A positive definite even Hermitian lattice is called even universal if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields Q( √ −m) for all positive square-free integers m and we list optimal criterions on even universality of Hermitian lattices over Q( √ −m) which admits even universal binary Hermit...

We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale diierences in the regime of moderate deviations.

The problem of regulating the transmission rate of an available bit rate (ABR) traÆc source in an ATM network is examined. Of particular interest is linear quadratic (LQ) rate regulation based on estimates of the round-trip propagation delay. The round trip delay is estimated using a nonlinear least mean square (NLMS) algorithm. Simulation results are used to demonstrate the method.

This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of complex polynomials using well-known results on a system of quadratic polynomial equations. Applying this method, a new proof for the upper bound of the Pythagoras number of real polynomials is also presented.

In this article the new method for the accounting singular point influence to the postprocessing error estimation is proposed. Solution improvement in singular zones is achieved modifying physical coordinate matrix used in least square problem equations: instead of the standard quadratic polynomial a new polynomial with singular elements is taken. Numerical examples demonstrate the advantages o...

Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F . We prove functoriality from globally generic cuspidal representations of GU(2, 2)(AF ) to automorphic representations of GL6(AF ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F , the twisted exterior square map red...

Quadratic growth curves of 2 degree polynomial are widely used in longitudinal studies. For a 2 degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under som...

We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale differences in the regime of moderate deviations.

Lower bound~ on the capacity and on the product of capacity and computation time are obtained for machines which recognize the set of squares. The bound on capacity is approached to within a factor of four by a specific machine which carries out a test based on the fact that every non-square is a quadratic non-residue of some rational prime. A machine which carries out a te st based on the stan...

The objective of positioning the fixture elements in the fixture is to make the workpiece stiff, so that geometric errors in the manufacturing process can be reduced. Most of the work for optimal fixture layout used the minimization of the sum of the nodal deflection normal to the surface as objective function. All deflections in other direction have been neglected. We propose a new method for ...