This note shows that we can recover any complex vector x0 ∈ C exactly from on the order of n quadratic equations of the form |〈ai,x0〉| = bi, i = 1, . . . ,m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. Further, we show that exact recovery holds for all input vectors s...

A development quadratic model of the heterogeneous biological population consisting of a few sub-populations is investigated. The classic stabilization problem of solutions for the system of ordinary quadratic differential equations, which describing this model, is solved. Examples are given. 2013 Elsevier Inc. All rights reserved.

In this paper, we completely solve the simultaneous Diophantine equations x − az = 1, y − bz = 1 provided the positive integers a and b satisfy b−a ∈ {1, 2, 4}. Further, we show that these equations possess at most one solutions in positive integers (x, y, z) if b − a is a prime or prime power, under mild conditions. Our approach is (relatively) elementary in nature and relies upon classical re...

The manuscript demonstrates that the solution of algebraic quadratic equations on the set of real numbers sometimes gives the results which contradict the transitional processes in oscillation systems. The solution of algebraic quadratic equations on the set of complex numbers, on the contrary, always agrees with the transitional processes in oscillation systems.

in this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. utilizing the generalized characterization theorem. then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. here neural network is considered as a part of large eld called n...

We give asymptotic formulas for the number of biquadratic extensions of Q that admit a quadratic extension which is a Galois extension of Q with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel–Walfisz theorem and the double osc...

Introduction Perceived waiting time (PWT) at signalized intersections differs from the real value of waiting time (WT), and varies with signal design. The onerousness of delay depends on the conditions under which it is experienced. Using weighted travel time may contribute to optimal signal control if its use can improve upon assuming that all time is weighted equally by users. This research e...

In this paper, an aggregate production-planning problem is formulated as a stochastic linear quadratic problem with chance constraints on state and control variables. The stochastic model proposed extends the classical aggregate model developed by Holt, Modigliani, Muth and Simon (HMMS). As an example of application, an equivalent deterministic problem is developed from the stochastic model. Th...

This paper presents partitional fuzzy clustering methods based on adaptive quadratic distances. The methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances. These distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. Moreover...

7 This paper presents partitional fuzzy clustering methods based on adaptive quadratic distances. The methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances. These 9 distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. More...