It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter : u′ = f(u)− h(t). Namely, there exists an 0 such that for 0 < < 0 there are two periodic solutions, for = 0 there is one periodic solution, and for > 0 there are no periodic solutions, provided that ∫ T 0 h(t)dt > 0. In this paper we look...

In 2006, Saito and Remy presented a new algorithm called polyharmonic local sine transform (PHLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain Ω. First we approximate f by a polyharmonic function u such that the residual component v = f −u vanishes in the boundary of Ω. Next, we do the odd extension for v, and then do the periodic extension,...

‎in this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear pdes in mathmatical physics; namely the one-‎dimensional modified complex ginzburg-landau equation by using the $ (g^{&apos;}/g) $ expansion method‎, homogeneous balance method, extended f-expansion method‎. ‎by ‎using homogeneous balance principle and the extended f-expansion, more periodic wave solutions expres...

Under reasonable assumptions on the data u, v and the function f , we show that the nonlinear periodic Goursat problem ∂u ∂x∂y (x, y) = f(x, y, u(x, y)); u(x, 0) = v(x); u(0, y) = w(y) which cannot be posed in the general theory of distributions, may be studied and solved in a differential algebra of periodic new generalized functions on R2. This algebra contains, in a canonical way, the space ...

We consider a bifurcation problem arising from population biology du(t) dt = f(u(t))− εh(t), where f(u) is a logistic type growth rate function, ε ≥ 0, h(t) is a continuous function of period T such that ∫ T 0 h(t)dt > 0. We prove that there exists an ε0 > 0 such that the equation has exactly two T -periodic solutions when 0 < ε < ε0, exactly one T -periodic solution when ε = ε0, and no T -peri...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the...

Reactions of CH(3)F have been surveyed systematically at room temperature with 46 different atomic cations using an inductively coupled plasma/selected-ion flow tube tandem mass spectrometer. Rate coefficients and product distributions were measured for the reactions of fourth-period atomic ions from K(+) to Se(+), of fifth-period atomic ions from Rb(+) to Te(+) (excluding Tc(+)), and of sixth-...

0. Introduction 1 1. Twisted orbits and zeta functions 3 2. Axiom A diieomorphisms 4 3. Symbolic dynamics and rationality 5 4. Zeta functions and for interval maps 9 5. The Ruelle zeta function 14 6. Zeta functions for hyperbolic ows 21 7. Zeta functions for analytic Anosov ows 25 8. L-functions and special values 26 9. counting closed orbits for ows 27 10. L-functions and homology 32 11. Pole ...

The lowest spectral gap of segments of a periodic waveguide in R2 is proportional to the square of the inverse length. The aim of this letter is a brief presentation of some results concerning spectral gaps in periodic waveguides. They are a representative example of the type of results derived in the forthcoming paper [5], see also the Closing Remark. Let γ : R → R be a C-function parameterise...

We prove that an automorphism φ : F → F of a finitely generated free group F is hyperbolic in the sense of Gromov if it has no nontrivial periodic conjugacy classes. This result was previously claimed (but not proved) in [BF92].