A global parametrix for the fundamental solution of a first order hyperbolic pseudodifferential operator

1987 ◽  
pp. 85-94
Author(s):  
Lars Gårding
Keyword(s):  
Fundamental Solution ◽  
Pseudodifferential Operator ◽  
First Order

scholarly journals Fractional-hyperbolic systems

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Anatoly Kochubei
Keyword(s):  
Cauchy Problem ◽  
Fundamental Solution ◽  
Fractional Derivative ◽  
Hyperbolic Systems ◽  
Time Variable ◽  
Spatial Variables ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
The Cauchy Problem ◽  
Evolution Systems

AbstractWe describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order α ∈ (0, 1) in the time variable t and the first order derivatives in spatial variables x = (x 1, …, x n), which can be considered as a fractional analogue of the class of hyperbolic systems. For such systems, we construct a fundamental solution of the Cauchy problem having exponential decay outside the fractional light cone {(t,x) : |t -α| ≤ 1}.

scholarly journals p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces overp-Adic Fields

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Bo Wu
Keyword(s):  
Sobolev Space ◽  
Fundamental Solution ◽  
Pseudodifferential Operator ◽  
Sobolev Type ◽  
Schwartz Function ◽  
Pseudodifferential Equations ◽  
Sobolev Type Spaces ◽  
Type Spaces

In this paper, we study the solutions of the pseudodifferential equations of typeDα u=voverp-adic fieldℚp, whereDαis ap-adic fractional pseudodifferential operator. Ifvis a Bruhat-Schwartz function, then there exists a distributionEα, a fundamental solution, such thatu=Eα*vis a solution. We also show that the solutionubelongs to a certain Sobolev space. Furthermore, we give conditions for the continuity and uniqueness ofu.

Representation of solution for first-order partial differential equation with Dzhrbashyan - Nersesyan operator of fractional differentiation

2020 ◽  
Vol 20 (2) ◽  
pp. 6-11
Author(s):  
F.T. Bogatyreva ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fundamental Solution ◽  
Order Partial Differential Equation ◽  
Fractional Differentiation ◽  
General Representation ◽  
Partial Differential ◽  
First Order

For a first-order partial differential equation with the Dzhrbashyan - Nersesyan operator of fractional differentiation, we construct a fundamental solution and derive a general representation of the solutions in rectangular domains.

scholarly journals Modal Formulation of Segmented Euler-Bernoulli Beams

2007 ◽  
Vol 2007 ◽  
pp. 1-18
Author(s):  
Rosemaira Dalcin Copetti ◽  
Julio C. R. Claeyssen ◽  
Teresa Tsukazan
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Fundamental Solution ◽  
Fourth Order ◽  
Fundamental Matrix ◽  
Block Matrix ◽  
Viscous Damping ◽  
Internal Damping ◽  
First Order ◽  
Order State

We consider the obtention of modes and frequencies of segmented Euler-Bernoulli beams with internal damping and external viscous damping at the discontinuities of the sections. This is done by following a Newtonian approach in terms of a fundamental response of stationary beams subject to both types of damping. The use of a basis generated by the fundamental solution of a differential equation of fourth-order allows to formulate the eigenvalue problem and to write the modes shapes in a compact manner. For this, we consider a block matrix that carries the boundary conditions and intermediate conditions at the beams and values of the fundamental matrix at the ends and intermediate points of the beam. For each segment, the elements of the basis have the same shape since they are chosen as a convenient translation of the elements of the basis for the first segment. Our method avoids the use of the first-order state formulation also to rely on the Euler basis of a differential equation of fourth-order and it allows to envision how conditions will influence a chosen basis.

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

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.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
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.

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

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.

Exact First Order Finite Element Modeling for Eddy Current NDE

1991 ◽  
Vol 3 (1) ◽  
pp. 235-253 ◽  
Author(s):  
L. D. Philipp ◽  
Q. H. Nguyen ◽  
D. D. Derkacht ◽  
D. J. Lynch ◽  
A. Mahmood
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Eddy Current ◽  
Element Modeling ◽  
First Order ◽  
Eddy Current Nde
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