has infinitely many solutions in rational numbers p/q. It follows from the theory of continued fractions that μ(ξ) is always greater than or equal to 2, and an easy covering argument shows that μ(ξ) is equal to 2 for almost all real numbers ξ (with respect to the Lebesgue measure). Furthermore, Roth’s theorem asserts that the irrationality exponent of every algebraic irrational number is equal ...

Ever since Kolmogorov’ introduced the intermittency exponent, more than a dozen attempts have been made to obtain its numerical value from experiments. The resulting estimates have varied from as low a value as 0.18 to as high as 0.7. (See Ref. 2 for a summary of early measurements, Table IV of Ref. 3 for measurements until about 1975 and Refs. 4-10 for experiments made thereafter.) It is unsat...

The Hurst Exponent is a dimensionless estimator for the self-similarity of a time series. Initially defined by Harold Edwin Hurst to develop a law for regularities of the Nile water level, it now has applications in medicine and finance. Meaningful values are in the range [0, 1]. Different methods for estimating the Hurst Exponent have been evaluated: The classical “Rescaled Range” method devel...

Primitive digraphs on n vertices with exponents at least b!n=2c + 2, where !n = (n 1) + 1, are considered. For n 3, all such digraphs containing a Hamilton cycle are characterized; and for n 6, all such digraphs containing a cycle of length n 1 are characterized. Each eigenvalue of any stochastic matrix having a digraph in one of these two classes is proved to be geometrically simple.

We initiate a study of the homomorphism domination exponent of a pair of graphs F and G, defined as the maximum real number c such that |Hom(F, T )| > |Hom(G,T )| for every graph T . The problem of determining whether HDE(F,G) > 1 is known as the homomorphism domination problem and its decidability is an important open question arising in the theory of relational databases. We investigate the c...

In this note, we investigate the behaviour of Łojasiewicz exponent under hyperplane sections and its relation to order tangency.

An allometric height-mass exponent γ gives an approximative power-law relation 〈M〉 ∝ H between the average mass 〈M〉 and the height H , for a sample of individuals. The individuals in the present study are humans but could be any biological organism. The sampling can be for a specific age of the individuals or for an age-interval. The body-mass index (BMI) is often used for practical purposes wh...

0. Initiated by Sekanina [6], in the sixties and more intensively in the seventies there were considered powers of undirected graphs with special respect to their Hamiltonian behaviour. These investigations have resulted in a lot of interesting and partly very profound propositions; we only remind of the (simple) result of Sekanina [6] that the cube of every finite connected graph is Hamiltonia...

Large strains, anisotropy of mechanical properties of materials and Coulomb friction in contact regions are some properties in the analysis of deep drawing process. In this research, the effects of different parameters such as anisotropy coefficient, work hardening exponent and friction coefficient on deep drawing process of drawing quality steel are studied. For this purpose, the finite elemen...

We study complex-temperature properties of the uniform and staggered susceptibilities χ and χ of the Ising model on the honeycomb lattice. From an analysis of low-temperature series expansions, we find evidence that χ and χ both have divergent singularities at the point z = −1 ≡ zl (where z = e), with exponents γ l = γ l,a = 5/2. The critical amplitudes at this singularity are calculated. Using...