We show that the quadratic matrix equation VW + η(W )W = I, for given V with positive real part and given analytic mapping η with some positivity preserving properties, has exactly one solution W with positive real part. Also we provide and compare numerical algorithms based on the iteration underlying our proofs. This work bears on operator-valued free probability theory, in particular on the ...

Let Σ be the algebraic universal cover of a closed surface of genus g > 1, T (Σ) its Teichmüller space, M(Σ,ℓ) the group of mapping classes stabilizing a fixed leaf ℓ. The L 1 Ehrenpreis conjecture asserts that M(Σ,ℓ) acts on T (Σ) with dense orbits in the L 1 topology (the topology coming from the L 1 norm on quadratic differentials). We give a proof of this weaker version of the Ehrenpreis co...

We prove that when n ≥ 5, the Dehn function of SL(n, Z) is at most quartic. The proof involves decomposing a disc in SL(n, R)/ SO(n) into a quadratic number of loops in generalized Siegel sets. By mapping these loops into SL(n, Z) and replacing large elementary matrices by “shortcuts,” we obtain words of a particular form, and we use combinatorial techniques to fill these loops.

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

Antiarrhythmic drug effects on maximal upstroke velocity (V^,) are frequency dependent, which implies that the effects of these drugs on conduction should also be rate dependent. Previous in vivo studies have been limited by assumptions about unchanging propagation pathway, and by the empirical use of a first-order recovery model. To explore time-dependent antiarrhythmic drug-induced conduction...

Security of electronic data has become indispensable to today’s global information society, and public-key cryptography, a key element to securing internet communication, has gained increasing interest as a vital subject of research. Numerous public-key cryptosystems have been proposed that use allegedly intractable number theoretic problems as a basis of their security. One example is NICE, in...

A pseudo-Boolean function is a real-valued function f(x) = f(x1, x2, . . . , xn) of n binary variables; that is, a mapping from {0, 1}n to R. For a pseudo-Boolean function f(x) on {0, 1}n, we say that g(x, y) is a quadratization of f if g(x, y) is a quadratic polynomial depending on x and on m auxiliary binary variables y1, y2, . . . , ym such that f(x) = min{g(x, y) : y ∈ {0, 1}m} for all x ∈ ...

Nonlinear rescaling (NR) methods alternate finding an unconstrained minimizer of the Lagrangian for the equivalent problem in the primal space (which is an infinite procedure) with Lagrange multipliers update. We introduce and study a proximal point nonlinear rescaling (PPNR) method that preserves convergence and retains a linear convergence rate of the original NR method and at the same time d...

This article is based on my lecture at the Complex Dynamics Workshop of the Research Institute of Mathematics at Kyoto University in October 2001. It is an exposition of joint work with Janina Kotus. The tangent family fλ(z) = λ tan(z) is the meromorphic analogue of the quadratic family z +c. The functions fλ(z) are characterized by their mapping properties: they are, up to scale, the only mero...