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1.
Hilbert–Kunz multiplicity is known to be a very mysterious invariant of a ring or an ideal. We will show a very beautiful
formula on Hilbert–Kunz multiplicity for integrally closed ideals in two-dimensional Gorenstein rational singularities. In
the proof, “McKay correspondence” and “Riemann–Roch formula” play essential roles. Also this formula gives a new significance
to “good ideals”.
Received: 25 October 2000 相似文献
2.
F. BRACKX N. DE SCHEPPER K. I. KOU F. SOMMEN 《数学学报(英文版)》2007,23(4):697-704
The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform. In this paper, we introduce a multi-dimensional Fractional Fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler's formula for the generalized Clifford-Hermite polynomials of Clifford analysis. 相似文献
3.
H. Nakaya 《Lithuanian Mathematical Journal》2000,40(2):156-165
We study an asymptotic formula of the DirichletL-functions in the critical strip. This is an analogy of the Atkinson-type formula for DirichletL-functions.
Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 201–213, April–June, 2000. 相似文献
4.
Fima C. Klebaner Zinoviy Landsman 《Methodology and Computing in Applied Probability》2009,11(3):339-357
We derive an option pricing formula on assets with returns distributed according to a log-symmetric distribution. Our approach
is consistent with the no-arbitrage option pricing theory: we propose the natural risk-neutral measure that keeps the distribution
of returns in the same log-symmetric family reflecting thus the specificity of the stock’s returns. Our approach also provides
insights into the Black–Scholes formula and shows that the symmetry is the key property: if distribution of returns X is log-symmetric then 1/X is also log-symmetric from the same family. The proposed options pricing formula can be seen as a generalization of the Black–Scholes
formula valid for lognormal returns. We treat an important case of log returns being a mixture of symmetric distributions
with the particular case of mixtures of normals and show that options on such assets are underpriced by the Black–Scholes
formula. For the log-mixture of normal distributions comparisons with the classical formula are given.
相似文献
5.
The Kirillov–Schilling–Shimozono (KSS) bijectionappearing in theory of the Fermionic formula gives an one-to-onecorrespondence between the set of elements of tensor productsof the Kirillov–Reshetikhin crystals (called paths) andthe set of rigged configurations. It is a generalization ofKerov–Kirillov–Reshetikhin bijection and plays inversescattering formalism for the box–ball systems. In thispaper, we give an algebraic reformulation of the KSS map fromthe paths to rigged configurations, using the combinatorialR and energy functions of crystals. It gives a characterizationof the KSS bijection as an intrinsic property of tensor productsof crystals. 相似文献
6.
Y. Sasaki 《Lithuanian Mathematical Journal》2007,47(3):311-326
In this article, we prove an explicit formula for |ζ(σ + iT)|2, where ζ(s) is the Riemann zeta-function and 1/2 < σ < 1, which is an analogue of Jutila’s formula. Our proof differs from that of Jutila.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 381–398, July–September, 2007. 相似文献
7.
Complex B-splines as introduced in Forster et al. (Appl. Comput. Harmon. Anal. 20:281–282, 2006) are an extension of Schoenberg’s cardinal splines to include complex orders. We exhibit relationships between these complex
B-splines and the complex analogues of the classical difference and divided difference operators and prove a generalization
of the Hermite–Genocchi formula. This generalized Hermite–Genocchi formula then gives rise to a more general class of complex
B-splines that allows for some interesting stochastic interpretations.
相似文献
8.
Shayne Waldron 《Numerische Mathematik》1998,80(3):461-494
Summary. The main result of this paper is an abstract version of the Kowalewski–Ciarlet–Wagschal
multipoint Taylor formula for representing the pointwise error in multivariate Lagrange interpolation. Several applications of this result are given
in the paper. The most important of these is the construction of a multipoint Taylor error formula for a general finite element, together with the corresponding –error bounds. Another application is the construction of a family of error formul? for linear interpolation (indexed by real
measures of unit mass) which includes some recently obtained formul?. It is also shown how the problem of constructing an
error formula for Lagrange interpolation from a D–invariant space of polynomials with the property that it involves only derivatives which annihilate the interpolating space
can be reduced to the problem of finding such a formula for a ‘simpler’ one–point interpolation map.
Received March 29, 1996 / Revised version received November 22, 1996 相似文献
9.
T. Kuzumaki 《The Ramanujan Journal》2011,24(3):331-343
In this paper, we shall reveal the hidden structure in recent results of Katsurada as the Meijer G-function hierarchy. In Sect. 1, we consider the holomorphic Eisenstein series and show that Katsurada’s two new expressions
are variants of the classical Chowla–Selberg integral formula (Fourier expansion) with or without the beta-transform of Katsurada
being incorporated. In Sect. 2, we treat the Taylor series expansion of the Lipschitz–Lerch transcendent in the perturbation
variable. In the proofs, we make an extensive use of the beta-transform (used to be called the Mellin–Barnes formula). 相似文献
10.
Masamichi Takase 《Mathematische Zeitschrift》2007,256(1):35-44
We show that for any given differentiable embedding of the three-sphere in six-space there exists a Seifert surface (in six-space)
with arbitrarily prescribed signature. This implies, according to our previous paper, that given such a (6,3)-knot endowed
with normal one-field, we can construct a Seifert surface so that the outward normal field along its boundary coincides with
the given normal one-field. This aspect enables us to understand the resemblance between Ekholm–Szűcs’ formula for the Smale
invariant and a formula in our previous paper for differentiable (6,3)-knots. As a consequence, we show that an immersion
of the three-sphere in five-space can be regularly homotoped to the projection of an embedding in six-space if and only if
its Smale invariant is even. We also correct a sign error in our previous paper: “A geometric formula for Haefliger knots”
[Topology 43: 1425–1447 2004].
相似文献
11.
A new numerical quadrature formula on the unit circle 总被引:1,自引:0,他引:1
In this paper we study a quadrature formula for Bernstein–Szegő measures on the unit circle with a fixed number of nodes and
unlimited exactness. Taking into account that the Bernstein–Szegő measures are very suitable for approximating an important
class of measures we also present a quadrature formula for this type of measures such that the error can be controlled with
a well-bounded formula.
This work was supported by Ministerio de Educación y Ciencia under grants number MTM2005-01320 (E. B. and A. C.) and MTM2006-13000-C03-02
(F. M.). 相似文献
12.
Alexandre I. Danilenko 《Monatshefte für Mathematik》2001,134(2):121-141
Inspired by [17], we develop an orbital approach to the entropy theory for actions of countable amenable groups. This is
applied to extend – with new short proofs – the recent results about uniform mixing of actions with completely positive entropy
[17], Pinsker factors and the relative disjointness problems [10], Abramov–Rokhlin entropy addition formula [19], etc. Unlike
the cited papers our work is independent of the standard machinery developed by Ornstein–Weiss [14] or Kieffer [12]. We do
not use non-orbital tools like the Rokhlin lemma, the Shannon–McMillan theorem, castle analysis, joining techniques for amenable
actions, etc. which play an essential role in [17], [19] and [10].
(Received 23 October 2000) 相似文献
13.
We present a relative trace formula approach to the Gross–Zagier formula and its generalization to higher-dimensional unitary
Shimura varieties. As a crucial ingredient, we formulate a conjectural arithmetic fundamental lemma for unitary Rapoport–Zink
spaces. We prove the conjecture when the Rapoport–Zink space is associated to a unitary group in two or three variables. 相似文献
14.
We give an Atkinson-type formula for the periodic zeta-function ζλ with rational parameter λ.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 504–516, October–December, 2007. 相似文献
15.
Manfred Reimer 《Results in Mathematics》2006,49(3-4):361-375
Discretized Newman–Shapiro-operators furnish a generalized hyperinterpolation method on the sphere with valuable mathematical
properties. Unfortunately the price is high numerical evaluation cost, which, however, can be reduced significantly, in a
first step, by a truncation method. The remaining, relevant terms, now small in number, are values of a (zonal) kernel function
with arguments near the pole. Here, and with respect to the degree, the kernel function satisfies an asymptotic formula. It
is based on a generalized Mehler–Heine-type formula which concerns certain ‘divided’ Gegenbauer-polynomials and Bessel-functions.
This formula is proved and used in order to reduce, in a second step, the evaluation cost once more, such that the discretized
Newman–Shapiro-operators become a competitive direct numerical polynomial approximation method on the sphere. For example,
the graph of a degree 160 approximation to a rather complicated spherical function has been calculated with a time (cost)
reduction, in total, by a factor about 10−4. 相似文献
16.
Masahiko Ito 《The Ramanujan Journal》2006,12(1):131-151
A new formula for an Askey–Wilson type integral associated with the root system F
4 is studied. A simple proof of the evaluation formula for the original Askey–Wilson integral is also stated.
2000 Mathematics Subject Classification Primary—33D67, 33D60
This work was supported in part by Grant-in-Aid for Scientific Research (C) No. 15540045 from the Ministry of Education, Culture,
Sports, Science and Technology (Japan). 相似文献
17.
The Bass–Heller–Swan formula is a basic calculational tool in pseudoisotopy K-theory. We describe the Nil-groups and the Bass–Heller–Swan splitting for the group of the pseudoisotopies of a closed manifold.
We use the methods of controlled topology used in the Bass–Heller–Swan splitting in K-theory. 相似文献
18.
A reduction formula for compressions of von Neumann algebra II–factors arising as free products is proved. This shows that the fundamental group is for some such algebras. Additionally, by taking a sort of free product with an unbounded semicircular element, continuous
one parameter groups of trace scaling automorphisms on II–factors are constructed; this produces type III factors with core , where can be a full II–factor without the Haagerup approximation property.
Received: 26 October 1998 / in final form 18 March 1999 相似文献
19.
Most standard textbooks about asymptotic approximations of integrals do not give explicit formulas for the coefficients of
the asymptotic methods of Laplace and saddle point. In these techniques, those coefficients arise as the Taylor coefficients
of a function defined in an implicit form, and the coefficients are not given by a closed algebraic formula. Despite this
fact, we can extract from the literature some formulas of varying degrees of explicitness for those coefficients: Perron’s
method (in Sitzungsber. Bayr. Akad. Wissensch. (Münch. Ber.), 191–219, 1917) offers an explicit computation in terms of the derivatives of an explicit function; in (de Bruijn, Asymptotic Methods in
Analysis. Dover, New York, 1950) we can find a similar formula for the Laplace method which uses derivatives of an explicit function. Dingle (in Asymptotic
Expansions: Their Derivation and Interpretation, Academic Press, New York, 1973) gives the coefficients of the saddle point method in terms of a contour integral. Perron’s method is rediscovered in (Campbell
et al., Stud. Appl. Math. 77:151–172, 1987), but they also go farther and compute the above mentioned derivatives by means of a recurrence. The most recent contribution
is (Wojdylo, SIAM Rev. 48(1):76–96, 2006), which rediscovers the Campbell, Fr?man and Walles’ formula and rewrites it in terms of Bell polynomials (in the Laplace
method) using new ideas of combinatorial analysis which efficiently simplify and systematize the computations. In this paper
we continue the research line of these authors. We combine the more systematic version of the saddle point method introduced
in (López et al., J. Math. Anal. Appl. 354(1):347–359, 2009) with Wojdylo’s idea to derive a new and more explicit formula for the coefficients of the saddle point method, similar to
Wojdylo’s formula for the coefficients of the Laplace method. As an example, we show the application of this formula to the
Bessel function. 相似文献
20.
Ricardo Abreu-Blaya Juan Bory-Reyes Michael Shapiro 《Complex Analysis and Operator Theory》2007,1(2):143-168
In this paper we discuss the notion of the Bochner–Martinelli kernel for domains with rectifiable boundary in
, by expressing the kernel in terms of the exterior normal due to Federer (see [17,18]). We shall use the above mentioned
kernel in order to prove both Sokhotski–Plemelj and Plemelj–Privalov theorems for the corresponding Bochner–Martinelli integral,
as well as a criterion of the holomorphic extendibility in terms of the representation with Bochner–Martinelli kernel of a
continuous function of two complex variables.
Explicit formula for the square of the Bochner–Martinelli integral is rediscovered for more general surfaces of integration
extending the formula established first by Vasilevski and Shapiro in 1989.
The proofs of all these facts are based on an intimate relation between holomorphic function theory of two complex variables
and some version of quaternionic analysis.
Submitted: September 6, 2006. Accepted: November 1, 2006. 相似文献