Related papers: On some problems concerning symmetrization operato…
We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.
We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…
This paper deals with four symmetrizations of a convex set $C$: the intersection, the harmonic and the arithmetic mean, and the convex hull of $C$ and $-C$. A well-known result of Firey shows that those means build up a subset-chain in the…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…
In this work, we study the well-posedness of certain sparse regularized linear regression problems, i.e., the existence, uniqueness and continuity of the solution map with respect to the data. We focus on regularization functions that are…
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…
The g-convexity of functions on manifolds is a generalization of the convexity of functions on Rn. It plays an essential role in both differential geometry and non-convex optimization theory. This paper is concerned with g-convex smooth…
In this paper, the asymptotic behavior of sequences of successive Steiner and Minkowski symmetrizations is investigated. We state an equivalence result between the convergences of those sequences for Minkowski and Steiner. Moreover, in the…
We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For…
In this paper, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when $\ell_0$-penalized models are fitted and usually lead to NP-Hard…
A new convenient method of describing flat convex compact sets is proposed. It generalizes classical trigonometric functions $\sin$ and $\cos$. Apparently, this method may be very useful for explicit description of solutions of optimal…
In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…
This paper focuses on the study of MS-Lipschitz p-summing operators, which were initially defined by the authors in <cite>14. Our objective is to establish relationships between T and its linearizations, namely T and T. Additionally, we…
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
The solution of a fine tuning problem is one of the principal motivations of Supersymmetry. However experimental constraints indicate that many Supersymmetric models are also fine tuned (although to a much lesser extent). We review the…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…