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...

– The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent ζ...

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...

We have previously presented the exponent for an upper bound on the error probability of a “peaky” signaling scheme that achieves the capacity of the Rayleigh fading channel under an average power constraint in the limit of infinite bandwidth. In the present work, we complement this result with a lower bound. We find that the exponents of the upper and lower bounds coincide in the wideband limi...

We derive the lower bound on squashed entanglement from a lower bound on the quantum conditional mutual information, which corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof of the lower bound is based on two recent resu...

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...