In Metric-measure Spaces Sobolev Embedding is Equivalent to a Lower Bound for the Measure

We study Sobolev inequalities on doubling metric measure spaces. We investigate the relation between Sobolev embeddings and lower bound for measure. In particular, we prove that if the Sobolev inequality holds, then the measure μ satisfies the lower bound, i.e. there exists b such that μ(B(x,r))≥b r ^α for r∈(0,1] and any point x from metric space.     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

Matrix-analytic solution of infinite,finite and level-dependent second-order fluid models

This paper presents a matrix-analytic solution for second-order Markov fluid models (also known as Markov-modulated Brownian motion) with level-dependent behavior. A set of thresholds is given that divide the fluid buffer into homogeneous regimes. The generator matrix of the background Markov chain, the fluid rates (drifts) and the variances can be regime dependent. The model allows the mixing of second-order states (with positive variance) and first-order states (with zero variance) and states with zero drift. The behavior at the upper and lower boundary can be reflecting, absorbing, or a combination of them. In every regime, the solution is expressed as a matrix-exponential combination, whose matrix parameters are given by the minimal nonnegative solution of matrix quadratic equations that can be obtained by any of the well-known solution methods available for quasi birth death processes. The probability masses and the initial vectors of the matrix-exponential terms are the solutions of a set of linear equations. However, to have the necessary number of equations, new relations are required for the level boundary behavior, relations that were not needed in first-order level dependent and in homogeneous (non-level-dependent) second-order fluid models. The method presented can solve systems with hundreds of states and hundreds of thresholds without numerical issues.     

Tandem Michael addition–Claisen-type condensation of anions of O-ethyl carbonates of cyanohydrins to cyclohex-2-en-1-one

A one pot method for the synthesis of ethyl 2-acetoxy-6-aroylcyclohex-1-ene-1-carboxylates and ethyl 2-acetoxy-6-heterocarbonylcyclohex-1-ene-1-carboxylates through Michael addition of the anions of ethyl carbonates of cyanohydrins to cyclohex-2-en-1-one and subsequent reaction with acetic anhydride is described. These compounds are potential intermediates for the synthesis of 9,10-anthraquinone and heterofused 1,4-naphthoquinone derivatives.     

Theoretical investigation of the molecular structure and spectroscopic properties of oxicams

Nonsteroidal anti-inflammatory drugs (NSAIDs) are among the most frequently prescribed drugs and have multiple therapeutic uses. These drugs are predominantly used for the treatment of musculoskeletal diseases because of their analgesic, antipyretic, and antiplatelet activities. Oxicams constitute an interesting class of organic compounds and have been investigated in the search for new analgesic and anti-inflammatory drugs. In the present work, a theoretical investigation of the molecular structure and spectroscopic properties of a series of five oxicams in different solvents was performed using density functional theory (DFT) methods. The geometric optimizations of the oxicams were carried out using the M06 density functional and the CBSB7 basis set. The infrared data were all obtained at the same theoretical level. The UV-Vis absorption and NMR data of some oxicams were calculated using the DFT and CBSB3 basis sets. The analysis of structural parameters, particularly the bond length and spectroscopic data, indicated that interactions occurred between the hydrogen bond types for 4-meloxicam, isoxicam, and normeloxicam. Stereoelectronic interactions caused by the substitution of alkyl groups caused the bond lengths to elongate. Similarly, the substitution of heteroatoms, such as nitrogen, sulfur, or oxygen, increased the bond lengths and angular stresses.     

Manifestation of the <Emphasis Type="Italic">gauche</Emphasis> effect in conformers of benzenesulfonic acid hydrazide

Conformational properties of a benzenesulfonic acid hydrazide molecule and its para-nitro and para-methyl derivatives, which have found wide application as porofors and biologically active compounds, are studied. It is found that the benzenesulfonic acid hydrazide molecule has six conformers with relative energies of 0//0 kcal/mol, 0.34//0.98 kcal/mol, 2.51//2.25 kcal/mol, 2.54//2.56 kcal/mol, 2.90//3.28 kcal/mol, 6.64//6.43 kcal/mol (MP2//DFT(B3LYP) with the cc-pVTZ basis set), each conformer has enantiomer. The conformers differ from each other in the relative orientation of the fragments of the–SO2NHNH2 group, the energies of the frontier orbitals, the direction and value of the dipole moments. It is shown that the introduction of a nitro or methyl group into the para-position practically does not affect the conformational properties of the sulfonyl hydrazide group. Change in the structure of benzenesulfonic acid hydrazide during the crystal–gas transition is considered and it is revealed that in the crystal the conformation similar in structure to one of the high-energy conformers of the free molecule is stabilized. The NBO analysis of the electron density distribution is performed and it is shown that the occurrence of the gauche effect in all conformers of the molecules under study can be interpreted by the manifestation of the total action of strong anomeric effects between the lone pairs of nitrogen atoms and antibonding orbitals of S=O, N–H, C–S, and N–S bonds.