We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically r...

The problem of existence of spacelike hypersurfaces with constant mean curvature in asymptotically flat spacetimes is considered for a class of asymptotically Schwarzschild spacetimes satisfying an interior condition. Using a barrier construction, a proof is given of the existence of complete hypersurfaces with constant mean cuvature which intersect null infinity in a regular cut. 1991 Mathemat...

It is proved that for any $0<\beta<\alpha$, bounded Ahlfors $\alpha$-regular space contains a $\beta$-regular compact subset embeds biLipschitzly in an ultrametric with distortion at most $O(\alpha/(\alpha-\beta))$. The bound on the asymptotically tight when $\beta\to \alpha$. main tool used proof regular form of skeleton theorem.

In this work, we construct a five-dimensional spherically symmetric, charged and asymptotically anti--de Sitter black hole with its singularity being pointlike strictly localized on our brane. addition, the induced brane geometry is described by Reissner-Nordstr\"om-(A)dS line element. We perform careful classification of horizons, demonstrate that all them are exponentially close to thus exhib...

We are concerned with the inviscid limit of Navier-Stokes equations to Euler for barotropic compressible fluids in $\mathbb{R}^3$. When viscosity coefficients obey a lower power-law density (i.e., $\rho^\delta$ $0<\delta<1$), we identify quasi-symmetric hyperbolic--singular elliptic coupled structure control behavior velocity near vacuum. Then this is employed prove that there exists unique reg...

In the maximum scatter traveling salesman problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting processes. We extend an algorithm by Arkin et al. that yields optimal solutions for nodes on a line to a regular m×n-grid. The new algorithm Weave(m,n) takes line...

Allelic association between pairs of loci is derived in terms of the association probability rho as a function of recombination theta, effective population size N, linear systematic pressure v, and time t, predicting both rho(rt), the decrease of association from founders and rho(ct), the increase by genetic drift, with rho(t) = rho(rt) + rho(ct). These results conform to the Malecot equation, ...

A generalization of Halpern’s iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term, an external sequence, and a continuous nondecreasing function of a distance of points of an external sequence, which is not necessarily related to the solution of Halpern’s iteration, a contractive mapping, and...

We give a new bound on the parameter λ (number of common neighbors of a pair of adjacent vertices) in a distance-regular graph G, improving and generalizing bounds for strongly regular graphs by Spielman (1996) and Pyber (2014). The new bound is one of the ingredients of recent progress on the complexity of testing isomorphism of strongly regular graphs (Babai, Chen, Sun, Teng, Wilmes 2013). Th...