New β-carotene-xylan complexes: preparation and characterization

Cellulose - The study aimed to propose a new system based on xylan for β-carotene delivery into aqueous environments. The xylan fraction of low molecular weight of...     

Approximation by generalized shifts of the Riemann zeta-function in short intervals

The Ramanujan Journal - We use the elliptic regulator to prove an identity between the Mahler measures of a genus 3 polynomial family and of a genus 1 polynomial family that was initially...     

Limit theorems in the space of analytic functions for the Hurwitz zeta-function with an algebraic irrational parameter

We prove a limit theorem in the space of analytic functions for the Hurwitz zeta-function with algebraic irrational parameter.     

Limit theorems for the Mellin transform of the fourth power of the Riemann zeta-function

We prove limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Mellin transform of {ie88-01}     

A hybrid method for multidimensional scaling using city-block distances

The problem of multidimensional scaling with city-block distances in the embedding space is reduced to a two level optimization problem consisting of a combinatorial problem at the upper level and a quadratic programming problem at the lower level. A hybrid method is proposed combining randomized search for the upper level problem with a standard quadratic programming algorithm for the lower level problem. Several algorithms for the combinatorial problem have been tested and an evolutionary global search algorithm has been proved most suitable. An experimental code of the proposed hybrid multidimensional scaling algorithm is developed and tested using several test problems of two- and three-dimensional scaling.     

Clustering analysis of different hop varieties according to their essential oil composition measured by GC/MS

This study describes the analysis of total hops essential oils from 18 cultivated varieties of hops, five of which were bred in Lithuania, and 7 wild hop forms using gas chromatography-mass spectrometry. The study sought to organise the samples of hops into clusters, according to 72 semi-volatile compounds, by applying a well-known method, k-means clustering analysis and to identify the origin of the Lithuanian hop varieties. The bouquet of the hops essential oil was composed of various esters, terpenes, hydrocarbons and ketones. Monoterpenes (mainly β-myrcene), sesquiterpenes (dominated by β-caryophyllene and α-humulene) and oxygenated sesquiterpenes (mainly caryophyllene oxide and humulene epoxide II) were the main compound groups detected in the samples tested. The above compounds, together with a-muurolene, were the only compounds found in all the samples. Qualitative and quantitative differences were observed in the composition of the essential oils of the hop varieties analysed. For successful and statistically significant clustering of the data obtained, expertise and skills in employing chemometric analysis methods are necessary. The result is also highly dependent on the set of samples (representativeness) used for segmentation into groups, the technique for pre-processing the data, the method selected for partitioning the samples according to the similarity measures chosen, etc. To achieve a large and representative data set for clustering analysis from a small number of measurements, numerical simulation was applied using the Monte Carlo method with normal and uniform distributions and several relative standard deviation values. The grouping was performed using the k-means clustering method, employing several optimal number of clusters evaluation techniques (Davies-Bouldin index, distortion function, etc.) and different data pre-processing approaches. The hop samples analysed were separated into 3 and 5 clusters according to the data filtering scenario used. However, the targeted Lithuanian hop varieties were clustered identically in both cases and fell into the same group together with other cultivated hop varieties from Ukraine and Poland.     

Universality of the Riemann zeta-function

In 1975, S.M. Voronin proved the universality of the Riemann zeta-function ζ(s). This means that every non-vanishing analytic function can be approximated uniformly on compact subsets of the critical strip by shifts ζ(s+iτ). In the paper, we consider the functions F(ζ(s)) which are universal in the Voronin sense.     

Nucleation and growth of Cu onto polycrystalline Pt electrode from acidic CuSO4 solution in the presence of H2SeO3

The early stages of Cu electrodeposition onto Pt(poly) have been investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] ≥ 2×10² using electrochemical and ex situ AFM techniques. The overpotential deposition of Cu has been performed onto a Pt surface precovered independently with Cu in amount close to an equivalent monolayer. Chronoamperometric results have been shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model. The values of diffusion coefficient D for Cu²⁺, number of nuclei N and average nuclei radius r _av have been calculated. In the local regions of the surface, the separate large agglomerates composed of the different diameter clusters have been revealed in both cases, but, in the presence of the H₂SeO₃, they attained a distinct chain-like configuration. Some morphological characteristics have been reported.