A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N=1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite num...

Generalizing the results of Thue (for n = 2) and of Klepinin and Sukhanov (for n = 3), we prove that for all n ≥ 2, the critical exponent of the Arshon word of order n is given by (3n− 2)/(2n− 2), and this exponent is attained at position 1.

A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N = 1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite n...

The upper bound on the exponent, ω, of matrix multiplication over a ring that was three in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the exponent of the algorithms known for the all pairs shortest path problem has stayed at three all these years even for the very special case of directed graphs with uniform edge lengths. In this paper we give an algor...

We prove that Alekhnovich’s algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ln log(n)) decoding algorithm for l-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent, improving in the exponent of n compared to previous results.

where Ω ⊂ R(N ≥ 4) is an open bounded domain with smooth boundary, β > 0, 0 ∈ Ω, 0 ≤ s < 2, 2∗(s) := 2(N − s) N − 2 is the critical Hardy-Sobolev exponent and, when s = 0, 2∗(0) = 2N N − 2 is the critical Sobolev exponent, 0 ≤ μ < μ := (N − 2) 4 . In [1] A. Ferrero and F. Gazzola investigated the existence of nontrivial solutions for problem (1.1) with β = 1, s = 0. In [2] D. S. Kang and S. J. ...

In this letter we establish a connection between two-exponent radius-mass power laws for cosmic objects and previously proposed two-exponent Regge-like spin-mass relations. A new, simplest method for establishing the coordinates of Chandrasekhar and Eddington points is proposed. In previous papers [2],[3] Muradian has suggested the two-exponent Regge-like relation J = ¯ h m m p 1+1/n (1) betwee...

We have used magnetically induced birefringence to study the susceptibility for the tilt order parameter in nonyloxybenzylidene butylaniline (90.4). This material is thought to undergo a smectic A-smectic F phase transition. The transition was observed to be first order, with Tc T* ~ 0.5 K, and the critical exponent 03B3 was consistent with the mean-field-like tilt susceptibility exponent chara...

A digraph G = (V; E) is primitive if, for some positive integer k, there is a u ! v walk of length k for every pair u; v of vertices of V. The minimum such k is called the exponent of G, denoted exp(G). The local exponent of G at a vertex u 2 V , denoted exp G (u), is the least integer k such that there is a u ! v walk of length k for each v 2 V. Let V = f1; 2; ; ng. Following Brualdi and Liu, ...

We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of N , N ≥ 2, symbols and with C1 diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic, exhibiting simultaneously ergodic measures with positive, negative, and zero exponents. We derive a multifractal analysis for the topological entropy of the level sets...