The Hydrogen–Deuterium Exchange at α-Carbon Atom in <Emphasis Type="BoldItalic">N,N,N</Emphasis>-Trialkylglycine Residue: ESI-MS Studies

Derivatization of peptides as quaternary ammonium salts (QAS) is a known method for sensitive detection by electrospray ionization tandem mass spectrometry. Hydrogens at α-carbon atom in N,N,N-trialkylglycine residue can be easily exchanged by deuterons. The exchange reaction is base-catalyzed and is dramatically slow at lower pH. Introduced deuterons are stable in acidic aqueous solution and are not back-exchanged during LC-MS analysis. Increased ionization efficiency, provided by the fixed positive charge on QAS group, as well as the deuterium labeling, enables the analysis of trace amounts of peptides.     

Construction of a porous homochiral coordination polymer with two types of Cu(n)I(n) alternating units linked by quinine: a solvothermal and a mechanochemical approach

The polymer network: The reaction of quinine (QN) with CuI under solvothermal, as well as liquid-assisted grinding, conditions afforded a unique 1D homochiral coordination polymer {[Cu(4)(μ(3)-I)(4)(QN)(2)][Cu(3)(μ(3)-I)(2)(μ(2)-I)(QN)(2)](2)}(n), containing both triangular Cu(3)I(3) and cubane Cu(4)I(4) clusters as connecting nodes (see scheme). Van der Waals interactions between the adjacent 1D polymer chains lead to an extended quasi-honeycomb homochiral pillared 3D network with solvent-free 1D channels.     

Influence of temperature and interactions with ligands on dissociation of dsDNA and ligand-dsDNA complexes of various types of binding. An electrochemical study

Several medicinally important compounds that bind to dsDNA strands via intercalation (C-1311, C-1305, EtBr), major groove binding (Hoechst 33258) and covalent binding (cis-Pt) were examined. The obtained results suggest that both the transfer of conformation B to C and the denaturation process, for the ligand-dsDNA complexes, except for covalently bound cis-Pt, took place at higher temperatures compared to the unbound helix. Furthermore, much lower currents of electrooxidation of guanine at 100 °C, compared to the currents obtained at this temperature for dsDNA in the absence of ligands, suggest that the binding of ligands affects the way the dsDNA denaturates at increased temperatures and leads to formation of different forms of DNA single strands. The voltammetric results were compared with the data of two spectroscopic techniques: UV-Vis and CD.     

Emulsion chamber observations of Centauros,aligned events and the long-flying component

The cosmic ray emulsion chamber community has reported several unusual phenomena which are also relevant to experiments at the current high-energy accelerators, in particular the Fermilab Tevatron Collider and the CERN Large Hadron Collider (LHC). A summary of the ”Cosmic Rays at Mountain Altitude” workshop held at Plock (Poland, September 2010) is given.     

On the measurability of functions with quasi-continuous and upper semi-continuous vertical sections

Let f: ?² → ? be a function with upper semicontinuous and quasi-continuous vertical sections f _x (t) = f(x, t), t, x ∈ ?. It is proved that if the horizontal sections f ^y (t) = f(t, y), y, t ∈ ?, are of Baire class α (resp. Lebesgue measurable) [resp. with the Baire property] then f is of Baire class α + 2 (resp. Lebesgue measurable and sup-measurable) [resp. has Baire property].     

On Family of Graphs with Minimum Number of Spanning Trees

We show that there is a well-defined family of connected simple graphs Λ(n, m) on n vertices and m edges such that all graphs in Λ(n, m) have the same number of spanning trees, and if ${G \in \Lambda(n, m)}$ then the number of spanning trees in G is strictly less than the number of spanning trees in any other connected simple graph ${H, H \notin \Lambda(n, m)}$ , on n vertices and m edges.     

Covering functions by countably many functions from some families

Let $ \mathcal{A} $ be a nonempty family of functions from $ \mathbb{R} $ to $ \mathbb{R} $ . A function $ f:\mathbb{R}\to \mathbb{R} $ is said to be strongly countably $ \mathcal{A} $ -function if there is a sequence (f _n ) of functions from $ \mathcal{A} $ such that $ \mathrm{Gr}(f)\subset {\cup_n}\mathrm{Gr}\left( {{f_n}} \right) $ (Gr(f) denotes the graph of f). If $ \mathcal{A} $ is the family of all continuous functions, the strongly countable $ \mathcal{A} $ -functions are called strongly countably continuous and were investigated in [Z. Grande and A. Fatz-Grupka, On countably continuous functions, Tatra Mt. Math. Publ., 28:57–63, 2004], [G. Horbaczewska, On strongly countably continuous functions, Tatra Mt. Math. Publ., 42:81–86, 2009], and [T.A. Natkaniec, On additive countably continuous functions, Publ. Math., 79(1–2):1–6, 2011]. In this article, we prove that the families $ \mathcal{A}\left( \mathbb{R} \right) $ of all strongly countably $ \mathcal{A} $ -functions are closed with respect to some operations in dependence of analogous properties of the families $ \mathcal{A} $ , and, in particular, we show some properties of strongly countably differentiable functions, strongly countably approximately continuous functions, and strongly countably quasi-continuous functions.     

Suita conjecture and the Ohsawa-Takegoshi extension theorem

We prove a conjecture of N. Suita which says that for any bounded domain D in ? one has $c_{D}^{2}\leq\pi K_{D}$ , where c _D (z) is the logarithmic capacity of ??D with respect to z∈D and K _D the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.     

B-spline solver for one-electron Schrödinger equation

A numerical algorithm for solving the one-electron Schrödinger equation is presented. The algorithm is based on the Finite Element method, and the basis functions are tensor products of univariate B-splines. The application of cubic or higher order B-splines guarantees that the searched solution belongs to a continuous and one time differentiable function space, which is a desirable property in the Kohn–Sham equation context from the Density Functional Theory with pseudopotential approximation. The theoretical background of the numerical algorithm is presented, and additionally, the implementation on parallel computers with distributed memory is described. The current implementation of the algorithm uses the MPI, HYPRE and ParMETIS libraries to distribute matrices on processing units. Additionally, the LOBPCG algorithm from HYPRE library is used to solve the algebraic generalized eigenvalue problem. The proposed algorithm works for any smooth interaction potential, where the domain of the problem is a finite subspace of the ?³ space. The accuracy of the algorithm is demonstrated for a selected interaction potential. In the current stage, the algorithm can be applied to solve the linearized Kohn–Sham equation for molecular systems.