Magnetic and Mössbauer spectral studies of nano crystalline cobalt substituted magnesium ferrites (MgxCo1 − xFe2O4)

The electronic structure of the heme unit of deoxyhemoglobin including the proximal imidazole has been studied using the first-principles Hartree-Fock procedure. Our results for the ^57mFe isomer shift and asymmetry parameter are in very good agreement with the values obtained from Mössbauer spectroscopy measurements. The ^57mFe nuclear quadrupole coupling constant is smaller than the experimental result and possible ways to improve the agreement in the future are discussed. Improved analysis of the Mössbauer data, removing some approximations made for deriving the magnetic hyperfine tensor for the ^57mFe nucleus, is suggested to allow quantitative comparison with our results in the future.     

A high resolution powder diffractometer using focusing optics

In this paper, we describe the design, construction and performance of a new high resolution neutron powder diffractometer that has been installed at the Dhruva reactor, Trombay, India. The instrument employs novel design concepts like the use of bent, perfect crystal monochromator and open beam geometry, enabling the use of smaller samples. The resolution curve of the instrument was found to have little variation over a wide angular region and a Δd/d ∼ 0.3% has been achieved. The instrument provides sample environment of very low temperatures and high magnetic fields using a 7 Tesla cryogen-free superconducting magnet with a VTI having a temperature range of 1.5–320 K. The special sample environment and high resolution make this neutron powder diffractometer a very powerful facility for studying magnetic properties of materials.      

Spectral graph wavelet optimized finite difference method for solution of Burger's equation with different boundary conditions

In this paper, spectral graph wavelet optimized finite difference method (SPGWOFD) has been proposed for solving Burger's equation with distinct boundary conditions. Central finite difference approach is utilized for the approximations of the differential operators and the grid on which the numerical solution is obtained is chosen with the help of spectral graph wavelet. Four test problems (with Dirichlet, Periodic, Robin and Neumann's boundary conditions) are considered and the convergence of the technique is checked. For assessing the efficiency of the developed technique, the computational time taken by the developed technique is compared to that of the finite difference method. It has been observed that developed technique is extremely efficient.     

On the Fučik spectrum of non-local elliptic operators

In this article, we study the Fu?ik spectrum of the fractional Laplace operator which is defined as the set of all \({(\alpha, \beta)\in \mathbb{R}^2}\) such that $$\quad \left.\begin{array}{ll}\quad (-\Delta)^s u = \alpha u^{+} - \beta u^{-} \quad {\rm in}\;\Omega \\ \quad \quad \quad u = 0 \quad \quad \quad \qquad {\rm in}\; \mathbb{R}^n{\setminus}\Omega.\end{array}\right\}$$ has a non-trivial solution u, where \({\Omega}\) is a bounded domain in \({\mathbb{R}^n}\) with Lipschitz boundary, n > 2s, \({s \in (0, 1)}\) . The existence of a first nontrivial curve \({\mathcal{C}}\) of this spectrum, some properties of this curve \({\mathcal{C}}\) , e.g. Lipschitz continuous, strictly decreasing and asymptotic behavior are studied in this article. A variational characterization of second eigenvalue of the fractional eigenvalue problem is also obtained. At the end, we study a nonresonance problem with respect to the Fu?ik spectrum.     

Fractional derivatives of the H-function of several variables

In the present paper we derive a number of key formulas involving fractional derivatives for the H-function of several variables, which was introduced and studied in a series of papers by 11., 12., 13., 14., 15., 9., 261–277].We make use of the generalized Leibniz rule for fractional derivatives in order to obtain one of the aforementioned results, which involves a product of two multivariable H-functions. Each of these results is shown to apply to yield interesting new results for certain multivariable hypergeometric functions and, in addition, several known results due, for example, to J. L. Lavoie, T. J. Osler and R. Tremblay [SIAM Rev.18 (1976), 240–268], 4., 5., 371–382] and R. K. Raina and C. L. Koul [Jñānābha7 (1977), 97–105].     

An FPTAS for minimizing the product of two non-negative linear cost functions

We consider a quadratic programming (QP) problem (Π) of the form min x ^T C x subject to Ax ≥ b, x ≥ 0 where \({C\in {\mathbb R}^{n \times n}_+, {\rm rank}(C)=1}\) and \({A\in {\mathbb R}^{m \times n}, b\in {\mathbb R}^m}\) . We present an fully polynomial time approximation scheme (FPTAS) for this problem by reformulating the QP (Π) as a parameterized LP and “rounding” the optimal solution. Furthermore, our algorithm returns an extreme point solution of the polytope. Therefore, our results apply directly to 0–1 problems for which the convex hull of feasible integer solutions is known such as spanning tree, matchings and sub-modular flows. They also apply to problems for which the convex hull of the dominant of the feasible integer solutions is known such as s, t-shortest paths and s, t-min-cuts. For the above discrete problems, the quadratic program Π models the problem of obtaining an integer solution that minimizes the product of two linear non-negative cost functions.