scholarly journals About almost geodesic curves

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1013-1018 ◽  
Author(s):  
Olga Belova ◽  
Josef Mikes ◽  
Karl Strambach
Keyword(s):  
Affine Connection ◽  
Algebraic Torus ◽  
Constant Coefficients

We determine in Rn the form of curves C for which also any image under an (n-1)-dimensional algebraic torus is an almost geodesic with respect to an affine connection ? with constant coefficients and calculate the components of ?.

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

scholarly journals Coarse cohomology with twisted coefficients

2020 ◽  
Vol 70 (6) ◽  
pp. 1413-1444
Author(s):  
Elisa Hartmann
Keyword(s):  
Sheaf Cohomology ◽  
Grothendieck Topology ◽  
Coarse Structure ◽  
Relative Cohomology ◽  
Number Of Ends ◽  
Constant Coefficients ◽  
Coarse Space ◽  
Grothendieck Topologies

AbstractTo a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on coarse spaces. We obtain that sheaf cohomology is a functor on the coarse category: if two coarse maps are close they induce the same map in cohomology. There is a coarse version of a Mayer-Vietoris sequence and for every inclusion of coarse spaces there is a coarse version of relative cohomology. Cohomology with constant coefficients can be computed using the number of ends of a coarse space.

scholarly journals Note on some representations of general solutions to homogeneous linear difference equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Stevo Stević ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Fibonacci Sequence ◽  
Linear Difference Equation ◽  
Linear Difference Equations ◽  
Second Order Difference Equation ◽  
Constant Coefficients ◽  
Order Difference Equation ◽  
Homogeneous Linear

Abstract It is known that every solution to the second-order difference equation $x_{n}=x_{n-1}+x_{n-2}=0$ x n = x n − 1 + x n − 2 = 0 , $n\ge 2$ n ≥ 2 , can be written in the following form $x_{n}=x_{0}f_{n-1}+x_{1}f_{n}$ x n = x 0 f n − 1 + x 1 f n , where $f_{n}$ f n is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally.

scholarly journals Adaptive Control Structure with Neural Data Processing Applied for Electrical Drive with Elastic Shaft

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3389
Author(s):  
Marcin Kamiński ◽  
Krzysztof Szabat
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Dynamic Properties ◽  
Experimental Studies ◽  
Drive System ◽  
Particle Swarm Optimizer ◽  
The Neural Network ◽  
Control Concept ◽  
Constant Coefficients ◽  
Selection Of

This paper presents issues related to the adaptive control of the drive system with an elastic clutch connecting the main motor and the load machine. Firstly, the problems and the main algorithms often implemented for the mentioned object are analyzed. Then, the control concept based on the RNN (recurrent neural network) for the drive system with the flexible coupling is thoroughly described. For this purpose, an adaptive model inspired by the Elman model is selected, which is related to internal feedback in the neural network. The indicated feature improves the processing of dynamic signals. During the design process, for the selection of constant coefficients of the controller, the PSO (particle swarm optimizer) is applied. Moreover, in order to obtain better dynamic properties and improve work in real conditions, one model based on the ADALINE (adaptive linear neuron) is introduced into the structure. Details of the algorithm used for the weights’ adaptation are presented (including stability analysis) to perform the shaft torque signal filtering. The effectiveness of the proposed approach is examined through simulation and experimental studies.

scholarly journals LAURENT POLYNOMIAL LANDAU–GINZBURG MODELS FOR COMINUSCULE HOMOGENEOUS SPACES

2021 ◽  
Author(s):  
PETER SPACEK
Keyword(s):  
Homogeneous Space ◽  
Homogeneous Spaces ◽  
Laurent Polynomial ◽  
Complete Intersections ◽  
Laurent Polynomials ◽  
Young Diagrams ◽  
Similar Shape ◽  
Algebraic Torus ◽  
The One ◽  
Polynomial Potentials

AbstractIn this article we construct Laurent polynomial Landau–Ginzburg models for cominuscule homogeneous spaces. These Laurent polynomial potentials are defined on a particular algebraic torus inside the Lie-theoretic mirror model constructed for arbitrary homogeneous spaces in [Rie08]. The Laurent polynomial takes a similar shape to the one given in [Giv96] for projective complete intersections, i.e., it is the sum of the toric coordinates plus a quantum term. We also give a general enumeration method for the summands in the quantum term of the potential in terms of the quiver introduced in [CMP08], associated to the Langlands dual homogeneous space. This enumeration method generalizes the use of Young diagrams for Grassmannians and Lagrangian Grassmannians and can be defined type-independently. The obtained Laurent polynomials coincide with the results obtained so far in [PRW16] and [PR13] for quadrics and Lagrangian Grassmannians. We also obtain new Laurent polynomial Landau–Ginzburg models for orthogonal Grassmannians, the Cayley plane and the Freudenthal variety.

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