and Applied Analysis 3 (2) If 0 < g < g0, we get a solitary wave solution u6 ( x, y, t ) c (√ 2 α − 1 β cosh θ ( x y − ct )) α − 1 ( 1 β − cosh 2θ ( x y − ct )) α ( −1 α β − α − 1 cosh 2θ ( x y − ct )) , 2.4 and two blow-up solutions u7± ( x, y, t ) c ( α ( 2 β ) − 2 − 2 α − 1 cosh θ ( x y − ct ) ± β 3/2 coth θ/2 ( x y − ct )) 2α ( −1 α β − α − 1 cosh θ ( x y − ct )) , 2.5 where β 6 − 6α α2 and...

The properties of the wave function for the Modified Pöschl-Teller (MPT) potential are outlined. The ladder operators are constructed directly from the wave functions without introducing any auxiliary parameter. It is shown that these operators are associated to the su(2) algebra. Analytical expressions for the functions sinh(αx) and cosh(αx) α d dx are evaluated from ladder operators. The expa...

Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of large-deviation principles. While Mark...

SB (a, b) = { √ b2−a2 cos−1(a/b) , a < b , √ a2−b2 cosh−1(a/b) , a > b . In this paper, we find the greatest values α1, α2, α3 and α4, and the least values β1, β2, β3 and β4 such that the double inequalities α1SAH(a, b) + (1 − α1)C(a, b) < A(a, b) < β1SAH(a, b) + (1 − β1)C(a, b), α2SHA(a, b) + (1 − α2)C(a, b) < A(a, b) < β2SHA(a, b) + (1 − β2)C(a, b), α3SCA(a, b) + (1 − α3)H(a, b) < A(a, b) < β...

We present a new approach, called a lazy matching, to the problem of on-line matching on bipartite graphs. Originally, each arriving element is irrevocably matched with some already existing one. In this paper we allow matching a new element to a group of elements (possibly decreasing other groups) with additional restrictions that every two groups have to be disjoint and decreasing a group is ...

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equatio...

In this paper, we will prove that all non-planar minimal surfaces of revolution can be generated by functions of the form f = 1 C cosh(Cx), x ∈ R (as illustrated in Figure 1). We will accomplish this by • Assuming a non-planar minimal surface of revolution exists • Showing that the surface must be given by the above form • Prove that such a surface is indeed minimal. By minimal surface, we mean...

Harmonic maps X:(S,h) --> N from a 2-manifold S with indefinite metric h to a semi-Riemannian manifold N are characterized, assuming that the induced metric I is nondegenerate. Except in one very special case, the characterizations involve a canonically determined holomorphic quadratic differential on a naturally chosen conformal structure. This is surprising because the Euler-Lagrange equation...

Let aIp(x) = ∑ n 0 (x/2)2n+p n!Γ(p + an + 1) be the Galué’s generalized modified Bessel function depending on parameters a = 0, 1, 2, . . . and p > −1. Consider the function aI p : R → R, defined by aI p(x) = 2pΓ(p+1)x−paIp(x). Motivated by the inequality of Lazarević, namely cosh x < ( sinh x x )3 for x = 0, in order to generalize this inequality we prove that the Turán-type, Lazarević-type in...