The spectrum of the non-selfadjoint system of difference operators of first order

We consider a singular differential-difference operator Λ on the real line which generalizes the one-dimensional Cherednik operator. We construct transmutation operators between Λ and first-order regular differential-difference operators on ℝ. We exploit these transmutation operators, firstly to establish a Paley–Wiener theorem for the Fourier transform associated with Λ, and secondly to introduce a generalized convolution on ℝ tied to Λ.

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Spectral analysis of discrete dirac equation with generalized eigenparameter in boundary condition

Filomat ◽

10.2298/fil1918039k ◽

2019 ◽

Vol 33 (18) ◽

pp. 6039-6054 ◽

Cited By ~ 1

Author(s):

Turhan Koprubasi ◽

Ram Mohapatra

Keyword(s):

Boundary Condition ◽

Spectral Analysis ◽

Dirac Equation ◽

Dirac Operator ◽

Spectral Properties ◽

Difference Operators ◽

Spectral Singularities ◽

First Order ◽

Complex Sequences

Let L denote the discrete Dirac operator generated in ?2 (N,C2) by the non-selfadjoint difference operators of first order (an+1y(2)n+1 + bny(2)n + pny(1)n = ?y(1)n, an-1y(1)n-1 + bny(1)n + qny(2)n = ?y(2)n, n ? N, (0.1) with boundary condition Xp k=0 (y(2)1?k + y(1)0 ?k)?k=0, (0.2) where (an), (bn), (pn) and (qn), n ? N are complex sequences, ?i; ?i ? C, i = 0, 1, 2,..., p and ? is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ?? n=1 |n|(|1-an| + |1+bn| + |pn| + |qn|) < ? holds.

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An inequality for first-order differences

Journal of Function Spaces and Applications ◽

10.1155/2005/214597 ◽

2005 ◽

Vol 3 (2) ◽

pp. 117-124

Author(s):

Gord Sinnamon

Keyword(s):

Difference Operators ◽

First Order

A question about comparing norms of difference operators that was raised in [1] and presented at the Fourth ISAAC Congress is answered in the affirmative.

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On semilocal convergence of three-step Kurchatov method under weak condition

Arabian Journal of Mathematics ◽

10.1007/s40065-020-00308-8 ◽

2021 ◽

Author(s):

Himanshu Kumar

Keyword(s):

Recurrence Relations ◽

Divided Difference ◽

Semilocal Convergence ◽

Weak Condition ◽

Theoretical Development ◽

Difference Operators ◽

Nonlinear System Of Equations ◽

First Order ◽

Type Integral ◽

Weaker Conditions

AbstractThe purpose of this paper to establish the semilocal convergence analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the $$\omega $$ ω condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the iterative method is shown by solving nonlinear system of equations and nonlinear Hammerstein-type integral equations. It illustrates the theoretical development of this study.

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HYERS-ULAM STABILITY OF FIRST ORDER LINEAR DIFFERENCE OPERATORS ON BANACH SPACE

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v14i1.7062 ◽

2018 ◽

Vol 14 (1) ◽

pp. 7475-7485

Author(s):

Arun Kumar Tripathy ◽

Pragnya Senapati

Keyword(s):

Banach Space ◽

Difference Operator ◽

Difference Operators ◽

Ulam Stability ◽

Order Linear ◽

First Order ◽

Linear Difference Operator

In this work, the Hyers-Ulam stability of first order linear difference operator TP defined by (Tpu)(n) = âˆ†u(n) - p(n)u(n); is studied on the Banach space X = lâˆž, where p(n) is a sequence of reals.

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The structure of the discrete spectrum of difference operators of first order

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics ◽

10.1501/commua1_0000000380 ◽

2000 ◽

pp. 069-075

Author(s):

C. COŞKUN

Keyword(s):

Discrete Spectrum ◽

Difference Operators ◽

First Order

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Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

Behavioral and Brain Sciences ◽

10.1017/s0140525x19000451 ◽

2019 ◽

Vol 42 ◽

Author(s):

Daniel J. Povinelli ◽

Gabrielle C. Glorioso ◽

Shannon L. Kuznar ◽

Mateja Pavlic

Keyword(s):

Temporal Reasoning ◽

Higher Order ◽

Important Case ◽

Human Cognition ◽

Relational Reasoning ◽

Dual Systems ◽

First Order ◽

Reasoning System ◽

Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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Stochasting modeling of planetary ring systems

International Astronomical Union Colloquium ◽

10.1017/s025292110010154x ◽

1984 ◽

Vol 75 ◽

pp. 461-469 ◽

Cited By ~ 1

Author(s):

Robert W. Hart

Keyword(s):

Maximum Entropy ◽

Ring System ◽

The Sun ◽

Ultimate State ◽

Interparticle Interactions ◽

Ring Systems ◽

First Order ◽

Planetary Ring ◽

Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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Morphological studies of linear (AB)n multiblock copolymers and their blends

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100122320 ◽

1992 ◽

Vol 50 (1) ◽

pp. 384-385

Author(s):

Richard J. Spontak ◽

Steven D. Smith ◽

Arman Ashraf

Keyword(s):

Electron Microscopy ◽

Microphase Separation ◽

Multiblock Copolymers ◽

First Order ◽

Morphological Studies ◽

Transmission Electron ◽

First Order Phase Transition ◽

Covalently Bonded ◽

Total Molecular Weight ◽

First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

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