. He has been honored with various awards including the Medal for Young Sci...
Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Electronic structure Kohn–Sham density functional theory Discontinuous Galerkin Adaptive local basis set Enrichment functions Eigenvalue problem
2015/7/14
Kohn–Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn–Sham Hamiltonian generally result...
Optimized local basis set for Kohn–Sham density functional theory
Electronic structure Kohn–Sham density functional theory Optimized local basis set Discontinuous Galerkin Trace minimization Molecular dynamics Pulay force GMRES Preconditioning
2015/7/14
We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local ...
Element orbitals for Kohn-Sham density functional theory
Element orbitals Kohn-Sham density functional theory
2015/7/14
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as plane wa...
A Functional Approach to FBSDEs and Its Application in Optimal Portfolios
FBSDEs Optimal Portfolios
2010/11/23
In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability s...
On the second inner variation of the Allen-Cahn Functional and its applications
Allen-Cahn functional second variation Morse index stability
2010/12/14
In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only a...
Permanence and periodic solution for a predator-prey model with mixed-type functional response
Predator-prey model mixed-type functional response
2010/9/14
In this paper, a predator-prey model with mixed-type functional response is investigated. Sufficient conditions are derived that guarantee the permanence of the system. Meanwhile, when the system is p...
Solving some functional and operational equations
functional equations functions of a real variable decreasing functions with interesting properties vis-a-vis to primes operational equations related to convex operators
2009/1/5
In the present work we recall some improved versions of some
general results ¯rst published in [14], concerning the functional equation
g = g ± f (g is a given function or operator, f being the...
In this paper we extend some statistical techniques of MANOVA, where the data are vectors in Rd, to the case where the observations are real functions.
Periodic solutions for a predator-prey system with dispersal and semi-ratio-dependent functional response
functional response periodic solution dispersal coincidence
2010/9/10
By using a continuation theorem of Mawhin’s coincidence degree , studied a periodic predator-prey system with dispersal and semi-ratiofunctional response, sufficient conditions are obtained for the ex...
A stage-structure predator-prey model with functional response
immature mature functional response Hamiltonian
2010/9/10
In this paper, a class of two species predator-prey model with functional response and harvesting, we consider a stage-structured population model with two life stages, immature and mature; and assume...
A Functional Inequality for the Survival Function of the Gamma Distribution
Error function Incomplete gamma function Density function Survival function Complete monotonicity
2008/7/3
In this note we give a completely different proof to a functional inequality established by Ismail and Laforgia for the survival function of the gamma distribution and we show that the inequality in t...
A Simultaneous System of Functional Inequalities and Mappings which are Weakly of a Constant Sign
Linear functional inequalities Kronecker's theorem Mappings of weakly constant sign
2008/7/3
A Simultaneous System of Functional Inequalities and Mappings which are Weakly of a Constant Sign.
A Stability of the Generalized Sine Functional Equations, II
Stability Superstability Functional equation Functional equality Sine functional equation
2008/7/3
A Stability of the Generalized Sine Functional Equations, II.
An Example of a Stable Functional Equation When the Hyers Method Does Not Work
Cauchy's functional equation Stability Hyers iteration
2008/7/3
An Example of a Stable Functional Equation When the Hyers Method Does Not Work.