Modeling of large flattened mode area fiber lasers

Potentialities of independent tailoring the index and gain profiles in fiber laser aiming to achieve a strong modal discrimination are theoretically examined. It is demonstrated by numerical simulations existence of fiber amplifier constructions which have the flattened fundamental mode profile in the gain region. It is shown that the fundamental mode retain the largest modal gain in comparison with modal gains of higher-order-modes for any depletion of the gain by the fundamental mode. The particular design is presented with the flattened fundamental mode area 6360 μm squared.     

Impedance of faradeic process with partial charge transfer

The electrochemical impedance of charge-transfer reaction involving the stages of adsorption and desorption of intermediate partially charged substance is analyzed theoretically in the frequency-potential plane in order to study the possibility for measuring the partial charge transfer. The simplest case of adsorption two-electron transfer, namely, the Langmuir adsorption with liner dependence of reaction rate on the coverage, is considered. It is assumed that the partial charge transfer is independent of the electrode potential.     

关于几类Menger型图

设Ｇ是一个简单图，若分离Ｇ的任一独立集Ｓ的最小点数等于连接Ｓ的点之间的内部不相交路的最大个数，则称Ｇ是Ｍｅｎｇｅｒ型图，本文讨论了几类Ｍｅｎｇｅｒ型图。     

Reduction of underdetermined systems of ordinary differential equations: II

We study the equivalence of underdetermined systems of ordinary differential equations and present a local classification of systems that are linear in derivatives, are sufficiently regular, and consist of two equations.     

Toughness and Matching Extension in {\mathcal{P}_3}-Dominated Graphs

Let G be a connected graph. For ${x,y\in V(G)}$ with d(x, y) = 2, we define ${J(x,y)= \{u \in N(x)\cap N(y)\mid N[u] \subseteq N[x] \,{\cup}\,N[y] \}}$ and ${J'(x,y)= \{u \in N(x) \cap N(y)\,{\mid}\,{\rm if}\ v \in N(u){\setminus}(N[x] \,{\cup}\, N[y])\ {\rm then}\ N[x] \,{\cup}\, N[y]\,{\cup}\,N[u]{\setminus}\{x,y\}\subseteq N[v]\}}$ . A graph G is quasi-claw-free if ${J(x,y) \not= \emptyset}$ for each pair (x, y) of vertices at distance 2 in G. Broersma and Vumar (in Math Meth Oper Res. doi:10.1007/s00186-008-0260-7) introduced ${\mathcal{P}_{3}}$ -dominated graphs defined as ${J(x,y)\,{\cup}\, J'(x,y)\not= \emptyset}$ for each ${x,y \in V(G)}$ with d(x, y) = 2. This class properly contains that of quasi-claw-free graphs, and hence that of claw-free graphs. In this note, we prove that a 2-connected ${\mathcal{P}_3}$ -dominated graph is 1-tough, with two exceptions: K _2,3 and K _1,1,3, and prove that every even connected ${\mathcal{P}_3}$ -dominated graph ${G\ncong K_{1,3}}$ has a perfect matching. Moreover, we show that every even (2p + 1)-connected ${\mathcal{P}_3}$ -dominated graph is p-extendable. This result follows from a stronger result concerning factor-criticality of ${\mathcal{P}_3}$ -dominated graphs.     

Computational and Synthetic Investigation of Cationic Rearrangement in the Putative Biosynthesis of Justicane Triterpenoids

A biomimetic cationic structural rearrangement of the oleanolic acid framework is reported for the gram‐scale synthesis and structural reassignment of justicioside E aglycone. The mechanism of the putative biosynthetic rearrangement is investigated with kinetic, computational, and synthetic approaches. The precursor to rearrangement was accessed through two strategic advancements: (1) synthesis of a 1,3‐diketone via oxidation of a β‐silyl enone, and (2) diastereoselective 1,3‐diketone reduction to form a syn‐1,3‐diol using SmI₂ with PhSH as a key additive.     

Theoretical Interpretation of the Vibrational Spectra of Carboxylic-Acid Dimers in the High-Frequency Range

An anharmonic band shift in the vibrational spectra of carboxylic-acid dimers is estimated on the basis of ab initio quantum calculations of anharmonic force constants. The implementation of ab initio quantum calculations taking into account the anharmonic nature of vibrations is connected with the choice of the atomic basis in the framework of a specific quantum method. All these factors together with the exclusion principle for bands in the infrared and Raman scattering spectra allow identification of the position of the bands of valence vibrations of CH bonds in the range of 2500–3500 cm^–1. The results of model calculations give reason to assert that the fundamental vibrations of the carboxylic fragment are the characteristic frequency and vibrational mode and, for OH bonds, also the characteristic intensity. Small doublet splitting and the exclusion principle for frequencies allow identification of the valence vibrations of CH bonds.     

Energy Fluctuations Shape Free Energy of Nonspecific Biomolecular Interactions

Understanding design principles of biomolecular recognition is a key question of molecular biology. Yet the enormous complexity and diversity of biological molecules hamper the efforts to gain a predictive ability for the free energy of protein-protein, protein-DNA, and protein-RNA binding. Here, using a variant of the Derrida model, we predict that for a large class of biomolecular interactions, it is possible to accurately estimate the relative free energy of binding based on the fluctuation properties of their energy spectra, even if a finite number of the energy levels is known. We show that the free energy of the system possessing a wider binding energy spectrum is almost surely lower compared with the system possessing a narrower energy spectrum. Our predictions imply that low-affinity binding scores, usually wasted in protein-protein and protein-DNA docking algorithms, can be efficiently utilized to compute the free energy. Using the results of Rosetta docking simulations of protein-protein interactions from Andre et al. (Proc. Natl. Acad. Sci. USA 105:16148, 2008), we demonstrate the power of our predictions.