Lower bounds of the Laplacian graph eigenvalues

In this paper we prove that all positive eigenvalues of the Laplacian of an arbitrary simple graph have some positive lower bounds. For a fixed integer k 1 we call a graph without isolated vertices k-minimal if its kth greatest Laplacian eigenvalue reaches this lower bound. We describe all 1-minimal and 2-minimal graphs and we prove that for every k 3 the path P_k+1 on k + 1 vertices is the unique k-minimal graph.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

Single-molecule nanopore sensing of actin dynamics and drug binding

Actin is a key protein in the dynamic processes within the eukaryotic cell. To date, methods exploring the molecular state of actin are limited to insights gained from structural approaches, providing a snapshot of protein folding, or methods that require chemical modifications compromising actin monomer thermostability. Nanopore sensing permits label-free investigation of native proteins and is ideally suited to study proteins such as actin that require specialised buffers and cofactors. Using nanopores, we determined the state of actin at the macromolecular level (filamentous or globular) and in its monomeric form bound to inhibitors. We revealed urea-dependent and voltage-dependent transitional states and observed the unfolding process within which sub-populations of transient actin oligomers are visible. We detected, in real-time, filament-growth, and drug-binding at the single-molecule level demonstrating the promise of nanopore sensing for in-depth understanding of protein folding landscapes and for drug discovery.

Nanopipettes were used for real-time investigation into actin dynamics and drug binding at single-molecule resolution, showing promise for a better understanding of the mechanism of protein–protein interactions and drug discovery.     

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.     

Photochemistry of β-(4-sydnonyl)-o-divinylbenzene: competitive cis-trans isomerization and photolysis

New cis- and trans-3-aryl-4-[2-(2-vinylphenyl)ethenyl]sydnones 2, aryl = phenyl, p-tolyl were prepared and transformed on irradiation in the presence of acrolein to a pyrazoline derivative that aromatized during isolation to trans-1-tolyl-3-[2-(2-vinylphenyl)ethenyl]pyrazole 7 and trans-5-formyl-1-tolyl-3-[2-(2-vinylphenyl)ethenyl]pyrazole 8.     

Synthesis and photochemistry of beta,beta'-di(2-furyl)-substituted o-divinylbenzenes: intra- and/or intermolecular cycloaddition as an effect of annelation

New heteroaryl-substituted o-divinylbenzenes, 2,2'-(1,2-phenylenedivinylene)difuran (9), 2,2'-(1,2-phenylenedivinylene)bisbenzo[b]furan (10), and 2,2'-(1,2-phenylenedivinylene)bisnaphtho[2,1-b]furan (11), were prepared and irradiated at various concentrations; intramolecular photocycloaddition and intermolecular [2+2] twofold photoaddition reactions took place to give bicyclo[3.2.1]octadiene derivatives 12-14 and cyclophane derivatives 15-17, respectively. Compound 11 was the most selective of these o-divinylbenzenes, which, owing to pi-pi intra- or intermolecular complexation, gave only the exo-bicyclo[3.2.1]octadiene derivative 14 at low concentrations, and only the cyclophane derivative 17 at high concentrations.     

Sums of reciprocals of certain additive functions

We obtain sharp estimates for sums of reciprocals and sums of quotients of certain non-negative integer-valued additive arithmetical functions.Research financed by the Mathematical Institute of Belgrade and Republika Zaj. of Serbia