Kinetic energy functional for Fermi vapors in spherical harmonic confinement

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure

Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions

Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. While all three methods predict final state distributions from explicit quasi-classical trajectory simulations with R$^2$ > 0.998, the grid-based approach performs best. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. The function-based approach also suffers from lacking a general set of model functions. Applications of the grid-based approach to nonequilibrium, multi-temperature initial state distributions are presented, a situation common to energy distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed

Metastable states of a ferromagnet on random thin graphs

We calculate the mean number of metastable states of an Ising ferromagnet on random thin graphs of fixed connectivity c. We find, as for mean field spin glasses that this mean increases exponentially with the number of sites, and is the same as that calculated for the +/- J spin glass on the same graphs. An annealed calculation of the number <N_{MS}(E)> of metastable states of energy E is carried out. For small c, an analytic result is obtained. The result is compared with the one obtained for spin glasses in order to discuss the role played by loops on thin graphs and hence the effect of real frustration on the distribution of metastable states.Comment: 15 pages, 3 figure

Marketing of sweet jelly seeds of palmyra fruit: A study covering the tribal region of South Gujarat, India

Palmyra is a naturally occurring vegetation in Gujarat’s southern region, spread randomly overall soil and land types. The major produce utilized from palmyra palm for a livelihood by the tribal community, contributing considerably to their income, is through sales of the immature soft jelly seed nuts of the fruit called “galeli”. The present investigation was carried out to study the marketing cost, margin, and price spread in galeli marketing. Primary data for the period initiating from 2015-16 to 2017-18 were pooled from 50 palmyra palm growers selected randomly representing five tribal villages of Mahua taluka of Surat district in the South Gujarat region. Two marketing channels viz., Channel-I: producer-consumer and Channel-II: producer - retailer - consumer were observed, and the marketing cost incurred on galeli marketing in these channels was worked out, which was `51.64 and 33.94 per hundred galeli, respectively. The highest producer’s share in consumer’s rupee was worked out in channel-I. The study showed that the major constraint faced by 78 per cent of the palmyra palm growers in the marketing of galeli was the poor functioning of the climber equipment and non-remunerative prices for galeli in the local market

Broad activation of the ubiquitin-proteasome system by Parkin is critical for mitophagy

Parkin, an E3 ubiquitin ligase implicated in Parkinson's disease, promotes degradation of dysfunctional mitochondria by autophagy. Using proteomic and cellular approaches, we show that upon translocation to mitochondria, Parkin activates the ubiquitin–proteasome system (UPS) for widespread degradation of outer membrane proteins. This is evidenced by an increase in K48-linked polyubiquitin on mitochondria, recruitment of the 26S proteasome and rapid degradation of multiple outer membrane proteins. The degradation of proteins by the UPS occurs independently of the autophagy pathway, and inhibition of the 26S proteasome completely abrogates Parkin-mediated mitophagy in HeLa, SH-SY5Y and mouse cells. Although the mitofusins Mfn1 and Mfn2 are rapid degradation targets of Parkin, we find that degradation of additional targets is essential for mitophagy. These results indicate that remodeling of the mitochondrial outer membrane proteome is important for mitophagy, and reveal a causal link between the UPS and autophagy, the major pathways for degradation of intracellular substrates

Stabilizability of Second Order Bilinear Systems

This note states necessary and sufficient conditions for the existence of a linear state feedback controller such that a second-order bilinear system has a globally asymptotically stable closed loop. A suitable controller is constructed for each system which satisfies the conditions

The Stability of Second Order Quadratic Differential Equations

This paper investigates the stability properties of second-order systems, x. = ƒ(x), where ƒ(x) contains either quadratic terms-system (1)-or linear and quadratic terms-system (2)-in x. The principal contributions are summarized in two theorems which give necessary and sufficient conditions for stability and asymptotic stability in the large of systems (1) and (2), respectively

DEVELOPMENT AND VALIDATION OF HPLC METHOD FOR SIMULTANEOUS DETERMINATION OF LIDOCAINE AND PRILOCAINE IN TOPICAL FORMULATION

  Objective: A simple, specific, accurate, and precise method, namely, reverse phase high-performance liquid chromatography was to develop for simultaneous estimation of Lidocaine (LDC) and prilocaine (PLC) in a topical local anesthetic cream.Method: The mixture of PLC and LDC was separated on Hi Q Sil C18 HS column, (250 mm × 4.6 mm, 5 μm), column temperature ambient and flow rate 1.2 mL/minutes. The mobile phase was acetonitrile: 0.01 M diethylamine solution (pH adjusts to 6.8 with orthophosphoric acid) (60:40) with detection at 225 nm.Results: The retention time was found to be 6.075±0.12 minutes for PLC and 8.642±0.15 minutes for LDC, respectively. Linearity was observed in the concentration range of 1-6 μg/mL for both LDC and PLC, respectively. The method was validated according to International Conference on Harmonization guideline and values of linearity, precision, robustness, limit of detection, limit of quantitation, selectivity, and recovery were found to be in good accordance with the prescribed value.Conclusion: The proposed method can be useful in the quality control of LDC and PLC in their topical formulation

Neural Modeling and Control of Diesel Engine with Pollution Constraints

The paper describes a neural approach for modelling and control of a turbocharged Diesel engine. A neural model, whose structure is mainly based on some physical equations describing the engine behaviour, is built for the rotation speed and the exhaust gas opacity. The model is composed of three interconnected neural submodels, each of them constituting a nonlinear multi-input single-output error model. The structural identification and the parameter estimation from data gathered on a real engine are described. The neural direct model is then used to determine a neural controller of the engine, in a specialized training scheme minimising a multivariable criterion. Simulations show the effect of the pollution constraint weighting on a trajectory tracking of the engine speed. Neural networks, which are flexible and parsimonious nonlinear black-box models, with universal approximation capabilities, can accurately describe or control complex nonlinear systems, with little a priori theoretical knowledge. The presented work extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. Considering the preliminary results, it appears that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation. Particularly, they are able to model nonlinear dynamics and outperform during transients the control schemes based on static mappings.Comment: 15 page