a modular $k$-coloring, $kge 2,$ of a graph $g$ without isolated vertices is a coloring of the vertices of $g$ with the elements in $mathbb{z}_k$ having the property that for every two adjacent vertices of $g,$ the sums of the colors of the neighbors are different in $mathbb{z}_k.$ the minimum $k$ for which $g$ has a modular $k-$coloring is the modular chromatic number of $g.$ except for some s...

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

We report a new illusion of elasticity in a rigid surface. A square frame is presented behind a concentric occluding cross. When the two surfaces are rotated rigidly, the square frame appears “rubbery”, that is, it appears to contract or expand during the rotation. The rubber square illusion is related to a number of other illusory phenomena involving motion and surface stratification. It is ge...

We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0, 1] that arrive from above, one at a time. The objective is to pack these items as they arrive, minimizing the resulting height. Just like in the classical game of Tetris, each square must be moved along a collision-free path to its final...

Coordinate, plural and predicative constructions of noun phrases are common and highly productive in natural languages. They are also related in intricate ways: conjunctive coordination is one of the simple means to form plural NP’s from singular ones; many coordinate and plural NP’s appear naturally in predicative positions. Any theory of grammar and semantic interpretation should account for ...

We present a simple, two dimensional example of a ”cat” – a body with zero angular momentum that can rotate itself with no external forces. This model is used to explain why this problem is known to be a gauge theory and to illustrate the importance of non-commutative operators. We will also show a comparison between the free-space ”cat” in Newtonian mechanics and the same problem in Aristoteli...

Starting from infinitely many supercompact cardinals, we force a model of ZFC where אω2+1 satisfies simultaneously a strong principle of reflection, called ∆-reflection, and a version of the square principle, denoted (אω2+1). Thus we show that אω2+1 can satisfy simultaneously a strong reflection principle and an anti-reflection principle.

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We present a technique for destroying stationary subsets of Pκκ using partial square sequences. We combine this method with Gitik’s poset for changing the cofinality of a cardinal without adding bounded sets to prove a variety of consistency results concerning saturated ideals and the set S(κ, κ+). In this paper we continue our study of consistency results concerning the set S(κ, κ) = {a ∈ Pκκ ...