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(R1499) Family of Surfaces with a Common Bertrand D-Curve as Isogeodesic, Isoasymptotic and Line of Curvature
Get PDFIn this paper, we establish the necessary and sufficient conditions to parameterize a surface family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic or curvature line in \mathbb{E}^3. Then, we calculate the fundamental forms of these surfaces and determine the developability and minimality conditions with the Gaussian and mean curvatures. We also extend this idea on ruled surfaces and provide the required conditions for those to be developable. Finally, we present some examples and graph the corresponding surfaces
(R1496) Impact of Electronic States of Conical Shape of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots
Get PDFSemiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs potential
Interactive effects of organic fertilizers and drought stress on growth and nutrient content of brassica juncea at vegetative stage
No full textWith the ongoing climate change scenario and alarmingly increased land degradation, understanding complex interactions of drought stress and organic fertilizers on morpho-physiological traits and dynamics of nutrient concentration is pivotal for sustainable production leafy vegetables such as mustard (Brassica juncea). Thus, this study evaluated the effect of drought stress and organic fertilizers on B. juncea growth, physiology, and dynamics of nutrient concentration at the vegetative stage. The plants were exposed to three water stress levels (well-watered (100% field capacity, FC), mild (50% FC), and severe (25% FC) supplemented with three organic fertilizers (chitosan, ultra green, and home-grown natural vegetable foods) either individually or in combination during the vegetative growth stage. Water stress had a negative effect on growth and physiological traits, and macro-and micronutrients of mustard. However, the ameliorative effects of fertilizer application were revealed by improved plant height, leaf area, relative water content, membrane stability index, and chlorophyll content from 9.7% to 26.9%, 28% to 32.72%, 7.97% to 39.51%, 7.93% to 39.66%, and 29.68% to 56.53%, respectively. Analysis of variance revealed a significant effect of soil moisture level, fertilizer type and their interaction on content of macronutrients (Ca, K, P, N, C, S, Na, Mg) and micronutrients (Fe, Zn) in mustard leaves. However, there was no significant effect detected for Cu across all factors as well the interaction effect on Mn. Overall, our results indicated that application of organic fertilizers enables mustard plant to withstand the deleterious effect of drought stress, resulting in improved growth and physiological traits as well as leaf nutrient content
Nonparametric Relative Error Estimation via Functional Regressor by the k Nearest Neighbors Smoothing Under Truncation Random Data
Get PDFThe relation between a functional random covariate and a scalar answer due to left truncation by a different random variable is evaluated in this study with the kNN method. In particular, in order to produce a nonparametric kNN regression operator of these functional truncated data as a loss function, we should use mean squared relative error. In number of neighbors, we establish an estimator and assess the uniform consistency performance with the convergence rate. Then, for different levels of computational truncated data, a simulation analysis was carried out on finite-sized samples to show the feasibility of our estimation procedure and to highlight its superiority to traditional kernel estimation
Orthogonality in Terms of 2-HH Norm and Bounded Linear Operators in Banach Spaces
Get PDFIn the present paper, the generalization of the Carlson orthogonality for functionals to operators in Banach spaces has been studied. We will also investigate various properties related to the Carlsson, Birkhoff-James, and Pythagorean orthogonality for operators. Kikianty and Dragomir (2010) mentioned in their paper by stating that Pythagorean and isosceles orthogonality through the medium of 2 − HH norm satisfies the non-degeneracy, symmetry and continuity properties without mentioning detailed proof. This paper provides the complete proof of these properties as well as the equivalency of additivity and homogeneity of the isosceles orthogonality with the help of 2 − HH norm. In the case of norm attaining bounded linear operators in a Hilbert space, we prove an equivalence relation between the Pythagorean and isosceles orthogonality including result that the Pythagorean implies Birkhoff-James, whereas the converse is not necessarily true. Furthermore, we will study a new particular case of Carlsson orthogonality and show that this orthogonality implies Birkhoff-James orthogonality, but the converse may not be true
Anti-synchronization Scheme for the Stability Analysis of a Newly Designed Hamiltonian Chaotic System Based on Hénon-Heiles Model Using Adaptive Control Method
Get PDFIn this paper, a systematic approach to investigate the anti-synchronization among identical Hamiltonian chaotic systems has been proposed by using adaptive control method (ACM). Initially an adaptive controller and parameter update law are described to achieve asymptotical stability of state variables of given system with uncertain parameters using Lyapunov stability theory (LST). In addition, numerical simulations using MATLAB software are performed to validate the efficacy and effectiveness of the designed technique. Moreover, the proposed technique has numerous applications in encryption and secure communication
A two-dimensional electron gas suspended above a neutralizing background
No full textWe consider a two-dimensional electron gas system consisting of a layer of electrons suspended above its jellium neutralizing background counterpart. We investigate the energy of the system in the Hartree–Fock approximation as a function of separation distance between the layer of electrons and the background. We find that the energy of the system is influenced by the separation distance in such a way that the new energy contribution originating from such a separation behaves as an effective kinetic energy term. The increase of the overall energy with increase of the separation distance adversely affects the stability of electron liquid states at high density. The results are derived for a fully spin-polarized (spinless) system of electrons in the thermodynamic limit, but can easily be generalized to a spin unpolarized state
New solution method for the problem of a uniformly charged straight wire
No full textA common problem in electrostatics is determining the electrostatic potential due to a uniformly charged straight wire. The solution of this problem illustrates well the types of calculations that one must perform in order to obtain the electrostatic potential or field of a given continuous charge distribution. In this work, we reconsider and solve the problem of a uniformly charged straight wire via a new method that is different from the popular direct integration approach found in the majority of physics textbooks. The outcomes of the two methods are compared and the results suggest several interesting mathematical formulas involving special functions
Variation Iteration Method for Solving Ethanol and Acetaldehyde Concentrations in a Fixed Bed Laboratory Reactor
Get PDFIn this paper, we investigate the effects of nonlinear behaviour of the dimensionless concentrations of the ethanol and acetaldehyde in a fixed bed laboratory reactor. The work is based on solving the nonlinear differential equation of concentration of the ethanol and acetaldehyde by means of the He’s variational iteration method (VIM). Also, the numerical simulation (4th order Runge – Kutta method) is reported using Matlab software. The analytical solutions are compared with numerical results in order to achieve conclusions based on not only for accuracy and efficiency of the solutions, but also the simplicity of the taken procedures which would have remarkable effects on the time devoted for solving process. The analytical result reported in this work is useful to understand the behaviour of the system. Furthermore, due to the accuracy and convergence of obtained solutions, it is proved that the VIM could be applied through other nonlinear problems even with high nonlinearity
Hybrid Algorithm for Singularly Perturbed Delay Parabolic Partial Differential Equations
Get PDFThis study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify the theoretical investigations