ions, as averages over populations of individuals) are not. Sober, rightly in my view, rejects both halves of this claim. (See Sober, ‘Evolution, Population Thinking, and Essentialism’, op. cit. note 18.) In the present context Mayr’s questionable metaphysical picture need not be a cause for concern. His key insight concerning the explanatory priority of individual variation in population think...

The dynamical properties of cos-Gaussian beams in strongly nonlocal nonlinear (SNN) media are theoretically investigated. Based on the moments method, the analytical expression for the rootmean-square (RMS) of the cos-Gaussian beam propagating in a SNN medium is derived. The critical powers that keep the RMS beam widths invariant during propagation in a SNN medium are discussed. The RMS beam wi...

Abstract For any Liouville number $\alpha $ , all of the following are transcendental numbers: ${e}^\alpha $\log _{e}\alpha $\sin \alpha $\cos $\tan $\sinh $\cosh $\tanh $\arcsin and inverse functions evaluated at listed trigonometric hyperbolic functions, noting that wherever multiple values involved, every such value is transcendental. This remains true if ‘Liouville number’ replaced by ‘ U -...

In this paper, the propagation properties of a vortex cosh-Gaussian beam (vChGB) in turbulent atmosphere are investigated. Based on extended Huygens–Fresnel diffraction integral and Rytov method, analytical expression for average intensity vChGB propagating atmospheric turbulence is derived. The effects strength parameters distribution spreading illustrated numerically analyzed detail. It shown...

Sharp bounds for cosh(x)x,sinh(x)x, and sin(x)x were obtained, as well one new bound ex+arctan(x)x. A situation to note about the obtained boundaries is symmetry in upper lower boundary, where boundary differs by a constant from boundary. New consequences of inequalities terms Riemann–Liovuille fractional integral standard integral.

In this paper, nearly perfect reconstruction (NPR) critically sampled cosine modulated M-channel filterbank (CMFB) and transmultiplexer systems are proposed. An improved design approach for a FIR low pass prototype filter that expoits spline function in the transition band of the ideal filter and takes the magnitude squared error function into account is considered. Prototype filter is designed...

In this paper, a computationally efficient iterative algorithm is presented for the design of multi-channel nearly perfect reconstruction nonuniform filter bank using the modified window functions such as Kaiser, Cosh and Exponential windows with exploiting a new perfect reconstruction condition of nonuniform filter banks instead of using complex objective functions. The cutoff frequency is opt...

Independent component analysis (ICA) The ICA algorithm has been applied successfully to modeling V1 simple cell receptive fields [1, 2]. It is closely related to sparse coding methods, and can be cast in terms of a simple generative model [3]: We suppose that our data x ∈ R is an unknown linear mixture of independent, non-Gaussian sources, i.e. x = As where A ∈ Rn×n is unknown. During learning,...