相关论文: Whitney's Theorem for oscillatiing on $R$ function…
Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional…
We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…
It is known that the M\"obius function in number theory is higher order oscillating. In this paper we show that there is another kind of higher order oscillating sequences in the form $(e^{2\pi i \alpha \beta^{n}g(\beta)})_{n\in \N}$, for a…
For v\in R^n let K be a compact set in R^n containing a suitable smooth surface and such that the intersection {tv+x:t\in R}\cap K is a closed interval or a single point for all x\in K. We prove that every linear first order differential…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…
In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.
Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory…
Original Whitham's method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of…
In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
We demonstrate the use of the Lorentz reciprocal theorem in obtaining corrections to the steady flow rate due to flow oscillations in rigid channels. Starting from the unsteady Stokes equations, we derive the suitable reciprocity relation,…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is…
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…
Quasi-toroidal oscillations in slowly rotating stars are examined in the framework of general relativity. The oscillation frequency to first order of the rotation rate is not a single value even for uniform rotation unlike the Newtonian…
We discuss the problem where the extremal function in embedding theorem of some (generally speaking, non-integer) order is the constant function. We obtain the necessary and sufficient conditions of this.
In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers…