Effective quadrature formula in solving linear integro-differential equations of order two

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods

Spin-flop quasi metamagnetic, anisotropic magnetic, and electrical transport behavior of Ho substituted kagome magnet ErMn6_6Sn6_6

We report on the magnetic and electrical properties of a (Mn$_3$Sn)$_2$ triangular network kagome structured high quality Ho substituted ErMn$_6$Sn$_6$ single-crystal sample by magneto-transport measurements. Er$_{0.5}$Ho$_{0.5}$Mn$_6$Sn$_6$ orders antiferromagnetically at N\'{e}el temperature $T_\mathrm{N} \sim$ 350 K followed by a ferrimagnetic (FiM) transition at $T_\mathrm{C} \sim$ 114 K and spin-orientation transition at $T_\mathrm{t} \sim$ 20 K. The field-manifestations of these magnetic phases in the \textit{ab}-basal plane and along the \textit{c}-axis are illustrated through temperature-field \textit{T-H} phase diagrams. In \textit{H}$\parallel$\textit{c}, narrow hysteresis between spin reorientation and field-induced FiM phases below $T_\mathrm{t}$, enhanced/strengthened FiM phase below $T_\mathrm{C}$ and stemming of FiM phase out of strongly coexisting AFM and FiM phases below $T_\mathrm{N}$ through a non-meta-magnetic transition are confirmed to arise from strong R-Mn sublattices interaction. In contrast, \textit{H}$\parallel$\textit{ab}-plane, between $T_\mathrm{N}$ and $T_\mathrm{C}$, individually contributing R-Mn sublattices with weak antiferromagnetic interactions undergo a field-induced spin-flop quasi-metamagnetic transition to FiM state. The temperature dependent electrical resistivity suggests metallic nature with Fermi liquid behavior at low temperatures. Essentially, the current study stimulates interest to investigate the magnetic and electrical properties of mixed rare-earth layered kagome magnetic metals for possible novel and exotic behavior.Comment: 9 pages, 6 figure

Negative refraction metamaterial with low loss property at millimeter wave spectrum

The design of the millimetre-wave (MMW) metamaterials (MMs) unit cell operates at 28 GHz is presented and numerically investigated. The proposed structure composed of a modified split ring resonator (MSRR) printed on both sides of the substrate layer. Popular MM structures such as S-shape, G-shape, and Ω-shape are adjusted to operate at the 28 GHz for comparison purpose. MSRR achieves a wide bandwidth of 1.1 GHz in comparison with its counterparts at the resonance frequency. Moreover, the proposed structure presents very low losses by providing the highest transmission coefficient, S21, at the corresponding frequency region. The radiation loss is substantially suppressed and the negativity of the constitutive parameters of the proposed MM structure is maintained. By applying the principle of the electromagnetically induced transparency (EIT) phenomenon, the MSRR unit cell induces opposite currents on both sides of the substrate which leads to cancelling out the scattering fields and suppresses the radiation loss. The constitutive parameters of the MM structures are retrieved using well-known retrieval algorithm. The proposed structure can be used to enhance the performance of fifth-generation (5G) antenna such as the gain and bandwidth

Response of Stock Markets to Monetary Policy: An Asian Stock Market Perspective

We estimate the response of Asian stock market prices to exogenous monetary policy shocks using a vector error correction model. In our paper, monetary policy transmits to stock market price through three routes: money by itself, exchange rate, and inflation. Our result points to the fact that stock prices increase persistently in response to an exogenous easing monetary policy. Variance deposition results show that, after 10 periods, the forecast error variance of beyond 53% of the Tehran Stock Exchange Price Index (TEPIX) can be explained by exogenous shocks to the US dollar-Iranian rial exchange rate, while this ratio for exogenous shocks to Iranian real gross domestic product was only 17%. We argue that such evidence can be accounted for by an endogenous response of the stock prices to the monetary policy shocks

Factors influencing students’ intention to use internet for academic purposes

This study aimed to investigate the factors influencing students’ intention to use the Internet for academic purposes amongst 204 final year business students in public universities in Malaysia.This study integrated theory of planned behavior (TPB) and theory of acceptance model (TAM) as the base model toward that purpose.The research model employs the variables from both theories namely attitudes, subjective norms, perceived behavioral control, perceived usefulness, perceived ease of use, intention, and behavior.A multiple regression analysis provides empirical support for the applicability of integration of TPB and TAM in predicting students’ intention to use the Internet for academic purposes.Results of the study show that attitudes, perceived behavioral control, and perceived usefulness are statistically significant in influencing intention to use the Internet for academic purposes.Based on the results, it can be concluded that students’ intention to use the Internet for academic purposes could be predicted from their attitudes, perceived behavioral control, and perceived usefulness at 49% level.In view of the results, several implications and recommendations are discussed

Conducting tests of hypotheses: the need for an adequate sample size

This article addresses the importance of obtaining a sample of an adequate size for the purpose of testing hypotheses. The logic underlying the requirement for a minimum sample size for hypothesis testing is discussed, as well as the criteria for determining it. Implications for researchers working with convenient samples of a fixed size are also considered, and suggestions are given about the steps that should be taken when they are not able to obtain a large enough sample. Finally, the implications of not having an adequate sample size for hypothesis testing are discussed to highlight the importance of determining sample size prior to conducting one’s study