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1.
A Dirichlet stereohedron for a crystallographic group G is the Voronoi region of any point with trivial stabilizer in the Voronoi diagram of its orbit.
We prove that Dirichlet stereohedra for three-dimensional crystallographic groups containing reflections in three, two or
one independent directions cannot have more than eight, eighteen and fifteen facets, respectively. We show examples where
the three bounds are attained.
As a tool for one of the cases, we study how many regions of a Dirichlet tesselation in the plane can be intersected by each
region of another Dirichlet tesselation for the same group. We find out that the number is at most seven for all planar crystallographic
groups except, perhaps, those of type pgg .
Received October 4, 1999, and in revised form May 30, 2000. Online publication December 4, 2000. 相似文献
2.
《Set-Valued Analysis》2008,16(2-3):199-227
The paper contains two groups of results. The first are criteria for calmness/subregularity for set-valued mappings between
finite-dimensional spaces. We give a new sufficient condition whose subregularity part has the same form as the coderivative
criterion for “full” metric regularity but involves a different type of coderivative which is introduced in the paper. We
also show that the condition is necessary for mappings with convex graphs. The second group of results deals with the basic
calculus rules of nonsmooth subdifferential calculus. For each of the rules we state two qualification conditions: one in
terms of calmness/subregularity of certain set-valued mappings and the other as a metric estimate (not necessarily directly
associated with aforementioned calmness/subregularity property). The conditions are shown to be weaker than the standard Mordukhovich–Rockafellar
subdifferential qualification condition; in particular they cover the cases of convex polyhedral set-valued mappings and,
more generally, mappings with semi-linear graphs. Relative strength of the conditions is thoroughly analyzed. We also show,
for each of the calculus rules, that the standard qualification conditions are equivalent to “full” metric regularity of precisely
the same mappings that are involved in the subregularity version of our calmness/subregularity condition.
The research of Jiří V. Outrata was supported by the grant A 107 5402 of the Grant Agency of the Academy of Sciences of the
Czech Republic. 相似文献
3.
W. Eckhaus 《Journal of Nonlinear Science》1993,3(1):329-348
Summary The Ginzburg-Landau modulation equation arises in many domains of science as a (formal) approximate equation describing the
evolution of patterns through instabilities and bifurcations. Recently, for a large class of evolution PDE's in one space
variable, the validity of the approximation has rigorously been established, in the following sense: Consider initial conditions
of which the Fourier-transforms are scaled according to the so-calledclustered mode-distribution. Then the corresponding solutions of the “full” problem and the G-L equation remain close to each other on compact intervals
of the intrinsic Ginzburg-Landau time-variable. In this paper the following complementary result is established. Consider
small, but arbitrary initial conditions. The Fourier-transforms of the solutions of the “full” problem settle to clustered
mode-distribution on time-scales which are rapid as compared to the time-scale of evolution of the Ginzburg-Landau equation. 相似文献
4.
Let X, Y be finite sets and T a set of functions X → Y which we will call “ tableaux”. We define a simplicial complex whose facets, all of the same dimension, correspond to these
tableaux. Such tableau complexes have many nice properties, and are frequently homeomorphic to balls, which we prove using vertex decompositions [BP79].
In our motivating example, the facets are labeled by semistandard Young tableaux, and the more general interior faces are
labeled by Buch’s set-valued semistandard tableaux. One vertex decomposition of this “Young tableau complex” parallels Lascoux’s
transition formula for vexillary double Grothendieck polynomials [La01, La03]. Consequently, we obtain formulae (both old
and new) for these polynomials. In particular, we present a common generalization of the formulae of Wachs [Wa85] and Buch
[Bu02], each of which implies the classical tableau formula for Schur polynomials. 相似文献
5.
We construct an asymptotics of the solution the Laplace equation in a “long” rectangle with the directional derivative given
on its “long sides” and Dirichlet data on its “short sides.” By using the asymptotics, we calculate one of the integral characteristics,
namely, the magnetoresistance. We obtain new formulas for the low-magnetic field magnetoresistance.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 520–532, April, 1999. 相似文献
6.
Jun Kigami 《Mathematische Annalen》2008,340(4):781-804
We study the standard Dirichlet form and its energy measure,called the Kusuoka measure, on the Sierpinski gasket as aprototype
of “measurable Riemannian geometry”. The shortest pathmetric on the harmonic Sierpinski gasket is shown to be thegeodesic
distance associated with the “measurable Riemannianstructure”. The Kusuoka measure is shown to have the volumedoubling property
with respect to the Euclidean distance and alsoto the geodesic distance. Li–Yau type Gaussian off-diagonal heatkernel estimate
is established for the heat kernel associated withthe Kusuoka measure. 相似文献
7.
We study pairs of Dirichlet series
and
in whicha(n) counts the number of objects of “size”n of some class of objects which is closed under formation of direct products and extraction of irreducible factors, andp(n) counts the number of objects of “size”n which are irreducible in this class. We prove Dirichlet series analogues of certain results about power series and use these
results to prove some conjectures of Burris concerning first-order 0–1 laws. 相似文献
8.
Matthias Schütt 《The Ramanujan Journal》2009,19(2):187-205
We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under
the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce tables
for weights 3 and 4, where finiteness holds unconditionally.
I am indepted to K. Hulek for his continuous interest and encouragement. Partial support by the DFG Schwerpunkt 1094 “Globale
Methoden in der komplexen Geometrie” is gratefully acknowledged. My thanks go also to the referee for helpful comments.
Part of the revising took place while I enjoyed the hospitality of the Dipartimento di Matematica “Frederico Enriques” of
Milano University. Funding from the network Arithmetic Algebraic Geometry, a Marie Curie Research Training Network, is gratefully
acknowledged. I particularly thank M. Bertolini and B. van Geemen. The final version was prepared while I was funded by DFG
under grant Schu 2266/2-2. 相似文献
9.
Vincent Astier 《Archive for Mathematical Logic》2007,46(5-6):481-488
Using sheaves of special groups, we show that a general local-global principle holds for every reduced special group whose
associated space of orderings only has a finite number of accumulation points. We also compute the behaviour of the Boolean
hull functor applied to sheaves of special groups.
The research leading to this note was carried out with the partial support of the European RTN Networks HPRN-CT-2002-00287
“Algebraic K-Theory, Linear Algebraic Groups and Related Structures”, and HPRN-CT-2001-00271 “Real Algebraic and Analytic
Geometry” 相似文献
10.
E. I. Timoshenko 《Algebra and Logic》2006,45(1):67-74
For a factor group with respect to periodic part of a group of the form F/[R′, F], an embedding in the matrix group is defined.
The criteria for a matrix to belong to an image of this group and for elements to be conjugate are specified. Some statements
having a direct bearing on groups of the form in question are proved. Application of the results obtained allows us to refine
the answer in [7] to a question by O. Chapuis concerning the universal classification of ∀-free soluble groups with two generators.
Supported by RFBR grant No. 02-01-00293 and by FP “Universities of Russia” grant No. UR.04.01.227.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 114–125, January–February, 2006. 相似文献
11.
Construction of large families of pseudorandom binary sequences 总被引:2,自引:0,他引:2
László Mérai 《The Ramanujan Journal》2009,18(3):341-349
Oon constructed large families of finite binary sequences with strong pseudorandom properties by using Dirichlet characters
of large order. In this paper Oon’s construction is generalized and extended. We prove that in our construction the well-distribution
and correlation measures are as “small” as in the case of the Legendre symbol.
相似文献
12.
V. A. Gritsenko 《Journal of Mathematical Sciences》1990,52(3):3056-3063
In the paper one computes the Fourier coefficients of the Eisenstein series of the orthogonal group of signature (1, 4). The
formulas show that the restriction of the Eisenstein series to the “imaginary” axis is a Dirichlet series, whose coefficients
are the products of the L-series by the number of the representations of the given number as a sum of three squares.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 82–90, 1987. 相似文献
13.
Jozsef Losonczy 《Annals of Combinatorics》2007,11(2):195-212
We introduce and study a class of “maximally clustered” elements for simply laced Coxeter groups. Such elements include as
a special case the freely braided elements of Green and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. We show that any reduced expression for a maximally clustered element is short-braid equivalent
to a “contracted” expression, which can be characterized in terms of certain subwords called “braid clusters”. We establish
some properties of contracted reduced expressions and apply these to the study of Schubert varieties in the simply laced setting.
Specifically, we give a smoothness criterion for Schubert varieties indexed by maximally clustered elements.
Received December 30, 2005 相似文献
14.
15.
We give an explicit form of a “good” Euler factor of a certain Dirichlet series attached to the Siegel-Eisenstein series.
The author was partially supported by Grant-in-Aid for Scientific Research, the Ministry of Education, Science, Sports and
Culture, Japan. 相似文献
16.
We consider a relaxed Dirichlet problem for a subelliptic p-Laplacian. We define the regular points for our problem and we
prove a Wiener type criterion (in terms of the μ-capacity related to the problem) for the regularity of a point. As consequence
of our result we obtain also a Wiener criterion for the regularity of boundary points.
Entrata in Redazione il 30 dicembre 1998.
The first Author has been partially supported by the MURST Research Project: “Non-Euclidean structures: Dirichlet forms and
Fractals”. 相似文献
17.
We calculate the distribution of the sextuple statistic over the hyperoctahedral group B
n
that involves the flag-excedance and flag-descent numbers “fexc” and “fdes,” the flag-major index “fmaj,” the positive and
negative fixed point numbers “
” and “
” and the negative letter number “neg.” Several specializations are considered. In particular, the joint distribution for
the pair
is explicitly derived.
相似文献
18.
For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime
graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set
with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders
on these sets; the information obtained is collected in tables. We consider several applications of these results to various
problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups.
Supported by RFBR grant No. 05-01-00797; by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1; by the RF Ministry of Education Developmental Program for Scientific Potential of the Higher
School of Learning, project No. 8294; by FP “Universities of Russia,” grant No. UR.04.01.202; and by Presidium SB RAS grant
No. 86-197.
__________
Translated from Algebra i Logika, Vol. 44, No. 6, pp. 682–725, November–December, 2005. 相似文献
19.
In this paper we describe vanishing and non-vanishing of cohomology of “most” line bundles over Schubert subvarieties of flag
varieties for rank 2 semisimple algebraic groups. 相似文献
20.
Andrzej Herdegen 《Annales Henri Poincare》2006,7(2):253-301
Casimir effect in most general terms may be understood as a backreaction of a quantum system causing an adiabatic change of
the external conditions under which it is placed. This paper is the second installment of a work scrutinizing this effect
with the use of algebraic methods in quantum theory. The general scheme worked out in the first part is applied here to the
discussion of particular models. We consider models of the quantum scalar field subject to external interaction with “softened”
Dirichlet or Neumann boundary conditions on two parallel planes. We show that the case of electromagnetic field with softened
perfect conductor conditions on the planes may be reduced to the other two. The “softening” is implemented on the level of
the dynamics, and is not imposed ad hoc, as is usual in most treatments, on the level of observables. We calculate formulas for the backreaction energy in these
models. We find that the common belief that for electromagnetic field the backreaction force tends to the strict Casimir formula
in the limit of “removed cutoff” is not confirmed by our strict analysis. The formula is model dependent and the Casimir value
is merely a term in the asymptotic expansion of the formula in inverse powers of the distance of the planes. Typical behaviour
of the energy for large separation of the plates in the class of models considered is a quadratic fall-of. Depending on the
details of the “softening” of the boundary conditions the backreaction force may become repulsive for large separations.
Communicated by Klaus Fredenhagen
submitted 9/09/04, accepted 1/07/05 相似文献