Search results for "Linear subspace"

showing 10 items of 65 documents

Communication: multireference equation of motion coupled cluster: a transform and diagonalize approach to electronic structure.

2014

The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective…

010304 chemical physicsChemistryGeneral Physics and AstronomyEquations of motionElectronic structure010402 general chemistry7. Clean energy01 natural sciencesLinear subspace0104 chemical sciencessymbols.namesakeCoupled clusterAtomic orbitalQuantum mechanics0103 physical sciencessymbolsComplete active spacePhysical and Theoretical ChemistryHamiltonian (quantum mechanics)Subspace topologyThe Journal of chemical physics
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Infinitesimal deformations of double covers of smooth algebraic varieties

2003

The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi--Yau threefolds which are non--singular models of do…

14B07; 14J3014J30Direct sum14B07General MathematicsInfinitesimalMathematical analysisAlgebraic varietySymbolic computationLinear subspaceequisingular deformationsMathematics - Algebraic GeometryMathematics::Algebraic GeometryFOS: MathematicsProjective spaceGravitational singularityLocus (mathematics)Algebraic Geometry (math.AG)double coveringsMathematics
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Variations of selective separability II: Discrete sets and the influence of convergence and maximality

2012

A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …

54D65 54A25 54D55 54A20H-separable spaceSubmaximalD+-separable spaceSequential spaceFUNCTION-SPACESSeparable spaceSpace (mathematics)INVARIANTSSeparable spaceCombinatoricsGN-separable spaceStrong fan tightnessM-separable spaceMaximal spaceConvergence (routing)Radial spaceFOS: MathematicsFréchet spaceCountable setStratifiable spaceWhyburn propertyTOPOLOGIESDH+-separable spaceTightnessMathematics - General TopologyMathematicsDH-separable spaceD-separable spaceSequenceExtra-resolvable spaceGeneral Topology (math.GN)Hausdorff spaceResolvableR-separable spaceLinear subspaceResolvable spaceSequentialDiscretely generated spaceSubmaximal spaceGeometry and TopologyTOPOLOGIES; FUNCTION-SPACES; INVARIANTSSS+ spaceFan tightnessCrowded spaceSubspace topologyTopology and its Applications
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Gabor systems and almost periodic functions

2017

Abstract Inspired by results of Kim and Ron, given a Gabor frame in L 2 ( R ) , we determine a non-countable generalized frame for the non-separable space AP 2 ( R ) of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of AP 2 ( R ) are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.

Almost periodic functionApplied Mathematics010102 general mathematicsAlmost-periodic functions010103 numerical & computational mathematicsGabor frame01 natural sciencesLinear subspaceFunctional Analysis (math.FA)Separable spaceCombinatoricsMathematics - Functional AnalysisFramesNorm (mathematics)42C40 42C15 42A75FOS: MathematicsAP-framesCountable set0101 mathematicsGabor systemsMathematicsAlmost-periodic functions; AP-frames; Frames; Gabor systems; Applied Mathematics
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Internal fe approximation of spaces of divergence-free functions in three-dimensional domains

1986

SUMMARY The space of divergence-free vector functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements having the same property. An easy way of generating basis functions in these subspaces is shown.

Applied MathematicsMechanical EngineeringMathematical analysisComputational MechanicsFluxBoundary (topology)Basis functionSpace (mathematics)Linear subspaceFinite element methodComputer Science ApplicationsMechanics of MaterialsDivergence (statistics)Vector-valued functionMathematicsInternational Journal for Numerical Methods in Fluids
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Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit

2017

In the present letter, it is demonstrated how full configuration interaction (FCI) results in extended basis sets may be obtained to within sub-kJ/mol accuracy by decomposing the energy in terms of many-body expansions in the virtual orbitals of the molecular system at hand. This extension of the FCI application range lends itself to two unique features of the current approach, namely that the total energy calculation can be performed entirely within considerably reduced orbital subspaces and may be so by means of embarrassingly parallel programming. Facilitated by a rigorous and methodical screening protocol and further aided by expansion points different from the Hartree-Fock solution, al…

Chemical Physics (physics.chem-ph)Physics010304 chemical physicsBasis (linear algebra)Embarrassingly parallelFOS: Physical sciences010402 general chemistry01 natural sciencesFull configuration interactionLinear subspace0104 chemical sciencesRange (mathematics)Atomic orbitalComputational chemistryPhysics - Chemical Physics0103 physical sciencesGeneral Materials ScienceLimit (mathematics)Statistical physicsPhysical and Theoretical ChemistryEnergy (signal processing)
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Distributed Pseudo-Gossip Algorithm and Finite-Length Computational Codes for Efficient In-Network Subspace Projection

2013

In this paper, we design a practical power-efficient algorithm for Wireless Sensor Networks (WSN) in order to obtain, in a distributed manner, the projection of an observed sampled spatial field on a subspace of lower dimension. This is an important problem that is motivated in various applications where there are well defined subspaces of interest (e.g., spectral maps in cognitive radios). As opposed to traditional Gossip Algorithms used for subspace projection, where separation of channel coding and computation is assumed, our algorithm combines binary finite-length Computational Coding and a novel gossip-like protocol with certain communication rules, achieving important savings in conve…

Cognitive radioTheoretical computer scienceComputationSignal ProcessingBinary numberEnergy consumptionElectrical and Electronic EngineeringLinear subspaceWireless sensor networkAlgorithmSubspace topologyMathematicsCoding (social sciences)IEEE Journal of Selected Topics in Signal Processing
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Baer cones in finite projective spaces

1987

Let R and V be two skew subspaces with dimensions r and v of P=PG(d,q). If q is a square, then there is a Baer subspace V* of V, i.e. a subspace of dimension v and order √q. We call the set C(R,V*)=\(\mathop \cup \limits_p \), where the union is taken over all PeV*, aBaer cone oftype (r,v).

CombinatoricsAlgebraDimension (vector space)Cone (topology)Projective spaceOrder (ring theory)Geometry and TopologyLinear subspaceSubspace topologySquare (algebra)MathematicsJournal of Geometry
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On Banaschewski functions in lattices

1991

hold for all x, y ~ X. We call such a function z a Banaschewski function or a B-function on X. A lattice L is a B-lattice or antitonely complemented, if there is a B-function defined on the whole lattice L. For instance, Boolean lattices as well as orthocomplemented lattices are B-lattices. On the other hand, a B-lattice is not necessarily Boolean or orthocomplemented, although a distributive B-lattice is a Boolean lattice. It is shown later that a matroid (geometric) lattice is also a B-lattice. Naturally, our results include the lemma of Banaschewski [ 1, Lemma 4], by which the lattice of the subspaces of a vector space is a B-lattice. It should be emphasized that a B-function is supposed…

CombinatoricsLemma (mathematics)Algebra and Number TheoryDistributive propertyHigh Energy Physics::LatticeLattice (order)Order (group theory)Function (mathematics)Linear subspaceMatroidVector spaceMathematicsAlgebra Universalis
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Operators on PIP-Spaces and Indexed PIP-Spaces

2009

As already mentioned, the basic idea of pip-spaces is that vectors should not be considered individually, but only in terms of the subspaces V r (r Є F), the building blocks of the structure. Correspondingly, an operator on a pipspace should be defined in terms of assaying subspaces only, with the proviso that only continuous or bounded operators are allowed. Thus an operator is a coherent collection of continuous operators. We recall that in a nondegenerate pip-space, every assaying subspace V r carries its Mackey topology \(\tau (V_r , V \bar{r})\) and thus its dual is \(V \bar{r}\). This applies in particular to \(V^{\#}\) and V itself. For simplicity, a continuous linear map between two…

CombinatoricsLinear mapsymbols.namesakeOperator (computer programming)Unitary representationBounded functionHilbert spacesymbolsProduct topologyLinear subspaceMathematicsMackey topology
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