A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity z f ′(z)/ f (z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and di...

We have expressed the nonlinear optical absorption of a semiconductor in terms of its linear spectrum. We determined that the two-photon absorption coefficient in a strong DCelectric field of a direct gap semiconductor can be expressed as the product of a differential operator times the convolution integral of the linear absorption without a DC-electric field and an Airy function. We have appli...

in this paper, the direct extrusion process of bimetallic rods in conical dies is analyzed by an improved upper bound method. the deformation zone is subdivided into six smaller zones and by considering a non-spherical entrance boundary to the deformation zone, a velocity field is presented which is different from velocity fields employed in previous studies. the total power consumption of the ...

The distribution of light scattered by finger joints is studied in the near-IR region. It is shown that variations in the optical parameters of the tissue (scattering coefficient fi^, absorption coefficient fi^, and anisotropy factor g) depend on the presence of the rheumatoid arthritis (RA). At the first stage, the distribution of scattered light was measured in diaphanoscopic experiments. The...

Keywords: Analytic functions Starlike and convex functions Multivalent functions Hadamard product (or convolution) Coefficient bounds Distortion inequalities Neighborhood properties Non-homogeneous Cauchy–Euler differential equations a b s t r a c t In this paper, by making use of the familiar concept of neighborhoods of p-valently analytic functions, we prove coefficient bounds, distortion ine...

Aims. We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Methods. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and comp...

13 In this paper, a user-defined inter-band correlation filter function was used to resample 14 hyperspectral data and thereby mitigate the problem of multicollinearity in classification 15 analysis. The proposed resampling technique convolves the spectral dependence information 16 between a chosen band-centre and its shorter and longer wavelength neighbours. Weighting 17 threshold of inter-ban...

We give a stability result for sparse convolutions on `(G)× `(G) for torsion-free discrete Abelian groups G such as Z. It turns out, that the torsion-free property prevents full cancellation in the convolution of sparse sequences and hence allows to establish stability in each entry, that is, for any fixed entry of the convolution the resulting linear map is injective with an universal lower no...

We study the asymptotic behavior of the terms in sequences satisfying recurrences of the form an = an−1 + n−d k=d f(n, k)akan−k where, very roughly speaking, f(n, k) behaves like a product of reciprocals of binomial coefficients. Some examples of such sequences from map enumerations, Airy constants, and Painlevé I equations are discussed in detail. 1 Main results There are many examples in the ...

It is shown that the closure of the set of Fourier coefficients of the Bernoulli convolution μθ parameterized by a Pisot number θ is countable. Combined with results of Salem and Sarnak, this proves that for every fixed θ > 1 the spectrum of the convolution operator f 7→ μθ∗f in L(S) (where S is the circle group) is countable and is the same for all p ∈ (1,∞), namely, {μ̂θ(n) : n ∈ Z}. Our resul...