Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]

In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that certain a variation of a Laplace method is applicable in this problem, hence the task reduces to a number of technical calculations.Comment: 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear

Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function

This paper continues investigations on the integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued fractions, though it has a hidden nice interpretation in terms of semi-regular continued fractions. The proof is self-contained and does not rely on previous results by the author.Comment: 8 page

The influence of moisture content variation on the withdrawal capacity of self-tapping screws

Due to high axial load-bearing capacity and economical application without pre-drilling, self-tapping screws are widely used in modern timber constructions nowadays. Their withdrawal behaviour, as one mechanism to be verified according to EN 1995-1-1 (2004), is discernibly influenced by the timber member and its moisture content. In case of increase of moisture content above 12 %, test results indicate a significant decrease in withdrawal capacity, which is actually not considered in design procedure. In our paper, we thus concentrate on these experimental studies, carried out in the frame of two research projects. Furthermore, we discuss two models developed for design procedure as well as for data assessment covering a large bandwidth of moisture content and compare them with results from previous investigations

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Skeletal muscle delimited myopathy and verapamil toxicity in SUR2 mutant mouse models of AIMS

ABCC9-related intellectual disability and myopathy syndrome (AIMS) arises from loss-of-function (LoF) mutations in the ABCC9 gene, which encodes the SUR2 subunit of ATP-sensitive potassium (

Phototransformation of halogenoaromatic derivatives in aqueous solution

The photochemical behaviour of monohalogeno-phenols and -anilines is highly dependent on the position of the halogen on the ring, but most often it is not significantly influenced by the nature of the halogen (Cl, Br, F). Photohydrolysis is the main reaction observed with 3-halogenated and it is almost specific. With 2-halogenated, photohydrolysis and photocontraction of the ring compete, the latter being very efficient with 2-halogeno-phenolates

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket