On a bicomplex induced by the variational sequence

2015 ◽  
Vol 12 (05) ◽  
pp. 1550057 ◽  
Author(s):  
Demeter Krupka ◽  
Giovanni Moreno ◽  
Zbyněk Urban ◽  
Jana Volná
Keyword(s):  
Finite Order ◽  
Infinite Order ◽  
Differential Forms ◽  
One Dimensional ◽  
Variational Sequence ◽  
Fibered Manifolds ◽  
Derivatives Of

The construction of a finite-order bicomplex whose morphisms are the horizontal and vertical derivatives of differential forms on finite-order jet prolongations of fibered manifolds over one-dimensional bases is presented. In particular, relationship between the morphisms and classes entering the variational sequence and the associated finite-order bicomplex is studied. Properties of classes entering the infinite-order bicomplex, induced from the finite-order variational sequences by means of an infinite canonical construction, are formulated as a remark, insisting further research.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

The combined effect of lattice’s uniaxial strains and electron–phonon interaction’s screening on TBEC of the intersite bipolarons

2016 ◽  
Vol 30 (26) ◽  
pp. 1650186
Author(s):  
B. Yavidov ◽  
SH. Djumanov ◽  
T. Saparbaev ◽  
O. Ganiyev ◽  
S. Zholdassova ◽  
...  
Keyword(s):  
Ideal Gas ◽  
Einstein Condensation ◽  
Chain Model ◽  
One Dimensional ◽  
Electron Phonon Interaction ◽  
Model Lattice ◽  
Experimental Values ◽  
Bose Einstein ◽  
Derivatives Of ◽  
The Ideal

Having accepted a more generalized form for density-displacement type electron–phonon interaction (EPI) force we studied the simultaneous effect of uniaxial strains and EPI’s screening on the temperature of Bose–Einstein condensation [Formula: see text] of the ideal gas of intersite bipolarons. [Formula: see text] of the ideal gas of intersite bipolarons is calculated as a function of both strain and screening radius for a one-dimensional chain model of cuprates within the framework of Extended Holstein–Hubbard model. It is shown that the chain model lattice comprises the essential features of cuprates regarding of strain and screening effects on transition temperature [Formula: see text] of superconductivity. The obtained values of strain derivatives of [Formula: see text] [Formula: see text] are in qualitative agreement with the experimental values of [Formula: see text] [Formula: see text] of La[Formula: see text]Sr[Formula: see text]CuO4 under moderate screening regimes.

Representation of the Variational Sequence by Differential Forms

2005 ◽  
Vol 88 (2) ◽  
pp. 177-199 ◽  
Author(s):  
Michael Krbek ◽  
Jana Musilová
Keyword(s):  
Differential Forms ◽  
Variational Sequence

On the question of whether f″+ e−zf′ + B(z)f = 0 can admit a solution f ≢ 0 of finite order

1986 ◽  
Vol 102 (1-2) ◽  
pp. 9-17 ◽  
Author(s):  
Gary G. Gundersen
Keyword(s):  
Entire Function ◽  
Finite Order ◽  
Infinite Order ◽  
Independent Interest ◽  
Partial Result ◽  
Transcendental Entire Function ◽  
Degree Polynomial ◽  
Odd Degree ◽  
Polynomial Of Odd Degree

SynopsisWe show that if B(z) is either (i) a transcendental entire function with order (B)≠1, or (ii) a polynomial of odd degree, then every solution f≠0 to the equation f″ + e−zf′ + B(z)f = 0 has infinite order. We obtain a partial result in the case when B(z) is an even degree polynomial. Our method of proof and lemmas for case (i) of the above result have independent interest.

Velocity Computation from Measures of Spatiotemporal Gradients at Multiple Orientations

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 77-77 ◽  
Author(s):  
A Johnston ◽  
P W McOwan
Keyword(s):  
Natural Extension ◽  
Image Brightness ◽  
Motion Patterns ◽  
One Dimensional ◽  
Aperture Problem ◽  
Motion Models ◽  
Temporal Domain ◽  
Moving Stimulus ◽  
Zero Values ◽  
Derivatives Of

Current models of speed and direction of motion which use measures of spatiotemporal gradients can suffer from ill-conditioning. This problem arises either because local measures of the derivatives of image brightness take zero values or because the motion equations cannot be solved for one-dimensional (1-D) signals in two-dimensional (2-D) images—the aperture problem. One way around this predicament is to select image points or introduce constants to deal with ill-conditioned calculations. Here we describe an analytic method that combines measures of speed in a range of directions to provide a well-conditioned measure of velocity at all points in the moving stimulus. This approach is a natural extension of a one-dimensional model which has been successful in predicting perceived motion in a variety of 1-D spatiotemporal motion patterns (Johnston, McOwan and Buxton 1992 Proceedings of the Royal Society of London, Series B250 297 – 306). Speed is computed with the use of biologically plausible filters that are derivatives of Gaussians in the spatial domain and log Gaussians in the temporal domain. Measures of speed and inverse speed are computed for a range of orientations consistent with the number of direction columns in MT/V5. The pattern of velocities measured over this set of orientations is then used to recover the speed and direction of motion of the stimulus. The model can correctly compute the velocity of moving 1-D patterns, such as gratings, patterns that prove a problem for many current 2-D motion models as they form degenerate cases, as well as the motion of rigid 2-D patterns.

Modified Unsplitted Perfectly Matched Layer Absorbing Boundary Conditions for Truncating Anisotropic Medium

2014 ◽  
Vol 900 ◽  
pp. 386-389
Author(s):  
Zhi Chao Cai ◽  
Li Xia Yang ◽  
Hao Chuan Deng ◽  
Xiao Wei ◽  
Hong Cheng Yin
Keyword(s):  
Boundary Conditions ◽  
Anisotropic Medium ◽  
Electromagnetic Wave Propagation ◽  
Simulation Analysis ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Derivatives Of ◽  
Difference Time

To simulate Electromagnetic wave propagation in anisotropic media, absorbing boundary conditions are needed to truncate the computation domains. Based on the finite difference time domain method in anisotropic medium, the implementation of the modified nearly perfectly matched layer absorbing boundary conditions for truncating anisotropic medium is presented. By using the partial derivatives of space variables stretched-scheme in the coordinate system, the programming complexity is reduced greatly. According to one dimensional numerical simulation analysis, the modified nearly perfectly matched layer absorbing boundary condition is validated.

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

The Poincaré-Cartan forms of one-dimensional variational integrals

2020 ◽  
Vol 70 (6) ◽  
pp. 1381-1412
Author(s):  
Veronika Chrastinová ◽  
Václav Tryhuk
Keyword(s):  
Differential Equations ◽  
Variational Problem ◽  
Ordinary Differential Equations ◽  
Differential Forms ◽  
Point Of View ◽  
Full Generality ◽  
One Dimensional ◽  
Variational Integrals

AbstractFundamental concepts for variational integrals evaluated on the solutions of a system of ordinary differential equations are revised. The variations, stationarity, extremals and especially the Poincaré-Cartan differential forms are relieved of all additional structures and subject to the equivalences and symmetries in the widest possible sense. Theory of the classical Lagrange variational problem eventually appears in full generality. It is presented from the differential forms point of view and does not require any intricate geometry.

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