In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

In this article, we have theoretically investigated the performance of graphene-hexagonal Boron Nitride (hBN) multilayer structure (hyper crystal) to demonstrate all angle negative refraction along with superior transmission. hBN, one of the latest natural hyperbolic materials, can be a very strong contender to form a hyper crystal with graphene due to its excellence as a graphene-compatible su...

In the field of representation learning on knowledge graphs (KGs), a hyper-relational fact consists main triple and several auxiliary attribute-value descriptions, which is considered more comprehensive specific than triple-based fact. However, currently available KG embedding methods in single view are limited application because they weaken hierarchical structure that represents affiliation b...

Table of Contents 1. Introduction. 2. The isomorphic classification of separable C(K) spaces. A. Milutin's Theorem. B. C(K) spaces with separable dual via the Szlenk index 3. Some Banach space properties of separable C(K) spaces. A. Weak injectivity. B. c 0-saturation of spaces with separable dual. C. Uncomplemented embeddings of C([0, 1]) and C(ω ω +) in themselves. 4. Operators on C(K)-spaces.

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual itera...

We present a geometric construction of a new class of hyper-Kähler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kähler geometry with torsion associated with the NS-5-brane along quaternionic planes in H k. We find the moduli space of these geometries and show that it can be constructed using the bundle space of the canonical quaternionic line bundle over...

Educational timetabling problem is a challenging real world problem which has been of interest to many researchers and practitioners. There are many variants of this problem which mainly require scheduling of events and resources under various constraints. In this study, a curriculum based course timetabling problem at Yeditepe University is described and an iterative selection hyper-heuristic ...

We investigated the effect of thyroid hormone status on renal handing of Ca2+. Further, like kinetics of Ca2+ transport across brush-border membrane (BBM) and basolateral membrane (BLM) of renal epithelial cells was carried out. FE(Ca) was decreased in hyperthyroid (Hyper-T) rats and increased in hypothyroid (Hypo-T) rats as compared to euthyroid (Eu-T) rats. Ca2+ uptake into renal brush-border...