Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at 1, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an a?rmative answer to a conjecture of Melham.     

Asymptotic behavior of functionals of cyclic long-range dependent random fields

Long-range dependent random fields with spectral densities, which are unbounded at some frequencies, are investigated. We demonstrate new examples of covariance functions, which do not exhibit a regular varying asymptotic behavior at infinity. However, the variances of averaged functionals of these fields are regularly varying. The limit theorems for weighted functionals of cyclic long-range dependent fields are obtained. The order of normalizing constants and relations between the weight functions and singularities in non-degenerative asymptotics are discussed.     

Motion analysis of two-link nonholonomic swimmers

Nonlinear Dynamics - This paper presents a tool for analyzing the motion of two-link nonholonomic swimmers. We refer to these systems as Land-sharks, which are a generalization of the well known...     

Resonant Leading Term Geometric Optics Expansions with Boundary Layers for Quasilinear Hyperbolic Boundary Problems

We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to show approximate solutions tend to the exact solutions in the small wavelength limit. Recent work [2 Coulombel, J.-F., Gues, O., and Williams, M., 2011. Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, Comm. Part. Diff. Eqs. 36 (2011), pp. 1797–1859.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] by Coulombel et al. studied the case of reflecting wave trains whose expansions involve only real phases. We treat generic boundary frequencies by incorporating into our expansions both real and nonreal phases. Nonreal phases introduce difficulties such as approximately solving complex transport equations and result in the addition of boundary layers with exponential decay. This also prevents us from doing an error analysis based on almost periodic profiles as in [2 Coulombel, J.-F., Gues, O., and Williams, M., 2011. Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, Comm. Part. Diff. Eqs. 36 (2011), pp. 1797–1859.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

The Synthesis and Properties of Some Fluorinated Dialkyl Phosphoramidates

The synthesis and physical properties of the first fluorinated dialkyl phosphoramidates of structure (RCH 2 O) 2 P(O)NHCH 2 R F , where R = CH 3 , CF 3 or CCl 3 and R F = CF 3 or C 2 F 5 , are described. They were obtained by treatment of the respective dialkyl phosphorochloridates with trifluoroethylamine or pentafluoropropylamine in ether in the presence of triethylamine.