We review the properties of the generalized entropies in our previous papers in the following way. (1)A generalized Fannes’ inequality is shown by the axiomatically characterized Tsallis entropy. (2)The maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for the nonnegative matrices in the framework of matrix ana...

The critical points of the generalized complementary energy variational principles are clariied. An open problem left by Hellinger and Reissner is solved completely. A pure complementary energy (involving the Kirchhoo type stress only) is constructed. We prove that the well-known generalized Hellinger-Reissner's energy L(u; s) is a saddle point functional if and only is the Gao-Strang gap funct...

This article proposes a generalized block control principle. The algorithm, developed in the framework of sliding mode control, offers insensitivity to parameter variations and external disturbances and simplification of the control design. In contrast to the known Block Control Principle, decomposing of the system into blocks where the dimension of state and control input coincide is not requi...

We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation to analyze the quantum theory of gravity or string theory from the perspective of a complex function. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function δ̃(∆x,∆k, ǫ). We arrived at the string uncertainty principle from the analyticit...

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q = 1=2 case. We show that, when the residual principle is considered as constraint, the q = 1=2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which correspo...

Let X=(X1 ,X2 ) be a continuous random vector. Under the assumption that the marginal distributions of X1 and X2 are given, we develop models for vector X when there is partial information about the dependence structure between X1  and X2. The models which are obtained based on well-known Principle of Maximum Entropy are called the maximum entropy (ME) mo...

Based on the κ-deformed functions (κ-exponential and κ-logarithm) and associated multiplication operation (κ-product) introduced by Kaniadakis (Phys. Rev. E 66 (2002) 056125), we present another one-parameter generalization of Gauss’ law of error. The likelihood function in Gauss’ law of error is generalized by means of the κ-product. This κ-generalized maximum likelihood principle leads to the...

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale of the running coupling αs(μ ). It is common practice to guess a physical scale μ = Q which is of order of a typical momentum transfer Q in the process, and then vary the scale over a range Q/2 and 2Q. This procedure is clearly problematic since the resulting fixed-order pQCD...