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1.
P. Kabaila 《Acta Appl Math》2003,78(1-3):185-192
We consider the problem of constructing a 1– upper confidence limit for the scalar parameter 0 in the presence of the nuisance parameter vector 0, when the data are discrete. The 'profile plug-in' upper confidence limit is introduced by Kabaila and Lloyd. This confidence limit is based on computing a P-value
from an estimator
of 0, replacing the nuisance parameter by the profile maximum likelihood estimate
for known, and equating to . Theoretical and numerical evidence for the good coverage properties of this confidence limit is presented by Kabaila and Lloyd. An upper confidence limit should be assessed not only by its coverage properties but also by how large this confidence limit is. We measure how large the profile plug-in upper limit is by using a large sample approximation to it. This large sample approximation is used to delineate further the good properties of this confidence limit. 相似文献
2.
Hendrik Grundling 《Acta Appl Math》1997,46(2):107-145
Given an inductive limit group
where each
is locally compact, and a continuous two-cocycle
, we construct a C*-algebra
group algebra
is imbedded in its multiplier algebra
, and the representations of
are identified with the strong operator continuous
of G. If any of these representations are faithful, the above imbedding is faithful. When G is locally compact,
is precisely
, the twisted group algebra of G, and for these reasons we regard
in the general case as a twisted group algebra for G. Applying this construction to the CCR-algebra over an infinite dimensional symplectic space (S,\,B),we realise the regular representations as the representation space of the C*-algebra
, and show that pointwise continuous symplectic group actions on (S,\, B) produce pointwise continuous actions on
, though not on the CCR-algebra. We also develop the theory to accommodate and classify 'partially regular' representations, i.e. representations which are strong operator continuous on some subgroup H of G (of suitable type) but not necessarily on G, given that such representations occur in constrained quantum systems. 相似文献
3.
David A. Richter 《Acta Appl Math》2001,66(1):41-65
Starting from the commutation relations in a complex semisimple Lie algebra
, one may obtain a space
of vector fields on Euclidean space such that
and
are isomorphic when
is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of
is a Borel subalgebra
. Furthermore, one may adjoin to the vector fields in
multiplication operators to obtain an
-parameter family of distinct presentations of
as spaces of differential operators, where
is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of
can be presented in this way. All of this is carried out explicitly for arbitrary
. In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight. 相似文献
4.
Jürg T. Marti 《Numerische Mathematik》1990,57(1):51-62
Summary The inverse Sturm-Liouville problem is the problem of finding a good approximation of a potential functionq such that the eigenvalue problem (*)–y
+qy=y holds on (0, ) fory(0)=y()=0 and a set of given eigenvalues . Since this problem has to be solved numerically by discretization and since the higher discrete eigenvalues strongly deviate from the corresponding Sturm-Liouville eigenvalues , asymptotic corrections for the 's serve to get better estimates forq. Let
k
(1kn) be the first eigenvalues of (*), let
k
be the corresponding discrete eigenvalues obtained by the finite element method for (*) and let
k
k
for the special caseq=0. Then, starting from an asymptotic correction technique proposed by Paine, de Hoog and Anderssen, new estimates for the errors
of the corrected discrete eigenvalues
are obtained and confirm and improve the knownO(kh
2)(h:=/(n+1)) behaviour. The estimates are based on new Sobolev inequalities and on Fourier analysis and it is shown that
for 4+c
2
k(n+1)/2, wherec
1 andc
2 are constants depending onq which tend to 0 for vanishingq. 相似文献
5.
Joël Merker 《Acta Appl Math》2006,92(2):125-207
We treat the problem of linearizability of a system of second order ordinary differential equations. The criterion we provide has applications to nonlinear Newtonian mechanics, especially in three-dimensional space. Let or , let , let , let and let
be a collection of m analytic second order ordinary differential equations, in general nonlinear. We obtain a new and applicable necessary and sufficient condition in order that this system is equivalent, under a point transformation
to the Newtonian free particle system .Strikingly, the explicit differential system that we obtain is of first order in the case , whereas according to a classical result due to Lie, it is of second order the case of a single equation . 相似文献
6.
Let
be a reductive Lie algebra over C. We say that a
-module M is a generalized Harish-Chandra module if, for some subalgebra
, M is locally
-finite and has finite
-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when
is a Cartan subalgebra. We also review the recent determination of which reductive in
subalgebras
are essential to a classification. Finally, we present in detail the emerging picture for the case when
is a principal 3-dimensional subalgebra. 相似文献
7.
Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad 《Acta Appl Math》2000,61(1-3):101-118
From the Erds–Turán theorem, it is known that if f is a continuous function on
and L
n
(f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then
Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in
and continuous on
and making use of algebraic interpolating polynomials in the roots of unity.In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent polynomials will be used as interpolants and, on the other hand, the interpolation points will be zeros of certain para-orthogonal functions with respect to a given measure on
. 相似文献
8.
Hans Zessin 《Probability Theory and Related Fields》1988,77(4):605-622
We consider the time evolved states
of the free motion
t
(q, v)=(q+tv,v),q,v
d
, starting in some non-equilibrium state
and look at the associated processX
t
of fluctuations of the actual number
t/
()
of particles of the realization in
with velocities inB at timet/ around its mean as 0 (i.e., in the hydrodynamic limit). It is shown that under natural conditions on the initial state
, especially a mixing condition in the space variables, for eacht the laws of the fluctuations become Gaussian in the hydrodynamic limit in the following sense:
as 0, where denotes weak convergence and
is a centered Gaussian state, which is translation invariant in the space variables. Furthermore the time evolution
is also given by the free motion in the sense that
On the other hand we shall see that
ast, whereP
z×
is the Poisson process with intensity measurez·×, i.e., the equilibrium state for the free motion with particle densityz and velocity distribution . In the hydrodynamic limit this behaviour corresponds to the ergodic theorem for the fluctuation process:
ast. Here
is a centered Gaussian state describing the equilibrium fluctuations, i.e., the fluctuations ofP
z×
. Thus we prove the central limit theorem for the ideal gas: fluctuations are Gaussian even in non-equilibrium. The proofs rest on an adaption of the method of moments for sequences of generalized fields. 相似文献
9.
Victor Kaftal 《Integral Equations and Operator Theory》1982,5(1):50-70
LetA be a von Neumann algebra,J be the ideal of compact operators relative toA and letF
+ be the left-Fredholm class ofA. We call almost left-Fredholm the class
= {A A: if P A is a projection and AP J then P J}. Then
and the inclusion is proper unlessA is semifinite and has a non-large center.
satisfies all of the algebraic properties ofF
+ but it is generally not open. IfA is semifinite then A
iff there are central projectionsG
with G = I such that AG F+(AG). Let :A A/J. Then the left almost essential spectrum ofA A,
, coincides with the set of eigenvalues of (A) 相似文献
10.
For a general nonlinear system and closed target set we study the value functions and
of the control problems of reaching and, respectively, its interior, in minimum time. Under no controllability assumptions on the system, we characterize them as, respectively, the minimal viscosity supersolution and the maximal viscosity subsolution of the Bellman equation with appropriate boundary conditions. Then we prove that
is the unique upper semicontinuous complete solution of such a boundary value problem, which means in particular that the (completed) graph of
contains the graph of any solution, as well as all the limits of reasonable approximating sequences. We give some applications to verifications theorems and to the stability of the minimum time function with respect to general perturbations.The authors are partially supported by the Italian National Projects Equazioni di evoluzione e applicazioni fisico-matematiche and Equazioni differenziali e calcolo delle variazioni, respectively. 相似文献
11.
E. V. Podsypanin 《Journal of Mathematical Sciences》1982,18(6):919-923
Let be a real quadratic irrational of discriminant D=f2Di>0, where Di is the fundamental discriminant of the field and h are the character and the number of classes of the field, respectively, and
proves the following estimate for the length l of the period of the expansion of into a continued fraction: where =1 if f=1 and =2 if f>1. A. S. Pen and B. F. Skubenko (Mat. Zametki, 5, No. 4, 413–482 (1969)) have proved this estimate in the case f=1, D10 (mod4).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 82, pp. 95–99, 1979. 相似文献
12.
A formula of a radial derivative
is obtained with the aid of derivatives with respect to and to of the functions closely connected with the spherical Poisson integral
and the boundary values are determined for
. The boundary values are also found for partial derivatives with respect to the Cartesian coordinates
. 相似文献
13.
We propose a generalization of a Drinfeld–Sokolov scheme of attaching integrable systems of PDEs to affine Kac–Moody algebras. With every affine Kac–Moody algebra
and a parabolic subalgebra
, we associate two hierarchies of PDEs. One, called positive, is a generalization of the KdV hierarchy, the other, called negative, generalizes the Toda hierarchy. We prove a coordinatization theorem which establishes that the number of functions needed to express all PDEs of the the total hierarchy equals the rank of
. The choice of functions, however, is shown to depend in a noncanonical way on
. We employ a version of the Birkhoff decomposition and a 2-loop formulation which allows us to incorporate geometrically meaningful solutions to those hierarchies. We illustrate our formalism for positive hierarchies with a generalization of the Boussinesq system and for the negative hierarchies with the stationary Bogoyavlenskii equation. 相似文献
14.
On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives
For 2-periodic functions
and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality
which takes into account the number of changes in the sign of the derivatives (x
(k)) over the period. Here, = (r – k + 1/q)/(r + 1/p),
r
is the Euler perfect spline of degree r,
and
. The inequality indicated turns into the equality for functions of the form x(t) = a
r
(nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines. 相似文献
15.
We show that the mean quadratic variation of a self-similar measure under certain open set condition exhibits asymptotic periodicity. Through a generalized Wiener's Tauberian Theorem, we obtain some new identities and equivalences of the mean quadratic variation of a bounded measurev and its Fourier average
. They are used to sharpen some recent results of Strichartz concerning the asymptotic behavior ofH
a(T); ) asT, where is the self-similar measure as above. In the development some results concerning the open set condition are also obtained. 相似文献
16.
Any transversally holomorphic foliated map
of Kählerianfoliations with
harmonic, is shown to be a transversallyharmonic map and an absolute minimum of the energy functional
inits foliated homotopy class. 相似文献
17.
We describe sequences of zeros of functions f 0 analytic in the half-plane
and satisfying the condition
where : [0; +) (0; +) is an increasing function such that the function ln (r) is convex with respect to ln r on [1; +). 相似文献
18.
Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(1):49-55
For families of probability measures (P
, )) generated by semimartingales, we consider the local density)(y, )=
t
(y, ))
t0 of a, measureP
y
with respect to the measureP
whose logarithm is the difference of a local martingale and a positive predictable increasing locally bounded process. Conditions are obtained under which the relations
and
hold, wherey
t
depends in some way ont, while
t
ast . Applications of these relations are exhibited and an example is given when the hypotheses of the theorems proved can be verified.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 48–55, 1986. 相似文献
19.
20.
We are interested in parabolic problems with L1 data of the type
with i, j=0, 1, (i, j) (0, 0), 0 = 0 and 1 = 1. Here, is an open bounded subset of
with regular boundary and
is a Caratheodory function satisfying the classical Leray-Lions conditions and is a monotone graph in
with closed domain and such that
We study these evolution problems from the point of view of semi-group theory, then we identify the generalized solution of the associated Cauchy problem with the entropy solution of
in the usual sense introduced in [5]. 相似文献