Bounded p-valent Robertson functions defined by using a differential operator

Let denote the class of functions analytic in U={z:|z|<1} which satisfy for fixed M, z=re^iθ∈U and

     

Order of convexity and univalency of general integral operator

In this paper, we introduce the integral operator of analytic functions. The order of convexity of this integral operator when γ=1 is determined. Furthermore, we derive sufficient conditions for this operator to be analytic and univalent in the open unit disc.     

On the asymptotic behavior of solutions of certain second-order differential equations

In this paper, the second order non-linear differential equation

     

On the control of solutions of a viscoelastic equation

In this paper we consider the semilinear viscoelastic equation

     

Stability and boundedness properties of certain second-order differential equations

In this paper, we investigated the differential equation

     

Pathwise estimation of the stochastic functional Kolmogorov-type system

In this paper we stochastically perturb the functional Kolmogorov-type system

     

An improved method for computing Hankel transform

The purpose of this paper is to compute the Hankel transform F_n(y) of order n of a function f(x) and its inverse transform using rationalized Haar wavelets. The integrand is replaced by its wavelet decomposition. Thus representing F_n(y) as a Fourier-Bessel series with coefficients depending strongly on the local behavior of the function , thereby getting an efficient algorithm for their numerical evaluation. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithm.     

Differential subordinations and argument inequalities

The main object of the present paper is to investigate certain properties of multivalent functions associated with a linear operator .     

Gauss quadrature formula: An extension via interpolating orthogonal polynomials

The n-point Gauss quadrature rule states that

     

Existence of solutions for a third-order multipoint boundary value problem with p-Laplacian

In this paper, we consider multipoint boundary value problem for third-order differential equations with p-Laplacian at resonance

     

VCO sweep-rate limit for a phase-lock loop

Phase-lock loops (PLLs) serve important roles in phase-lock receivers, coherent transponders, and similar applications. For many of these uses, the bandwidth of the loop must be kept small to limit the detrimental influence of noise, and this requirement makes the natural PLL pull-in phenomenon too slow and/or unreliable. For each such case, the phase-lock acquisition process can be aided by the application of an external sweep voltage to the loop voltage controlled oscillators (VCOs). The goal is to have the applied sweep voltage rapidly decrease the closed-loop frequency error to a point where phase lock occurs quickly. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep-rate magnitude, denoted here as R_m rad/s², for which phase lock is guaranteed. If the applied VCO sweep rate is less than R_m, the loop cannot sweep past a stable phase-lock point, and it will phase lock. On the other hand, for an applied sweep-rate magnitude that is greater than R_m, the PLL may sweep past a lock point and fail to phase lock. In the existing PLL literature, only a trial-and-error approach has been described for estimating R_m, given values of loop damping factor ζ and natural frequency ω_n. Furthermore, no plots exist of computed versus ζ and versus ζ (B_L denotes loop-noise bandwidth). These deficiencies are dealt with in this paper. A new iterative numerical technique is given that converges to the maximum sweep-rate magnitude R_m. It is used to generate data for plots of and versus ζ, the likes of which have never appeared before in the PLL literature.     

On certain meromorphic p-valent starlike functions

A certain differential operator D^n+p is introduced for functions of the form