A standard technique for solving the recursion xn+1 = g (xn) where g : C→ C is a complex function is to first find a fairly simple function g : C→ C and a bijection f : C→ C such that g = f◦g◦f−1 where ◦ is the composition of functions. Then xn = g (x0) = (f ◦ g ◦ f−1) (x0) where g and g are the n-fold composition of functions and g is fairly easy to compute. With this motivation we find all pa...

M. Antonowicz and A. P. Fordy (1988) introduced the second-order polynomial eigenvalue problem Lφ = (∂2 +∑i=1 viλ)φ = αφ (∂ = ∂/∂x, α = constant) and discussed its multi-Hamiltonian structures. For n= 1 and n= 2, the associated finite-dimensional integrable Hamiltonian systems (FDIHS) have been discussed by Xu and Mu (1990) using the nonlinearization method and Bargmann constraints. In this pap...

Accurate data on gross domestic product (GDP) at pixel level are needed to understand the dynamics of regional economies. GDP spatialization is the basis of quantitative analysis on economic diversities of different administrative divisions and areas with different natural or humanistic attributes. Data from the Visible Infrared Imaging Radiometer Suite (VIIRS), carried by the Suomi National Po...

This paper proposes statistical analysis of phase-only correlation functions based on linear statistics and directional statistics. We derive the expectation and variance of the phase-only correlation functions assuming phase-spectrum differences of two input signals to be probability variables. We first assume linear probability distributions for the phasespectrum differences. We next assume c...

Let f(z) = P n a(n)n e(nz) ∈ Sk(N,χ) be a cusp form for Γ0(N), weight k > 4 and character χ. Let q(x) = x + sx+ t ∈ Z[x] be a quadratic polynomial. It is shown that

We consider polynomial differential systems in the plane with Liouvillian first integrals. It is shown that all such systems have Darbouxian integrating factors, and that the search for such integrals can be reduced to a search for the invariant algebraic curves of the system and their ‘degenerate’ counterparts.

RC6 has been submitted as a candidate for the Advanced Encryption Standard (AES). Two important features of RC6 that were absent from its predecessor RC5 are a quadratic function and a fixed rotation. By examining simplified variants that omit these features we clarify their essential contribution to the overall security of RC6.

In 2011 ISO standardized [2] a family of deterministic pseudorandom bit generators MQ—DRBG, based on multivariate quadratic functions satisfying certain properties. The security of the generator could be described in terms of complexity of solving the corresponding system of multivariate quadratic equations. In our previous article [1] we proposed two different techniques for constructing syste...

Let q : Ĉ → Ĉ be any quadratic polynomial and r : C2 ∗ C3 → PSL(2,C) be any faithful discrete representation of the free product of finite cyclic groups C2 and C3 (of orders 2 and 3) having connected regular set. We show how the actions of q and r can be combined, using quasiconformal surgery, to construct a 2 : 2 holomorphic correspondence z → w, defined by an algebraic relation p(z,w) = 0.

The topic of our research is unconstrained 0-1 quadratic programming. We find some properties of the Boolean Quadric Polytope, which is obtained from the standard linearization of the given 0-1 quadratic function. By using a result obtained by Deza and Laurent on a class of hypermetric inequalities for the Cut Polytope, we find a necessary and sufficient condition for a class of inequalities to...