A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formulation. An analytic mome...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

As very powerful and important tools in the study of nonlinear sciences, fixed point methods have attracted so much attention. Over the last decades, fixed point techniques have been applied extensively in such diverse fields as biology, chemistry, economics, engineering, game theory, physics, and so on. The thorough study of the fixed point theory and its approach methods contained in the lite...

In this paper, we formulate two classes of problems, the colored range query problems and the colored point enclosure query problems to model multi-dimensional range and point enclosure queries in the presence of categorical information. Many of these problems are difficult to solve using traditional data structural techniques. Based on a new framework of combining sketching techniques and trad...

Detecting approximate symmetries of parts of a model is important when attempting to determine the geometric design intent of approximate boundary-representation (B-rep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the model to improve its shape, to simplify its analysis, or to constrain it during editing. We give an...

* Correspondence: madjid. [email protected]; [email protected]. kr Center of excellence in nonlinear analysis and applications, Department of mathematics, Semnan university, P.O. Box 35195363, Semnan, Iran Department of mathematics education and the rins, Gyeongsang national university, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract The aim of t...

This paper presents a framework for reasoning about robust geoemtric algorithms. Robustness is formally deened and a data structure called an approximate polygon is introduced and used to reason about polygons constructed of edges whose positions are uncertain. A robust algorithm for point location in an approximate polygon is presented. The algorithm uses only the signature of the point (not i...

and Applied Analysis 3 Proof. As T and S form a K-Cyclic map, d x1, x2 d Tx0, Sx1 ≤ k d x0, Tx0 d x1, Sx1 1 − 2k d A,B k d x0, x1 d x1, x2 1 − 2k d A,B . 3.1 So, it follows that d x1, x2 ≤ k/ 1 − k d x0, x1 1 − k/ 1 − k d A,B . Similarly, it can be seen that d x2, x3 ≤ ( k 1 − k )2 d x0, x1 [ 1 − ( k 1 − k )2] d A,B . 3.2 Hence, it follows by induction that d xn, xn 1 ≤ ( k 1 − k )n d x0, x1 [ ...

Let P be a polygonal curve in R of length n, and S be a point set of size k. The Curve/Point Set Matching problem consists of finding a polygonal curve Q on S such that the Fréchet distance from P is less than a given ε. We consider eight variations of the problem based on the distance metric used and the omittability and repeatability of the points. We provide closure to a recent series of com...