an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, statistics, computer vision, system identification and control, and it is NP-hard. It is known that under some restricted isometry property (RIP) conditions we can obtain the exact low-rank matrix solution by solving its convex relaxation, the nuclear norm minimization. In this paper, we consider the n...

Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...

Let G be a connected linear Lie group which finitely covers the isometry group of X. Furthermore, let Γ ⊂ G be a discrete subgroup. We assume that Γ is geometrically finite. We refer to Definition 2.1 for a precise explanation of this notion. If X is a real hyperbolic space, then Γ is geometrically finite iff it admits a fundamental domain with finitely many totally geodesic faces. In the other...

The Malliavin calculus is an infinite dimensional calculus on a Gaussian space, which is mainly applied to establish the regularity of the law of nonlinear functionals of the underlying Gaussian process. Suppose that H is a real separable Hilbert space with scalar product denoted by 〈·, ·〉H . The norm of an element h ∈ H will be denoted by ‖h‖H . Consider a Gaussian family of random variables W...

We attempt to convey a sense of compressed sensing. Specifically, we discuss how `1 minimization and the restricted isometry property for matrices can be used for sparse recovery of underdetermined linear systems even in the presence of noise.

This paper studies the recovery guarantees of the models of minimizing ‖X‖∗ + 1 2α‖X‖F where X is a tensor and ‖X‖∗ and ‖X‖F are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing ‖X‖∗ under the conditions on the sensing operator such as its null-space property...

The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the null space of the measurement procedure and as such, any two matrices which have the same null space will have NSP if either one of them does. On the other h...