Maximal flows reach at least a 1/2 approximation of the maximum flow in client-server networks. By adding 1 additional time round to any distributed maximal flow algorithm we show how this 1/2-approximation can be improved on boundeddegree networks. We call these modified maximal flows ‘locally fair’ since there is a measure of fairness prescribed to each client and server in the network. Let N...

implying C = 1 and δ (p) = δ (p̃). (b) Note that assuming p = ωp� dp� 1 dp � 2 2� � 0� (2π) 3 2ωp� f (p) = (2π) 3 δ p + m θ p f (p) d4p� � 2 2� � 0� = 3 δ p� + m θ p� f (p�) (2) (2π) dp � 2 2� � 0� dp� 1 = 3 δ p + m θ p f (p�) = 3 f (p�) (2π) (2π) 2ωp� In the second line we renamed p → p�, in the third we used | det Λ| = 1, p�2 = p and θ p�0 = θ p for Lorentz transformations connected to the ide...

A wide range of glassy and disordered materials exhibit complex, nonexponential, structural relaxation (aging). We propose a simple nonlinear rate equation δ = a[1-exp(b δ)], where δ is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural r...

We provide a new proof of a Frĕıman-type theorem. Specifically, suppose that G is a locally compact abelian group with a Haar measure μG. The δ-ball Bδ of a translation invariant metric is called d-dimensional if μG(B2δ′ ) 6 2 dμG(Bδ′ ) for all δ ′ ∈ (0, δ]. We show that if A is a compact neighborhood with μG(nA) 6 n μG(A) for all n > d log d, then A is contained in a O(d log d)-dimensional bal...

In this paper G will always be a finitely generated, infinite group and S will always be a symmetric generating set for G. Let M be a right G-module. A 1cocycle with values in M is a map δ : G → M such that δ(gh) = (δ(h)) g + δ(g) for any g, h ∈ G; a 1-coboundary is a 1-cocycle of the form δ(g) = xg − x for some x ∈ M and for all g ∈ G. We denote by Z (G,M) the vector space of all 1-cocycles an...

We propose a general formalism for galaxy biasing and apply it to methods for measuring cosmological parameters, such as regression of light versus mass, the analysis of redshift distortions, measures involving skewness and the cosmic virial theorem. The common linear and deterministic relation g=bδ between the density fluctuation fields of galaxies g and mass δ is replaced by the conditional d...

The diffusion-weighted magnetic resonance imaging (DWI) technique enables quantification of water mobility for probing microstructural properties of biological tissue and has become an effective tool for collecting information about the underlying pathology of cancerous tissue. Measurements using multiple b-values have indicated biexponential signal attenuation, ascribed to "fast" (high ADC) an...

The kinetics and mechanism of the reaction between benzaldehyde 1, malononitrile 2 and dimedone 3 in a mixture of ethanol and water as solvents in the presence of fructose as a biodegradable catalyst has been studied by the spectroscopic method (UV-Vis spectrophotometry method). The influence of various parameters (temperature, solvent and concentration) was studied on the reaction by means of ...

We consider multilinear operators T (f1, . . . , fl) given by determinants of matrices of the form (Xkfj)1≤j,k≤l, where the Xk’s are C∞ vector fields on Rn. We give conditions on the Xk’s so that the corresponding operator T map products of Lebesgue spaces L p1×· · ·×Lpl into some anisotropic space H1, when 1 p1 + · · · + 1 pl = 1. 0. Introduction and statement of results. A well known Theorem ...

The title compound, C(3)H(12)BN, was solved using data collected from a multiple crystal (note incomplete data shell). The cell packing is dominated by bifurcated attractive N-H(δ+)⋯(δ-)H-B inter-actions.