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1.
2.
We investigate the spectral properties of the time‐dependent linear transport equation with bounce‐back boundary conditions. A fine analysis of the spectrum of the streaming operator is given and the explicit expression of the strongly continuous streaming semigroup is derived. Next, making use of a recent result from Sbihi (J. Evol. Equations 2007; 7 :689–711), we prove, via a compactness argument, that the essential spectrum of the transport semigroup and that of the streaming semigroup coincide on all Lp‐spaces with 1<p<∞. Application to the linear Boltzmann equation for granular gases is provided. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
3.
Adam Bobrowski 《Semigroup Forum》2010,81(3):435-445
We show that Lord Kelvin’s method of images is a way to prove generation theorems for semigroups of operators. To this end
we exhibit three examples: a more direct semigroup-theoretic treatment of abstract delay differential equations, a new derivation
of the form of the McKendrick semigroup, and a generation theorem for a semigroup describing kinase activity in the recent
model of Kaźmierczak and Lipniacki (J. Theor. Biol. 259:291–296, 2009). 相似文献
4.
This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in
L
1-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C
0-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup
is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will
be estimated for smooth initial data is given. 相似文献
5.
We discuss the spectral properties of collisional semigroups associated to various models from transport theory by exploiting the links between the so‐called resolvent approach and the semigroup approach. Precisely, we show that the essential spectrum of the full transport semigroup coincides with that of the collisionless transport semigroup in any Lp‐spaces (1 <p < ∞) for three 2D‐transport models with Maxwell‐boundary conditions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d. random variables chosen from a fixed probability
distribution p of mean 0, variance 1, and finite higher moments. Previous work (Bryc et al., Ann. Probab. 34(1):1–38, 2006; Hammond and Miller, J. Theor. Probab. 18(3):537–566, 2005) showed that the spectral measures (the density of normalized eigenvalues) converge almost surely to a universal distribution
almost that of the Gaussian, independent of p. The deficit from the Gaussian distribution is due to obstructions to solutions of Diophantine equations and can be removed
(see Massey et al., J. Theor. Probab. 20(3):637–662, 2007) by making the first row palindromic. In this paper we study the case where there is more than one palindrome in the first
row of real symmetric Toeplitz matrices. Using the method of moments and an analysis of the resulting Diophantine equations,
we show that the spectral measures converge almost surely to a universal distribution. Assuming a conjecture on the resulting
Diophantine sums (which is supported by numerics and some theoretical arguments), we prove that the limiting distribution
has a fatter tail than any previously seen limiting spectral measure. 相似文献
7.
Giovanni Ranieri 《Archiv der Mathematik》2002,79(6):472-478
In 1980, J. Esterle proved the Wiener theorem forL
1 (—) by a completely new method using analytic semigroup techniques. We show here how to extend the method in two different
ways. First, it is shown that spectral synthesis for points on the real line is also provided by analytic semigroup techniques.
Second, Esterle's proof may also be adapted to provide Wiener theorem for some elementary hypergroups.
Eine überarbeitete Fassung ging am 24. 4. 2001 ein 相似文献
8.
Aref Jeribi Hatem Megdiche Nedra Moalla 《Mathematical Methods in the Applied Sciences》2005,28(2):127-145
This paper deals with Rotenberg's models of cell populations with general boundary conditions. It is shown, first, that the associated Cauchy problem is governed by a C0‐semigroup. Second, we have proved that if the boundary operator is positive, the transport semigroup is irreducible. And finally, a spectral decomposition of the solution into an asymptotic term was derived. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Convergence to equilibrium for linear spatially homogeneous Boltzmann equation with hard and soft potentials: A semigroup approach in L1‐spaces
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We investigate the large time behavior of solutions to the spatially homogeneous linear Boltzmann equation from a semigroup viewpoint. Our analysis is performed in some (weighted) L1‐spaces. We deal with both the cases of hard and soft potentials (with angular cut‐off). For hard potentials, we provide a new proof of the fact that, in weighted L1‐spaces with exponential or algebraic weights, the solutions converge exponentially fast towards equilibrium. Our approach uses weak‐compactness arguments combined with recent results of the second author on positive semigroups in L1‐spaces. For soft potentials, in L1‐spaces, we exploit the convergence to ergodic projection for perturbed substochastic semigroup to show that, for very general initial datum, solutions to the linear Boltzmann equation converges to equilibrium in large time. Moreover, for a large class of initial data, we also prove that the convergence rate is at least algebraic. Notice that, for soft potentials, no exponential rate of convergence is expected because of the absence of spectral gap. 相似文献
10.
We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin [S.H. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. Theor. Biol. 60 (1976) 449–457] to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction–diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation. 相似文献
11.
Let S be a grading monoid with quotient group q(S) , let F(S) be the set of fractional ideals of S . For A ∈ F(S) , define A
w
= {x ∈ q(S) \mid J+x \subseteq A for some f.g. ideal J of S with J
-1
=S} and A_ \overline w ={x ∈ q(S)\mid J+x \subseteq A for some ideal J of S with J
-1
=S} . Then w and \overline w are star-operations on F(S) such that w ≤ \overline w . Using these star-operations, we give characterizations of Krull semigroups and pre-Krull semigroups. Also we show that
for every maximal * -ideal P of S , if S
P
is a valuation semigroup, then * -cancellation ideals are * -locally principal ideals, where * is a star-operation on S of finite character. Finally, we show that S is a pre-Krull semigroup (H-semigroup) if and only if the polynomial semigroup S[x] is a pre-Krull semigroup (H-semigroup).
October 15, 1999 相似文献
12.
In Macheras and Strauss (Atti Sem Math Fis Univ Modena, L, pp 349–361, 2002) and Musial et al. (J Theor Probab 20:545–560,
2007) various products for primitive liftings in the factors of a product of probability spaces have been considered. In this
paper we settle for the d-dimensional Lebesgue densities open problems from Macheras and Strauss (Atti Sem Math Fis Univ Modena, L, pp 349–361, 2002)
and Musial et al. (J Theor Probab 20:545–560, 2007) by applying results relying on the metrical group structure of
\mathbb Rd{{\mathbb R}^d}, if
d ? \mathbb N{d\in{\mathbb N}}. In particular, a lifting problem from Musial et al. (Arch Math 83:467–480, 2004), Question 3.3, is decided to the negative
for the Lebesgue densities. The relation of the Lebesgue density in the product space and the results of the products taken
for the Lebesgue densities in the factors under order is discussed. The results can be carried over to densities and liftings
dominating Lebesgue densities and to multiplicative and positive linear liftings on function spaces. 相似文献
13.
We consider a Rees matrix semigroup S = M[U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that pU 1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup. 相似文献
14.
In this article, we study a second-order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called regular and nonregular cases, we prove that the resolvent decreases with respect to the spectral parameter in L p ?(0,?1), but there is no maximal decreasing at infinity for p?>?1. Furthermore, the studied operator generates in L p ?(0,?1) an analytic semigroup for p?=?1 in regular case, and an analytic semigroup with singularities for p?>?1 in both cases, and for p?=?1 in the nonregular case only. The obtained results are then used to show the correct solvability of a mixed problem for a parabolic partial differential equation with nonregular boundary conditions. 相似文献
15.
S.M. Maepa 《Quaestiones Mathematicae》2016,39(3):307-318
We study the character amenability of semigroup algebras. We work on general semigroups and certain semigroups such as inverse semigroups with a finite number of idempotents, inverse semigroups with uniformly locally finite idempotent set, Brandt and Rees semigroup and study the character amenability of the semigroup algebra l1(S) in relation to the structures of the semigroup S. In particular, we show that for any semigroup S, if ?1(S) is character amenable, then S is amenable and regular. We also show that the left character amenability of the semigroup algebra ?1(S) on a Brandt semigroup S over a group G with index set J is equivalent to the amenability of G and J being finite. Finally, we show that for a Rees semigroup S with a zero over the group G, the left character amenability of ?1(S) is equivalent to its amenability, this is in turn equivalent to G being amenable. 相似文献
16.
《代数通讯》2013,41(6):2461-2479
Superabundant semigroups are generalizations of completely regular semigroups written the class of abundant semigroups. It has been shown by Fountain that an abundant semigroup is superabundant if and only if it is a semilattice of completely J *-simple semigroups. Reilly and Petrich called a semigroup S cryptic if the Green's relation H is a congruence on S. In this paper, we call a superabundant semigroup S a regular crypto semigroup if H * is a congruence on S such that S/H * is a regular band. It will be proved that a superabundant semigroup S is a regular crypto semigroup if and only if S is a refined semilattice of completely J *-simple semigroups. Thus, regular crypto semigroups are generalization of the cryptic semigroups as well as abundant semigroups. 相似文献
17.
Humberto Prado 《Semigroup Forum》2008,77(3):456-462
We study stability properties of certain evolution equations including the fractional Cauchy problem. Under some spectral
assumptions these equations are governed either by a resolvent or a regularized resolvent or a k-convoluted semigroup. We investigate the long time behavior for bounded solutions by a direct application of the ergodic
theorems for regularized resolvents of Lizama and Prado (J. Approx. Theory 122:42–61, 2003), Prado (Semigroup Forum 73:243–252, 2006). We apply our results to the qualitative study of the fractional diffusion-wave equation on L
p
(ℝ).
The author is partially supported under FONDECYT Grant no 1070127. 相似文献
18.
Yu. A. Kordyukov 《Acta Appl Math》1991,23(3):223-260
This paper is devoted to some of the properties of uniformly elliptic differential operators with bounded coefficients on manifolds of bounded geometry in L
pspaces. We prove the coincidence of minimal and maximal extensions of an operator of a considered type with a positive principal symbol, the existence of holomorphic semigroup, generated by it, and the estimates of L
p-norms of the operators of this semigroup. Some spectral properties of such operators in L
pspaces are also studied. 相似文献
19.
A semigroup is called type-E if the band of its idempotents can be expressed as a direct product of a rectangular band and an ω-chain. For brevity, we call an IC *-bisimple quasi-adequate semigroup of type-E a q
*-bisimple IC semigroup of type-E. In this paper, we characterize q
*-bisimple semigroups by using some kind of generalized Bruck-Reilly extensions. As a consequence, some results concerning
*-bisimple type-A
ω-semigroups given by Asibong-Ibe (Semigroup Forum 31:99–117, 1985) are generalized. 相似文献
20.
Sachs (Can J Math 14:451–460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular
lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundations of quantum mechanics initiated by Butterfield and Isham (Int J
Theor Phys 37(11):2669–2733, 1998, Int J Theor Phys 38(3):827–859, 1999), at least in the case where L is the orthomodular lattice of projections of a Hilbert space, or von Neumann algebra. The results here may add some additional
perspective to this line of work. 相似文献