Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

In this paper, a numerical scheme is proposed for the multi-fluid compressible flows. This method is applied to the problem of underwater explosion. The proposed scheme is basically the extension of Godunov method in gas dynamic problems to the multifluid environments and is second-order accurate in space. In this method, also, the problem of artificial mixing of two different phases on Euleria...

In this paper, a numerical scheme is proposed for the multi-fluid compressible flows. This method is applied to the problem of underwater explosion. The proposed scheme is basically the extension of Godunov method in gas dynamic problems to the multifluid environments and is second-order accurate in space. In this method, also, the problem of artificial mixing of two different phases on Euleria...

An order-theoretic forest is a countable partial order such that the set of elements larger than any element linearly ordered. It an tree if two have upper-bound. The type branch (a maximal ordered subset) can be linear order. Such generalized infinite trees yield convenient definitions rank-width and modular decomposition graphs. We define algebra based on only four operations generate up to i...

TmVO$_{4}$ exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity that can be tuned continuously to quantum phase transition via magnetic fields along $c$-axis. Here we present $^{51}$V nuclear resonance data in perpendicular $c$-axis single crystal has been carefully cut by plasma focused ion beam an ellipsoidal shape mi...