where λis are the eigenvalues of the Hessian D 2u. Namely, any global convex solution to (1.1) in R must be a quadratic polynomial. Recall the classical result, any global convex solution in R to the Laplace equation △u = λ1+ · · ·+λn = c or the Monge-Ampère equation log detD2u = log λ1+ · · ·+ log λn = c must be quadratic. Equation (1.1) originates from special Lagrangian geometry [HL]. The (L...

In this paper we study the quadratic regulator problem for a process governed by a Volterra integral equation in IR. Our main goal is the proof that it is possible to associate a Riccati differential equation to this quadratic control problem, which leads to the feedback form of the optimal control. This is in contrast with previous papers on the subject, which confine themselves to study the F...

It is shown that an even partition A∪B of the set R = {1, 2, . . . , p− 1} of positive residues modulo an odd prime p is the partition into quadratic residues and quadratic non-residues if and only if the elements of A and B satisfy certain additive properties, thus providing a purely additive characterization of the set of quadratic residues. 1 Additive properties of quadratic residues An inte...

in this study we produced a new method for solving regular dierential equations with step size h and taylor series. this method analyzes a regular dierential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coecients and cubic and second- level equations.

The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the discrete-time generalised Riccati equation, but, differently from the discrete case, to date the importance of this equation in the context of optimal contro...

In this paper a control problem for a controlled linear stochastic equation in a Hilbert space and an exponential quadratic cost functional of the state and the control is formulated and solved. The stochastic equation can model a variety of stochastic partial differential equations with the control restricted to the boundary or to discrete points in the domain. The solution method does not req...

Within last century the study of cycles of twodimensional quadratic systems was stimulated by 16th Hilbert’s problem and its different variants [Hilbert, 1902; Lloyd, 1988; Blows & Perko, 1994; Ilyashenko, 2002; Chen & Wang, 1979; Shi, 1980]. The development of asymptotical methods for investigation of cycles of quadratic systems is facilitated by the fractionally-quadratic transformations, whi...

In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Banaś and L. Olszowy, a...

This paper considers quadratic approximation as a narrowing tool in an interval branch-and-prune method. We seek the roots of such an approximate equation – a quadratic equation with interval parameters. Heuristics to decide, when to use the developed operator, are proposed. Numerical results for some benchmark problems are presented and analyzed.

Global attractivity in a quadratic-linear rational difference equation with delay C.M. Kent & H. Sedaghat To cite this article: C.M. Kent & H. Sedaghat (2009) Global attractivity in a quadratic-linear rational difference equation with delay, Journal of Difference Equations and Applications, 15:10, 913-925, DOI: 10.1080/10236190802040992 To link to this article: http://dx.doi.org/10.1080/1023619...