We study the existence of sign changing solutions to following problem(0.1){Δu+|u|p−1u=0inΩε;u=0on∂Ωε, where p=n+2n−2 is critical Sobolev exponent and Ωε a bounded smooth domain in Rn, n≥3, form Ωε=Ω\B(0,ε). Here Ω containing origin 0 B(0,ε) denotes ball centered at with radius ε>0. construct new type sign-changing high energy problem (0.1), when parameter ε small enough.

nanofibrous scaffolds produced by electrospinning have attracted much attention, recently. aligned and random nanofibrous scaffolds of poly (vinyl alcohol) (pva), poly (ε-caprolactone) (pcl) and nanohydroxyapatite  (nha) were fabricated by electrospinning method in this study. the composite nanofibrous scaffolds were subjected to detailed analysis. morphological investigations revealed that the...

We investigate the power of migration in online scheduling for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. Once we decide to accept a job, we have to complete it before its deadline d that satisfies d ≥ (1 + ε) · p + r, where p is the processing time, r the submission time and the slack ε > 0 a system parameter. Typically, the hard case ...

We show that every n-point tree metric admits a (1 + ε)-embedding into ` C(ε) logn 1 , for every ε > 0, where C(ε) ≤ O ( ( 1ε ) 4 log 1ε ) ) . This matches the natural volume lower bound up to a factor depending only on ε. Previously, it was unknown whether even complete binary trees on n nodes could be embedded in ` O(logn) 1 with O(1) distortion. For complete d-ary trees, our construction ach...

We show that for any ε > 0 there is an XOR game G = G(ε) with Θ(ε−1/5) inputs for one player and Θ(ε−2/5) inputs for the other player such that Ω(ε−1/5) ebits are required for any strategy achieving bias that is at least a multiplicative factor (1 − ε) from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self...

We prove that any extended formulation that approximates the matching polytope on nvertex graphs up to a factor of (1 + ε) for any 2 n ≤ ε ≤ 1 must have at least ( n α/ε ) defining inequalities where 0 < α < 1 is an absolute constant. This is tight as exhibited by the (1 + ε) approximating linear program obtained by dropping the odd set constraints of size larger than (1 + ε)/ε from the descrip...

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2ε) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue λ(ε) and the eigenvector angular frequency k(ε) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on th...

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( ε log 3/2 1 ε ) by Agarwal et a...

Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...