More than forty years ago, Igusa proved in [Ig] a “Fundamental Lemma”, according to which, theta constants give an explicit generically injective map from some modular varieties related to the symplectic group Sp(n, R) into the projective space. The embedded varieties satisfy some quartic relations, the so called Riemann’s relations. We expect that similar results hold for orthogonal instead of...

A theorem of Mumford’s states that for a smooth cubic threefold X, the intermediate Jacobian JX is a principally polarized abelian variety of dimension 5 whose theta divisor has a unique singular point, which has multiplicity three. This talk describes joint work with R. Friedman, in which we prove a converse: if A is a principally polarized abelian variety of dimension 5 whose theta divisor ha...

We introduce the class of variable anisotropic singular integral operators associated to a continuous multi-level ellipsoid cover $$\Theta $$ $$\mathbb {R}^n$$ introduced by Dahmen et al. (Constr Approx 31:149–194, 2010). This is an extension classical isotropic on $${\mathbb R}^n$$ arbitrary smoothness and their analogues for general expansive matrices first author Bownik (Mem Am Math Soc 164(...

in the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{f}_{c,theta}$-mappings and $mathscr{f}_{c,theta}$-majorized mappings are established‎. ‎as applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎our results unify and generalize most known results‎ ‎in recent literature‎.

We introduce and analyze a new finite-difference scheme, relying on the theta-method, for solving monotone second-order mean field games. These games consist of coupled system Fokker–Planck Hamilton–Jacobi–Bellman equation. The theta-method is used discretizing diffusion terms: we approximate them with convex combination an implicit explicit term. On contrast, use centered scheme first-order te...

WinBUGS code to fit the multivariate Bayesian relative risk model: model{ for( i in 1 : N ) { for( j in 1 : K ) { Y[i, j] ~ dpois(lambda[i, j]) # distribution of observations lambda[i, j] E[i, j] * theta[i, j] theta[i, j] exp(phi[ i, j]) # log parametrization } phi[i, 1:K ] ~ dmnorm(mu[ ], Omega[, ]) } for(j in 1:K){ mu[j] ~ dunif( 2,2) } Omega[1:K, 1:K ] ~ dwish(R[, ], 12) # Wishart on prec. m...

We analyze the generalized symmetric exclusion process, which allows at most $\alpha$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $\theta\in\mathbb R$. prove that hydrodynamic behavior given heat equation depending on value of $\theta$, supplemented different boundary conditions. Setting $\alpha = 1$ find results known [1] f...

We study the convergence and rates of a multi-block proximal alternating direction method multipliers (PADMM) for solving linearly constrained separable nonconvex nonsmooth optimization problems. This algorithm is an important variant (ADMM) which includes term in each subproblem, to cancel out complicated terms applications where subproblems are not easy solve or do admit simple closed form so...

Let $K=\mathbb{Q}(\theta)$ be a number field generated by complex root $\theta$ of monic irreducible trinomial $F(x) = x^n+ax+b \in \mathbb{Z}[x]$. There is an extensive literature on monogenity fields defined trinomials. For example, Gaál studied the multi-monogenity sextic Jhorar and Khanduja provide some explicit conditions $a$, $b$ $n$ for $(1, \theta, \ldots, \theta^{n-1})$ to power integr...