Variational Formulation of the Schrödinger Field

The variational formulation of the Schrödinger field was investigated and the applicability of the chain method was analyzed. Using Batalin-Fradkin-Tyutin formalism a gauge invariant theory was constructed.     

Multicomponent quantitative resolution of binary mixtures by using continuous wavelet transform

Continuous 1-dimensional wavelet transform (WT) was applied to the quantitative analysis of a vitamin combination of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) with strongly overlapping signals. Absorbance data from the UV-Vis absorption spectrum of width 1150 were subjected to Gauss1 and Gauss2 WTs. Because of its flexibility, data processing, and its high signal amplitude, the continuous WT method is a powerful tool for analysis of multicomponent mixtures. By measuring the amplitude signals corresponding to the selected zero-crossing points of the transformed signal, we obtained the calibration curve. The validation of the calibration graphs was confirmed with different mixtures of THI and PYR at various concentration ratios. A brief explanation of the continuous wavelet method is given. MATLAB 6.5 software was used to perform the calculations. The results of our study were compared with those obtained by spectroscopic, chemometric, and liquid chromatographic methods, and good agreement was found.     

Discrete fractional logistic map and its chaos

A discrete fractional logistic map is proposed in the left Caputo discrete delta’s sense. The new model holds discrete memory. The bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.     

New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials

This paper reports a new numerical approach for numerically solving types of fractional variational problems. In our approach, we use the fractional integrals operational matrix, described in the sense of Riemann–Liouville, with the help of the Lagrange multiplier technique for converting the fractional variational problem into an easier problem that consisting of solving an algebraic equations system in the unknown coefficients. Several numerical examples are introduced, combined with their approximate solutions and comparisons with other numerical approaches, for confirming the accuracy and applicability of the proposed approach.     

Improve the heat exchanger efficiency via examine the Graphene Oxide nanoparticles: a comprehensive study of the preparation and stability,predict the thermal conductivity and rheological properties,convection heat transfer and pressure drop

Journal of Thermal Analysis and Calorimetry - In this research, the effect of using GO/ water nanofluid as a coolant fluid in an isothermal heat transfer system was studied. At first, to evaluate...     

A new fractional derivative involving the normalized sinc function without singular kernel

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.     

Hamilton–Jacobi Treatment of Chiral Schwinger Model

We investigate the path integral quantization of the bosonic chiral Schwinger model using multi-Hamilton–Jacobi procedure. The integrability conditions require the extension of the initial phase space. The Wess–Zumino term was recovered calculating the action corresponding to the extended system.     

Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics

We present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.