We used Wick’s normal-ordering technique, squeezed creation and annihilation operators, and a variation method, to find the eigenvalues of the general pure ?x2m potential. Numerical results for low-lying energy levels of pure quadratic, quartic, sextic, octic and decatic potentials, for different values of ? were obtained. Some interesting features of these energy levels are explained.

A new kind of quasi-quartic trigonometric polynomial base functions with a shape parameter λ over the space Ω=span {1, sint, cost, sint2t, cos2t} is presented, and the corresponding quasi-quartic trigonometric Bézier curves and surfaces are defined by the introduced base functions. The quasi-quartic trigonometric Bézier curves inherit most of properties similar to those of quartic Bézier curves...

We present some explicit formulas for queue length and waiting time distributions of customers in the MfHE,,,/l queue. The formulas are obtained with the aid of roots of quadratic, cubic, and quartic polynomials constructed from a recurrence equation. With an example, we demonstrate that the formulas for queueing dishbutions are exhemely accurate, while the corresponding infinite history M IGII...

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-...

In this paper we investigate the generalized HyersUlam stability of the functional equation f(2x + y) + f(2x − y) = f(x + y) + f(x − y) + 2f(2x)− 2f(x) in fuzzy Banach spaces.

This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a bounded time interval. An integro-differential equation is obtained for the time evolution of this quadratic-ex...

Last time we have seen that the proof of Fermat’s Last Theorem for the exponent 4 provides us with two elliptic curves (y = x + x and y = x − 4x) in the guise of the quartic equations (X + Y 4 = Z and X − 4Y 4 = Z). Moreover, in the actual proof we used connections between these quartic curves and the ‘underlying conic’, namely the quadratic curves x+ y = z and x− 4y = z, which actually both re...

Wewill define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam– Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, co...

and Applied Analysis 3 vector spaces X and Y is a solution of 1.5 if and only if there exists a unique function C : X × X × X → Y such that f x C x, x, x for all x ∈ X, and C is symmetric for each fixed one variable and is additive for fixed two variables see also 20 . The quartic functional equation 1.6 was introduced by Rassias 21 in 2000 and then in 2005 was employed by Park and Bae 22 and o...