In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Hölder-type global error bound with an explicit Hölder exponent. Our result extends the corresponding results of [25] from piecewise convex quadratic functions to piecewise convex polynomials.

We outline the small amplitude asymptotic approximation for breathers for one-dimensional chains, and two-dimensional lattices with square, triangular/hexagonal, and honeycomb geometries. Two-dimensional lattices are complicated due to the resulting NLS-type equation being either elliptic or hyperbolic in nature. This gives rise to an additional constraint in addition to the usual condition on ...

This article examines the relationships between interaction (product) terms and curvilinear (quadratic) terms in regression models in which the independent variables are correlated. The author uses 2 substantive examples to demonstrate the following outcomes: (a) If the appropriate quadratic terms are not added to the estimated model, then the observed interaction may indicate a synergistic (of...

Last time we have seen that the proof of Fermat’s Last Theorem for the exponent 4 provides us with two elliptic curves (y = x + x and y = x − 4x) in the guise of the quartic equations (X + Y 4 = Z and X − 4Y 4 = Z). Moreover, in the actual proof we used connections between these quartic curves and the ‘underlying conic’, namely the quadratic curves x+ y = z and x− 4y = z, which actually both re...

We consider negabent Boolean functions that have Trace representation. We completely characterize quadratic negabent monomial functions. We show the relation between negabent functions and bent functions via a quadratic function. Using this characterization, we give infinite classes of bent-negabent Boolean functions over the finite field F2n , with the maximum possible degree, n 2 . These are ...

We consider the problem of minimizing an indefinite quadratic objective function subject to twosided indelinite quadratic constraints. Under a suitable simultaneous diagonalization assumption {which trivially holds for trust region type problems), we prove that the original problem is equivalent to a convex minimization problem with simple linear constraints. We then consider a special problem ...

In this paper we consider the problem of minimizing a quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the rst part of the paper, we show that (i) the number of values of the objective function at KKT points is bounded by 3n + 1 where n is the dimension of the problem; (ii) given a KKT point that is not a global minimizer, it is ...

     The quadratic loss function has been used by decision-theoretic statisticians and economists for many years.  In this paper  the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant ...

MPC or model predictive control is representative of control methods which are able to handle inequality constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global asymptotic stability can be obtained; until recently, use of infinite...

We describe several cryptographic schemes in quadratic function fields of odd characteristic. In both the real and the imaginary representation of such a field, we present a Diffie-Hellman-like key exchange protocol as well as a public-key cryptosystem and a signature scheme of ElGamal type. Several of these schemes are improvements of systems previously found in the literature, while others ar...