We consider minimization of a quadratic objective function subject to a sign-indefinite quadratic equality constraint. We derive necessary and sufficient conditions for the existence of solutions to the constrained minimization problem. These conditions involve a generalized eigenvalue of the matrix pencil consisting of a symmetric positivesemidefinite matrix and a symmetric indefinite matrix. ...

A concise introduction to the Normalized Quadratic expenditure or cost function is provided so that the interested reader will have the necessary information to understand and use this functional form. The Normalized Quadratic is an attractive functional form for use in empirical applications as correct curvature can be imposed in a parsimonious way without losing the desirable property of flex...

We construct martingales whose 1-dimensional marginals are those of a centered selfdecomposable variable multiplied by some power of time t. Many examples involving quadratic functionals of Bessel processes are discussed.

In this article, we will discuss geometric quantization of 2d QCD with fermionic and bosonic matter fields. We identify the respective large-Nc phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The Hamiltonians are quadratic functions, and the resulting equations of motion for these classical systems are nonlinear. In [33], it was shown that the linearizat...

We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. Though this model can be considered simple, its mathematical analysis i...

D.H. Lehmer found a quadratic polynomial such that 326 is a primitive root for the first 206 primes represented by this polynomial. It is shown that this is related to the class number one problem and prime producing quadratics. More impressive examples in the same spirit are given using recent results on prime producing quadratics. Y. Gallot holds the current record in which 206 is being repla...

A standard technique for solving the recursion xn+1 = g (xn) where g : C→ C is a complex function is to first find a fairly simple function g : C→ C and a bijection f : C→ C such that g = f◦g◦f−1 where ◦ is the composition of functions. Then xn = g (x0) = (f ◦ g ◦ f−1) (x0) where g and g are the n-fold composition of functions and g is fairly easy to compute. With this motivation we find all pa...

M. Antonowicz and A. P. Fordy (1988) introduced the second-order polynomial eigenvalue problem Lφ = (∂2 +∑i=1 viλ)φ = αφ (∂ = ∂/∂x, α = constant) and discussed its multi-Hamiltonian structures. For n= 1 and n= 2, the associated finite-dimensional integrable Hamiltonian systems (FDIHS) have been discussed by Xu and Mu (1990) using the nonlinearization method and Bargmann constraints. In this pap...

Accurate data on gross domestic product (GDP) at pixel level are needed to understand the dynamics of regional economies. GDP spatialization is the basis of quantitative analysis on economic diversities of different administrative divisions and areas with different natural or humanistic attributes. Data from the Visible Infrared Imaging Radiometer Suite (VIIRS), carried by the Suomi National Po...