Consider two (n−1)-dimensional manifolds, S and S in R. We say that they are normalcompatible when the closest projection of each one onto the other is a homeomorphism. We give a tight condition under which S and S are normal-compatible. It involves the minimum feature size of S and of S and the Hausdorff distance between them. Furthermore, when S and S are normal-compatible, their Frechet dist...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

yielding elements (ye) are among those devices that not only help control structural damages, but make better seismic behavior by concentrating the frames in some removable part of the structures. ye are located at the intersection of concentric braced frame (cbf) in a rectangular shape. in this paper, seismic behavior of the frames with ye will be investigated. for this reason, 5 braced steel ...

Finite tight frames have many applications and some interesting physical interpretations. One of the important subjects in this area is the ways for constructing such frames. In this article we give a concrete method for constructing finite normalized frames using Platonic solids.

Some basic concepts for functions defined on subsets of the unit sphere, such as s-directional derivative, s-gradient and s-Gateaux s-Frechet differentiability etc, are introduced investigated. These different from usual ones Euclidean spaces, however, results obtained here very similar. Then, applications, we provide some criterions s-convexity spheres which improvements or refinements known r...

It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

response modification factor (r-factor) is one of the seismic design parameters to consider nonlinear performance of building structures during strong earthquake. relying on this, many seismic design codes led to reduce earthquake loads imposed to the structure. the present paper tries to evaluate the r-factors of conventional concentric braced frames (cbfs) and special moment frames (mrfs) in ...

1. N o t a t i o n a n d pre l iminary ideas . A sequence space is a vector subspace of the space co of all real (or complex) sequences. A sequence space E with a locally convex topology r is called a Kspace if the inclusion map E —* co is continuous, when co is endowed with the product topology (co = II^Li (R)*). A i£-space E with a Frechet (i.e., complete, metrizable and locally convex) topol...

We provide a new analysis framework for the adversarial multi-armed bandit problem. Using the notion of convex smoothing, we define a novel family of algorithms with minimax optimal regret guarantees. First, we show that regularization via the Tsallis entropy, which includes EXP3 as a special case, matches the O( √ NT ) minimax regret with a smaller constant factor. Second, we show that a wide ...