Related papers: On the irrationality measure function in average
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
We study the asymptotics of the moments of arithmetic functions that have a limit distribution, not necessarily normal, defined on a subset of the natural series that satisfies certain requirements. Several assertions are proved on…
The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient…
The irrationality exponent $\mu(t)$ of an irrational number t, defined using the irrationality measure $1/q^\mu$, distinguishes among non-Liouville numbers and is infinite for Liouville numbers. Using the irrationality measure $1/\beta^q$,…
We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups.
We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the…
We completely describe the asymptotic behaviour of the Riemann mapping function and its derivatives at an analytic cusp. We achieve the same for the inverse of the mapping function.
Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…
The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the…
This paper is a short overview of the main Abelian- and Tauberian-type results from [4, 14, 26] regarding the asymptotic analysis of different classes of generalized functions in terms of appropriate frames. The Tauberian-type results…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
Research performance values are not certain. Performance indexes should therefore be accompanied by uncertainty measures, to establish whether the performance of a unit is truly outstanding and not the result of random fluctuations. In this…
The mean value inequality is characteristic for upper semicontinuous functions to be subharmonic. Quasinearly subharmonic functions generalize subharmonic functions. We find the necessary and sufficient conditions under which subsets of…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
The Cantor ladder is naturally included into various families of self-similar functions. In the frame of these families we study the asymptotics of some parametric integrals.
For a class of random band matrices of band width $W$, we prove regularity of the average spectral measure at scales $\epsilon \geq W^{-0.99}$, and find its asymptotics at these scales.
We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of…
For $\alpha>\beta-1>0$, we obtain two sided inequalities for the moment integral $I(\alpha,\beta)= \int_{\mathbb{R}} |x|^{-\beta}|\sin x|^{\alpha}dx$. These are then used to give the exact asymptotic behavior of the integral as $\alpha \to…