It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent χ and the wandering exponent ξ are related through the universal relation χ = 2ξ − 1, irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. This article gives a rigorous proof of this conjecture assuming that th...

Results of large-scale Monte Carlo simulations of three-dimensional Ising models with edges and corners are reviewed. At the ordinary transition, angle dependent critical exponents are observed, whereas at the surface transition edge and corner critical exponents are non-universal and depend on the details of the model. The results obtained at the surface transition are compared to exact findin...

I describe how we can understand the classical appearance of our world from a universal quantum theory. The essential ingredient is the process of decoherence. I start with a general discussion in ordinary quantum theory and then turn to quantum gravity and quantum cosmology. There is a whole hierarchy of classicality from the global gravitational field to the fluctuations in the cosmic microwa...

accurate analysis and interpolation of heavy metals, especially arsenic concentrationin ground watercan play a significant role in planning and continuous monitoring of water resources. the analysis may also prevent human health issues.the purpose of this paper was to evaluate newly published sugeno type fuzzy inference system as an interpolation method for estimating the amount of arsenic in k...

We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator Λ = θ + ∑∞ i=−2 Uiθ , as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super W -algebra incorporating all known extended superconformal WN algebras by reduction. We also construct the super BKP hierarchy by imposing a set of an...

The spatial distribution of precipitation is one the most important climatic variables used in geographic and environmental studies. However, when there a lack full coverage meteorological stations, estimations are necessary to interpolate for larger areas. purpose this research was find best interpolation method mapping partly densely populated Khorasan Razavi province northeastern Iran. To ac...

It is discussed whether some of the consistency problems of present–day physics could be solved by replacing special relativity, whose underlying kinematics is ruled by the Poincaré group, by de Sitter relativity, with underlying kinematics ruled by the de Sitter group. In contrast to ordinary special relativity, which seems to fail at the Planck scale, this new relativity is “universal” in the...

We describe a step toward quantizing deformation theory. The L∞ operad is encoded in a Hochschild cocyle ◦1 in a simple universal algebra (P, ◦0). This Hochschild cocyle can be extended naturally to a star product ⋆ = ◦0+~◦1+~ 2 ◦2+ · · · . The algebraic structure encoded in ⋆ is the properad Ω(coFrob) which, conjecturally, controls a quantization of deformation theory—a theory for which Froben...

The specializations of the motivic elliptic polylogarithm on the universal elliptic curve to the modular curve are referred to as Eisenstein classes. In this paper, we prove that the syntomic realizations of the Eisenstein classes restricted to the ordinary locus of the modular curve may be expressed using p-adic Eisenstein-Kronecker series, which are p-adic modular forms defined using the two-...

drought monitoring is a fundamental component of drought risk management. it is normally performed using various drought indices that are effectively continuous functions of rainfall and other hydrometeorological variables. in many instances, drought indices are used for monitoring purposes. geostatistical methods allow the interpolation of spatially referenced data and the prediction of values...