We prove a new structural property regarding the “skyline” of uniform radius disks and use this to derive a number of new sequential and distributed approximation algorithms for well-known optimization problems on unit disk graphs (UDGs). Specifically, the paper presents new approximation algorithms for two problems: domatic partition and weighted minimum dominating set (WMDS) on UDGs, both of ...

Abstract We give short elementary expositions of combinatorial proofs some variants Euler's partition identity that were first addressed analytically by George Andrews, and later combinatorially others. The method using certain matrices to concisely explain these bijections, based on ideas used in a previous manuscript the author, enables us also new generalizations two results.

We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.

Acetic acid was separated from a dilute mixture using a commercial polyvinyl alcohol (PVA) membrane.  Intrinsic separation characteristics of the membrane were studied as a function of temperature.  The degree of membrane swelling decreased marginally with increase in feed temperature. At 25oC the maximum degree of swelling was found out to be 46.3%, which reduced to 39.5%...

The theme of the present paper is numerical integration $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First initial interval partitioned into subintervals and integrand approximated by a piecewise polynomial interpolant based on obtained partition. Then approximation applied difference its interpolant. final integral sum both. optima...

with Ei the energy of the microstate labeled by i, β = 1/kBT the inverse temperature (T ), kB Boltzmann’s constant, and ZBG the partition function. The exponential term FBG = exp (−βE) is, of course, called the BG factor. Recently Beck and Cohen [3, 4] have advanced a generalization (called “superstatistics”) of this BG factor, assuming that the inverse temperature β is a stochastic variable. T...

in the present study, natural convective heat transfer in a partitioned square cavity utilizing nanofluids is studied. the vertical left and right walls are considered as the hot and cold walls, respectively and the partitions assumed to be adiabatic. the nanofluid used in this study is al2o3 with the volume fraction of 20%. it is assumed that nanofluid is a single phase fluid. fluent 6.3.26 is...