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1.
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the
convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary
dimension. The algorithm has the following properties:
For example, the algorithm finds thev vertices of a polyhedron inR
d defined by a nondegenerate system ofn inequalities (or, dually, thev facets of the convex hull ofn points inR
d, where each facet contains exactlyd given points) in timeO(ndv) andO(nd) space. Thev vertices in a simple arrangement ofn hyperplanes inR
d can be found inO(n
2
dv) time andO(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming. 相似文献
(a) | Virtually no additional storage is required beyond the input data. |
(b) | The output list produced is free of duplicates. |
(c) | The algorithm is extremely simple, requires no data structures, and handles all degenerate cases. |
(d) | The running time is output sensitive for nondegenerate inputs. |
(e) | The algorithm is easy to parallelize efficiently. |
2.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
1. | It does not self-overlap: it is a simple polygon. |
2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
• | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
• | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
• | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
3.
Belmesnaoui Aqzzouz 《Rendiconti del Circolo Matematico di Palermo》2006,55(2):147-162
We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK
x with the followings properties:
相似文献
1 | The categoryK is a full subcategory ofK x. |
2 | The free objects ofK are projectives inK x. |
3 | A sequence ofK-morphismes isK-exact if, and only if, it isK x-exact. |
4 | To each objectU ofK x we can associate a surjections:X→U whereX is an object ofK. |
4.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
相似文献
(1) | Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|. |
(2) | |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group. |
(3) | |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group. |
5.
6.
We show that the following two problems are polynomially equivalent:
As a consequence, an optimality testing oracle may be used to design a polynomial time algorithm for approximately solving the (weighted) Max-Cut Problem. 相似文献
1) | Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not. |
2) | Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC. |
7.
Joseph Corneli Neil Hoffman Paul Holt George Lee Nicholas Leger Stephen Moseley Eric Schoenfeld 《Journal of Geometric Analysis》2007,17(2):189-212
We prove the double bubble conjecture in the three-sphereS
3 and hyperbolic three-spaceH
3 in the cases where we can apply Hutchings theory:
A balancing argument and asymptotic analysis reduce the problem inS
3 andH
3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces. 相似文献
– | • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. |
– | • inH 3, when the smaller volume is at least 85% that of the larger. |
8.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB
n andC
n and obtain the following main results:
For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB
n orC
n overk.
相似文献
(a) | We give the configuration ofZB n andZC n. |
(b) | We show that Λ is standard. |
(c) | Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n. |
9.
M. K. Sen 《Semigroup Forum》1992,44(1):149-156
A pair (S, P) of a regular semigroupsS and a subsetP ofE
s
whereE
s
is the set of all idempotent elements ofS is called aP-regular semigroupS(P) if it satisfies the following:
The class of orthodox semigroups and the class of regular *-semigroups are within the class ofP-regular semigroups. This paper gives a characterisation of theP-kernel of aP-congruence. 相似文献
(1) | P 2 ⊆E S |
(2) | qPq⊆P for allq∈P |
(3) | for anyx∈S there existsx †∈V(x) (the set of inverses ofx), such thatxP 1 x †⊆P andx † P 1 x⊆P whereP 1=P∩{1}. |
10.
For any two 2-regular spanning subgraphs G and H of the complete multipartite graph K, necessary and sufficient conditions are found for the existence of a 2-factorization of K in which
in the case where K has an odd number of vertices. 相似文献
1. | the first and second 2-factors are isomorphic to G and H respectively, and |
2. | each other 2-factor is a hamilton cycle |
11.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
(1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
(2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
(3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
(4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |
12.
Yuji Kobayashi 《Archiv der Mathematik》2005,85(3):227-232
Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family
of finitely presented groups Gn over a fixed finite alphabet with solvable word problem such that
Received: 22 July 2004 相似文献
(1) | the center of Gn is trivial for every |
(2) | the dimension d(n) of the center of the group algebra K · Gn over K is either 1 or k, and |
(3) | it is undecidable given n whether d(n) = 1 or d(n) = k. |
13.
We prove that if a closed planar setS is not a countable union of convex subsets, then exactly one of the following holds:
We show that an analogous theorem is impossible for dimension greater than 2. We give an example of a compact planar set with
countable degree of visual independence which is not a countable union of convex subsets, and give a combinatorial criterion
for a closed set inR
d
not to be a countable union of convex sets. We also prove a conjecture of G. Kalai, namely, that a closed planar set with
the property that each of its visually independent subsets has at most one accumulation point, is a countable union of convex
sets. We also give examples of sets which possess a (small) finite degree of visual independence which are not a countable
union of convex subsets. 相似文献
(a) | There is a perfect subsetP⊆S such that for every pair of distinct pointsx, yεP, the convex closure ofx, y is not contained inS. |
(b) (a) | does not hold and there is a perfect subsetP⊆S such that for every pair of pointsx, yεP the convex closure of {x, y} is contained inS, but for every triple of distinct pointsx, y, zεP the convex closure of {x, y, z} is not contained inS. |
14.
P. Moszkowski 《Periodica Mathematica Hungarica》1989,20(2):147-154
The major sequences of lengthn are defined as the words withn letters taken from the integers 1, 2, ,n and containing at least
相似文献
1. | letter equal ton |
2. | letters equal or more thann – 1,n – 1 letters equal or more than 2. |
15.
16.
Ronen Peretz 《Israel Journal of Mathematics》1999,109(1):181-187
LetF(X, Y) be a two dimensional polynomial map overC. We show how to use the notion of induced resultants in order to give short and elementary proofs to the following three
theorems:
相似文献
1. | If the Jacobian of F is a non-zero constant, then the image of F contains all of C2 except for a finite set. |
2. | If F is invertible, then the inverse map is determined by the free terms of the induced resultants. |
3. | If F is invertible, then the degree of F equals the degree of its inverse. |
17.
A nearlattice S is a meet semilattice together with the property that any two elements possessing a common upper bound have a supremum. Here the authors have introduced the notion of sectionally semicomplemented distributive nearlattices and given several characterizations of them. The skeleton SCon(S) of Con(S), the congruence lattice, consists of all those nearlattice congruences which are the pseudocomplements of members of Con(S). The relationship between skeletal congruences and kernel of skeletal congruences leads to numerous characterizations of sectionally semicomplemented distributive nearlattices and semiboolean algebras. For example we prove, for a distributive nearlattice S with 0, the following conditions are equivalent:
AMS Subject Classifications (1991): 06A12, 06A99, 06B10. 相似文献
(i) | S is sectionally semicomplemented |
(ii) | The map Θ Θ ̸ker Θ of SCon(S) onto KSCon(S) is one-to-one. |
(iii) | The map Θ Θ ̸ker Θ of SCon(S) onto KSCon(S) preserves finite joins. |
(iv) | The map Θ Θ ker ̸Θ is a lattice isomorphism of SCon(S) onto KSCon(S), whose inverse is the map J ̸ Θ(J)**. |
18.
Michel Brion 《manuscripta mathematica》1993,80(1):347-371
Two conjectures made by II.O. Foulkes in 1950 can be stated as follows.
相似文献
1) | Denote byV a finite-dimensional complex vector space, and byS m V itsm-th symmetric power. Then the GL(V)-moduleS n (S m V ) contains the GL(V)-moduleS n (S m V ) forn > m. |
2) | For any (decreasing) partition λ = (λ1,λ2,λ3,...), denote byS λ V the associated simple, polynomial GL(V)-module. Then the multiplicity of in the GL(V)-moduleS n (S m+p Y) is an increasing function ofp. We show that Foulkes' first conjecture holds forn large enough with respect tom (Corollary 1.3). Moreover, we state and prove two broad generalizations of Foulkes' second conjecture. They hold in the framework of representations of connected reductive groups, and they lead e.g. to a general analog of Hermite's reciprocity law (Corollary 1 in 3.3). |
19.
In this paper, we show the equivalence of somequasi-random properties for sparse graphs, that is, graphsG with edge densityp=|E(G)|/(
2
n
)=o(1), whereo(1)→0 asn=|V(G)|→∞. Our main result (Theorem 16) is the following embedding result. For a graphJ, writeN
J(x) for the neighborhood of the vertexx inJ, and letδ(J) andΔ(J) be the minimum and the maximum degree inJ. LetH be atriangle-free graph and setd
H=max{δ(J):J⊆H}. Moreover, putD
H=min{2d
H,Δ(H)}. LetC>1 be a fixed constant and supposep=p(n)≫n
−1
D
H. We show that ifG is such that
Moreover, we discuss a setting under which an arbitrary graphH (not necessarily triangle-free) can be embedded inG. We also present an embedding result for directed graphs.
Research supported by a CNPq/NSF cooperative grant.
Partially supported by MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997-4) and by CNPq (Proc. 300334/93-1 and 468516/2000-0).
Partially supported by NSF Grant 0071261.
Supported by NSF grant CCR-9820931. 相似文献
(i) | deg G (x)≤C pn for allx∈V(G), | ||
(ii) |
for all 2≤r≤D
H and for all distinct verticesx
1, ...,x
r ∈V(G), |
||
(iii) |
for all but at mosto(n
2) pairs {x
1,x
2} ⊆V(G), |
20.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献