On the Asymptotic Spectrum of a Transport Operator with Elastic and Inelastic Collision Operators

2020 ◽  
Vol 40 (3) ◽  
pp. 805-823
Author(s):  
Abdul-Majeed Al-Izeri ◽  
Khalid Latrach
Keyword(s):  
Inelastic Collision ◽  
Asymptotic Spectrum ◽  
Transport Operator

scholarly journals Some Compactness and Interpolation Results for Linear Boltzmann Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Nadjeh Redjel ◽  
Abdelkader Dehici
Keyword(s):  
Boltzmann Equation ◽  
Spectral Theory ◽  
Neutron Transport ◽  
Transport Equations ◽  
Physical Models ◽  
Linear Boltzmann Equation ◽  
Radon Measures ◽  
Asymptotic Spectrum ◽  
Transport Operator ◽  
Neutron Transport Equations

We discuss some compactness results inLp  (1≤p<∞)spaces related to the spectral theory of neutron transport equations for general classes of collision operators and Radon measures having velocity spaces as supports covering most physical models. We show in particular that the asymptotic spectrum of the transport operator is independent ofp.

scholarly journals A Generalization of Strassen’s Theorem on Preordered Semirings

Order ◽  
2021 ◽  
Author(s):  
Péter Vrana
Keyword(s):  
Compact Hausdorff Space ◽  
Polynomial Growth ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Equivalent Condition ◽  
Real Numbers ◽  
Asymptotic Spectrum ◽  
Ring Of Continuous Functions ◽  
Archimedean Property ◽  
Locally Compact Hausdorff Space

AbstractGiven a commutative semiring with a compatible preorder satisfying a version of the Archimedean property, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is an essentially unique compact Hausdorff space together with a map from the semiring to the ring of continuous functions. Strassen’s theorem characterizes an asymptotic relaxation of the preorder that asymptotically compares large powers of the elements up to a subexponential factor as the pointwise partial order of the corresponding functions, realizing the asymptotic spectrum as the space of monotone semiring homomorphisms to the nonnegative real numbers. Such preordered semirings have found applications in complexity theory and information theory. We prove a generalization of this theorem to preordered semirings that satisfy a weaker polynomial growth condition. This weaker hypothesis does not ensure in itself that nonnegative real-valued monotone homomorphisms characterize the (appropriate modification of the) asymptotic preorder. We find a sufficient condition as well as an equivalent condition for this to hold. Under these conditions the asymptotic spectrum is a locally compact Hausdorff space satisfying a similar universal property as in Strassen’s work.

Inelastic Collision Processes of Methane and Ethane Molecules at a Pt(111) Surface Studied by Molecular Beam Scattering Techniques

1999 ◽  
Vol 38 (Part 1, No. 12A) ◽  
pp. 6910-6914 ◽  
Author(s):  
Shinjiro Yagyu ◽  
Yasunobu Kino ◽  
Toshiyuki Ikeuchi ◽  
Tomomi Hiraoka ◽  
Takahiro Kondo ◽  
...  
Keyword(s):  
Molecular Beam ◽  
Inelastic Collision ◽  
Molecular Beam Scattering ◽  
Beam Scattering ◽  
Collision Processes

Comment on an Inelastic Collision Service

1970 ◽  
Vol 38 (12) ◽  
pp. 1490-1490
Author(s):  
Charles Jacobs
Keyword(s):  
Inelastic Collision

Transport operator in the space of vector functions

2020 ◽  
Vol 18 (0) ◽  
Author(s):  
H. V. Ivasyk ◽  
E. V. Cheremnykh
Keyword(s):  
Transport Operator
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