In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

introduction the chemical characteristic of groundwater as a major source of water supply for human life is an important factor in determining the usage of it for agriculture, industry and drinking. useful techniques and different methods of studying the chemical composition of groundwater such as correlation coefficient, descriptive statistics, factor analysis and cluster analysis provide an u...

We investigate DOA (direction-of-arrival) estimation for arbitrary linear arrays, where the antenna positions may be non-integer values in half-wavelength units. We introduce an approach based on arbitrary virtual linear arrays to resolve manifold ambiguity and estimate DOA's in the superior case. These virtual arrays adopt the set of covariance lags speci ed by the original array and so themse...

Digital databases can be represented by matrices, where rows (say) correspond to numerical sensors readings, or features, and columns correspond to data points. Recent data analysis methods describe the local geometry of the data points using a weighted affinity graph, whose vertices correspond to data points. We consider two geometries, or graphs one on the rows and one on the columns, such th...

Highlights Work was continued on exact counting of black hole states and comparison with the quantum corrected macroscopic entropy. A method was developed to exactly bosonize a system of finite number of non-relativistic fermions in one dimension, with applications to many problems in field theory, string theory and condensed matter physics including the classic Tomonaga problem of bosonization...

The geometries and binding energies of a recent buckyball tweezers (C(60)H(28)) and its supramolecular complexes are investigated using recently developed density functionals (M06-L and M06-2X) that include an accurate treatment of medium-range correlation energy. The pincer part of the tweezers, corannulene, has a strong attractive interaction with C(60). However, due to the entropy penalty, t...

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theor...

We revisit the 4D generalized black hole geometries, obtained by us [1], with a renewed interest, to unfold some aspects of effective gravity in a noncommutative D3-brane formalism. In particular, we argue for the existence of extra dimensions in the gravity decoupling limit in the theory. We show that the theory is rather described by an ordinary geometry and is governed by an effective string...