In this paper we propose a new numerically reliable computational approach to determine the inner-outer factorization of a rational transfer matrix G of a linear descriptor system. In contrast to existing computationally involved “one-shot” methods which require the solution of Riccati or generalized Riccati equations, the new approach relies on an efficient recursive zeros dislocation techniqu...

In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional ...

In this paper we study Jordan-structure-preserving perturbations of matrices selfadjoint in the indefinite inner product. The main result of the paper is Lipschitz stability of the corresponding similitude matrices. The result can be reformulated as Lipschitz stability, under small perturbations, of canonical Jordan bases (i.e., eigenvectors and generalized eigenvectors enjoying a certain flipp...

Abstract. Following Rankin’s method, D. Zagier computed the n-th Rankin-Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2 and then computed the inner product of this Rankin-Cohen bracket with a cusp form f of weight k = k1 + k2 + 2n and showed that this inner product gives, upto a constant, the special value of the Rankin-Selberg convolution of f and g. This...

We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation” that is satisfied by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. T...

Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H ;〈·,·〉), r,s > 0, p ∈ (0,s], D = {x ∈ H ,‖rx− sa‖ ≤ p}, x1,x2 ∈D−{0}, and αr,s = min{(r2‖x...

Abstract—The holographic transformation is generalized to problems in quantum information science. In this work, the partition function is represented by an inner product of two highdimensional vectors both of which can be decomposed to tensor products of low-dimensional vectors. On the representation, the holographic transformation is clearly understood by using adjoint linear maps. Furthermor...

We discuss two closely related interval arithmetic systems: i) the system of directed (generalized) intervals studied by E. Kaucher, and ii) the system of normal intervals together with the outer and inner interval operations. A relation between the two systems becomes feasible due to introduction of special notations and a so-called normal form of directed intervals. As an application, it has ...

Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H; 〈., .〉), r, s > 0, p ∈ (0, s],D = {x ∈ H, ‖rx− sa‖ ≤ p}, x1, x2 ∈ D − {0} and αr,s ...

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is inve...