共查询到20条相似文献,搜索用时 31 毫秒
1.
Eitan Altman Arie Hordijk Lodewijk C. M. Kallenberg 《Mathematical Methods of Operations Research》1996,44(3):387-399
It is known that the value function in an unconstrained Markov decision process with finitely many states and actions is a piecewise rational function in the discount factor a, and that the value function can be expressed as a Laurent series expansion about = 1 for close enough to 1. We show in this paper that this property also holds for the value function of Markov decision processes with additional constraints. More precisely, we show by a constructive proof that there are numbers O = o <1 <... < m–1 < m = 1 such that for everyj = 1, 2, ...,m – 1 either the problem is not feasible for all discount factors in the open interval (j–1, j) or the value function is a rational function in a in the closed interval [j–1, j]. As a consequence, if the constrained problem is feasible in the neighborhood of = 1, then the value function has a Laurent series expansion about = 1. Our proof technique for the constrained case provides also a new proof for the unconstrained case. 相似文献
2.
Summary In each lattice point , of a rectangular net a numerical valueu
is given. A bicubical and twice continuously differentiable function is constructed interpolating the valuesu
. The method is known as «spline interpolation». 相似文献
3.
A measure for the denseness of sequences (an) mod 1, irrational, is the dispersion constantD() introduced byH. Niederreiter. In this paper the smallest accumulation point 1 of the set of theD() is determined and all those are explicitely given for whichD () < 1 holds. 相似文献
4.
Kevin O'Bryant 《Journal of Algebraic Combinatorics》2004,19(1):91-115
A Sturmian word is a map W :
{0,1} for which the set of {0, 1}-vectors F
n(W) {(W(i), W(i + 1),...,W(i + n – 1))
T
: i
} has cardinality exactly n + 1 for each positive integer n. Our main result is that the volume of the simplex whose n + 1 vertices are the n + 1 points in F
n(W) does not depend on W. Our proof of this motivates studying algebraic properties of the permutation ,n
(where is any irrational and n is any positive integer) that orders the fractional parts {}, {2},...,{n}, i.e., 0 < {,n
(1)} < {,n
(2)} < ··· < {,n
(n)} < 1. We give a formula for the sign of ,n
, and prove that for every irrational there are infinitely many n such that the order of ,n
(as an element of the symmetric group S
n) is less than n. 相似文献
5.
Hölder classes of variable order (x) are introduced and it is shown that the fractional integralI
0+
has Hölder order (x)+ (0 < , +, ++ < 1, + = sup (x)). 相似文献
6.
Dr. Abul Maksud Sayied 《Mathematische Zeitschrift》1970,114(1):22-32
Summary The partial differential fields most suited for the purpose of construction of Galois theory for the family (1) are endowed with the symmetric bilinear form (2iv) and are called -differential fields. In Section 1 are defined certain algebraic notions related to the symmetric bilinear form (2iv) and which are necessary for the construction of any Galois theory. Necessary and sufficient condition for the extension of the domain of the operator (this operator is not a derivation although it commutes with the partial derivations of the -differential field) from an -differential fieldK to a finitely generated -differential extension field is given in Theorem 1.Section 2 defines the notion of -differential mapping as linear mappings which preserve the symmetric bilinear form and commute with the partial derivations. The group properties of the set of -differential mappings are discussed and the Galois correspondence theorems set up for -differential fields.Section 3 sets up the notion of -Liouvillian extensions of -differential fields and briefly discusses the Galois groups associated with these -Liouvillian extension fields.Section 4 points to the procedure for the algebraic characterization of -simple--differential field extensions by elementary solutions of the partial differential equation
m
=0. 相似文献
7.
Živorad Tomovski 《Analysis Mathematica》2003,29(2):165-170
In this paper equivalent classes of the classes M'
and S'
p
r, p >1, 0,r {0,1,2,...,[]} defined by Sheng [5] are obtained. Then it is shown that the classes of Fourier coefficients S
p, S'
p(case r==0) and S
p(), p>1, defined by . V. Stanojevi, V. B. Stanojevi Sheng and the author of the present note are identical. As a corollary of this result, the L
1-estimate for cosine series, obtained in [10], is refined. 相似文献
8.
We construct an asymptotic formula for a sum function for
a
(), where
a
() is the sum of the ath powers of the norms of divisors of the Gaussian integer on an arithmetic progression 0 (mod ) and in a narrow sector 1 arg < 2. For this purpose, we use a representation of
a
(n) in the form of a series in the Ramanujan sums. 相似文献
9.
A. B. Aleksandrov 《Journal of Mathematical Sciences》1993,63(2):115-129
Let be an inner function, let C, ¦¦=1. Then the harmonic function [(+)]/(–)] is the Poisson integral of a singular measure
D. N. Clark's known theorem enables us to identify in a natural manner the space H2 H2 with the space L2
(
).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 7–33, 1989. 相似文献
10.
N. A. Vavilov 《Journal of Mathematical Sciences》1982,19(1):987-998
It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group G
(, R) of twisted type =Al,l odd, Dl, E6 over a commutative semilocal ring R with involution are in one-to-one correspondence with the -invariant parabolic nets of ideals of R of type , i.e., with the sets, of ideals
of R such that: (l)
whenever; (2)
=
for all ; (3)
=R for > 0. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 94, pp. 21–36, 1979. 相似文献
11.
Scott W. Weeks Graham C. Sander Ian G. Lisle Jean-Yves Parlange 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(6):841-853
When both the diffusivityD and fractional flow functionf have a power law dependence on the water content , i.e.D=D
o andf=+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionV
wo and comparison with experimental data are given. In particular, when the fluxV
wo and a are related byV
wo( + 1)/D
o=2, a new fully explicit analytical solution is found as (r, t)=(1 – r
2/4D
ot)1/ forr
2 < 4D
ot/ and (r, t)=0 forr
2 4D
ot/ We show that the existence of this exact soution is due to the presence of a Lagrangian symmetry. 相似文献
12.
Let :=. The following are known: two -sets of power are isomorphic. Let >0. Two ordered divisible Abelian groups that are -sets of power are isomorphic, two real closed fields that are -sets of power are isomorphic. The following is shown: (1) there exist 2 nonisomorphic ordered Abelian groups (respectively ordered fields) that are -sets of power ; (2) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) of power all having the same order type; (3) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) that are -sets having the same order type. 相似文献
13.
JirÍ Adámek 《Applied Categorical Structures》1996,4(1):121-126
For a topological category over Set we prove that if a functor T: has a fixed cardinal (i.e. for each object K with card (UK)= we have card (UTK)), then T has a least fixed point, and if T has a successive pair of fixed cardinals and +, then T has a greatest fixed point. This extends results of Adámek and Koubek.Partial financial support of the Grant Agency of the Czech Republic under Grant No. 201/93/0950 is gratefully acknowledged. 相似文献
14.
Catherine Bandle René P. Sperb 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1973,24(5):709-720
Zusammenfassung Mit Hilfe der Rellichschen Störungstheorie wird die analytische Abhängigkeit der Lösungen eines Randwert- und eines Eigenwertproblems gezeigt, sowie des tiefsten Eigenwertes 1() von einem Parameter , der in den Randbedingungen auftritt.Als Anwendung ergeben sich Schranken für das Energieintegral und 1(). Ferner wird die Definition der RobinfunktionR(P, Q; ) erweitert auf negative Werte von , insbesondere singuläre Werte –p
j
.
Neu-Technikum Buchs 相似文献
Neu-Technikum Buchs 相似文献
15.
In-Suk Wee 《Probability Theory and Related Fields》1990,85(4):469-488
Summary Let {X
t
} be a 1 process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x
–L
1
(x), v{yy<–x}=x
–L
2
(x) whereL
1,L
2 are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf
a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University 相似文献
16.
Toru Nakahara 《Monatshefte für Mathematik》1982,94(2):125-132
In this note we shall prove that there exist infinitely many cyclic biquadratic fieldsK whose integral bases are neither {1, , 2, } nor {1, , , 3) for any numbers , inK. Next, we shall construct infinitely many cyclic biquadratic fieldsK which have the index 1, but still have not the integral basis {1, , 2, 3) for every inK. Finally we shall give a class of biquadratic fields for a problem of Hasse concerning an integral basis. 相似文献
17.
Gérard A. Philippin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1976,27(5):545-551
Zusammenfassung Das Ziel dieser Arbeit ist die Konstruktion von unteren und oberen Schranken für
D
hu dx dy mith=r
sin . Dabei istu die erste Eigenfunktion einer auf dem Rande gebundenen Membran, deren Gebiet vollständig im Winkel 0/ liegt. Am Schluss der Arbeit werden zwei einfache Beispiele vorgeschlagen.
This research was supported by the Swiss Nationalfonds. 相似文献
Résumé L'objet de cet article est de construire des bornes inférieures et supérieures pour D hu dx dy avech=r sin , et oùu est la première fonction propre d'une membrane vibrante fixée sur son contour D, complètement contenu dans l'angle 0/. Comme conclusion, deux applications simples sont présentées.
This research was supported by the Swiss Nationalfonds. 相似文献
18.
Keijo Väänänen 《manuscripta mathematica》1977,21(2):173-180
The paper considers polynomials in ,f1(),...,fs(), where is an algebraic number satisfying certain conditions and f1(z),...,fs(z) are some E-functions, algebraically independent over the field of rational functions. Explicit lower bounds in terms of the heights of and the polynomial are obtained for the absolute values of these polynomials. The result is proved by using the method of Siegel and idlovskii.This work was carried out while the author was a research fellow of the Alexander von Humboldt Foundation. 相似文献
19.
Yves Péraire 《Archive for Mathematical Logic》1995,34(4):269-277
The results established in this paper are in connection with the Relative Internal Set Theory (R.I.S.T.). The main result is the general principle of choice: Let be a level and let (x, y) be anexternalbounded formula of the language of R.I.S.T.. Suppose that to each elementx, dominated by , corresponds an elementy
x
such that (x, y
x
) holds, then there exists a function of choice such that, which is a very general principle of choice, for everyx dominated by , (x, (x)) holds. More than that, we establish that if all the elementsy
x
are uniformly dominated by a level then we can prescribe that the function of choice is also dominated by . 相似文献
20.
G. S. Karkarashvili 《Journal of Mathematical Sciences》1993,66(3):2236-2242
We consider numerical solution of an integro-differential equation with nonsmooth initspaial values. Unique solvability in Sobolev spaceW
2
(0, 1), =1,2, is proved. We establish the rate of convergence of the approximate solution to the exact solution in fractional spacesW
2
+1
, 01, with approximation order O(h
++1/2
) for 01/2 andO(h
+1
|ln h|1/2, for 1/2 #x2264;1.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 8–16, 1988. 相似文献