In this paper we prove a common fixed point theorem for compatible maps of type (β) on fuzzy metric spaces with arbitrary continuous t-norm.

We propose a first-order augmented Lagrangian algorithm (FALC) to solve the composite norm minimizationproblemminX∈Rm×n μ1‖σ(F(X)−G)‖α +μ2‖C(X)− d‖β ,subject to A(X)− b ∈ Q,where σ(X) denotes the vector of singular values of X ∈ Rm×n, the matrix norm‖σ(X)‖α denotes either the Frobenius,the nuclear, or the `2-operator norm of X, the vector norm‖.‖β denotes either ...

We present a new estimator for precision matrix in high dimensional Gaussian graphical models. At the core of the proposed estimator is a collection of node-wise linear regression with nonconvex penalty. In contrast to existing estimators for Gaussian graphical models with O(s √ log d/n) estimation error bound in terms of spectral norm, where s is the maximum degree of a graph, the proposed est...

We establish an L×L → L norm estimate for a bilinear oscillatory integral operator along parabolas incorporating oscillatory factors e −β .

The ring Z consists of the integers of the field Q, and Dedekind takes the theory of unique factorization in Z to be clear and well understood. The problem is that unique factorization can fail when one considers the integers in a finite extension of the rationals, Q(α). Kummer showed that when Q(α) is a cyclotomic extension (i.e. α is a primitive pth root of unity for a prime number p), one ca...

Let XN = (X (N) 1 , . . . , X (N) p ) be a family of N × N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices YN = (Y (N) 1 , . . . , Y (N) q ), possibly random but independent of XN , for which the operator norm of P (XN ,YN ,Y∗ N) converges almost surely for all polynomials P . Limits are described by operator norms of object...

Given i.i.d. observations of a random vector X ∈ R, we study the problem of estimating both its covariance matrix Σ, and its inverse covariance or concentration matrix Θ = (Σ). When X is multivariate Gaussian, the non-zero structure of Θ is specified by the graph of an associated Gaussian Markov random field; and a popular estimator for such sparse Θ is the l1-regularized Gaussian MLE. This est...

Consider a non-negative function f : R → R+ such that ∫ f dγn = 1, where γn is the ndimensional Gaussian measure. If f is semi-log-convex, i.e. if there exists a number β ≥ 1 such that for all x ∈ R, the eigenvalues of ∇ log f(x) are at least −β, then f satisfies an improved form of Markov’s inequality: For all α ≥ e, γn ( {x ∈ R : f(x) > α} ) ≤ 1 α · Cβ(log logα) 4 √ logα , where C is a univer...

Let ϕ(z) = (ϕ 1 (z),...,ϕ n (z)) be a holomorphic self-map of D n and ψ(z) a holomorphic function on D n , where D n is the unit polydiscs of C n. Let 0 < α, β < 1, we compute the essential norm of a weighted composition operator ψC ϕ between α-Bloch space Ꮾ α (D n) and β-Bloch space Ꮾ β (D n).