ISSN 1439-8516 CN 11-2039/O1
We develop a new method to perturb singular circuits in configuration Space B with trivial isotropy groups, and construct a homomorphism Φ* between its circuit cobordism groups and pseudohomology groups. This work can be viewed as a counterpart to Zinger's construction.
In this paper, we investigate the intersection numbers of nearly Kirkman triple systems. JN[v] is the set of all integers k such that there is a pair of NKTS(v)s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that JN[v]={0, 1,..., (v(v-2))/(6)-6,(v(v-2))/(6)-4,(v(v-2))/(6)} for any integers v≡0 (mod 6) and v≥66. For v≤60, there are 8 cases left undecided.
Let γ be a hyperbolic closed orbit of a C1 vector field X on a compact C∞ manifold M of dimension n≥3, and let HX(γ) be the homoclinic class of X containing γ. In this paper, we prove that C1-generically, if HX(γ) is expansive and isolated, then it is hyperbolic.
Let G be a finite group and let N be a nilpotent normal subgroup of G such that G/N is cyclic. It is shown that under some conditions all Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.
We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor) following Lawson's original idea in his 72' Trans. A.M.S. paper "The equivariant Plateau problem and interior regularity". Moreover, each of them enjoys (coflat) calibrations singular only at the origin.
In this paper, for the purpose of measuring the non-self-centrality extent of non-selfcentered graphs, a novel eccentricity-based invariant, named as non-self-centrality number (NSC number for short), of a graph G is defined as follows:N(G)=Σvi,vj∈V(G)|ei-ej|where the summation goes over all the unordered pairs of vertices in G and ei is the eccentricity of vertex vi in G, whereas the invariant will be called third Zagreb eccentricity index if the summation only goes over the adjacent vertex pairs of graph G. In this paper, we determine the lower and upper bounds on N(G) and characterize the corresponding graphs at which the lower and upper bounds are attained. Finally we propose some attractive research topics for this new invariant of graphs.
In this paper, we mainly explore fractal dimensions of fractional calculus of continuous functions defined on closed intervals. Riemann-Liouville integral of a continuous function f(x) of order v(v>0) which is written as D-vf(x) has been proved to still be continuous and bounded. Furthermore, upper box dimension of D-vf(x) is no more than 2 and lower box dimension of D-vf(x) is no less than 1. If f(x) is a Lipshciz function, D-vf(x) also is a Lipshciz function. While f(x) is differentiable on[0, 1], D-vf(x) is differentiable on[0, 1] too. With definition of upper box dimension and further calculation, we get upper bound of upper box dimension of Riemann-Liouville fractional integral of any continuous functions including fractal functions. If a continuous function f(x) satisfying Hölder condition, upper box dimension of Riemann-Liouville fractional integral of f(x) seems no more than upper box dimension of f(x). Appeal to auxiliary functions, we have proved an important conclusion that upper box dimension of Riemann-Liouville integral of a continuous function satisfying Hölder condition of order v(v>0) is strictly less than 2-v. Riemann-Liouville fractional derivative of certain continuous functions have been discussed elementary. Fractional dimensions of Weyl-Marchaud fractional derivative of certain continuous functions have been estimated.
The current paper is devoted to stochastic Burgers equation with driving forcing given by white noise type in time and periodic in space. Motivated by the numerical results of Hairer and Voss, we prove that the Burgers equation is stochastic stable in the sense that statistically steady regimes of fluid flows of stochastic Burgers equation converge to that of determinstic Burgers equation as noise tends to zero.
Positive entire solutions of the equation Δpu=u-q in RN (N≥2) where 1 < p≤N, q>0, are classified via their Morse indices. It is seen that there is a critical power q=qc such that this equation has no positive radial entire solution that has finite Morse index when q>qc but it admits a family of stable positive radial entire solutions when 0 < q≤qc. Proof of the stability of positive radial entire solutions of the equation when 1 < p < 2 and 0 < q≤qc relies on Caffarelli-Kohn-Nirenberg's inequality. Similar Liouville type result still holds for general positive entire solutions when 2 < p≤N and q>qc. The case of 1 < p < 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p=2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.
In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.
