Connections of KP, qKP, and Moyal type dKP constructions are developed. Some expansion of the Moyal KP constructions of Kemmoku-Saito is given with clarification of the role of spectral variables as a phase space.

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-B...

 (b− a)M, for all x ∈ [a, b] . The constant 14 is best possible in the sense that it cannot be replaced by a smaller constant. In [2], the author has proved the following Ostrowski type inequality. Theorem 2. Let f : [a, b] → R be continuous on [a, b] with a > 0 and differentiable on (a, b) . Let p ∈ R\ {0} and assume that Kp (f ) := sup u∈(a,b) { u |f ′ (u)| } < ∞. Then we have the inequality...

We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the r-matrix framework. An r-matrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader’s convenience. All relativistic constructions are regular one-parameter perturbations of the nonrelativistic ones. We derive in a simple way the linear Hamiltonian structure of the re...

and denote by KP the complete graph of p vertices . A well known theorem of TUR.áN [6] states that every 9(n ; m(n, p) + 1) contains a Kp and that this result is best possible. Thus in particular every á(2n ; n 2 + 1) contains a triangle. Denote by f„(p ; 1) the largest integer so that every W(n; m(n, p) + 1) contains at least fn(p ; l) distinct K p 's. RADEMACHER proved that fn(3 ; 1) = [n/2] ...

Tretinoin is known to be a pharmaceutical drug for treating acne vulgaris, keratosis pilaris, and acute promyelocytic leukemia. In order to reveal the possible conformers of tretinoin, the energies of all the conformers through rotational bonds have been evaluated by systematic rotor search analysis. The intramolecular interactions ranging from strong hydrogen bonds to weak van der Waals forces...

Figure 3: Simulated metabolism using an outer region with ρP=0.027, kP-L=0.018, kL-P=0.125, P∞=1.733, and an inner region with ρP=0.027, kP-L=0.088, kL-P=0.17, P∞=2.5. The default sampling is 30 samples between t=0 and 29 s and a flip angle of 10°. The optimal sampling over the range given above suggests samples at 0, 2.9, 13.1, 41.9 s and flip angles of 23.2, 36.6, 47.3, and 90°. Note the decr...

We discuss a differential integrable hierarchy, which we call the (N,M)–th KdV hierarchy, whose Lax operator is obtained by properly adding M pseudo–differential terms to the Lax operator of the N–th KdV hierarchy. This new hierarchy contains both the higher KdV hierarchy and multi– field representation of KP hierarchy as sub–systems and naturally appears in multi–matrix models. The N + 2M − 1 ...

Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the ...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of th...