The main object of this paper is to study the subclass SC(γ, λ, β) of analytic univalent functions with negative coefficients in unit disc U = {z : |z| < 1}. Further coefficient estimates, distortion theorem and integral operators for this class are also obtained. We also discuss radii of convexity and closure properties for functions belonging to the class SC(γ, λ, β). 2000 Mathematics Subject...

A working wind turbine generates a large amount of multivariate time-series data, which contain abundant operation state information and can predict impending anomalies. The anomaly detection the nacelle that houses all generating components in have been challenging due to its inherent complexities, systematic oscillations noise. To address these problems, this paper proposes an unsupervised ap...

In the paper, by virtue of convolution theorem for Laplace transforms and analytic techniques, author finds necessary sufficient conditions complete monotonicity, inequalities several functions involving polygamma functions. By these results, derives a lower bound function related to sectional curvature Fisher–Rao manifold beta distributions.

We consider the set Ω2 of double zeros in (0, 1) for power series with coefficients in {−1, 0, 1}. We prove that Ω2 is disconnected, and estimate minΩ2 with high accuracy. We also show that [2 − η, 1) ⊂ Ω2 for some small, but explicit η > 0 (this was only known for η = 0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine...

The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a market in long terms, such as year intervals, is different from that in short terms. A diffusion equation with a time dependent diffusion coefficient that des...

We develop new mathematical results based on the spherical harmonic convolution framework for reflection from a curved surface. We derive novel identities, which are the angular frequency domain analogs to common spatial domain invariants such as reflectance ratios. They apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting c...

Let F (z1, . . . zd) = ∏n j=1 η lj(z1,...,zd) nj be the quotient of an analytic function by a product of linear functions lj := 1− ∑ bijzi. We compute asymptotic formulae for the Taylor coefficients of F via the multivariate residue approach begun by [BM93]. By means of stratified Morse theory, we are able to give a short and fully implementable algorithm for determining an asymptotic series ex...

In the convolution model Zi = Xi + εi, we give a model selection procedure to estimate the density of the unobserved variables (Xi) 1≤i≤n , when the sequence (Xi) i≥1 is strictly stationary but not necessarily independent. This procedure depends on wether the density of εi is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the in...

We consider acoustic pulse propagation in inhomogeneous media over relatively long propagation distances. Our main objective is to characterize the spreading of the travelling pulse due to microscale variations in the medium parameters. The pulse is generated by a point source and the medium is modelled by a smooth three-dimensional background that is modulated by stratified random fluctuations...