Search

In 2014, Jleli and Samet [6] introduced a contraction mapping called θ-contraction. After this, many authors had given their contribution on φ − θ-contraction (see [7, 8]). Motivated by [[6, 9]], we introduce the notion of generalized φ − θ contraction and establish some new fixed point theorems for this contraction in the setting of complete partial metric spaces. [ABSTRACT FROM AUTHOR]

Faults are unwanted events in any industrial production system. Early detection and diagnosis of faults in automated systems is important in order to prevent equipment damage, loss of performance and profits. For this purpose, more and more sophisticated and complex systems for observation and monitoring of basic characteristics in automated processes are being built. Preconditions for increasing their efficiency are processing and analysis of process information is obtained through a significant number of sensors. For pneumatic systems in addition to the identification of certain faults that may affect the normal production process, it is important to consider the possibilities to improve their energy efficiency. In this regards, the work focuses on the detection of leaks. The fault detection is based on the measurement of the compressed air consumption at the inlet of the pneumatic module and synchronization with signal from the PLC to the valve, and controlled the pneumatic cylinder. The experimental study aims to develop methods for automatic detection and classification of leaks that may be used in machine learning algorithms. [ABSTRACT FROM AUTHOR]

In this article, we propose a generalization of both b -metric and dislocated metric, namely, dislocated extended b -metric space. After getting some fixed point results, we suggest a relatively simple solution for a Volterra integral equation by using the technique of fixed point in the setting of dislocated extended b -metric space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems. [ABSTRACT FROM AUTHOR]

Metrizability of Furstenberg topology on integers gives some strange consequences. Besides a primality test for an integer to be a prime, it shows that primes are not dense in integers. It illustrates the construction of a series of positive numbers having a negative sum. Furthermore, it re-establishes the fact that the probability of a randomly chosen integer being prime is zero. [ABSTRACT FROM AUTHOR]

We prove that certain classes of metrically homogeneous graphs omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and we describe their Ramsey expansions. [ABSTRACT FROM AUTHOR]

Fixed point theory is very wide field, which have many applications in different areas. The concept of altering distance to find fixed point results have been explored by many authors. In the present paper, we achieve unique common fixed point results for two self-mappings using a generalization of altering distance and a rational type contractive condition. An example has also been given in support of our result. [ABSTRACT FROM AUTHOR]

In this paper we obtain some stability results for fixed point sets associated with a sequence of multivalued mappings. We define multivalued α-ψ contractions and multivalued α-admissible mappings. We use Hausdorff distance in our definition. We show that the fixed point sets of uniformly convergent sequences of multivalued α-ψ contractions which are also assumed to be multivalued α-admissible, are stable under certain conditions. The multivalued mappings we define here are not necessarily continuous. We present two illustrative examples and one open problem. [ABSTRACT FROM AUTHOR]

The comprehensive performance of the marine current turbine is an important issue in the ocean energy development. Its key is the performance of the hydrofoil, which is used to form the turbine blade. A multi-point optimization method of the hydrofoil is proposed in this paper. In this method, the Bezier curve is used to parameterize the hydrofoil. The geometrical parameters are used as variables while the lift-drag ratio and the cavitation performance of the hydrofoil are used as the objective functions. The NSGA-II algorithm is chosen as the optimization algorithm. In order to resolve the difficulty of this high-dimensional multi-objective optimi- zation problem, the conception of the distance metric in the metric space is introduced to unify the lift-drag ratio and the cavitation performance under different working conditions. And then, the above optimization method is applied in the NACA63-815 hydro- foil's optimal design under three typical conditions. Finally, the results from the performance comparison of the original and optimi- zed hydrofoils obtained by using the CFD simulation are analyzed in detail. It is indicated that the optimized hydrofoils enjoy a better hydrodynamic performance than the original ones under the three conditions. The feasibility and the theoretical validity of this optimization method are confirmed by the results. [ABSTRACT FROM AUTHOR]

Sintunavarat and Kumam (W. Sintunavarat, P. Kumam, Gregus-type common fixed point theorems for tangential multi-valued mappings of integral type in metric spaces, Int. J. Math. Math. Sci. 2011 12 (Article ID 923458)) extended the tangential property to hybrid pair of mappings which generalizes the idea of tangential property due to Pathak and Shahzad (H.K. Pathak, N. Shahzad, Gregus type fixed point results for tangential mappings satisfying contractive conditions of integral type, Bull. Belg. Math. Soc. Simon Stevin 16(2) (2009) 277–288). In the present paper, we introduce the notion of strong tangential property and utilize the same to prove an integral type metrical common fixed point theorem for non-self mappings. An illustrative example is also furnished to support our main result. Our results are corrected, improved and generalized versions of a multitude of relevant common fixed point theorems of the existing literature. [ABSTRACT FROM AUTHOR]

With the technology advance and the growth of Internet, the information that can be found in this net, as well as the number of users that access to look for specific data is bigger. Therefore, it is desirable to have a search system that allows to retrieve information at a reasonable time and in an efficient way. In this paper we show two computing paradigms appropriate to apply in the treatment of large amounts of data consisting of objects such as images, text, sound and video, using hybrid computing over MPI+OpenMP and GPGPU. The proposal is developed through experience gained in the construction of various indexes and the subsequent search, through them, of multimedia objects. [ABSTRACT FROM AUTHOR]

Abstract: This paper proves the existence of periodic and fixed points for contractive conditions in metric (symmetric) space. [Copyright &y& Elsevier]

Copyright of Mathématiques & Sciences Humaines is the property of Editions du CNRS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract: Distance-based indexing exploits only the triangle inequality to answer similarity queries in metric spaces. Lacking coordinate structure, mathematical tools in can only be applied indirectly, making it difficult to theoretically study metric-space indexing. Toward solving this problem, a common algorithmic step is to select a small number of special points, called pivots, and map the data objects to a low-dimensional space, one dimension for each pivot, where each dimension represents the distances of a pivot to the data objects. We formalize a “pivot space model” where all the data objects are used as pivots such that data is mapped from metric space to , preserving all the pairwise distances under . With this model, it can be shown that the indexing problem in metric space can be equivalently studied in . Further, we show the necessity of dimension reduction for and that the only effective form of dimension reduction is to select existing dimensions, i.e. pivot selection. The coordinate structure of makes the application of many mathematical tools possible. In particular, Principle Component Analysis (PCA) is incorporated into a heuristic method for pivot selection and shown to be effective over a large range of workloads. We also show that PCA can be used to reliably measure the intrinsic dimension of a metric space. [Copyright &y& Elsevier]

Property A UB is the notion in metric geometry which has applications in higher index problems. In this paper, the permanence property of property A UB of metric spaces under large scale decompositions of finite depth is proved. [ABSTRACT FROM AUTHOR]

A fixed point theorem in three metric spaces is proved. This result extends the results obtained in [6] from two metric spaces to three metric spaces. It generalizes the results obtained in [8, 4, 5]. A several corollaries are obtained according as the forms of implicit functions [ABSTRACT FROM AUTHOR]

Abstract: Distance permutation indexes support fast proximity searching in high-dimensional metric spaces. Given some fixed reference sites, for each point in a database the index stores a permutation naming the closest site, the second-closest, and so on. We examine how many distinct permutations can occur as a function of the number of sites and the size of the space. We give theoretical results for tree metrics and vector spaces with , , and metrics, improving on the previous best known storage space in the vector case. We also give experimental results and commentary on the number of distance permutations that actually occur in a variety of vector, string, and document databases. [Copyright &y& Elsevier]