scholarly journals A Second-Order TV-Type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data

2016 ◽  
Vol 55 (3) ◽  
pp. 401-427 ◽  
Author(s):  
Ronny Bergmann ◽  
Andreas Weinmann
Keyword(s):  
Vector Space ◽  
Second Order ◽  
Higher Dimensional ◽  
Space Data

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

scholarly journals New gedanken experiment on higher-dimensional asymptotically AdS Reissner–Nordström black hole

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Ming Zhang ◽  
Jie Jiang
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Order Approximation ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Matter Field ◽  
Second Order ◽  
Field Perturbation ◽  
Higher Dimensional ◽  
Dynamical Quantity

AbstractViewing the negative cosmological constant as a dynamical quantity derived from the matter field, we study the weak cosmic censorship conjecture for the higher-dimensional asymptotically AdS Reissner–Nordström black hole. To this end, using the stability assumption of the matter field perturbation and the null energy condition of the matter field, we first derive the first-order and second-order perturbation inequalities containing the variable cosmological constant and its conjugate quantity for the black hole. We prove that the higher-dimensional RN-AdS black hole cannot be destroyed under a second-order approximation of the matter field perturbation process.

Linear Property of the Screw Surface of the Spatial RPRP Linkage

2005 ◽  
Vol 128 (3) ◽  
pp. 581-586 ◽  
Author(s):  
Chintien Huang ◽  
Han-Tsung Tu
Keyword(s):  
Vector Space ◽  
Ruled Surface ◽  
Second Order ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Reference Position ◽  
Finite Displacements ◽  
Screw Surface ◽  
Intersection Operation ◽  
Linear Property

This paper investigates the screw surface of the RPRP linkage, an overconstrained linkage with mobility one. The screw surface is a ruled surface containing screws for displacing the coupler of the RPRP linkage from one reference position to all reachable positions. In this paper, two types of RPRP linkages, in folded and unfolded forms, are constructed by using hexahedrons in accordance with Delassus’ criteria. It is shown that the screw surfaces of both types of RPRP linkages can be represented by screw systems of the second order. These novel finite screw systems are obtained by intersecting two 3-systems corresponding to the finite displacements of the RP and PR dyads. The intersection of finite screw systems is conducted by employing the intersection operation of vector subspaces of the six-dimensional vector space.

scholarly journals A COMPARISON OF ONE- AND TWO-SIDED KRYLOV–ARNOLDI PROJECTION METHODS FOR FULLY COUPLED, DAMPED STRUCTURAL-ACOUSTIC ANALYSIS

2013 ◽  
Vol 21 (02) ◽  
pp. 1350004 ◽  
Author(s):  
R. SRINIVASAN PURI ◽  
DENISE MORREY
Keyword(s):  
Coupled System ◽  
Dimensional Subspace ◽  
Second Order ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Frequency Moments ◽  
Arnoldi Algorithm ◽  
Higher Dimensional ◽  
Fully Coupled

The two-sided second-order Arnoldi algorithm is used to generate a reduced order model of two test cases of fully coupled, acoustic interior cavities, backed by flexible structural systems with damping. The reduced order model is obtained by applying a Galerkin–Petrov projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving the low frequency moments of the coupled system. The basis vectors for projection are computed efficiently using a two-sided second-order Arnoldi algorithm, which generates an orthogonal basis for the second-order Krylov subspace containing moments of the original higher dimensional system. The first model is an ABAQUS benchmark problem: a 2D, point loaded, water filled cavity. The second model is a cylindrical air-filled cavity, with clamped ends and a load normal to its curved surface. The computational efficiency, error and convergence are analyzed, and the two-sided second-order Arnoldi method shows better efficiency and performance than the one-sided Arnoldi technique, whilst also preserving the second-order structure of the original problem.

Periodic solutions of higher-dimensional discrete systems

2004 ◽  
Vol 134 (5) ◽  
pp. 1013-1022 ◽  
Author(s):  
Zhan Zhou ◽  
Jianshe Yu ◽  
Zhiming Guo
Keyword(s):  
Positive Integer ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Second Order ◽  
Higher Dimensional ◽  
Image Position

Consider the second-order discrete system where f ∈ C (R × Rm, Rm), f(t + M, Z) = f(t, Z) for any (t, Z) ∈ R × Rm and M is a positive integer. By making use of critical-point theory, the existence of M-periodic solutions of (*) is obtained.

scholarly journals The Manin constant in the semistable case

2018 ◽  
Vol 154 (9) ◽  
pp. 1889-1920 ◽  
Author(s):  
Kęstutis Česnavičius
Keyword(s):  
Vector Space ◽  
Elliptic Curve ◽  
Abelian Varieties ◽  
Higher Dimensional ◽  
Special Cases ◽  
Modular Parametrization ◽  
De Rham ◽  
Neron Models ◽  
General Relations ◽  
Néron Models

For an optimal modular parametrization $J_{0}(n){\twoheadrightarrow}E$ of an elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$, Manin conjectured the agreement of two natural $\mathbb{Z}$-lattices in the $\mathbb{Q}$-vector space $H^{0}(E,\unicode[STIX]{x1D6FA}^{1})$. Multiple authors generalized his conjecture to higher-dimensional newform quotients. We prove the Manin conjecture for semistable $E$, give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral $p$-adic étale and de Rham cohomologies of abelian varieties over $p$-adic fields and exhibit a new exactness result for Néron models.

scholarly journals Higher Dimensional Automata

2002 ◽  
Vol 9 (44) ◽  
Author(s):  
Zoltán Ésik ◽  
Zoltán L. Németh
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Dimensional Theory ◽  
Higher Dimensional ◽  
Second Order Logic ◽  
Rational Sets ◽  
Monadic Second Order Logic

We provide the basics of a 2-dimensional theory of automata on series-parallel biposets. We define recognizable, regular and rational sets of series-parallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.

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