In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spac...

In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical syste...

A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that families of binary block codes with appropriately rescaled binomial multiplicity enumerators used on binary classical-quantum channels and decoded by the su...

In this work, we introduce the notion of the error exponent region for a multi-user channel. This region specifies the set of error-exponent vectors that are simultaneously achievable by all users in the multi-user channel. This is done by associating different probabilities of error for different users, contrary to the traditional approach where a single probability of system error is consider...

We are interesting in the error exponent for source coding with fidelity criterion. For each fixed distortion level ∆, the maximum attainable error exponent at rate R, as a function of R, is called the reliability function. The minimum rate achieving the given error exponent is called the minimum achievable rate. For memoryless sources with finite alphabet, Marton (1974) gave an expression of t...

The classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [F = 1 exp( kt)“] for nucleation and growth transformations works very well for most solid state transformations but fails regularly when applied to recrystallization of plastically deformed metals. Under conditions of near constant growth rate, a high exponent (n 2 3) is predicted but low exponents (n < 2) are typically measured. Ano...

The effect of Y2O3, CeO2, P2O5, ZrO2 and TiO2 in single, double and triple form on crystallization mechanism of Li2OAl2O3- SiO2(LAS) glass-ceramic system was investigated .The nucleation and crystallization peak temperatures of optimized samples in each group were determined by Ray & Day method .The crystalline phase was determined by the X-ray diffractometery .The micro-structure of the sample...

We estimated Hurst exponent of twelve stock index series from across the glove using daily values of for past ten years and found that the Hurst exponent value of the full series is around 0.50 confirming market efficiency. But the Hurst exponent value is found to vary widely when the full series is split into smaller series of 60 trading days. Later, we tried to find relationship between Hurst...

a watershed management program is usually based on the results of watershed modeling. accurate modeling results are decided by the appropriate parameters and input data. precipitation is the most important input for watershed modeling. precipitation characteristics usually exhibit significant spatial variation, even within small watersheds. therefore, properly describing the spatial variation o...