scholarly journals Moment Problems on Bounded and Unbounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Octav Olteanu
Keyword(s):  
Quadratic Forms ◽  
Necessary Conditions ◽  
Unbounded Domains ◽  
Continuous Functions ◽  
Moment Problems ◽  
Two Dimensional ◽  
Space Of Continuous Functions ◽  
One Dimensional ◽  
Sufficient And Necessary Conditions ◽  
The One

Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional case. For the bounded domain case, one considers a space of complex analytic functions in a disk and a space of continuous functions on a compact interval. The latter result seems to give sufficient (and necessary) conditions for the existence of a multiplicative solution.

scholarly journals Boundedness of one-dimensional branching Markov processes

1997 ◽  
Vol 10 (4) ◽  
pp. 307-332 ◽  
Author(s):  
F. I. Karpelevich ◽  
Yu. M. Suhov
Keyword(s):  
Markov Processes ◽  
Necessary Conditions ◽  
Random Variable ◽  
Expected Number ◽  
One Dimensional ◽  
Sufficient And Necessary Conditions ◽  
Type Boundary ◽  
The One ◽  
Branching Diffusions ◽  
Jump Markov Processes

A general model of a branching Markov process on ℝ is considered. Sufficient and necessary conditions are given for the random variable M=supt≥0max1≤k≤N(t)Ξk(t) to be finite. Here Ξk(t) is the position of the kth particle, and N(t) is the size of the population at time t. For some classes of processes (smooth branching diffusions with Feller-type boundary points), this results in a criterion stated in terms of the linear ODEσ2(x)2f″(x)+a(x)f′(x)=λ(x)(1−k(x))f(x). Here σ(x) and a(x) are the diffusion coefficient and the drift of the one-particle diffusion, respectively, and λ(x) and k(x) the intensity of branching and the expected number of offspring at point x, respectively. Similarly, for branching jump Markov processes the conditions are expressed in terms of the relations between the integral μ(x)∫π(x,dy)(f(y)−f(x)) and the product λ(x)(1−k(x))f(x), where λ(x) and k(x) are as before, μ(x) is the intensity of jumping at point x, and π(x,dy) is the distribution of the jump from x to y.

scholarly journals Some inequalities and superposition operator in the space of regulated functions

2019 ◽  
Vol 9 (1) ◽  
pp. 1278-1290 ◽  
Author(s):  
Leszek Olszowy ◽  
Tomasz Zając
Keyword(s):  
Hausdorff Measure ◽  
Necessary Conditions ◽  
Continuous Functions ◽  
Superposition Operator ◽  
Space Of Continuous Functions ◽  
Measures Of Noncompactness ◽  
Nemytskii Operator ◽  
Sufficient And Necessary Conditions ◽  
Regulated Functions

Abstract Some inequalities connected to measures of noncompactness in the space of regulated function R(J, E) were proved in the paper. The inequalities are analogous of well known estimations for Hausdorff measure and the space of continuous functions. Moreover two sufficient and necessary conditions that superposition operator (Nemytskii operator) can act from R(J, E) into R(J, E) are presented. Additionally, sufficient and necessary conditions that superposition operator Ff : R(J, E) → R(J, E) was compact are given.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

2022 ◽  
Author(s):  
Bharti bharti ◽  
Debabrata Deb
Keyword(s):  
Molecular Dynamics ◽  
Liquid Crystals ◽  
Molecular Dynamics Simulations ◽  
Liquid Crystalline ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Dynamics Simulations

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the...

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

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