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Basis Set Functions
In this chapter, we discuss the basis set functions for standard molecular quantum mechanics calculations. Furthermore, the basis sets for quantum...
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The impact of spectral basis set composition on estimated levels of cingulate glutamate and its associations with different personality traits
Background1 H-MRS is increasingly used in basic and clinical research to explain brain function and alterations respectively. In psychosis research...
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The Basis Pursuit as a Set Selector
Success in the solution of under-constrained problems where sparsity is an appropriate regularization is typically judged by comparing the solution...
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Automatic purpose-driven basis set truncation for time-dependent Hartree–Fock and density-functional theory
Real-time time-dependent density-functional theory (RT-TDDFT) and linear response time-dependent density-functional theory (LR-TDDFT) are two...
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Basis Set Superposition Error: Effects of the Boys‒Bernardi Correction on the DFT Modeling of Hydrogen Sorption on Low-Dimensional Carbon Nanomaterials
AbstractDFT modeling of hydrogen sorption on graphene and C 2 N monolayers using the SIESTA and VASP packages demonstrates the need for optimizing the...
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A complete set of the dimension-8 Green’s basis operators in the Standard Model effective field theory
We present a complete and independent off-shell Green’s basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We...
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The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics
AbstractUsing an example of Pearson type IV distributions, we propose a procedure of completing the classical probability distribution to a quantum...
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The effect of the electronic structure method and basis set on the accuracy of the electric multipoles computed with the distributed multipole analysis (DMA)
ContextAn accurate description of the molecular charge density is crucial for investigating intra- and inter-molecular properties. Among the...
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Rough-Set-Base Data Analysis: Theoretical Basis and Applications
Rough set theory, originally proposed by Z. Pawlak, provides a mathematical basis of set-based approximation of concepts and logical data analysis....
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On the Raleigh–Ritz variational method. Non-orthogonal basis set
We overview the main equations of the Rayleigh–Ritz variational method and discuss their connection with the problem of simultaneous diagonalization...
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Problems of Choosing a Basis Set for Quantum-Chemical Modeling of Samarium-Containing Model Systems
Abstract —The main problems that appear in the quantum-chemical modeling of complex lanthanide (Ln) ions are considered. The main difficulty is the...
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Stress-based topology optimization with the parameterized level-set method based on radial basis functions
Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for stress...
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A Training Set Subsampling Strategy for the Reduced Basis Method
We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline...
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On Active-Set LP Algorithms Allowing Basis Deficiency
An interesting phenomenon in linear programming (LP) is how to deal with solutions in which the number of nonzero variables is less than the number...
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A coupled meshless element-free Galerkin and radial basis functions method for level set-based topology optimization
This paper presents a meshless element-free Galerkin method coupled with the radial basis functions (RBFs)-based level set algorithm for topology...
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Basis, Basis Vectors, and Inner Product
We begin this chapter with a romantic story to familiarize ourselves with the basis vectors and bra–ket notation. Then we will have an in-depth...
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Flexibilities of Wavelets as a Computational Basis Set for Large-Scale Electronic Structure Calculations
The BigDFT project started in 2005 with the aim of testing the advantages of using a Daubechies wavelet basis set for Kohn–Sham density functional...
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Amplitude basis for conformal correlators
We present a classification of conformally-invariant three-point tensor structures in d dimensions that parallels the classification of...