共查询到20条相似文献,搜索用时 31 毫秒
1.
We give a counterexample of Bowers–Stephenson’s conjecture in the spherical case: spherical inversive distance circle packings
are not determined by their inversive distances. 相似文献
2.
Andrzej Lenarcik 《manuscripta mathematica》2008,125(3):309-324
We investigate the Jacobian Newton polygon of plane curve singularities. This invariant was introduced by Teissier in the
more general context of hypersurfaces. The Jacobian Newton polygon determines the topological type of a branch (Merle’s result)
but not of an arbitrary reduced curve (Eggers example). Our main result states that the Jacobian Newton Polygon determines
the topological type of a non-degenerate unitangent singularity. The Milnor number, the Łojasiewicz exponent, the Hironaka
exponent of maximal contact and the number of tangents are examples of invariants that can be calculated by means of the Jacobian
Newton polygon. We show that the number of branches and the Newton number defined by Oka do not have this property.
Dedicated to Professor Arkadiusz Płoski on his 60th birthday 相似文献
3.
The B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on
the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov, and Varchenko. For flag varieties,
Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this
paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture
for flag varieties, when Sottile’s monotonicity conditions are not satisfied. 相似文献
4.
Jacob Rasmussen 《Inventiones Mathematicae》2010,182(2):419-447
We use Lee’s work on the Khovanov homology to define a knot invariant s. We show that s(K) is a concordance invariant and that it provides a lower bound for the smooth slice genus of K. As a corollary, we give a purely combinatorial proof of the Milnor conjecture. 相似文献
5.
Harvey Friedman 《Israel Journal of Mathematics》1973,14(2):205-212
We prove that the Beth definability theorem fails for a comprehensive class of first-order logics with cardinality quantifiers.
In particular, we give a counterexample to Beth’s theorem forL(Q), which is finitary first-order logic (with identity) augmented with the quantifier “there exists uncountably many”.
This research was partially supported by NSF GP29254. 相似文献
6.
Moritz Kerz 《Inventiones Mathematicae》2009,175(1):1-33
We prove that the n-th Milnor K-group of an essentially smooth local ring over an infinite field coincides with the (n,n)-motivic cohomology of the ring. This implies Levine’s generalized Bloch–Kato conjecture. 相似文献
7.
A. Melle-Hernández 《Israel Journal of Mathematics》2000,115(1):29-50
An additive formula for the Milnor number of an isolated complex hypersurface singularity is shown. We apply this formula
for studying surface singularities. Durfee's conjecture is proved for any absolutely isolated surface and a generalization
of Yomdin singularities is given.
This work was supported in part by a Spanish FPI'91 grant and by the Spanish project PB94-0291. 相似文献
8.
We prove a new formula about local control of the number of p-regular conjugacyclasses of a finite group. We then relate the results to Alperins weight conjecture to obtain newresults describing the number of simple modules for a finite group in terms of weights of solvablesubgroups. Finally, we use the results to obtain new formulations of Alperins weight conjecture,and to obtain restrictions on the structure of a minimal counterexample. 相似文献
9.
David B. Massey 《Proceedings of the American Mathematical Society》2006,134(7):2049-2060
We show how some of our recent results clarify the relationship between the Lê numbers and the cohomology of the Milnor fiber of a non-isolated hypersurface singularity. The Lê numbers are actually the ranks of the free Abelian groups--the Lê modules--appearing in a complex whose cohomology is that of the Milnor fiber. Moreover, the Milnor monodromy acts on the Lê module complex, and we describe the traces of these monodromy actions in terms of the topology of the critical locus.
10.
Based on Ostrowski’s fourth order method, we derive a family of eighth order methods for the solution of nonlinear equations.
In terms of computational cost the family requires three evaluations of the function and one evaluation of first derivative.
Therefore, the efficiency index of the present methods is 1.682 which is better than the efficiency index 1.587 of Ostrowski’s
method. Kung and Traub conjectured that multipoint iteration methods without memory based on n evaluations have optimal order
2
n − 1. Thus, the family agrees with Kung–Traub conjecture for the case n = 4. The efficacy of the present methods is tested on a number of numerical examples. It is observed that our methods are
competitive with other similar robust methods and very effective in high precision computations. 相似文献
11.
Thomas A. Willging 《Archiv der Mathematik》2008,91(4):323-329
In this work we discuss Schmutz’s conjecture that in dimension 2 to 8 the distinct norms that occur in the lattices with the
best known sphere packings are strictly greater than those in any other lattice of the same covolume. We see that the ternary
conjecture is not true. However, it seems that there is but one exception: one lattice, where for one length the conjecture
fails.
Received: 11 February 2008, Revised: 20 May 2008 相似文献
12.
We use Klee’s Dehn–Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove
Kalai’s conjecture providing lower bounds on the f-vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify Kühnel’s conjecture that
gives an upper bound on the middle Betti number of a 2k-dimensional manifold in terms of k and the number of vertices, and (iii) partially prove Kühnel’s conjecture providing upper bounds on other Betti numbers of
odd- and even-dimensional manifolds. For manifolds with boundary, we derive an extension of Klee’s Dehn–Sommerville relations
and strengthen Kalai’s result on the number of their edges.
I. Novik research partially supported by Alfred P. Sloan Research Fellowship and NSF grant DMS-0500748.
E. Swartz research partially supported by NSF grant DMS-0600502. 相似文献
13.
A. Stoimenow 《Transactions of the American Mathematical Society》2002,354(10):3927-3954
We give examples of knots with some unusual properties of the crossing number of positive diagrams or strand number of positive braid representations. In particular, we show that positive braid knots may not have positive minimal (strand number) braid representations, giving a counterpart to results of Franks-Williams and Murasugi. Other examples answer questions of Cromwell on homogeneous and (partially) of Adams on almost alternating knots.
We give a counterexample to, and a corrected version of, a theorem of Jones on the Alexander polynomial of 4-braid knots. We also give an example of a knot on which all previously applied braid index criteria fail to estimate sharply (from below) the braid index. A relation between (generalizations of) such examples and a conjecture of Jones that a minimal braid representation has unique writhe is discussed.
Finally, we give a counterexample to Morton's conjecture relating the genus and degree of the skein polynomial.
14.
A topological approach to evasiveness 总被引:6,自引:0,他引:6
The complexity of a digraph property is the number of entries of the vertex adjacency matrix of a digraph which must be examined
in worst case to determine whether the graph has the property. Rivest and Vuillemin proved the result (conjectured by Aanderaa
and Rosenberg) that every graph property that is monotone (preserved by addition of edges) and nontrivial (holds for some
but not all graphs) has complexity Ω(v
2) wherev is the number of vertices. Karp conjectured that every such property is evasive, i.e., requires that every entry of the incidence
matrix be examined. In this paper the truth of Karp’s conjecture is shown to follow from another conjecture concerning group
actions on topological spaces. A special case of the conjecture is proved which is applied to prove Karp’s conjecture for
the case of properties of graphs on a prime power number of vertices.
Supported in part by an NSF postdoctoral fellowship
Supported in part by NSF under grant No. MCS-8102248 相似文献
15.
Jianbei An 《Israel Journal of Mathematics》1999,112(1):109-134
This paper is part of a program to study Alperin’s weight conjecture and Dade’s conjecture on counting ordinary characters
in blocks for several finite groups. The classifications of radical subgroups and certain radical chains and their local structures
of the simple Conway’s third group have been obtained by using the computer algebra system CAYLEY. The Alperin weight conjecture
and the Dade final conjecture have been confirmed for the group. 相似文献
16.
G. G. Ilyuta 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):139-155
We obtain several formulas for the Poincaré series defined by B. Kostant for Klein groups (binary polyhedral groups) and some
formulas for Coxeter polynomials (characteristic polynomials of monodromy in the case of singularities). Some of these formulas—the
generalized Ebeling formula, the Christoffel-Darboux identity, and the combinatorial formula—are corollaries to the well-known
statements on the characteristic polynomial of a graph and are analogous to formulas for orthogonal polynomials. The ratios
of Poincaré series and Coxeter polynomials are represented in terms of branched continued fractions, which are q-analogs of continued fractions that arise in the theory of resolution of singularities and in the Kirby calculus. Other formulas
connect the ratios of some Poincaré series and Coxeter polynomials with the Burau representation and Milnor invariants of
string links. The results obtained by S.M. Gusein-Zade, F. Delgado, and A. Campillo allow one to consider these facts as statements
on the Poincaré series of the rings of functions on the singularities of curves, which suggests the following conjecture:
the ratio of the Poincaré series of the rings of functions for close (in the sense of adjacency or position in a series) singularities
of curves is determined by the Burau representation or by the Milnor invariants of a string link, which is an intermediate
object in the transformation of the knot of one singularity into the knot of the other. 相似文献
17.
David P. Hunt 《Acta Analytica》2007,22(1):3-15
The most serious challenge to Frankfurt-type counterexamples to the Principle of Alternate Possibilities (PAP) comes in the
form of a dilemma: either the counterexample presupposes determinism, in which case it begs the question; or it does not presuppose
determinism, in which case it fails to deliver on its promise to eliminate all alternatives that might plausibly be thought
to satisfy PAP. I respond to this challenge with a counterexample in whichconsidering an alternative course of action is anecessary condition fordeciding to act otherwise, and the agent does not in fact consider the alternative. I call this a “buffer case,” because the morally
relevant alternative is “buffered” by the requirement that the agent first consider the alternative. Suppose further that
the agent’s considering an alternative action—entering the buffer zone—is what would trigger the counterfactual intervener.
Then it would appear that PAP-relevant alternatives are out of reach.
I defend this counterexample to PAP against three objections: that considering an alternative isitself a morally relevant alternative; that buffer cases can be shown to containother alternatives that arguably satisfy PAP; and that even if the agent’spresent access to PAP-relevant alternatives were eliminated, PAP could still be satisfied in virtue ofearlier alternatives. I conclude that alternative possibilities are a normal symptom, but not an essential constituent, of moral
agency. 相似文献
18.
Cyclic orders of graphs and their equivalence have been promoted by Bessy and Thomassé’s recent proof of Gallai’s conjecture.
We explore this notion further: we prove that two cyclic orders are equivalent if and only if the winding number of every
circuit is the same in the two. The proof is short and provides a good characterization and a polynomial algorithm for deciding
whether two orders are equivalent.
We then derive short proofs of Gallai’s conjecture and a theorem “polar to” the main result of Bessy and Thomassé, using the
duality theorem of linear programming, total unimodularity, and the new result on the equivalence of cyclic orders. 相似文献
19.
From the assumption that Leopoldt’s conjecture fails and some mild extra assumptions, we deduce the existence of multiple $$\mathbb {Z}_p$$-extensions whose Iwasawa modules are “large” in a precise sense. We are not aware of any constructions of such extensions that avoid our preposterously strong hypothesis. 相似文献
20.
We propose relaxed lower semicontinuity properties for set-valued mappings, using weak τ-functions, and employ them to weaken known lower semicontinuity assumptions to get enhanced Ekeland’s variational principle
for Pareto minimizers of set-valued mappings and underlying minimal-element principles. Our results improve and recover recent
ones in the literature. 相似文献