On the spectrum of the hierarchical Laplacian

Let (X, d) be a locally compact separable ultrametric space. We assume that (X, d) is proper, that is, any closed ball B?X is a compact set. Given a measure m on X and a function C(B) defined on the set of balls (the choice function) we define the hierarchical Laplacian L _C which is closely related to the concept of the hierarchical lattice of F.J. Dyson. L _C is a non-negative definite self-adjoint operator in L ²(X, m). In this paper we address the following question: How general can be the spectrum \(\mathsf {Spec}(L_{C})\subseteq \mathbb {R}_{+}?\) When (X, d) is compact, S p e c(L _C ) is an increasing sequence of eigenvalues of finite multiplicity which contains 0. Assuming that (X, d) is not compact we show that under some natural conditions concerning the structure of the hierarchical lattice (≡ the tree of d-balls) any given closed subset S ? ?₊, which contains 0 as an accumulation point and is unbounded if X is non-discrete, may appear as S p e c(L _C ) for some appropriately chosen function C(B). The operator ?L _C extends to L ^q (X, m), 1 ≦ q < ∞, as Markov generator and its spectrum does not depend on q. As an example, we consider the operator ?? ^α of fractional derivative defined on the field ? _p of p-adic numbers.     

Physical sorption and thermogravimetry as the methods used to analyze linear polymeric structure

An increased interest in polymer optical fibers can be observed in the last years. One of the main problems in the technology of these fibers is achieving good optical and thermal stability of used polymer materials. This paper presents a series of manufactured poly(methyl methacryalte) samples which quality was investigated using the physical sorption and the thermogravimetry methods. Studies were carried out to optimize the composition of the starting mixtures used to obtain proper polymer optical fibers.     

Herbicidal Activity of Phosphonic,Phosphinic and Phosphinous Acid Analogues of Aromatic Amino Acids

Abstract

Over 40 phosphonic, phosphinic and phosphinous acid analogues of phenylglycine and phenylalanine were synthesized and screened for their herbicidal activity on Lepidium sativum (crest) and Cucumis sativus (cucumber). The most active appeared to be 2-amino-1-hydroxy-3-phenylpropylphosphonic acid which was equipotent with popular herbicide glyphosate. Also aminobenzylphosphonic acids, analogues of phenylglycine, exhibited notable herbicidal activity and thus represent a group of the most active herbicides found among simple aminophosphonic acids. Other compounds showed moderate herbicidal activity. Preliminary results indicate that analogues of aromatic amino acids display their activity as effectors of biosynthesis of aromatic amino acids.     

Comparison of the sensitivity of mass spectrometry atmospheric pressure ionization techniques in the analysis of porphyrinoids

The porphyrinoids chemistry is greatly dependent on the data obtained in mass spectrometry. For this reason, it is essential to determine the range of applicability of mass spectrometry ionization methods. In this study, the sensitivity of three different atmospheric pressure ionization techniques, electrospray ionization, atmospheric pressure chemical ionization and atmospheric pressure photoionization, was tested for several porphyrinods and their metallocomplexes. Electrospray ionization method was shown to be the best ionization technique because of its high sensitivity for derivatives of cyanocobalamin, free‐base corroles and porphyrins. In the case of metallocorroles and metalloporphyrins, atmospheric pressure photoionization with dopant proved to be the most sensitive ionization method. It was also shown that for relatively acidic compounds, particularly for corroles, the negative ion mode provides better sensitivity than the positive ion mode. The results supply a lot of relevant information on the methodology of porphyrinoids analysis carried out by mass spectrometry. The information can be useful in designing future MS or liquid chromatography–MS experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

Vertex-edge domination in graphs

Aequationes mathematicae - We establish that for any connected graph G of order $$n \ge 6$$ , a minimum vertex-edge dominating set of G has at most n/3 vertices, thus affirmatively answering the...     

Enantioseparation on a chiral nanostructured surface: Effect of molecular shape

In this paper we use the Monte Carlo simulation method to study adsorption of chiral molecules on a solid surface with periodic distribution of active sites. Namely, equilibrium adsorption of a racemic mixture of enantiomers represented by homonuclear tetramers is modeled on a square lattice with a chiral pattern of active sites. We consider two possible chiral structures of the tetramers which differ only by chain geometry but have equal adsorption energies. The effect of the chain geometry on the effectiveness of separation is assessed by comparing the corresponding adsorption selectivities obtained from the simulations. We present results of model calculations in which the parameters do not refer to any particular experimental system. These results indicate that the model chiral surface can, in general, adsorb preferentially the complementary enantiomer, regardless of its chain conformation. Specifically, it was shown that changes in the tetramer geometry, from S-shaped to -shaped, lead to marginal changes in the shape of both single component and mixed adsorption isotherms calculated for the enantioselective surface. In this context, the enantiomer separation on the surface proposed in this work was shown to be insensitive to molecular shape of the adsorbing species.     

Correction to: There is at most one continuous invariant mean

Aequationes mathematicae - A mistake in the formulation of Lemma&nbsp;1 has been corrected. A preliminary section to the proof of Theorem&nbsp;1 is added.     

Predictive tracking of an object by a pan–tilt camera of a robot

Nonlinear Dynamics - Moving-object tracking using a pan–tilt camera setup is quite a well-known task in robotics. However, the presented research addresses specific properties of the tracked...     

Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins

We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 μs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.