Abstract. In this paper we explore finite rank perturbations of unilateral weighted shifts Wα. First, we prove that the subnormality of Wα is never stable under nonzero finite rank pertrubations unless the perturbation occurs at the zeroth weight. Second, we establish that 2-hyponormality implies positive quadratic hyponormality, in the sense that the Maclaurin coefficients ofDn(s) := detPn [(W...

The two-body interactions in the Biswas-Hamann (BH) and Murrell-Mottram (MM) potential functions are analytically related in this paper by equating the zeroth to second differentials at equilibrium bond length. By invoking the Maclaurin series expansion for the exponential term, the MM potential function could be expressed in a manner that enables comparison of repulsive and attractive terms. A...

In this paper we verify a conjecture of M. Vuorinen that the Muir approximation is a lower approximation to the arc length of an ellipse. Vuorinen conjectured that f(x) = 2F1( 1 2 ,− 1 2 ; 1;x) − [(1 + (1 − x)3/4)/2]2/3 is positive for x ∈ (0, 1). The authors prove a much stronger result which says that the Maclaurin coefficients of f are nonnegative. As a key lemma, we show that 3F2(−n, a, b; ...

The Maclaurin symmetric mean (MSM) was originally introduced by Maclaurin. The prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments. However, the researches on MSM are very rare, especially in fuzzy decision making. In this paper, we investigate the MSM operator and extend the MSM operator to hesitant fuzzy environment and develop the ...

The celebrated Turán inequalities P 2 n(x) − Pn−1(x)Pn+1(x) ≥ 0, x ∈ [−1, 1], n ≥ 1, where Pn(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ2 n − γn−1γn+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the L...

In this paper in the space L (m) 2 (0, 1) the problem of construction of optimal quadrature formulas is considered. Here the quadrature sum consists on values of integrand at nodes and values of first derivative of integrand at the end points of integration interval. The optimal coefficients are found and norm of the error functional is calculated for arbitrary fixed N and for any m ≥ 2. It is ...

The Möbius inversion technique is applied to the Poisson summation formula. This results in expressions for the remainder term in the Fourier coefficient asymptotic expansion as an infinite series. Each element of this series is a remainder term in the corresponding Euler-Maclaurin summation formula, and the series has specified convergence properties. These expressions may be used as the basis...

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...