We develop new techniques to incorporate the recently proposed “short code” (a low-degree version of the long code) into the construction and analysis of PCPs in the classical “LABEL-COVER + Fourier Analysis” framework. As a result, we obtain more size-efficient PCPs that yield improved hardness results for approximating CSPs and certain coloring-type problems. In particular, we show a hardness...

This paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring of vector invariants of m copies of that representation is not Cohen-Macaulay for m ≥ 3. In the second section of the paper we use Poincaré series methods to produce upper bounds...

The principles of finiteness and reduction of couplings can be applied to achieve GaugeYukawa Unification. It is found that the observed top-bottom hierarchy and the top quark mass naturally follow if there exists Gauge-Yukawa Unification which is a simple functional relation among the gauge coupling and the Yukawa couplings of the third generation in various susy unified gauge models. We brief...

and Applied Analysis 3 By 2.2 , we get μf,−q ( a pZp ) 2 q 2 qp −qa ∫ Zp f ( a px ) dμ−qpn x . 2.3 Therefore, by 2.3 , we obtain the following theorem. Theorem 2.1. For f, g ∈ C Zp , one has μαf βg,−q αμf,−q βμg,−q, 2.4 where α, β are constants. From 2.2 and 2.4 , we note that ∣μf,−q ( a pZp )∣∣ ≤ M‖f‖∞, 2.5 where ‖f‖∞ supx∈Zp |f x | and M is some positive constant. Now, we recall the definitio...

A numerical set S with Frobenius number g is a set of integers with min(S) = 0 and max(Z − S) = g, and its atom monoid is A(S) = {n ∈ Z | n+ s ∈ S for all s ∈ S}. Let γg be the number of numerical sets S having A(S) = {0} ∪ (g,∞) divided by the total number of numerical sets with Frobenius number g. We show that the sequence {γg} is decreasing and converges to a number γ∞ ≈ .4844 (with accuracy...

Assuming that the string inspired, universal sum rules for soft supersymmetry-breaking terms, which have been recently found both in a wide class of four-dimensional superstrings and in supersymmertic gauge-Yukawa unified gauge models, are satisfied above and at the grand unification scale, we investigate their low energy consequences and derive sum rules in the superpartner spectrum of the min...

We discuss the Dirac quantization of two dimensional gravity with bosonic matter fields. After defining the extended Hamiltonian it is possible to fix the gauge completely. The commutators can all be obtained in closed form; nevertheless, the results are not particularly simple. Universidade de São Paulo IFUSP-preprint-1041 March 1993 ∗ Present Address: Instituto de F́ısica, Universidade Federal...

Markov and quantum information processing models are compared with respect to their capability of explaining two different puzzling findings from empirical research on human inference and decision making. Both findings involve a task that requires making an inference about one of two possible uncertain states, followed by decision about two possible courses of action. Two conditions are compare...

and Applied Analysis 3 for all x, y ∈ C. A mapping A : C → H is said to be α-inverse strongly g-monotone if and only if 〈 Ax −Ay, g x − gy ≥ α∥Ax −Ay∥2, 2.2 for some α > 0 and for all x, y ∈ C. A mapping g : C → C is said to be strongly monotone if there exists a constant γ > 0 such that 〈 g x − gy, x − y ≥ γ∥x − y∥2, 2.3 for all x, y ∈ C. Let B be a mapping ofH into 2 . The effective domain of...

We present a rigorous analysis and numerical evidence indicating that a recently developed methodology for detecting unstable periodic orbits is capable of yielding all orbits up to periods limited only by the computer precision. In particular, we argue that an efficient convergence to every periodic orbit can be achieved and the basin of attraction can be made finite and accessible for typical...