共查询到20条相似文献,搜索用时 25 毫秒
1.
In this paper we seek particular representations for absolutely continuous Phase-type distributions with 3 distinct real poles.
First, we define subsets of these Phase-type distributions given the 3 distinct poles. One subset contains distributions that
have upper triangular PH representation of order n, but do not have a triangular one of PH order n−1. This is done by using the invariant polytope approach. For any distribution in our subsets we give an invariant polytope
containing the corresponding distribution by finding the vertices of the polytope. Second, we propose a method that actually
constructs the generator matrix of the required PH representation from the invariant polytope. Consequently, our method constructs
an upper triangular PH representation that has minimal order among the upper triangular PH representations given the probability
density function of a PH distribution. 相似文献
2.
We provide a purely local computation of the (elliptic) twisted (by “transpose-inverse”) character of the representationπ=I(1) of PGL(3) over ap-adic field induced from the trivial representation of the maximal parabolic subgroup. This computation is independent of
the theory of the symmetric square lifting of [IV] of automorphic and admissible representations of SL(2) to PGL(3). It leads
— see [FK] — to a proof of the (unstable) fundamental lemma in the theory of the symmetric square lifting, namely that corresponding
spherical functions (on PGL(2) and PGL(3)) are matching: they have matching orbital integrals. The new case in [FK] is the
unstable one. A direct local proof of the fundamental lemma is given in [V]. 相似文献
3.
Gary F. Birkenmeier Henry E. Heatherly Jin Yong Kim Jae Keol Park 《Journal of Algebra》2000,230(2):1018
In this paper we develop the theory of generalized triangular matrix representation in an abstract setting. This is accomplished by introducing the concept of a set of left triangulating idempotents. These idempotents determine a generalized triangular matrix representation for an algebra. The existence of a set of left triangulating idempotents does not depend on any specific conditions on the algebras; however, if the algebra satisfies a mild finiteness condition, then such a set can be refined to a “complete” set of left triangulating idempotents in which each “diagonal” subalgebra has no nontrivial generalized triangular matrix representation. We then apply our theory to obtain new results on generalized triangular matrix representations, including extensions of several well known results. 相似文献
4.
A. Krzysztof Kwaśniewski 《Advances in Applied Clifford Algebras》2008,18(1):57-73
We introduce a natural partial order ≤ in structurally natural finite subsets of the cobweb prefabs sets recently constructed
by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers’
triangular array — are then calculated and the explicit formula for them is provided. Next — in the second construction —
we endow the set sums of prefabiants with such an another partial order that their Bell-like numbers include Fibonacci triad
sequences introduced recently by the present author in order to extend famous relation between binomial Newton coefficients
and Fibonacci numbers onto the infinity of their relatives among whom there are also the Fibonacci triad sequences and binomial-like
coefficients (incidence coefficients included). The first partial order is F-sequence independent while the second partial order is F-sequence dependent where F is the so-called admissible sequence determining cobweb poset by construction. An F-determined cobweb poset’s Hasse diagram becomes Fibonacci tree sheathed with specific cobweb if the sequence F is chosen to be just the Fibonacci sequence. From the stand-point of linear algebra of formal series these are generating
functions which stay for the so-called extended coherent states of quantum physics. This information is delivered in the last
section.
Presentation (November 2006) at the Gian-Carlo Rota Polish Seminar . 相似文献
5.
A. V. Vasilyev 《Algebra and Logic》1996,35(6):371-383
A minimal permutation representation of a group is a faithful permutation representation of least degree. Well-studied to
date are the minimal permutation representations of finite sporadic and classical groups for which degrees, point stabilizers,
as well as ranks, subdegrees, and double stabilizers, have been found. Here we attempt to provide a similar account for finite
simple ezceptional groups of types G2 and F4.
Supported by RFFR grant No. 96-01-01893, the program “Universities of Russia,” and by International Science Foundation and
Government of Russia grant No. RPC300.
Translated fromAlgebra i Logika, Vol. 35, No. 6, pp. 663–684, November–December, 1996. 相似文献
6.
A. V. Vasilyev 《Algebra and Logic》1997,36(5):302-310
A minimal permutation representation of a group is its faithful permutation representation of least degree. We will find degrees
and point stabilizers, as well as ranks, subdegrees, and double stabilizers, for groups of types E6, E7, and E8. This brings to a close the study of minimal permutation representations of finite simple Chevalley groups.
Supported by RFFR grant No. 93-01-01501, through the program “Universities of Russia,” and by grant No. RPC300 of ISF and
the Government of Russia.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 518–530, September–October, 1997. 相似文献
7.
Approximation with generalized hyperexponential distributions: Weak convergence results 总被引:1,自引:0,他引:1
Generalized hyperexponential (GH) distributions are linear combinations of exponential CDFs with mixing parameters (positive and negative) that sum to unity. The denseness of the class GH with respect to the class of all CDFs defined on [0, ) is established by showing that a GH distribution can be found that is as close to a given CDF as desired, with respect to a suitably defined metric. The metric induces the usual topology of weak convergence so that, equivalently, there exists a sequence of GH CDFs that converges weakly to a given CDF. This result is established by using a similar result for weak convergence of Erlang mixtures. Various set inclusion relations are also obtained relating the GH distributions to other commonly used classes of approximating distributions, including generalized Erlang (GE), mixed generalized Erlang (MGE), those with reciprocal polynomial Laplace transforms (K
n
), those with rational Laplace transforms (R
n
), and phase-type (PH) distributions. A brief survey of the history and use of approximating distributions in queueing theory is also included.This research was partially supported by the Office of Naval Research under Contract No. N00014-86-K0029. Much of this work is taken from the first-named author's doctoral dissertation, accepted by the faculty at the University of Virginia. 相似文献
8.
A. V. Vasilyev 《Algebra and Logic》1998,37(1):9-20
A minimal permutation representation of a group is its faithful permutation representation of least degree. Here the minimal
permutation representations of finite simple exceptional twisted groups are studied: their degrees and point stabilizers,
as well as ranks, subdegrees, and double stabilizers, are found. We can thus assert that, modulo the classification of finite
simple groups, the aforesaid parameters are known for all finite simple groups.
Supported by RFFR grant No. 96-01-01893, through the program “Universities of Russia”, and by grant No. RPC300 of ISF and
the Government of Russia.
Translated fromAlgebra i Logika, Vol. 37, No. 1, pp. 17–35, January–February, 1998. 相似文献
9.
M. M. Chip 《Journal of Mathematical Sciences》1998,90(5):2416-2420
We propose studying generalized moment representations of a form in which it suffices to apply a system of orthogonal polynomials
in order to procure the biorthogonality conditions in the construction of superdiagonal Padé polynomials using generalized
moment representations. The algebraic polynomials in the moment representation are to be sought as the linear forms of biorthogonal
polynomials. We obtain the relations between the coefficients of these linear forms and the generalized moments, and we also
establish conditions for the existence and uniqueness of generalized moment representations of polynomial form.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 110–115. 相似文献
10.
Dimitris Bertsimas 《Queueing Systems》1988,3(4):305-320
A closed form expression for the waiting time distribution under FCFS is derived for the queueing system MGEk/MGEm/s, where MGEn is the class of mixed generalized Erlang probability density functions (pdfs) of ordern, which is a subset of the Coxian pdfs that have rational Laplace transform. Using the calculus of difference equations and based on previous results of the author, it is proved that the waiting time distribution is of the form 1-
, under the assumption that the rootsU
j
are distinct, i.e. belongs to the Coxian class of distributions of order
. The present approach offers qualitative insight by providing exact and asymptotic expressions, generalizes and unifies the well known theories developed for the G/G/1,G/M/s systems and leads to an
algorithm, which is polynomial if only one of the parameterss orm varies, and is exponential if both parameters vary. As an example, numerical results for the waiting time distribution of the MGE2/MGE2/s queueing system are presented. 相似文献
11.
Benjamin Schraen 《Israel Journal of Mathematics》2010,176(1):307-361
We construct some locally ℚ
p
-analytic representations of GL2(L), L a finite extension of ℚ
p
, associated to some p-adic representations of the absolute Galois group of L. We prove that the space of morphisms from these representations to the de Rham complex of Drinfel’d’s upper half space has
a structure of rank 2 admissible filtered (φ, N)-module. Finally, we prove that this filtered module is associated, via Fontaine’s theory, to the initial Galois representation. 相似文献
12.
Let V be a Euclidean Jordan algebra, Гthe associated symmetric cone and G be the identity component of the linear automorphism group of Г.In this paper we associate to a certain class of spherical representations (ρ, ɛ) of G certain ɛ-valued Riesz distributions
generalizing the classical scalar valued Riesz distributions on V. Our construction is motivated by the analytic theory of
unitary highest weight representations where it permits to study certain holomorphic families of operator valued Riesz distributions
whose positive definiteness corresponds to the unitarity of a representation of the automorphism group of the associated tube
domain Г +iV. 相似文献
13.
M. Guerra 《Journal of Mathematical Sciences》2009,156(3):440-567
This text presents a complete theory of existence/uniqueness and the structure of generalized solutions for singular linear-quadratic
optimal control problems. Generalized optimal controls are distributions of order r and the corresponding generalized trajectories are distributions of order (r − 1). r is the “order of singularity” of the problem, an integer no greater than the dimension of the state space. Its value is obtained
through a certain reduction procedure. In the final section, some perspectives and partial results concerning the extension
of these results to nonlinear problems are briefly discussed.
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 27, Optimal Control, 2007. 相似文献
14.
Two approximative fixed-point iterative methods based on decomposition for closed queueing networks with Coxian service distributions
and arbitrary buffer sizes are extended to include phase-type service distributions. The irreducible Markov chain associated
with each subnetwork in the respective decompositions is represented hierarchically using Kronecker products. The two methods
are implemented in a software tool capable of computing the steady-state probability vector of each subnetwork by a multilevel
method at each fixed-point iteration and are compared with other methods for accuracy and efficiency. Numerical results indicate
that there is a niche filled by the two approximative methods.
The authors thank Jean-Michel Fourneau for pointing out Marie’s method and Brouwer’s fixed-point theorem. The first author
gratefully acknowledges grant TüBA-GEBİP from the Turkish Academy of Sciences. 相似文献
15.
In this paper, we consider Bayesian inference and estimation of finite time ruin probabilities for the Sparre Andersen risk model. The dense family of Coxian distributions is considered for the approximation of both the inter‐claim time and claim size distributions. We illustrate that the Coxian model can be well fitted to real, long‐tailed claims data and that this compares well with the generalized Pareto model. The main advantage of using the Coxian model for inter‐claim times and claim sizes is that it is possible to compute finite time ruin probabilities making use of recent results from queueing theory. In practice, finite time ruin probabilities are much more useful than infinite time ruin probabilities as insurance companies are usually interested in predictions for short periods of future time and not just in the limit. We show how to obtain predictive distributions of these finite time ruin probabilities, which are more informative than simple point estimations and take account of model and parameter uncertainty. We illustrate the procedure with simulated data and the well‐known Danish fire loss data set. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
16.
In this paper we exhibit a new method of proving non-unitarity of representations, based on semi simplicity of unitarizable
representations. Non-unitarity is proved for a half of all irreducible representations of classical p-adic groups whose infinitesimal character is the same as the infinitesimal character of a generalized Steinberg representation
(as defined in Tadić, Am J Math 120:159–210, 1998). Only the Steinberg representation and its Aubert dual are expected to
be unitary here. In this way we partially generalize a result of Casselman to the case of classical groups. Our argument is
completely different from Casselman’s argument (which is hard to extend to this case). It requires a very limited knowledge
of the inducing cuspidal representation. 相似文献
17.
Discrete components of some complementary series representations 总被引:2,自引:0,他引:2
We show that the restriction of the complementary series representations of SO(n, 1) to SO(m, 1) (m < n) contains complementary series representations of SO(m, 1) discretely, provided that the continuous parameter is sufficiently close to the first point of reducibility and the representation
of M — the compact part of the Levi- is a sufficiently small fundamental representation. 相似文献
18.
We define the notion of admissible pair for an algebra A, consisting on a couple (Γ, R), where Γ is a quiver and R a unital, splitted and factorizable representation of Γ, and prove that the set of admissible pairs for A is in one to one correspondence with the points of the variety of twisting maps TAn:=T(Kn,A)\mathcal{T}_A^n:=\mathcal{T}(K^n,A). We describe all these representations in the case A = K
m
. 相似文献
19.
In this paper, we study asymptotic properties (large deviations and functional central limit theorem) of generalized record
processes built on a triangular array of continuous and exchangeable random variables. As an application of these results,
the links with the Kendall's rank correlation statistic are studied and testing exchangeability is discussed.
AMS 2000 Subject Classification Primary—60F10
Secondary—60F17, 62G10 相似文献
20.
In this note we give elementary examples of the naturalness of generalized Clifford algebras appearance, in some particular
quantum mechanical models.
First Weyl’s program [1] for quantum kinematics for the case of simplest Galois fieldsZ
n
is realized in terms of generalized Clifford algebras. Dynamics might then be introduced, following the ideas of Hanney and
Berry [2], as shown in [3].
Second the coherent state picture of the finite dimensional “Z
n
— Quantum Mechanics” is presented.
In the last part the known coherent states ofq-deformed quantum oscillators (q≡ω) are explicitly shown in the generalized Grassman algebras and the generalized Clifford algebras settings.
Presented atThe Polish-Mexican Seminar, Kazimierz Dolny, August 1998 — Poland. 176 相似文献