On modules which force homogeneous maps to be linear

Let be a ring with identity. We characterize in terms of the left ideal structure of when every homogeneous map between nonsingular -modules is linear and answer some earlier questions of the author that remained open.

     

Conformal boundary conditions and three-dimensional topological field theory

We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.     

Enhancing Auxiliary-Mediated Native Chemical Ligation at Challenging Junctions with Pyridine Scaffolds

To expand the scope of native chemical ligation (NCL) beyond reactions at cysteine, ligation auxiliaries are appended to the peptide N-terminus. After the introduction of a pyridine-containing auxiliary, which provided access to challenging junctions (proline or β-branched amino acids), we herein probe the role of the pyridine-ring nitrogen. We observed side reactions leading to preliminary auxiliary loss. We describe a new easy to attach β-mercapto-β-(4-methoxy-2-pyridinyl)-ethyl (MMPyE) auxiliary, which 1) has increased stability; 2) enables NCL at sterically encumbered junctions (e. g., Leu-Val); and 3) allows removal under mildly basic (pH 8.5) conditions was introduced. The synthesis of a 120 aa long peptide containing eight MUC5AC tandem repeats via ligation of two 60mers demonstrates the usefulness. Making use of hitherto unexplored NCL to tyrosine, the MMPyE auxiliary provided access to a head-to-tail-cyclized 21-mer peptide and a His₆-tagged hexaphosphorylated peptide comprising 6 heptapeptide repeats of the RNA polymerase II C-terminal domain.     

Variants of the Stokes Problem: the Case of Anisotropic Potentials

We investigate the smoothness properties of local solutions of the nonlinear Stokes problem$\begin{eqnarray*}-\diverg \{T(\eps(v))\} + \nabla \pi &=& g \msp \mbox{on $\Omega$,}\\\diverg v&\equiv & 0 \msp \mbox{on $\Omega$,}\end{eqnarray*}$where v: ⁿ is the velocity field, $\pi$: $ denotes the pressure function, and g: ⁿ represents a system of volume forces, denoting an open subset of ⁿ . The tensor T is assumed to be the gradient of some potential f acting on symmetric matrices. Our main hypothesis imposed on f is the existence of exponents 1 < p q < \infty such that\lambda (1+|\eps|^{2})^{\frac{p-2}{2}} |\sigma|^{2} \leq D^{2}f(\eps)(\sigma ,\sigma) \leq \Lambda (1+|\eps|^{2})^{\frac{q-2}{2}} |\sigma|^{2}holds with suitable constants , > 0, i.e. the potential f is of anisotropic power growth. Under natural assumptions on p and q we prove that velocity fields from the space W ¹ _{p, loc} (; ⁿ ) are of class C ^1, on an open subset of with full measure. If n = 2, then the set of interior singularities is empty.Dedicated to O. A. Ladyzhenskaya on the occasion of her 80th birthday     

On the interaction between two fixed spherical particles

The variation of the drag (C_D) and lift coefficients (C_L) of two fixed solid spherical particles placed at different positions relative each other is studied. Simulations are carried out for particle Reynolds numbers of 50, 100 and 200 and the particle position is defined by the angle between the line connecting the centers of the particles and the free-stream direction (α) and the separation distance (d₀) between the particles. The flow around the particles is simulated using two different methods; the Lattice Boltzmann Method (LBM), using two different computational codes, and a conventional finite difference approach, where the Volume of Solid Method (VOS) is used to represent the particles. Comparisons with available numerical and experimental data show that both methods can be used to accurately resolve the flow field around particles and calculate the forces the particles are subjected to. Independent of the Reynolds number, the largest change in drag, as compared to the single particle case, occurs for particles placed in tandem formation. Compared to a single particle, the drag reduction for the secondary particle in tandem arrangement is as high as 60%, 70% and 80% for Re = 50, 100 and 200, respectively. The development of the recirculation zone is found to have a significant influence on the drag force. Depending on the flow situation in-between the particles for various particle arrangements, attraction and repulsion forces are detected due to low and high pressure regions, respectively. The results show that the inter-particle forces are not negligible even under very dilute conditions.     

Influence of the hall effect on plasma compressibility in a strong toroidal magnetic field

The development of the tearing instability is studied in the presence of a high toroidal magnetic field and a high plasma conductivity. The variation of the plasma density is shown to be significant in this case. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 3–9, March–April, 1998.     

Electrochemical Proton Intercalation in Vanadium Pentoxide Thin Films and its Electrochromic Behavior in the near-IR Region

This work examines the proton intercalation in vanadium pentoxide (V₂O₅) thin films and its optical properties in the near-infrared (near-IR) region. Samples were prepared via direct current magnetron sputter deposition and cyclic voltammetry was used to characterize the insertion and extraction behavior of protons in V₂O₅ in a trifluoroacetic acid containing electrolyte. With the same setup chronopotentiometry was done to intercalate a well-defined number of protons in the H_xV₂O₅ system in the range of x=0 and x=1. These films were characterized with optical reflectometry in the near-IR region (between 700 and 1700 nm wavelength) and the refractive index n and extinction coefficient k were determined using Cauchy ’s dispersion model. The results show a clear correlation between proton concentration and n and k.     

Evaluation of mass spectrometric data using principal component analysis for determination of the effects of organic lakes on protein binder identification

Matrix‐assisted laser desorption/ionisation–time of flight (MALDI‐TOF) mass spectrometry is commonly used for the identification of proteinaceous binders and their mixtures in artworks. The determination of protein binders is based on a comparison between the m/z values of tryptic peptides in the unknown sample and a reference one (egg, casein, animal glues etc.), but this method has greater potential to study changes due to ageing and the influence of organic/inorganic components on protein identification. However, it is necessary to then carry out statistical evaluation on the obtained data. Before now, it has been complicated to routinely convert the mass spectrometric data into a statistical programme, to extract and match the appropriate peaks. Only several ‘homemade’ computer programmes without user‐friendly interfaces are available for these purposes. In this paper, we would like to present our completely new, publically available, non‐commercial software, ms‐alone and multiMS‐toolbox, for principal component analyses of MALDI‐TOF MS data for R software, and their application to the study of the influence of heterogeneous matrices (organic lakes) for protein identification. Using this new software, we determined the main factors that influence the protein analyses of artificially aged model mixtures of organic lakes and fish glue, prepared according to historical recipes that were used for book illumination, using MALDI‐TOF peptide mass mapping. Copyright © 2015 John Wiley & Sons, Ltd.     

Speeding up the Dreyfus–Wagner algorithm for minimum Steiner trees

The Dreyfus–Wagner algorithm is a well-known dynamic programming method for computing minimum Steiner trees in general weighted graphs in time O ^*(3 ^k ), where k is the number of terminal nodes to be connected. We improve its running time to O ^*(2.684 ^k ) by showing that the optimum Steiner tree T can be partitioned into T = T ₁∪ T ₂ ∪ T ₃ in a certain way such that each T _i is a minimum Steiner tree in a suitable contracted graph G _i with less than terminals. In the rectilinear case, there exists a variant of the dynamic programming method that runs in O ^*(2.386 ^k ). In this case, our splitting technique yields an improvement to O ^*(2.335 ^k ).     

Laser-foil acceleration of high-energy protons in small-scale plasma gradients

Proton beams laser accelerated from thin foils are studied for various plasma gradients on the foil rear surface. The beam maximum energy and spectral slope reduce with the gradient scale length, in good agreement with numerical simulations. The results also show that the jxB mechanism determines the temperature of the electrons driving the ion expansion. Future ion-driven fast ignition of fusion targets will use multikilojoule petawatt laser pulses, the leading part of which will induce target preheat. Estimates based on the data show that this modifies by less than 10% the ion beam parameters.