We study the Isomorphism of Polynomial (IP2S) problem with m = 2 homogeneous quadratic polynomials of n variables over a finite field of odd characteristic: given two quadratic polynomials (a,b) on n variables, we find two bijective linear maps (s, t) such that b = t◦a◦s. We give an algorithm computing s and t in time complexity Õ(n) for all instances. The IP2S problem was introduced in cryptog...

We consider the 3-D system defined by jerk equation $\dddot{x} = -a \ddot{x} + x \dot{x}^2 -x^3 -b c \dot{x}$, with $a, b, c\in \mathbb{R}$. When $a=b=0$ and $c < 0$ equilibrium point localized at origin is a zero-Hopf equilibrium. analyse Bifurcation that occur this when we persuade quadratic perturbation of coefficients, prove one, two or three periodic orbits can born parameter goes to $0$.

In this paper, we derive some algebraic identities on right and left neighbors R(F ) and L(F ) of an indefinite binary quadratic form F = F (x, y) = ax + bxy + cy of discriminant Δ = b − 4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F . Keywords—Quadratic form, indefinite form, cy...

the superiority of the quadratic images to second harmonic (SH) images in phantoms, both in terms of spatial and contrast resolutions. Furthermore, we have shown that the quadratic images produce contrast-to-tissue ratios (CTRs) at the same level of those produced by pulse inversion (PI) without the need for multiple transmission. The imaging results have also shown that quadratic imaging also ...

We provide a new analytical approach to operator splitting for equations of the type ut = Au + B(u) where A is a linear operator and B is quadratic. A particular example is the Korteweg–de Vries (KdV) equation ut−uux +uxxx = 0. We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.

We consider the problem of efficient estimation for the drift of fractional Brownian motion B := ( B t ) t∈[0,T ] with hurst parameter H less than 1 2 . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

We prove a general theorem that evaluates the Legendre symbol (A+B √ m p) under certain conditions on the integers A, B, m and the prime p. The evaluation is in terms of parameters appearing in a binary quadratic form representing p. The theorem has applications to quartic residuacity.

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...