Gravitational energy-momentum density in teleparallel gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Moller's canonical energy-momentum density of the gravitational field.     

Nitration of substituted chromans

The nitration of substituted chromans has been studied and the structure of the nitro compounds has been confirmed by chemical and spectral data.     

Nonenzymic polycyclization of analogues of oxidosqualene with a preformed C-ring

Some nonenzymic epoxide-initiated polyolefin cyclization are reported. The presented molecules are partially constrained analogues of (3S)-oxidosqualene, the natural substrate to many important cyclase enzymes. These model compounds feature a preformed C-ring with built-in stereochemical information. The experimental results allow for an instructive comparison with the enzymic processes, particularly those of the cyclases in steroid biosynthesis (i.e. lanosterol synthase).     

Nonlinear compression of optical solitons

In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.     

Structural study of the solid-state photoaddition reaction of arylidenoxindoles

The photochemistry of isomeric 2-furyliden- and benzylidenoxindoles (2H-indol-2-ones) is examined. In solution E-Z isomerization is the only process via the excited singlet state (which fluoresces in glassy solution at 77 K and not at room temperature). In the crystalline state, the two (Z) derivatives are photostable, in accordance with the prediction based on the structural determination of the furylidene derivative, which adopts the unreactive Schmidt's gamma type arrangement. The (E) furylidene derivative (1a) gives efficiently (Phi = 0.3) the head-to-tail dimer, as indicated by the crystal structure, which is of the reactive alpha type, in full accord with the topochemical principles. In contrast, the corresponding benzylidene (1b) derivative reacts sluggishly (Phi < 0. 01) and mainly gives polymers, despite the fact that crystal structure determination shows that it likewise pertains to the alpha type and complies with the topochemical rules. The difference in reactivity is explained on the basis of (i) the twist of the phenyl ring with respect to the indole plane, and (ii) the higher overall cohesion energy and the lower interaction energy between facing molecules, as found from the charge density analysis for the crystals of 1b in comparison to those of 1a. This evidences a further stringent requirement for the occurrence of topochemical photodimerizations.     

Inversion of simulated positron annihilation lifetime spectrum using a neural network

Inversion of positron annihilation lifetime spectroscopy, based on a neural network Hopfield model, is presented in this paper. From a previous reported density function for lysozyme in water a simulated spectrum, without the superposition of statistical fluctuation and spectrometer resolution effects, was generated. These results were taken as the exact results from which the neural network was trained. The precision of the inverted density function was analyzed taking into account the number of neurons and the learning time of the neural network. A fair agreement was obtained when comparing the neural network results with the exact results. For example, the maximum of the density function, with a precision of 0.4% for the percentual relative error, was obtained for 64 neurons.     

Metric and isoperimetric problems in symplectic geometry

Our first result is a reduction inequality for the displacement energy. We apply it to establish some new results relating symplectic capacities and the volume of a Lagrangian submanifold in a number of different settings. In particular, we prove that a Lagrange submanifold always bounds a holomorphic disc of area less than , where is some universal constant. We also explain how the Alexandroff-Bakelman-Pucci inequality is a special case of the above inequalities. Our inequality on displacement of reductions is also applied to yield a relation between length of billiard trajectories and volume of the domain. Two simple results concerning isoperimetric inequalities for convex domains and the closure of the symplectic group for the norm are included.
     

SC List-Flip Decoding of Polar Codes by Shifted Pruning: A General Approach

In the successive cancellation (SC) list decoding, the tree pruning operation retains the L best paths with respect to a metric at every decoding step. However, the correct path might be among the L worst paths due to the imposed penalties. In this case, the correct path is pruned and the decoding process fails. shifted pruning (SP) scheme can recover the correct path by additional decoding attempts when decoding fails, in which the pruning window is shifted by κ≤L paths over certain bit positions. A special case of the shifted pruning scheme where κ=L is known as SCL-flip decoding, which was independently proposed in 2019. In this work, a new metric that performs better in particular for medium and long codes is proposed, and nested shift-pruning schemes are suggested for improving the average complexity.