Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph Γ. We calculate the Lagrangian gluing conditions at vertices v ∈ Γ for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum,...

We give a polynomial time algorithm that given a graph which admits a bisection cutting a fraction (1 − ε) of edges, finds a bisection cutting a (1 − g(ε)) fraction of edges where g(ε) → 0 as ε→ 0. One can take g(ε) = O( 3 √ ε log(1/ε)). Previously known algorithms for Max Bisection could only guarantee finding a bisection that cuts a fraction of edges bounded away from 1 (in fact less than 3/4...

A symmetric subset of the reals is one that remains invariant under some reflection x 7→ c − x. We consider, for any 0 < ε ≤ 1, the largest real number ∆(ε) such that every subset of [0, 1] with measure greater than ε contains a symmetric subset with measure ∆(ε). In this paper we establish upper and lower bounds for ∆(ε) of the same order of magnitude: for example, we prove that ∆(ε) = 2ε − 1 ...

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...