Homo- and heteronuclear 2D NMR approaches to analyse a mixture of deuterated unlike/like stereoisomers using weakly ordering chiral liquid crystals

We describe several homo- and heteronuclear 2D NMR strategies dedicated to the analysis of anisotropic (2)H spectra of a mixture of dideuterated unlike/like stereoisomers with two remote stereogenic centers, using weakly orienting chiral liquid crystals. To this end, we propose various 2D correlation experiments, denoted "D(H)(n)D" or "D(H)(n)C" (with n=1, 2), that involve two heteronuclear polarization transfers of INEPT-type with one or two proton relays. The analytical expressions of correlation signals for four pulse sequences reported here were calculated using the product-operators formalism for spin I=1 and S=1/2. The features and advantages of each scheme are presented and discussed. The efficiency of these 2D sequences is illustrated using various deuterated model molecules, dissolved in organic solutions of polypeptides made of poly-gamma-benzyl-L-glutamate (PBLG) or poly-epsilon-carbobenzyloxy-L-lysine (PCBLL) and NMR numerical simulations.     

Efficient visible-light-induced photocatalytic degradation of MO on the Cr-nanocrystalline titania-S

In order to improve visible light photocatalytic activities of the nanometer TiO₂, a novel and efficient Cr,S-codoped TiO₂ (Cr-TiO₂-S) photocatalyst was prepared by precipitation-doping method. The crystalline structure, morphology, particle size, and chemical structure of Cr-TiO₂-S were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and Fourier transform infrared (FT-IR) techniques, respectively. Results indicate that the doping of Cr and S, cause absorption edge shifts to the visible light region (λ > 420 nm) compare to the pure TiO₂, reduces average size of the TiO₂ crystallites, enhances desired lattice distortion of Ti, promotes separation of photo-induced electron and hole pair, and thus improves pollutant decomposition under visible light irradiation. The photocatalytic activities of Cr-TiO₂-S nanoparticles were evaluated using the photodegradation of methyl orange (MO) as probe reaction under the irradiation of UV and visible light and it was observed that the Cr-TiO₂-S photocatalyst shows higher visible photocatalytic activity than the pure TiO₂. The optimal Cr-TiO₂-S concentration to obtain the highest photocatalytic activity was 5 mol% for both of Cr and S.     

Detection of corrosion beneath a paint layer by use of spectral polarization optical imaging

The spectral and polarization properties of scattered light were used to image corrosion beneath the surface of a painted aluminum plate. The quality of imaging of the corrosion on the metal surface was significantly enhanced by the spectral polarization optical imaging technique. Depolarization scattered light was used to detect and image corrosion beneath the paint layer.     

Minimal ranks of some quaternion matrix expressions with applications

Suppose that p(X, Y) = A − BX − X^(∗)B^(∗) − CYC^(∗) and q(X, Y) = A − BX + X^(∗)B^(∗) − CYC^(∗) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(X, Y) with respect to pair of matrices X and Y = Y^(∗), and the minimal rank formula of q(X, Y) with respect to pair of matrices X and Y = −Y^(∗). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed.     

On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms

Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed.In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end.     

Aspiration Based Simulated Annealing Algorithm

An aspiration based simulated annealing algorithm for continuousvariables has been proposed. The new algorithm is similar to the one givenby Dekkers and Aarts (1991) except that a kind of memory is introduced intothe procedure with a self-regulatory mechanism. The algorithm has beenapplied to a set of standard global optimization problems and a number ofmore difficult, complex, practical problems and its performance comparedwith that of the algorithm of Dekkers and Aarts (1991). The new algorithmappears to offer a useful alternative to some of the currently availablestochastic algorithms for global optimization.     

On some problems of Petrich concerning Bruck and Reilly semigroups

For an inverse semigroupS with its idempotents dually well-ordered, we prove thatS is isomorphic to the semigroup of all one-to-one partial right translations ofS. Also, we prove for a Bruck semigroupS=B(T, α) thatS isE-unitary if and only ifT isE-unitary and α is an idempotent pure homomorphism. Moreover, we characterize allE-unitary covers ofB(T, α), whereT is a finite chain of groups.     

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data,using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.     

The Quantum-Classical Comparison of the Arrival-Time Distribution Through the Probability Current

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.     

Transverse Wave Propagation in Relativistic Two-Fluid Plasmas around Reissner–Nordström Black Hole

We investigate transverse electromagnetic waves propagating in a plasma influenced by the gravitational field of the Reissner–Nordström black hole. Applying 3+1 spacetime split we reformulate the relativistic two-fluid equations to take account of gravitational effects due to the event horizon and describe the set of simultaneous linear equations for the perturbations. Using a local approximation we investigate the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves. We derive the dispersion relation for these waves and solve it for the wave number k numerically.