Weyl asymptotics for perturbed functional difference operators

2019 ◽  
Vol 60 (10) ◽  
pp. 103505
Author(s):  
Ari Laptev ◽  
Lukas Schimmer ◽  
Leon A. Takhtajan
Keyword(s):  
Difference Operators ◽  
Functional Difference ◽  
Weyl Asymptotics

scholarly journals A Sharp Lieb-Thirring Inequality for Functional Difference Operators

2021 ◽  
Author(s):  
Ari Laptev ◽  
◽  
Lukas Schimmer ◽  
Keyword(s):  
Essential Spectrum ◽  
Resonance State ◽  
Difference Operators ◽  
Functional Difference ◽  
One Dimensional

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators is a resonance state.

scholarly journals Force Generation on the Hallux Is More Affected by the Ankle Joint Angle than the Lesser Toes: An In Vivo Human Study

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 48
Author(s):  
Junya Saeki ◽  
Soichiro Iwanuma ◽  
Suguru Torii
Keyword(s):  
Repeated Measures ◽  
Joint Angle ◽  
Plantar Flexion ◽  
Human Study ◽  
Force Generation ◽  
Functional Difference ◽  
Multiple Comparison Test ◽  
The Difference ◽  
Metatarsophalangeal Joints

The structure of the first toe is independent of that of the other toes, while the functional difference remains unclear. The purpose of this study was to investigate the difference in the force generation characteristics between the plantar-flexion of the first and second–fifth metatarsophalangeal joints (MTPJs) by comparing the maximal voluntary plantar-flexion torques (MVC torque) at different MTPJs and ankle positions. The MVC torques of the first and second–fifth MTPJs were measured at 0°, 15°, 30°, and 45° dorsiflexed positions of the MTPJs, and at 20° plantar-flexed, neutral, and 20° dorsiflexed positions of the ankle. Two-way repeated measures analyses of variance with Holm’s multiple comparison test (MTPJ position × ankle position) were performed. When the MTPJ was dorsiflexed at 0°, 15°, and 30°, the MVC torque of the first MTPJ when the ankle was dorsiflexed at 20° was higher than that when the ankle was plantar-flexed at 20°. However, the ankle position had no significant effect on the MVC torque of the second–fifth MTPJ. Thus, the MVC torque of the first MTPJ was more affected by the ankle position than the second–fifth MTPJs.

New fractional order discrete Grüss type inequality

2021 ◽  
Vol 71 (1) ◽  
pp. 33-42
Author(s):  
Serkan Asliyüce ◽  
A. Feza Güvenilir
Keyword(s):  
Fractional Order ◽  
Type Inequality ◽  
Difference Operators

Abstract The aim of this study is to establish new discrete Grüss type inequality using fractional order h-sum and h-difference operators that generalize the fractional sum and difference operators.

scholarly journals NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1430001 ◽  
Author(s):  
V. K. DOBREV
Keyword(s):  
Representation Theory ◽  
Theoretical Perspective ◽  
Explicit Construction ◽  
Intertwining Operators ◽  
Difference Operators ◽  
Semisimple Lie Groups ◽  
Boundary Operators ◽  
Boundary Fields ◽  
Theoretical Results ◽  
Schrödinger Algebra

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.

scholarly journals Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

scholarly journals An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Masatoshi Noumi ◽  
Ayako Sano
Keyword(s):  
Infinite Family ◽  
Type A ◽  
Higher Order ◽  
Difference Operators ◽  
Order Difference

AbstractWe introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’ operators through a formula of Wronski type.

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