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1.
Satoru Fujishige 《Mathematical Programming》1984,29(2):125-141
The present paper shows that for any submodular functionf on a crossing family
with
, if the polyhedron
is nonempty, then there exist a unique distributive lattice
with
and a unique submodular function
with
such thatB(f) coincides with the base polyhedron
associated with the submodular system
. Here, iff is integer-valued, thenf
1 is also integer-valued.
Based on this fact, we also show the relationship between the independent-flow problem considered by the author and the minimum
cost flow problem considered by J. Edmonds and R. Giles. 相似文献
2.
E. Steingrímsson 《Discrete and Computational Geometry》1994,12(1):465-479
The 2-weak vertex-packing polytope of a loopless graphG withd vertices is the subset of the unitd-cube satisfyingx
i
+x
j
≤1 for every edge (i,j) ofG. The dilation by 2 of this polytope is a polytope
with integral vertices. We triangulate
with lattice simplices of minimal volume and label the maximal simplices with elements of the hyperoctahedral groupB
d
. This labeling gives rise to a shelling of the triangulation
of
, where theh-vector of
(and the Ehrharth
*-vector of
can be computed as a descent statistic on a subset ofB
d
defined in terms ofG. A recursive way of computing theh-vector of
is also given, and a recursive formula for the volume of
.
This work was partially supported by grants from the Icelandic Council of Science and the Royal Swedish Academy of Sciences,
respectively. 相似文献
3.
Automatic groups were introduced in connection with geometric problems, in particular with the study of fundamental groups
of 3-manifolds. In this article the class of automatic groups is extended to include the fundamental group of every compact
3-manifold which satisfies Thurston's geometrization conjecture. Toward this end, the class
of asynchronously
groups is introduced and studied, where
is an arbitrary full abstract family of languages. For example
may be the family of regular languagesReg, context-free languagesCF, or indexed languagesInd. The class
consists of precisely those groups which are asynchronously automatic. It is proved that
contains all of the above fundamental groups, but that
does not. Indeed a virtually nilpotent group belongs to
if and only if it is virtually abelian.
The first author was partially supported by NSF grant DMS-9203500 and FNRS (Suisse). He also wishes to thank the University
of Geneva for its hospitality while this paper was being written. The second author thanks the Institute for Advanced Study
for its hospitality while this paper was being written. 相似文献
4.
It
and
are two families of pairwise disjoint simple closed curves in the plane such that each curve in
intersects each curve in
, then the total number of points of intersection in
is at least 2(m−1)n, where
, and this bound is best possible. We use this to show that the cartesian product of two 5-cycles has crossing number 15. 相似文献
5.
Evgeni Ja. Gabovič 《Semigroup Forum》1972,4(1):335-340
A semigroup S is calledE-semigroup (
-semigroup) if every (finitely generated) subsemigroup of S is an endomorphic image of S and Ē-semigroup (
-semigroup) if every subsemigroup of S is an E-semigroup
-semigroup. All classes X ε {Ē,
, E,
} are distinct even in the case of semilattices. It is established when a free band (semilattice) is an X-semigroup.
-,
- and Ē-chains and E-chains with identity or zero, Ē-and
, X-bands with identity and X-semigroups with identity and zero are found. 相似文献
6.
K. R. Apt 《Israel Journal of Mathematics》1978,29(2-3):221-238
The connections between inductive definability and models of comprehension are studied. Let
= 〈A, R
l, ...,R
n 〉 be an infinite structure and letI
φ
be a set inductively defined by a formulaφ of the second order language
. We prove that if
is a model of Δ
1
1
-Comprehension relativized toφ, andφ is
-absolute, then for everyη smaller than the height of
(h(
)),I
φ
is in
. If
is aβ-structure which satisfies Σ
1
1
-Comprehension relativized toφ and WF(X), and φ is
-absolute, thenI
φ
is in
and ‖φ| <h (
). These results imply that Barwise-Grilliot theorem is false in the case of uncountable acceptable structures. We also study
the notion of invariant definability over models1 of Δ
1
1
-Comprehension.
This paper is registered as Report ZW 69/76 of the Mathematical Centre. 相似文献
7.
Let
be a family of two-valued functions defined on ann-element set in which each pair of functions in
satisfy a given intersection condition. For certain intersection conditions we determine the maximal value of
. 相似文献
8.
Given a self-concordant barrier function for a convex set
, we determine a self-concordant barrier function for the conic hull
of
. As our main result, we derive an “optimal” barrier for
based on the barrier function for
. Important applications of this result include the conic reformulation of a convex problem, and the solution of fractional
programs by interior-point methods. The problem of minimizing a convex-concave fraction over some convex set can be solved
by applying an interior-point method directly to the original nonconvex problem, or by applying an interior-point method to
an equivalent convex reformulation of the original problem. Our main result allows to analyze the second approach showing
that the rate of convergence is of the same order in both cases. 相似文献
9.
William M. Kantor 《Israel Journal of Mathematics》1976,23(1):8-18
Generalized quadrangles
are studied in whichs ort is prime and Aut
has rank 3 on points.
This research was supported in part by NSF grant GP 37982X. 相似文献
10.
For an arbitrary uniformly continuous completely positive semigroup (
t
:t0) on the space of bounded operators on a Hilbert space, we construct a family (U(t)t0) of unitary operators on a Hilbert space and a conditional expectation from to, such that, for arbitraryt0,. The unitary operatorsU(t) satisfy a stochastic differential equation involving a noncommutative generalisation of infinite dimensional Brownian motion. They do not form a semigroup.Part of this work was completed when the first author was visiting research associate at the Center for Relativity, Physics Department, The University of Texas at Austin, Austin, TX 78712, U.S.A., supported in part by NSF PHY 81-01381. 相似文献
11.
Z. A. Arushanyan 《Journal of Mathematical Sciences》1981,16(3):1161-1167
One finds conditions which ensure the possibility of weighted mean-square approximation of a vector-function defined on the
boundary of an n-dimensional domain
by vector-functions of the form
, where u is, the solution of the equation Δm
u=0 in
while∂/∂v denotes differentiation along the normal. The weight function is continuous and positive everywhere on
with the point
whose relative neighborhood
is contained in some (n-1)-dimensional plane. The solution of this approximation problem is closely related with a certain
uniqueness theorem for the solution of the Cauchy problem for the polyharmonic equation, also proved in the paper.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR,
Vol. 65, pp. 164–171, 1976. 相似文献
12.
William R. Nico 《Semigroup Forum》1972,5(1):145-153
Let S be a monoid such that every left S-operand satisfies the ascending chain condition on orbits. Let X be an indecomposable
[0-indecomposable] left S-operand. There is a descending chain of suboperands of X defined in terms of maximal orbits. If
this chain terminates after a finite number of terms, the last non-empty [non-zero] term defines a distinguished collection
(X) [
0(X)] of disjoint [0-disjoint] orbits in X. The assumption that
(X) [
0(X)] is finite for all appropriate X, together with the additional assumption that every left S-operand satisfies the d.c.c.
on orbits, implies that S has a unique minimal left ideal [that the principal left ideals outside of the minimal ideal are
linearly ordered].
This research supported in part by the National Science Foundation. 相似文献
13.
R. Schneider 《Discrete and Computational Geometry》1995,13(1):609-627
Let
be an infinite discrete system ofk-dimensional flats inn-dimensional Euclidean space. If the totalk-dimensional volume of the flats in
intersected with the ball of center 0 and radiusr, divided by the volume of that ball, tends to a limit forr→∞, then this limit is called thedensity of
. We consider isoperimetric problems of the following kind. If
is a hyperplane system of positive density, find sharp upper bounds for the density of the system ofk-flats (k∈{0, ...,n−2}) that are generated as intersections of hyperplanes in
. Ideas from the theory of uniform distribution of sequences are employed to define a large class of hyperplane systems, calleduniform, for which all necessary densities exist, isperimetric inequalities can be proved, and systems with extremal intersection
densities can be characterized. 相似文献
14.
K. L. Malyshev 《Journal of Mathematical Sciences》1994,71(1):2281-2287
A representation of the algebra
(3)=t(3) S0(3, ) by differential Schaefer's operators is proposed, and an external algebra of
(3)-valued differential forms is constructed. The requirement of local gauge invariance is formulated in the model of the
(3)-valued field, which enables a group of gauge transformations of the continual theory of defects to be obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 173–184, 1991.I wish to thank V. N. Popov for his interest. 相似文献
15.
Jean-Eric Pin 《Semigroup Forum》1980,20(1):11-47
Résumé On étudie le mono?de des parties
d'un mono?de fini M. On montre en particulier que pour tout groupe non commutatif fini G et pour tout mono?de fini M, il
existe un entier n tel que M divise
où Gn=G×G×...×G (n fois). Les résultats obtenus permettent d'autre part de décrire toutes les variétés de langages (au sens d'Eilenberg)
qui sont fermées par morphisme littéral (resp. par substitution inverse). On étudie également les variétés fermées par mélange. 相似文献
16.
Jim Lawrence 《Discrete and Computational Geometry》1988,3(1):307-324
Given a collection of convex polytopes, let() denote the set of all convex transversals of. If and are two such collections, of finite cardinality, then there is a simple, arithmetical condition which holds precisely when ()=(). Another such condition, involving what we call the Sallee-Shephard mapping, characterizes those pairs and for which (())=().As these results are established, several distributive lattices involving convex sets are introduced, and relationships between their valuation modules are determined. In particular, it is proven that the Sallee-Shephard mapping is an isomorphism of the additive, abelian group of simple functions generated by the characteristic functions of the open, convex sets and that generated by those of the closed, convex sets. 相似文献
17.
V. V. Peller 《Journal of Mathematical Sciences》1985,31(1):2709-2712
In this paper there is given a sufficient condition for a Hankel matrix F to belong to the space of Schur multipliers of all bounded operators in
2 (or, what is the same, to the tensor algebra V2). It is shown that ifw is a nonnegative function on T, such that is a sequence of integers, {Fi}j1 is a sequence of polynomials,) and, then FV2. It follows from this that under these conditions F is a multiplier of the space H1, i.e.,.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 113–119, 1984 相似文献
18.
This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category:
and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of
and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give
a sufficient and necessary condition for the braid of,
Hℳ to induce the braid of
, or equivalently, the braid of
, whereA is a quantum commutativeH-module algebra 相似文献
19.
Geoffrey S. Watson 《Annals of the Institute of Statistical Mathematics》1983,35(1):303-319
Summary A distribution on the unit sphere inℝ
q
with a densityf(‖x
v
‖) is considered where
is ans(<q) dimensional subspace andx
v
is the part ofx in
. For a large sample the estimation of
, a test that
and a test for rotational symmetry within
is given. For several samples with possibly different subspaces
but the samef, a test that
is given. For all tests power functions for contiguous alternatives are given. For the special density proportional to expk‖x
v
‖
2, additional results are given.
Research supported in part by a Contract with the Office of Naval Research N00014-81-K-0146 awarded to Princeton University,
Princeton, New Jersey 08544. 相似文献
20.
Le Tu Quoc Thang 《Discrete and Computational Geometry》1995,14(1):31-70
The existence of different kinds of local rules is established for many sets of pentagonal quasi-crystal tilings. For eacht∈ℝ there is a set
of pentagonal tilings of the same local isomorphism class; the caset=0 corresponds to the Penrose tilings. It is proved that the set
admits a local rule which does not involve any colorings (or markings, decorations) if and only ift=m+nτ. In other words, this set of tilings is totally characterized by patches of some finite radius, orr-maps. When
the set
admits a local rule which involvescolorings. For the set of Penrose tilings the construction here leads exactly to the Penrose matching rules. Local rules for the caset=1/2 are presented. 相似文献