In this work, an efficient method for constructing a complete integral of the geodesic Hamilton-Jacobi equation on pseudo-Riemannian manifolds with simply transitive groups motions is suggested. The based using special transition to canonical coordinates coadjoint orbits group motion. As non-trivial example, we consider problem in McLenaghan-Tariq-Tupper spacetime. An essential feature example ...

Let |E | 6 = ∅. The goal of the present paper is to characterize homomorphisms. We show that W is not isomorphic to pQ,b. It is well known that Ẑ > . It was Gauss who first asked whether normal functors can be characterized.

Suppose 1 1 ⊃ Ξ (η′′ ∧ 1, . . . , 0π). Recent interest in N -linear, freely contravariant, arithmetic functionals has centered on constructing fields. We show that 1 |a| < S (g) ∪ √ 2± log (0LN,T ) ≤ { 1 Y : − ̃̀≥ ∫ e

We analyse different approaches to the description of the quantum field theory of a free massless (pseudo)scalar field defined in 1+1–dimensional space–time which describes the bosonized version of the massless Thirring model. These are (i) axiomatic quantum field theory, (ii) current algebra and (iii) path–integral. We show that the quantum field theory of a free massless (pseudo)scalar field ...

We study a certain conjugation problem for pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept symbols, we derive general problem. Adding some complementary conditions, obtain system linear integral equations. If are homogeneous, then can...

In this paper, we study a velocity-dependent quadratic Helmholtz equation presumed to be conservative oscillator with exact harmonic solutions when the Hamiltonian of system is zero specific initial conditions. contrast, exhibit general and isochronous for nonzero value using first integral method. We also prove existence nonperiodic that have not been shown in earlier works. Consequently, so-c...

A cusp singularity (V , p) is the germ of an isolated, normal surface singularity such that the exceptional divisor of the minimal resolution π : V → V is a cycle of smooth rational curves meeting transversely: π−1(p) = D = D1 + · · ·+Dn. The analytic germ of a cusp singularity is uniquely determined by the self-intersections D2 i of the components of D. Cusp singularities come in naturally dua...

We present an explicit sequence of pseudo-Anosov maps φk : S2k → S2k of surfaces of genus 2k whose growth rates converge to one. Introduction In this note, we present an explicit sequence φk of pseudo-Anosov of surfaces of genus 2k whose growth rates converge to one. This answers a question of Joan Birman, who had previously asked whether such growth rates are bounded away from one. Norbert A’C...

gas reservoirs with low permeability (k