The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein-Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin-1/2 field. © 1988 American Institute of Physics.

Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Dynamics characterization of modified Gross-Pitaevskii equation

The dynamics of dissipative and coherent N-body systems, such as a Bose-Einstein condensate, which can be described by an extended Gross-Pitaevskii formalism, is investigated. In order to analyze chaotic and unstable regimes, two approaches are considered: a metric one, based on calculations of Lyapunov exponents, and an algorithmic one, based on the Lempel-Ziv criterion. The consistency of both approaches is established, with the Lempel-Ziv algorithmic found as an efficient complementary approach to the metric one for the fast characterization of dynamical behaviors obtained from finite sequences. © 2013 Elsevier B.V. All rights reserved.

Scattering and bound states of fermions in the modified Hulthen potential

In the present work the scattering of a fermion in the modified Hulthen potential is considered with a general vector and scalar and we solved the Dirac equation in the one-dimensional space. The transmission and reflection coefficients are reported. The bound-state solution is also given. The study shows the asymptotic behavior of the wave function in bound-state and scattering states solutions.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Simulating the effect of acoustic treatment types for residential balconies with road traffic noise

Development of design guides to estimate the difference in speech interference level due to road traffic noise between a reference position and balcony position or façade position is explored. A previously established and validated theoretical model incorporating direct, specular and diffuse reflection paths is used to create a database of results across a large number of scenarios. Nine balcony types with variable acoustic treatments are assessed to provide acoustic design guidance on optimised selection of balcony acoustic treatments based on location and street type. In total, the results database contains 9720 scenarios on which multivariate linear regression is conducted in order to derive an appropriate design guide equation. The best fit regression derived is a multivariable linear equation including modified exponential equations on each of nine deciding variables, (1) diffraction path difference, (2) ratio of total specular energy to direct energy, (3) distance loss between reference position and receiver position, (4) distance from source to balcony façade, (5) height of balcony floor above street, (6) balcony depth, (7) height of opposite buildings, (8) diffusion coefficient of buildings, and; (9) balcony average absorption. Overall, the regression correlation coefficient, R2, is 0.89 with 95% confidence standard error of ±3.4 dB.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

Electrocatalytic oxidation of ascorbic acid using a single layer of gold nanoparticles immobilized on 1,6-hexanedithiol modified gold electrode

This paper describes the electrocatalytic oxidation of ascorbic acid (AA) in phosphate buffer solution by the immobilized citrate capped gold nanoparticles (AuNPs) on 1,6-hexanedithiol (HDT) modified Au electrode. X-ray photoelectron spectrum (XPS) of HDT suggests that it forms a monolayer on Au surface through one of the two single bondSH groups and the other single bondSH group is pointing away from the electrode surface. The free single bondSH groups of HDT were used to covalently attach colloidal AuNPs. The covalent attachment of AuNPs on HDT monolayer was confirmed from the observed characteristic carboxylate ion stretching modes of citrate attached with AuNPs in the infra-red reflection absorption spectrum (IRRAS) in addition to a higher reductive desorption charges obtained for AuNPs immobilized on HDT modified Au (Au/HDT/AuNPs) electrode in 0.1 M KOH when compared to HDT modified Au (Au/HDT) electrode. The electron transfer reaction of [Fe(CN)6]4−/3− was markedly hindered at the HDT modified Au (Au/HDT) electrode while it was restored with a peak separation of 74 mV after the immobilization of AuNPs on Au/HDT (Au/HDT/AuNPs) electrode indicating a good electronic communication between the immobilized AuNPs and the underlying bulk Au electrode through a HDT monolayer. The Cottrell slope obtained from the potential-step chronoamperometric measurements for the reduction of ferricyanide at Au/HDT/AuNPs was higher than that of bare Au electrode indicating the increased effective surface area of AuNPs modified electrode. The Au/HDT/AuNPs electrode exhibits excellent electrocatalytic activity towards the oxidation of ascorbic acid (AA) by enhancing the oxidation peak current to more than two times with a 210 mV negative shift in the oxidation potential when compared to a bare Au electrode. The standard heterogeneous electron transfer rate constant (ks) calculated for AA oxidation at Au/HDT/AuNPs electrode was 5.4 × 10−3 cm s−1. The oxidation peak of AA at Au/HDT/AuNPs electrode was highly stable upon repeated potential cycling. Linear calibration plot was obtained for AA over the concentration range of 1–110 μM with a correlation coefficient of 0.9950. The detection limit of AA was found to be 1 μM. The common physiological interferents such as glucose, oxalate ions and urea do not show any interference within the detection limit of AA. The selectivity of the AuNPs modified electrode was illustrated by the determination of AA in the presence of uric acid.

Predictors of condom use behaviour among male street labourers in urban Vietnam using a modified Information-Motivation-Behavioral Skills (IMB) model

HIV risk in vulnerable groups such as itinerant male street labourers is often examined via a focus on individual determinants. This study provides a test of a modified Information-Motivation-Behavioral Skills (IMB) model to predict condom use behaviour among male street workers in urban Vietnam. In a cross-sectional survey using a social mapping technique, 450 male street labourers from 13 districts of Hanoi, Vietnam were recruited and interviewed. Collected data were first examined for completeness; structural equation modelling was then employed to test the model fit. Condoms were used inconsistently by many of these men, and usage varied in relation to a number of factors. A modified IMB model had a better fit than the original IMB model in predicting condom use behaviour. This modified model accounted for 49% of the variance, versus 10% by the original version. In the modified model, the influence of psychosocial factors was moderately high, whilst the influence of HIV prevention information, motivation and perceived behavioural skills was moderately low, explaining in part the limited level of condom use behaviour. This study provides insights into social factors that should be taken into account in public health planning to promote safer sexual behaviour among Asian male street labourers.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Catalyst effectiveness factor for redox model kinetic equation

A generalized isothermal effectiveness factor correlation has been proposed for catalytic reactions whose intrinsic kinetics are based on the redox model. In this correlation which is exact for asymptotic values of the Thiele parameter the effect of the parameters appearing in the model, the order of the reaction and particle geometry are incorporated in a modified form of Thiele parameter. The relationship takes the usual form: Image and predicts effectiveness factor with an error of less than 2% in a range of Thiele parameter that accommodates both the kinetic and diffusion control regimes.

Modified design procedure for a sparger reactor sequence

In an earlier communication[l] we have indicated a general graphical design procedure for a sequence of sparger reactors in which a second order liquid phase reaction proceeds in a stagewise fashion. The prediction of the reactant concentration in each stage and hence the conversion depended on a search procedure initiated along a straight line representing the mass balance equation at the given stage and drawn from the known feed stage located on the abscissa in a E-IU diagram for the given system.

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.