In the formulation of Cachazo, He, and Yuan, tree-level amplitudes for massless particles in gauge theory and gravity can be expressed as rational functions of the Lorentz invariants ka · kb, ǫa · kb, and ǫa · ǫb, valid in any number of spacetime dimensions. We use dimensional reduction of higher-dimensional amplitudes of particles with internal momentum κ to obtain amplitudes for massive parti...

The Palaeolithic sequence from Sodmein Cave in the Egyptian Eastern Desert, near Quseir, contains seven stratified archaeological levels from the Middle and Upper Palaeolithic. The lowest archaeological level (Middle Palaeolithic level 5) consists of huge fireplaces associated with a lithic assemblage in which Nubian Levallois technology and bifacial tools are present. From this level, six frag...

Abstract Wave scattering by many (M = M(a)) small bodies, at the boundary of which an interface boundary condition is imposed, is studied. Smallness of the bodies means that ka << 1, where a is the characteristic dimension of the body and k = 2π λ is the wave number in the medium in which small bodies are embedded. Equation for the effective field is derived in the limit as a → 0, M(a)→∞, at a ...

The theoretical case is considered where the total amount of plasma protein is conserved, but the drug is eliminated after its single application. After a single drug application at time t = 0, the total drug concentration is measured at times ti,...,tk and the total drug concentration at time ti is denoted by φi. Our discussion is limited to one protein binding site. The quantity of plasma pro...

It has been showed in [4] that any bipartite graph Ka,b, where a, b are even is decomposable into closed trails of prescribed even lengths. In this article we consider the corresponding question for open trails. We prove a necessary and sufficient condition for graphs Ka,b to be decomposable into edge-disjoint open trails of positive lengths (less than ab) whenever these lengths sum up to the s...

Let Ka,b be a complete bipartite multigraph. We show a necessary and sufficient condition for a multigraph Ka,b to be arbitrarily decomposable into open trails. A motivation for us to investigated this problem is a paper of Balister [1].

The purpose of this note is to obtain some congruences modulo a power of a prime p involving the truncated hypergeometric series p−1 � k=1 (x)k(1− x)k (1)k · 1 ka for a = 1 and a = 2. In the last section, the special case x = 1/2 is considered.

The initial expansion of anatomically modern humans (AMH) occurred during a hyperarid event in Africa that occurred 135-75 ka. Large-scale AMH spread in northern Eurasia started during the Middle Weichselian glacial maximum, and proceeded during the subsequent mild interstadial (60-40 ka ago). This expansion which encompassed the polar regions and southern Siberia proceeded at a remarkably rapi...