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1.
Let w be an element of the Weyl group of sl
n + 1. We prove that for a certain class of elements w (which includes the longest element w0 of the Weyl group), there exist a lattice polytope R
l(w)
, for each fundamental weight i of sl
n + 1, such that for any dominant weight =
i = 1
n
a
i
i
, the number of lattice points in the Minkowski sum
w
=
i = 1
n
a
i
i
w
is equal to the dimension of the Demazure module E
w
(). We also define a linear map A
w
: R
l(w)
P Z R where P denotes the weight lattice, such that char E
w
() = e
e–A(x)
where the sum runs through the lattice points x of
w
. 相似文献
2.
Exact estimates for partially monotone approximation 总被引:2,自引:0,他引:2
G. L. Iliev 《Analysis Mathematica》1978,4(3):181-197
f(x) — , - [–1,1], (f, ) — , as— f, . . (- ) (x
i,x
i+ 1) (i=0, 1, ...,s–1; =–1,x
s,=1), f(x) . , n=0,1,...
n() , [– 1,1] signf(x) sign
n(x) 0, ¦f(x)–
n(x)¦ C(s) (f, 1/n+1, C(s) s. , - , « » . 相似文献
3.
Like dismantling for finite posets, a perfect sequence = P
: of a chain complete posetP represents a canonical procedure to produce a coreP
. It has been proved that if the posetP contains no infinite antichain then this coreP
is a retract ofP andP has the fixed point property iffP
has this property. In this paper the condition of having no infinite antichain is replaced by a weaker one. We show that the same conclusion holds under the assumption thatP does not contain a one-way infinite fence or a tower.Supported by a grant from The National Natural Science Foundation of China. 相似文献
4.
Let denote a distance-regular graph with vertex set X, diameter D 3, valency k 3, and assume supports a spin model W. Write W = i = 0D ti Ai where Ai is the ith distance-matrix of . To avoid degenerate situations we assume is not a Hamming graph and ti {t0, –t0 } for 1 i D. In an earlier paper Curtin and Nomura determined the intersection numbers of in terms of D and two complex parameters and q. We extend their results as follows. Fix any vertex x X and let T = T(x) denote the corresponding Terwilliger algebra. Let U denote an irreducible T-module with endpoint r and diameter d. We obtain the intersection numbers ci(U), bi(U), ai(U) as rational expressions involving r, d, D, and q. We show that the isomorphism class of U as a T-module is determined by r and d. We present a recurrence that gives the multiplicities with which the irreducible T-modules appear in the standard module. We compute these multiplicites explicitly for the irreducible T-modules with endpoint at most 3. We prove that the parameter q is real and we show that if is not bipartite, then q > 0 and is real.AMS 2000 Subject Classification: Primary 05E30 相似文献
5.
M. Lemańczyk 《Probability Theory and Related Fields》1988,78(4):491-507
Summary A new method for construction of transformations T
i: (X
i, B
i,
i) , i=1,2, that are factors of each other but that are not measuretheoretically isomorphic is provided. This method uses ergodic product cocycles of the form S
i
1xS
i
2x...,, where : XZ
2 is a cocycle, S belongs to the centralizer of T and T is an ergodic translation on a compact, monothetic group X. 相似文献
6.
M. J. Grimble 《Journal of Optimization Theory and Applications》1978,26(3):427-451
In the development of a roll force model for cold rolling, techniques were developed for solving the system equations which are of general interest. This paper gives a brief introduction to the physical model but concentrates on the solution of the model equations and the simulation. An unusual feature of the model was that the calculated profiles had to satisfy a number of boundary conditions at different points throughout the roll arc. A new method was developed for calculating these profiles and for determining the gradient functions which satisfied the boundary constraints.Nomenclature
p()
pressure at roll angle
-
h()
gauge
-
a()
roll radius
-
y()
yield stress
-
g
i
()
gradient function on iterationi
-
e()
gauge error
- (, )
transition function
-
H(–)
Heaviside unit step function at =
-
(–)
unit impulse function at =
-
H(,
1,
2)
defined asH( –
1) –H( –
2)
-
angular position from the roll center line
-
T
angular limits of roll arc represented
-
n
angular position of the neutral angle
-
i
angular position ofith strip elastic-plastic boundary
-
pi
pressure change at the boundaryi
-
i
,
i
,
i
constants defined in Appendix A
-
k
1,k
2
elastic region constants
-
k
total number of strip boundaries (elastic-plastic and entry and exit points)
-
R
undeformed work roll radius
-
R
s
roll separation—distance between roll centers
-
h
01
unstrained gauge in an elastic region
-
h
in
gauge of the strip at the entry to the roll gap
-
J
gauge error cost function
- <x, y>
inner product ofx andy
- x
norm ofx
-
L
2[0,
T
]
the space of Lebesgue square-integrable functions defined on the interval [0,
T
]
- JUVY
denotes (Dx)() =dx()/d
The author would like to acknowledge the help given by Dr. G. F. Bryant, Director, and Mr. M. A. Fuller, Senior Research Engineer, the Industrial Automation Group, Imperial College of Science and Technology, London. He is also grateful to M. J. G. Henderson of the University of Birmingham for his advice and encouragement during the project. He would like to thank the Directors of GEC Electrical Projects Limited for allowing him to undertake the work and also Mr. J. McTaggart and Mr. C. McKenzie (GEC), Professor H. A. Prime of the University of Birmingham, and Dr. G. F. Bryant for arranging the project. 相似文献
7.
The Dual of the martingale Hardy space ℋΦ with general Young function Φwith general Young function Φ
Bui Khoi Dam 《Analysis Mathematica》1988,14(4):287-294
[10], 1 . [4] K
q-, , 1p2 pp K
q, q=p/p–1)(q=+, p=1 K
= ). — p ⊃<<. , , , — , K
. , ( ) , q . 相似文献
8.
U. Goginava 《Analysis Mathematica》2000,26(3):209-226
In this paper we prove that if f C
(0, 1
N
) and the function f is of bounded partial variation, then the N-dimensional Walsh-Fourier series of the function f is uniformly (C,–) summable (1 +...+
N
< 1,
i
> 0, i = 1,...,N) in the sense of Pringsheim. If 1 +...+
N
= 1,
i
> 0, i = 1,2,...,N, then there exists a continuous function f
0 of bounded partial variation on [0, 1]
N
such that the Cesàro (C,–) means
m
–
(f0,Õ) of the N-dimensional Walsh-Fourier series of f
0 diverge over cubes. 相似文献
9.
Michael Lin 《Probability Theory and Related Fields》1981,55(2):231-236
Summary Let P be a Markov operator on L
(X, , m). Theorem 1: (i) P is weakly mixing (ii) For every fL
there is a sequence {nt} of density 1 such that all w
*-cluster points of
are constants (iii) For every fL
there is a {kj} with
w
*-convergent to a constant. Theorem 2: If P is induced by a non-singular transformation , P is weakly mixing For every A, {
–n(A)} has a remotely trivial subsequence. The existence of a finite invariant measure is not required in these results. 相似文献
10.
The essence of this article lies in a demonstration of the fact that for some random search methods (r.s.m.) of global optimization, the number of the objective function evaluations required to reach a given accuracy may have very slow (logarithmic) growth to infinity as the accuracy tends to zero. Several inequalities of this kind are derived for some typical Markovian monotone r.s.m. in metric spaces including thed-dimensional Euclidean space
d
and its compact subsets. In the compact case, one of the main results may be briefly outlined as a constructive theorem of existence: if
is a first moment of approaching a good subset of-neighbourhood ofx
0=arg maxf by some random search sequence (r.s.s.), then we may choose parameters of this r.s.s. in such a way that E
c(f) In2 . Certainly, some restrictions on metric space and functionf are required. 相似文献
11.
N. M. Ivochkina 《Journal of Mathematical Sciences》1984,26(6):2349-2359
One proves that a priori boundedness of the norm
of the solution of the problem det(Uxx)=f(x,u,ux)>>0,u¦=0. The magnitudes of the exponents,() depends on whether the arguments u p occur or not in f (x,u,p).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 74–90, 1983. 相似文献
12.
W. C. Stephen Suen 《Combinatorica》1993,13(2):209-229
We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let
i
be thei
th vertex encountered by DFS andL(i, m, n) be the height of
i
in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree. 相似文献
13.
Let bea distance-regular graph with diameter d. For vertices x and y of at distancei, 1 i d, we define the setsC
i(x,y) = i–1(x) (y), A
i
(x,y) =
i
(x) (y) and B
i
(x,y) =
i+1(x) (y).Then we say has the CABj property,if the partition CAB
i
(x,y) = {C
i
(x,y),A
i
(x,y),B
i
(x,y)}of the local graph of y is equitable for each pairof vertices x and y of at distance i j. We show that in with the CABj property then the parameters ofthe equitable partitions CAB
i(x,y) do not dependon the choice of vertices x and y atdistance i for all i j. The graph has the CAB property if it has the CAB
d
property. We show the equivalence of the CAB property and the1-homogeneous property in a distance-regular graph with a
1 0. Finally, we classify the 1-homogeneous Terwilligergraphs with c
2 2. 相似文献
14.
Tassilo Küpper 《Numerische Mathematik》1976,25(2):201-214
Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea
2 and for given functions = we require =C
0[0, 1] C
2([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and . 相似文献
15.
An overall bounded orthonormal set of functions
n
(x) is constructed for which there exists a series
m
=1 ann(x) with coefficients an=o(ln'n/n), which diverges to + almost everywhere. The bibliography contains 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 483–494, November, 1967. 相似文献
16.
We consider measurable subsets {ofR}n with 0<m()<, and we assume that has a spectral set . (In the special case when is also assumed open, may be obtained as the joint spectrum of a family of commuting self-adjoint operators {H
k: 1kn} in L
2 () such that each H
k is an extension of i(/x
k) on C
c
(), k=1, ..., n.)It is known that is a fundamental domain for a lattice if is itself a lattice. In this paper, we consider a class of examples where is not assumed to be a lattice. Instead is assumed to have a certain inhomogeneous form, and we prove a necessary and sufficient condition for to be a fundamental domain for some lattice in {ofR}n. We are thus able to decide the question, fundamental domain or not, by considering only properties of the spectrum . Our criterion is obtained as a corollary to a theorem concerning partitions of sets which have a spectrum of inhomogeneous form.Work supported in part by the NSF.Work supported in part by the NSRC, Denmark. 相似文献
17.
H. Roloff 《Journal of Mathematical Sciences》1984,27(4):2968-2974
Over a commutative ring R with invertible element 2 and with radical , nets (i.e., tables =(ij) of ideals ij such that irrj ij) such that
ii
are considered. Such nets are called pseudoradical. The groups of the lower central series and the derived series are explicitly constructed for the corresponding net subgroups G () (of the general linear group GL (n,R)) in terms of .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 180–186, 1982. 相似文献
18.
Cindy de Volder 《Geometriae Dedicata》2001,85(1-3):237-251
We consider the blowing-up Y
k
of the projective plane along k general points P
1,...,P
k
. Let
k
: Y
k
2 be the projection map and E
i
the exceptional divisor corresponding to P
i
for 1ik. For m2 and km(m+3)/2–4 let
k
be the invertible sheaf
k
*(
2(m))
Y
k
(–E
1–···–E
k
) on Y
k
, and let k: Y
k
N
be the morphism corresponding to
k
. As
k
is a local embedding, the Gauss map
k
corresponding to
k
is defined on Y
k
by
k
(x)=(d
x
k
)(T
x
(Y
k
)) for all xY
k
. We prove that this Gauss map
k
is injective. 相似文献
19.
I. A. Pushkarev 《Journal of Mathematical Sciences》1999,96(5):3590-3599
Let G SN be the wreath product of a finite group G and the symmetric group SN. The aim of this paper is to prove the branching theorem for the increasing sequence of finite groups G S1 G S2 ... G SN ... and the analog of Young's orthogonal form for this case, using the inductive approach invented by A. Vershik and A. Okounkov for the case of symmetric group.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 229–244. 相似文献
20.
Résumé Soit (V
)0 une résolvante définie sur un espace mesurable telle que le noyau initial est borné; on trouve une condition nécéssaire et suffisante pour qu'un noyau borné U possède une résolvante (U
)0 telle que U
V
pour tout 0. On donne plusieurs applications de ce résultat. 相似文献