A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators
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97 MATHEMATICS AND COMPUTING↗
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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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Upstreamness and downstreamness in input–output analysis from local and aggregate information
Abstract Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in input–output (I–O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I–O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-1 approximation to the I–O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the world input–output database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I–O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytically tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Mean-field limit of a hybrid system for multi-lane multi-class traffic
This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with autonomous vehicles possibly influenced by external policymakers. First, a finite-dimensional hybrid system is developed based on the continuous Bando-Follow-the-Leader dynamics coupled with discrete events due to lane-change maneuvers. Then the mean-field limit of the finite-dimensional hybrid system is rigorously derived for the dynamics of the human-driven vehicles. The microscopic lane-change maneuvers of the human-driven vehicles generate a source term for the mean-field PDE. This leads to an infinite-dimensional hybrid system described by coupled Vlasov-type PDE, ODEs, and discrete events.
97 MATHEMATICS AND COMPUTING↗
Existence of multi-bump solutions for a class of Kirchhoff type problems in R{sup 3}
Using variational methods, we establish existence of multi-bump solutions for a class of Kirchhoff type problems −(a+b∫{sub R{sup 3}}|∇u|{sup 2}dx)Δu+λV(x)u=f(u), where f is a continuous function with subcritical growth, V(x) is a critical frequency in the sense that inf{sub x∈R{sup 3}}V(x)=0. We show that if the zero set of V(x) has several isolated connected components Ω{sub 1}, …, Ω{sub k} such that the interior of Ω{sub i} is not empty and ∂Ω{sub i} is smooth, then for λ > 0 large there exists, for any non-empty subset J ⊂ (1, …, k), a bump solution is trapped in a neighborhood of ∪{sub j∈J}Ω{sub j}.
97 MATHEMATICS AND COMPUTING↗
Supersymmetric quantum mechanics and Painlevé equations
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
97 MATHEMATICS AND COMPUTING↗
Certification and the potential energy landscape
Typically, there is no guarantee that a numerical approximation obtained using standard nonlinear equation solvers is indeed an actual solution, meaning that it lies in the quadratic convergence basin. Instead, it may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the corresponding stationary point when further optimization is attempted. In some cases, these non-solutions could be misleading. Proving that a numerical approximation will quadratically converge to a stationary point is termed certification. In this report, we provide details of how Smale's α-theory can be used to certify numerically obtained stationary points of a potential energy landscape, providing a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Isopermutation group
The concept of ‘Isotopy’ as formulated by Ruggero Maria Santilli [1, 2, 3] plays a vital role in the development of Iso mathematics. Santilli defined iso-fields of characteristic zero. In this paper we extend this definition to define Iso-Galois fields [4] which are essentially of non-zero characteristic. Isotopically isomorphic realizations of a group define isopermutation group which gives a clear cut distinction between automorphic groups and isotopic groups.
97 MATHEMATICS AND COMPUTING↗
New approach to information fusion for Lipschitz classifiers ensembles: Application in multi-channel C-OTDR-monitoring systems
This paper presents new results concerning selection of an optimal information fusion formula for an ensemble of Lipschitz classifiers. The goal of information fusion is to create an integral classificatory which could provide better generalization ability of the ensemble while achieving a practically acceptable level of effectiveness. The problem of information fusion is very relevant for data processing in multi-channel C-OTDR-monitoring systems. In this case we have to effectively classify targeted events which appear in the vicinity of the monitored object. Solution of this problem is based on usage of an ensemble of Lipschitz classifiers each of which corresponds to a respective channel. We suggest a brand new method for information fusion in case of ensemble of Lipschitz classifiers. This method is called “The Weighing of Inversely as Lipschitz Constants” (WILC). Results of WILC-method practical usage in multichannel C-OTDR monitoring systems are presented.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Generalizations of γ-open set in topological spaces
The main aim of this work is to study three generalized forms of γ-open set due to D. Andrijevic (D. Andrijevic, On the Topology Generated by pre-open sets, Presented at the Sixth Prague Topological Symposium, 39 (1987), 367-376)in a topological space. Out of which the dual appearance of one is the stronger form of b-locally closed set in the sense of Arafa A. Nasef (A. A Nasef,On b-locally closed sets and related topics, CHAOS SOLITONS & FRACTALS 12(2001) 1909-1915). Also, we introduce the concept of different types of continuity and study their basic properties by using these newly defined sets. Finally, we establish the interrelationships among themselves together with some already existing generalized forms of continuity.
97 MATHEMATICS AND COMPUTING↗
Metriplectic foundations of gyrokinetic Vlasov–Maxwell–Landau theory
Here, this Letter reports on a metriplectic formulation of a collisional, nonlinear full-f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Khovanov homology of graph-links
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
97 MATHEMATICS AND COMPUTING↗
Factorizations in finite groups
A necessary condition for uniqueness of factorizations of elements of a finite group G with factors belonging to a union of some conjugacy classes of G is given. This condition is sufficient if the number of factors belonging to each conjugacy class is big enough. The result is applied to the problem on the number of irreducible components of the Hurwitz space of degree d marked coverings of P{sup 1} with given Galois group G and fixed collection of local monodromies. Bibliography: 9 titles.
97 MATHEMATICS AND COMPUTING↗
Solution blow-up for a class of parabolic equations with double nonlinearity
We consider a class of parabolic-type equations with double nonlinearity and derive sufficient conditions for finite time blow-up of its solutions in a bounded domain under the homogeneous Dirichlet condition. To prove the solution blow-up we use a modification of Levine's method. Bibliography: 13 titles.
97 MATHEMATICS AND COMPUTING↗
Fano threefolds of large Fano index and large degree
We classify Q-Fano threefolds of Fano index >2 and sufficiently big degree. Bibliography: 20 titles.
97 MATHEMATICS AND COMPUTING↗
Existence of a Lipschitz selection of the Chebyshev-centre map
The paper is concerned with the existence of a Lipschitz selection for the operator T{sub C} (the Chebyshev-centre map) that assigns to any bounded subset M of a Banach space X the set T{sub C}(M) of its Chebyshev centres. It is proved that if the unit sphere S(X) of X has an exposed smooth point, then T{sub C} does not have a Lipschitz selection. It is also proved that if X is finite dimensional the operator T{sub C} has a Lipschitz selection if and only if X is polyhedral. The operator T{sub C} is also shown to have a Lipschitz selection in the space c{sub 0}(K) and c-spaces. Bibliography: 4 titles.
97 MATHEMATICS AND COMPUTING↗
On spectral synthesis on zero-dimensional Abelian groups
Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace H⊆C(G) is said to be an invariant subspace if it is invariant with respect to the translations τ{sub y}:f(x)↦f(x+y), y∈G. In the paper, it is proved that any invariant subspace H admits spectral synthesis, that is, H coincides with the closed linear span of the characters of G belonging to H. Bibliography: 25 titles.
97 MATHEMATICS AND COMPUTING↗
Spectral analysis of difference and differential operators in weighted spaces
This paper is concerned with describing the spectrum of the difference operator K:l{sub α}{sup p}(Z,X)→l{sub α}{sup p}(Z......athscrKx)(n)=Bx(n−1), n∈Z, x∈l{sub α}{sup p}(Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that K acts in the weighted space l{sub α}{sup p}(Z,X), 1≤p≤∞, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum σ(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles.
97 MATHEMATICS AND COMPUTING↗
Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation
We provide a complete list of real Lie algebras with generic orbits of dimension 2 in the coadjoint representation. Bibliography: 20 titles.
97 MATHEMATICS AND COMPUTING↗