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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries

We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) irredundant decompositions are characterized.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels

A group G is said to be rigid if it contains a normal series G = G{sub 1} > G{sub 2} > . . . > G{sub m} > G{sub m+1} = 1, whose quotients G{sub i}/G{sub i+1} are Abelian and, treated as right ℤ[G/G{sub i}]- modules, are torsion-free. A rigid group G is divisible if elements of the quotient G{sub i}/G{sub i+1} are divisible by nonzero elements of the ring ℤ[G/G{sub i}]. Every rigid group is embedded in a divisible one. Previously, it was stated that the theory 𝔗{sub m} of divisible m-rigid groups is complete. Here, it is proved that this theory is ω-stable. Furthermore, we describe saturated models, study elementary submodels of an arbitrary model, and find a representation for a countable saturated model in the form of a limit group in the Fraïssé system of all finitely generated m-rigid groups. Also, it is proved that the theory 𝔗{sub m} admits quantifier elimination down to a Boolean combination of ∀∃-formulas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Indecomposable p-Local Torsion-Free Groups with Quadratic and Cubic Splitting Fields

Indecomposable torsion-free p-local Abelian groups of finite rank with quadratic and cubic splitting field K are characterized. As a consequence, for groups with quadratic splitting field K it is proved that K-decomposable p-local torsion-free Abelian groups of finite rank are isomorphic if and only if their endomorphism rings are isomorphic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Quasi-Endomorphism Rings of Quasi-Decomposable Torsion-Free Abelian Groups of Rank 4 with a Strongly Indecomposable Quasi-Summand of Rank 2

We obtain a description of quasi-endomorphism rings of torsion-free Abelian groups G of rank 4 that are quasi-decomposable into a direct sum of groups A{sub 1} and A{sub 2} of rank 1 and a strongly indecomposable group B of rank 2 in the case where the quasi-homomorphism group ℚ ⨂ Hom(B,A{sub 2}) has rank 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components

We study the boundary values of conformal mappings of plane finitely connected domains. We present a complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Vector Bundles on P{sup 1}{sub ℤ} with Simple Jumps

Vector bundles of rank 2 on the projective line over ℤ are considered. It is assumed that such a bundle E is trivial on a generic fiber, and its restriction to any special fiber is isomorphic either to O{sup 2} or to O(−1)⊕O(1). Under these assumptions it is proved that an exact sequence of the form 0→O(−2) → E →O(2) → 0 exists.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Determinantal Range of Matrix Products

Let matrices A,C ∈ M{sub n} have eigenvalues α{sub 1}, . . ., α{sub n} and γ{sub 1}, . . . , γ{sub n}, respectively. The set of complex numbers D{sub C}(A) = {det(A−UCU*) : U ∈ M_n, U*U = I_n} is called the C-determinantal range of A. The paper studies various conditions under which the relation D{sub C}(R S) = D{sub C}(S R) holds for some matrices R and S.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Atomic Theory of Division and Intersection of Semiring Ideals

We consider two-sided ideals of semirings. More precisely, we study the theory of two-sided ideals in the signature consisting of the predicate symbol ⊆ and three function symbols that denote the intersection, right division, and left division of ideals. We prove the decidability of the set of those atomic formulas in this signature that are valid for all semirings and all valuations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On T-Amorphous Association Schemes

An association scheme is said to be T-amorphous if it is antisymmetric and any tournament obtained by an appropriate merging of its classes is doubly regular. The goal of this paper is to study basic properties of T-amorphous schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Cyclic codes over the ring F{sub 2}+uF{sub 2}+vF{sub 2}

In this paper, we study linear and cyclic codes over the ring F{sub 2}+uF{sub 2}+vF{sub 2}. The ring F{sub 2}+uF{sub 2}+vF{sub 2} is the smallest non-Frobenius ring. We characterize the structure of cyclic codes over the ring R=F{sub 2}+uF{sub 2}+vF{sub 2} using of the work Abualrub and Saip (Des Codes Cryptogr 42:273–287, 2007). We study the rank and dual of cyclic codes of odd length over this ring. Specially, we show that the equation |C||C{sup ⊥}|=|R|{sup n} does not hold in general for a cyclic code C of length n over this ring. We also obtain some optimal binary codes as the images of cyclic codes over the ring F{sub 2}+uF{sub 2}+vF{sub 2} under a Gray map, which maps Lee weights to Hamming weights. Finally, we give a condition for cyclic codes over R that contains its dual and find quantum codes over F{sub 2} from cyclic codes over the ring F{sub 2}+uF{sub 2}+vF{sub 2}.

97 MATHEMATICS AND COMPUTING↗