In [1] D. Harrington and R. Whitley examined several questions of seminormality for composition operators. In that article they raise the question of finding a measure theoretic characterization of hyponormality for composition operators. In this article we establish criteria for hyponormality for weighted composition operators. By restricting attention to the case of weight function equal to 1...

a = semimajor axis b = magnetic field vector e = eccentricity e = orbital element vector e · = matrix exponential f = true anomaly h = angular momentum magnitude i = inclination J = cost Jn = nth zonal harmonic coefficient M = mean anomaly m = mass m = magnetic dipole vector N − 1 = number of thrusts n = mean motion p = semilatus rectum q = electrical charge r = orbit radius magnitude r = posit...

Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday

In this paper, we prove some basic results for Cauchy dual of weighted composition operators. Also introduce new classes operators, called ?-hyponormal, ?-quasi-hyponormal, and provide necessary sufficient conditions MP-inverse operators on L2(?) to belong these classes. addition, study the complex symmetry types Moreover, examples are provided illustrate obtained results.

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

in this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-fide) is proposed. in fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-fide is obtained. some examples show the efficiency of the proposed method.

We theoretically show that an astigmatic transformation of nth-order edge dislocation (a zero-intensity straight line) produces n optical elliptical vortices (spiral dislocations) with unit topological charge at the double focal distance from cylindrical lens, located on a line perpendicular to dislocation, points whose coordinates are roots Hermite polynomial. The orbital angular momentum is p...

Let H and K be complex Hilbert spaces, let L(H,K) be the set of bounded linear operators from H to K and write L(H) := L(H,H). An operator T ∈ L(H) is said to be normal if T ∗T = TT ∗, hyponormal if T ∗T ≥ TT ∗, and subnormal if T = N |H, where N is normal on some Hilbert space K ⊇ H. If T is subnormal then T is also hyponormal. Recall that the Hilbert space L2(T) has a canonical orthonormal ba...