Search results for "basis"
showing 10 items of 760 documents
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
2015
The theory of HenstockâKurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.
Hepatitis B core particles as a universal display model: a structure-function basis for development
1999
AbstractBecause it exhibits a remarkable capability to accept mutational intervention and undergo correct folding and self-assembly in all viable prokaryotic and eukaryotic expression systems, hepatitis B core (HBc) protein has been favored over other proposed particulate carriers. Structurally, the unusual α-helical organization of HBc dimeric units allows introduction of foreign peptide sequences into several areas of HBc shells, including their most protruding spikes. Progress toward full resolution of the spatial structure as well as accumulation of chimeric HBc-based structures has brought closer the knowledge-based design of future vaccines, gene therapy tools and other artificial par…
Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene
1993
The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…
Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals
2021
In this contribution, we present the implementation of a second-order complete active space–self-consistent field (CASSCF) algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called norm-extended optimization, guarantees convergence of the optimization, but it involves the full Hessian and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance …
On Sets of Words of Rank Two
2019
Given a (finite or infinite) subset X of the free monoid A∗ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆ F∗. A submonoid M generated by k elements of A∗ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆ A∗ primitive if it is the basis of a |X|-maximal submonoid. This extends the notion of primitive word: indeed, w is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆ Y∗. The set Y is therefore called a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive …
On the Intrinsic Complexity of Learning
1995
AbstractA new view of learning is presented. The basis of this view is a natural notion of reduction. We prove completeness and relative difficulty results. An infinite hierarchy of intrinsically more and more difficult to learn concepts is presented. Our results indicate that the complexity notion captured by our new notion of reduction differs dramatically from the traditional studies of the complexity of the algorithms performing learning tasks.
Slow roll in simple non-canonical inflation
2007
17 pages, 4 figures.-- ISI Article Identifier: 000245945000008.-- ArXiv pre-print available at: http://arxiv.org/abs/astro-ph/0701343
ON THE DEFORMATION QUANTIZATION OF AFFINE ALGEBRAIC VARIETIES
2004
We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space.
Analytic result for the nonplanar hexa-box integrals.
2019
In this paper, we analytically compute all master integrals for one of the two non-planar integral families for five-particle massless scattering at two loops. We first derive an integral basis of 73 integrals with constant leading singularities. We then construct the system of differential equations satisfied by them, and find that it is in canonical form. The solution space is in agreement with a recent conjecture for the non-planar pentagon alphabet. We fix the boundary constants of the differential equations by exploiting constraints from the absence of unphysical singularities. The solution of the differential equations in the Euclidean region is expressed in terms of iterated integral…
Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
2018
We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by explicitly carrying out the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to a basis of 73 master integrals.