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1.
Guido Walz 《BIT Numerical Mathematics》1997,37(1):189-201
In this paper we investigate some properties of trigonometric B-splines. We establish a complex integral representation for
these functions, which is in certain analogy to the polynomial case, but the proof of which has to be done in a different
and more complicated way. Using this integral representation, we can prove some identities concerning the evaluation of a
trigonometric B-spline, its derivative and its partial derivative w.r.t. the knots. Finally we show that—in the case of equidistant
knots—the trigonometric B-splines of odd order form a partition of a constant, and therefore the corresponding B-spline curve
possesses the convex-hull property. This is illustrated by a numerical example. 相似文献
2.
A new proof of Lévy’s version of the Absoluteness Lemma is given—a proof which avoids dependent choices and leads to stronger
versions of the lemma.
Research partially supported by N.S.F. Grant GP-8625. 相似文献
3.
Summary The concepts of the asymptotic maximum likelihood estimates—AMLEs in short—and their asymptotic identity are introduced in
section 1. They seem to be more adequate than the usual one for uses in the large sample theory. The AMLE is a slightly weakened
version of the usual maximum likelihood estimate and therefore it should have a bit wider applicability than the original
one. The asymptotic normality of a consistent AMLE and Wilks’ theorem concerning the asymptotic distribution of the statistic
—2 log λ, where λ is the likelihood ratio, can be obtained under the regularity conditions due to Doob in section 2. A set
of conditions which assure the existence of a unique and consistent AMLE is presented in section 3 and in the final section
4 the proof of the existence of the unique and consistent AMLE under those conditions is given.
This work has been motivated by the work of Ogawa, Moustafa and Roy [3]. 相似文献
4.
Cilanne E. Boulet 《The Ramanujan Journal》2006,12(3):315-320
We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrews in
which he considers the generating function for partitions with respect to size, number of odd parts, and number of odd parts
of the conjugate.
2000 Mathematics Subject Classification Primary—05A17; Secondary—11P81 相似文献
5.
We give a new proof of a theorem of Zudilin that equates a very-well-poised hypergeometric series and a particular multiple
integral. This integral generalizes integrals of Vasilenko and Vasilyev which were proposed as tools in the study of the arithmetic
behaviour of values of the Riemann zeta function at integers. Our proof is based on limiting cases of a basic hypergeometric
identity of Andrews.
Dedicated to Richard Askey on the occasion of his 70th birthday.
Research partially supported by the programme “Improving the Human Research Potential” of the European Commission, grant HPRN-CT-2001-00272,
“Algebraic Combinatorics in Europe”.
2000 Mathematics Subject Classification Primary—33C20; Secondary—11J72 相似文献
6.
Guy Alfandary 《Israel Journal of Mathematics》1994,86(1-3):211-220
LetG be a finite group. Attach toG the following two graphs: Γ — its vertices are the non-central conjugacy classes ofG, and two vertices are connected if their sizes arenot coprime, and Γ* — its vertices are the prime divisors of sizes of conjugacy classes ofG, and two vertices are connected if they both divide the size of some conjugacy class ofG. We prove that whenever Γ* is connected then its diameter is at most 3, (this result was independently proved in [3], for
solvable groups) and Γ* is disconnected if and only ifG is quasi-Frobenius with abelian kernel and complements. Using the method of that proof we give an alternative proof to Theorems
in [1],[2],[6], namely that the diameter of Γ is also at most 3, whenever the graph is connected, and that Γ is disconnected
if and only ifG is quasi-Frobenius with abelian kernel and complements. As a result we conclude that both Γ and Γ* have at most two connected
components. In [2],[3] it is shown that the above bounds are best possible.
The content of this paper corresponds to a part of the author’s Ph.D. thesis carried out at the Tel Aviv University under
the supervision of Prof. Marcel Herzog. 相似文献
7.
Gilles Godefroy 《Israel Journal of Mathematics》1988,61(3):301-331
We study the class of the Riesz subsets of abelian discrete groups, that is, the sets for which the F. and M. Riesz theorem
extends. We show that the “classical” tools of the theory — Riesz projections, localization in the Bohr sense, products —
are leading to Riesz sets which are satisfying nice additional properties, e.g., the Mooney-Havin result extends to this class.
We give an alternative proof of a result of A. B. Alexandrov, and we improve a construction of H. P. Rosenthal. The connection
is made between this class and theM-structure theory. We show a result of convergence at the boundary for holomorphic functions on the polydisc. The Bourgain-Davis
result on convergence of analytic martingales is improved. 相似文献
8.
G. Salomonsen 《Geometric And Functional Analysis》2001,11(5):1031-1095
We construct self-adjoint extensions of Dirac operators on manifolds with corners of codimension 2, which generalize the
Atiyah—Patodi—Singer boundary conditions. The boundary conditions are related to geometric constructions, which convert problems
on manifolds with corners into problems on manifolds with boundary and wedge singularities. In the case, where the Dirac bundle
is a super-bundle, we prove two general index theorems, which differ by the splitting formula for -invariants. Further we work out the de Rham, signature and twisted spin complex in closer detail. Finally we give a new proof
of the splitting formula for the -invariant.
Submitted: October 1999, Revised version: March 2001. 相似文献
9.
David W. Barnette 《Israel Journal of Mathematics》1971,9(3):290-298
Steinitz’ theorem states that a graph is the graph of a 3-dimensional convex polytope if and only if it is planar and 3-connected.
Grünbaum has shown that Steinitz’ proof can be modified to characterize the graphs of polytopes that are centrally symmetric
or have a plane of symmetry. We show how to modify Steinitz’ proof to take care of the remaining involutory case—polytopes
that are symmetric about a line.
Research supported by NSF Grant GP-3470. 相似文献
10.
XILIFENG 《高校应用数学学报(英文版)》1998,13(2):231-240
In this paper the derivative and its exceptional set according to the alternatively jumping function and self-similar function respectively are discussed. And in the appendix, a proof of the statement 1.2(2) of “Calculus on Cantor triadic set (Ⅱ)—derivative” which is important to the discussion of exceptional set is given. 相似文献
11.
Youssef Hamadi Sa?d Jabbour Lakhdar Sa?s 《4OR: A Quarterly Journal of Operations Research》2012,10(1):15-32
Learning is a general concept, playing an important role in many Artificial intelligence domains. In this paper, we address
the learning paradigm used to explain failures or conflicts encountered during search. This explanation, derived by conflict
analysis, and generally expressed as a new constraint, is usually used to dynamically avoid future occurrences of similar
situations. Before focusing on clause learning in Boolean satisfiability (SAT), we first overview some important works on
this powerful reasoning tool in other domains such as constraint satisfaction and truth maintenance systems. Then, we present
a comprehensive survey of the most important works having led to what is called today—conflict driven clause learning (CDCL)—which
is one of the key components of modern SAT solvers. In theory, current SAT solvers with clause learning are as powerful as
general resolution proof systems. In practice, real-world SAT instances with millions of variables and clauses are now in
the scope of this solving paradigm. 相似文献
12.
Wenchang Chu 《The Ramanujan Journal》2007,13(1-3):221-225
The Pfaff-Euler Transform for hypergeometric 2
F
1-series is applied to provide a direct and elementary proof that the hypergeometric representation with algebraic parameters
of Pollaczek polynomials are indeed polynomials.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—33C45; Secondary—33C05 相似文献
13.
We present here a (weak) axiom which implies some of the consequences of MA, but is consistent with GCH. We use the method
of Jensen in his proof of consis (ZFC+GCH+SH).
The third author wishes to thank the United States—Israel Binational Foundation for partially supporting this research by
Grant 1110. 相似文献
14.
The seminal contribution of Debreu and Scarf (Int Econ Rev 4:235–246, 1963) connects the two concepts of core and competitive
equilibrium in exchange economies. In effect, their core-equilibrium equivalence result states that, when the set of economic
agents is replicated, the set of core allocations of the replica economy shrinks to the set of competitive allocations. Florenzano
(J Math Anal Appl 153:18–36, 1990) defines the fuzzy core as the set of allocations which cannot be blocked by any coalition
with an arbitrary rate of participation and then shows the asymptotic limit of cores of replica economies coincides with the
fuzzy core. In this note, we provide an elementary proof of the non-emptiness of the fuzzy core for an exchange economy. Hence,
in motivation, our result is similar to the contribution of Vohra (On Scarf’s theorem on the non-emptiness of the core: a
direct proof through Kakutani’s fixed point theorem. Brown University Working Paper, 1987) and Shapley and Vohra (Econ Theory
1:108–116, 1991) for the core. Unlike the classical Debreu–Scarf limit theorem (Debreu and Scarf in Int Econ Rev 4:235–246,
1963) and its numerous extensions our result does not require any asymptotic intersection—or limit—of the set of core allocations
of replica economies.
The author would like to thank the Netherlands Organisation for Scientific Research (NWO) for financial support. 相似文献
15.
Mourad E. H. Ismail 《The Ramanujan Journal》2006,11(3):349-353
We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved
by W. Chu. We also give an elementary proof of a generalization of an identity originally proved using modular functions and
used to study a generating function for the number of partitions with specified crank.
Research partially supported by NSF grant DMS 99-70865.
2000 Mathematics Subject Classification Primary—39A70, 11P83; Secondary—33C20 相似文献
16.
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
17.
If disks are moved so that each center—center distance does not increase, must the area of their union also be nonincreasing?
We show that the answer is yes, assuming that there is a continuous motion such that each center—center distance is a nonincreasing
function of time. This generalizes a previous result on unit disks. Our proof relies on a recent construction of Edelsbrunner
and on new isoperimetric inequalities of independent interest. We go on to show analogous results for the intersection and
for holes between disks.
Received November 6, 1996, and in revised form June 16, 1997, and September 23, 1997. 相似文献
18.
We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is
the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex Δn is homotopy equivalent to a wedge of (n−2)! spheres of dimension n−4. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex
and the Hilbert series of the associated pre-WDVV ring.
2000 Mathematics Subject Classification: Primary—13F55, Secondary—05E99, 55P15 相似文献
19.
Hjalmar Rosengren 《The Ramanujan Journal》2006,12(2):155-166
Recently, Kajihara gave a Bailey-type transformation relating basic hypergeometric series on the root system A
n
, with different dimensions n. We give, with a new, elementary proof, an elliptic extension of this transformation. We also obtain further Bailey-type
transformations as consequences of our result, some of which are new also in the case of basic and classical hypergeometric
series.
2000 Mathematics Subject Classification Primary—33D67; Secondary—11F50 相似文献
20.
Yu. L. Ershov 《Algebra and Logic》1998,37(4):215-222
We introduce the concept of a projective family of subgroups, which behaves well under passage to subgroups, and then relate
it to the notion of a wreath product. This does indeed deliver a new proof of the Kurosh theorem on subgroups of a free product,
in which use is actually made of just categorical properties of a free product—all earlier proofs had a combinatorial bearing.
Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 381–393, July–August, 1998. 相似文献