Confirming a conjecture by Ivančo and Jendrol’ for a large class of graphs we prove that for every graph G = (V,E) of order n, size m and maximum degree ∆ with m > 111000∆ there is a function f : V ∪ E → { 1, 2, ..., ⌈ m+2 3 ⌉} such that f(u) + f(uv) + f(v) 6= f(u′) + f(u′v′) + f(v′) for every uv, u′v′ ∈ E with uv 6= u′v′. Furthermore, we prove the existence of such a function with values up to...

A speech production experiment was conducted to investigate how well native Japanese speakers can produce a non-contrastive sound in American English, namely, intervocalic alveolar flaps, and how their production varies as a function of language experience. Native Japanese speakers who have prior experience living in the US produced English sentences containing potentially flappable segments. R...

We study a relativistic anyon model with a spin-j matter field minimally coupled to a statistical gauge potential governed by the Chern-Simons dynamics with a statistical parameter α. A spin and statistics transmutation is shown in terms of a continuous random walk method. An integer or odd-half-integer part of α can be reabsorbed by change of j. We discuss the equivalence of a large class of (...

One can prove the following propositions: (1) For all real numbers a, b and for every natural number c holds (ab ) c = a c bc . (2) For every real number a and for all integer numbers b, c such that a 6= 0 holds ab+c = ab · ac. (3) For every natural number n and for every real number a such that n is even and a 6= 0 holds (−a)n = an. (4) For every natural number n and for every real number a su...

/*@ public normal_behavior @ requires !isEmpty(); @ ensures \old(queue).has(\result) && @ queue.equals(\old(queue).remove(\result)) && @ (\forall Comparable o; queue.has(o); @ \result.compareTo(o) <= 0); @ modifies queue; @*/ public Comparable removeFirst() { Comparable first = elems[0]; Comparable last = elems[--numElems]; int pos = 0; int child = 1; while (child < numElems) { if (child + 1 < ...

Given a graph H, we say a graph G is H-saturated if G does not contain H as a subgraph and the addition of any edge e′ 6∈ E(G) results in H as a subgraph. In this paper, we construct (K4 − e)-saturated graphs with |E(G)| either the size of a complete bipartite graph, a 3-partite graph, or in the interval [ 2n− 4, ⌊ n 2 ⌋ ⌈ n 2 ⌉ − n+ 6 ] . We then extend the (K4−e)-saturated graphs to (Kt − e)-...

Geoffrey Grimmett Abstra t. The problem of how to allocate to states the seats in the US House of Representatives is the most studied instance of what is termed the ‘apportionment problem’. We propose a new method of apportionment which is stochastic, which meets the quota condition, and which is fair in the sense of expectations. Two sources of systematic unfairness are identified, firstly the...

Beatty sequences [nα1 + β1]n∈Z and [mα2 + β2]m∈Z are recorded by two athletes running in opposite directions in a round stadium. This approach suggests a nice interpretation for well known partitioning criteria: such sequences (eventually) partition the integers essentially when the athletes have the same starting point. A remarkable observation due to S. Beatty says that if w is any positive i...

Information and communication technologies (ICTs) have increasingly become an integral part of society, enhancing, changing, supporting, and complicating human lives. Although the disregard of technology inventors and designers for the users of ICTs has resulted in disjunctures between ICTs and users, users have refused to become mere agents of the designers. Individual users have developed the...

Both the degree to which the left-hemisphere is specialized for language and the relative ability of the right-hemisphere to subserve language function are underspecified. The present study sought to identify whether the right-frontal fMRI activation seen in a number of case studies in patients with left-sided brain lesions exists as a group-level trend in patients with left-frontal tumors. It ...