Search results for: partial metric space

Authors: Hemant Kumar Pathak

Abstract:

In 1994, Matthews (S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197) introduced the concept of a partial metric as a part of the study of denotational semantics of data flow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory. In this paper, we introduce the concept of almost partial Hausdorff metric. We prove a fixed point theorem for multi-valued mappings on partial metric space using the concept of almost partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. In the sequel, we derive a homotopy result as an application of our main result.

Keywords: fixed point, partial metric space, homotopy, physical sciences

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Authors: J. C. Riaño-Rojas, J. D. Alzate-Cardona, E. Restrepo-Parra

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In this work, a study of generic magnetic nanoparticles varying the metric space is presented. As the metric space is changed, the nanoparticle form and the inner product are also varied, since the energetic scale is not conserved. This study is carried out using Monte Carlo simulations combined with the Wolff embedding and Metropolis algorithms. The Metropolis algorithm is used at high temperature regions to reach the equilibrium quickly. The Wolff embedding algorithm is used at low and critical temperature regions in order to reduce the critical slowing down phenomenon. The ions number is kept constant for the different forms and the critical temperatures using finite size scaling are found. We observed that critical temperatures don't exhibit significant changes when the metric space was varied. Additionally, the effective dimension according the metric space was determined. A study of static behavior for reaching the static critical exponents was developed. The objective of this work is to observe the behavior of the thermodynamic quantities as energy, magnetization, specific heat, susceptibility and Binder's cumulants at the critical region, in order to demonstrate if the magnetic nanoparticles describe their magnetic interactions in the Euclidean space or if there is any correspondence in other metric spaces.

Keywords: nanoparticles, metric, Monte Carlo, critical behaviour

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: Loai Abdallah, Malik Yousef

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A domain space for the data should reflect the actual similarity between objects. Since objects belonging to the same cluster usually share some common traits even though their geometric distance might be relatively large. In general, the Euclidean distance of data points that represented by large number of features is not capturing the actual relation between those points. In this study, we propose a new method to construct a different space that is based on clustering to form a new distance metric. The new distance space is based on ensemble clustering (EC). The EC distance space is defined by tracking the membership of the points over multiple runs of clustering algorithm metric. Over this distance, we train the decision trees classifier (DT-EC). The results obtained by applying DT-EC on 10 datasets confirm our hypotheses that embedding the EC space as a distance metric would improve the performance.

Keywords: ensemble clustering, decision trees, classification, K nearest neighbors

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Authors: A. Anandha Selvan, B. Malarvizhi

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In recent year the problem of space debris have become very serious. The mass of the artificial objects in orbit increased quite steadily at the rate of about 145 metric tons annually, leading to a total tally of approximately 7000 metric tons. Now most of space debris object orbiting in LEO region about 97%. The catastrophic collision can be mostly occurred in LEO region, where this collision generate the new debris. Thus, we propose a concept for cleaning the space debris in the region of thermosphere by passing the Extreme Ultraviolet (EUV) radiation to in front of space debris object from the re-orbiter. So in our concept the Extreme Ultraviolet (EUV) radiation will create the thermosphere expansion by reacting with atmospheric gas particles. So the drag is produced in front of the space debris object by thermosphere expansion. This drag force is high enough to slow down the space debris object’s relative velocity. Therefore the space debris object gradually reducing the altitude and finally enter into the earth’s atmosphere. After the first target is removed, the re-orbiter can be goes into next target. This method remove the space debris object without catching debris object. Thus it can be applied to a wide range of debris object without regard to their shapes or rotation. This paper discusses the operation of re-orbiter for removing the space debris in thermosphere region.

Keywords: active space debris removal, space debris, LEO, extreme ultraviolet, re-orbiter, thermosphere

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Authors: Abdul Hakim Khan

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The aim of the present paper is to study the Banach Space and Combinatorial Algebraic Structure of R. It is further aimed to study algebraic structure of set of all q-extension of classical formula and function for 0 < q < 1.

Keywords: integral functions, q-extensions, q numbers of metric space, algebraic structure of r and banach space

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Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

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Authors: Awais Asif

Abstract:

This article investigates fixed point theorems of Chatterjea type F-contraction in the setting of F-metric space. We relax the conditions of F-contraction and define modified F-contraction for two mappings. The study provides fixed point results for both single-valued and multivalued mappings. The results are further extended to common fixed point theorems for two mappings. Moreover, to discuss the applicability of our results, an application is provided, which shows the role of our results in finding the solution to functional equations in dynamic programming. Our results generalize and extend the existing results in the literature.

Keywords: Chatterjea type F-contraction, F-cauchy sequence, F-convergent, multi valued mappings

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Authors: S. Ravichandra, D. V. L. N. Somayajulu

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Requirement of stakeholders for adding more details to the database is the main cause of the schema evolution in the relational database. Further, this schema evolution causes the instability to the database. Hence, it is aimed to define a metric suite for schema evolution of a relational database. The metric suite will calculate the metrics based on the features of the database, analyse the queries on the database and measures the coupling, cohesion and component dependencies of the schema for existing and evolved versions of the database. This metric suite will also provide an indicator for the problems related to the stability and usability of the evolved database. The degree of change in the schema of a database is presented in the forms of graphs that acts as an indicator and also provides the relations between various parameters (metrics) related to the database architecture. The acquired information is used to defend and improve the stability of database architecture. The challenges arise in incorporating these metrics with varying parameters for formulating a suitable metric suite are discussed. To validate the proposed metric suite, an experimentation has been performed on publicly available datasets.

Keywords: cohesion, coupling, entropy, metric suite, schema evolution

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Authors: T. Francis Thamburaj, A. Aloysius

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Polymorphism is one of the main pillars of the object-oriented paradigm. It induces hidden forms of class dependencies which may impact software quality, resulting in higher cost factor for comprehending, debugging, testing, and maintaining the software. In this paper, a new cognitive complexity metric called Cognitive Weighted Polymorphism Factor (CWPF) is proposed. Apart from the software structural complexity, it includes the cognitive complexity on the basis of type. The cognitive weights are calibrated based on 27 empirical studies with 120 persons. A case study and experimentation of the new software metric shows positive results. Further, a comparative study is made and the correlation test has proved that CWPF complexity metric is a better, more comprehensive, and more realistic indicator of the software complexity than Abreu’s Polymorphism Factor (PF) complexity metric.

Keywords: cognitive complexity metric, object-oriented metrics, polymorphism factor, software metrics

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Authors: Santu Dey, Arindam Bhattacharyya

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The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, Φ-symmetric, Φ-projectively at Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quartersymmetric metric connection satisfying P.S = 0, where P denote the projective curvature tensor with respect to quarter-symmetric metric connection.

Keywords: quarter-symmetric metric connection, Lorentzian alpha-Sasakian manifold, quasi-projectively flat Lorentzian alpha-Sasakian manifold, phi-symmetric manifold

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Authors: M. Hussain, Aqsa Farooq

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Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network.

Keywords: Resolving set, Metric dimension, Honeycomb network, Line graph

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Syed M. Jawwad Riaz

Abstract:

There has been a lot of interest in exploring the thermodynamic properties at the horizon of a black hole geometry. Earlier, it has been shown, for different spacetimes, that the Einstein field equations at the horizon can be expressed as a first law of black hole thermodynamics. In this paper, considering r = constant slices, for the Kerr-Newman black hole, shown that the Einstein field equations for the induced 3-metric of the hypersurface is expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can only be written as a first law of black hole thermodynamics. It is to be mentioned here that the procedure adopted is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime.

Keywords: black hole space-times, Einstein's field equation, foliation, hyper-surfaces

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Authors: D. S. Palimkar

Abstract:

Random fixed point theory has received much attention in recent years, and it is needed for the study of various classes of random equations. The study of random fixed point theorems was initiated by the Prague school of probabilistic in the 1950s. The existence and uniqueness of fixed points for the self-maps of a metric space by altering distances between the points with the use of a control function is an interesting aspect in the classical fixed point theory. In a new category of fixed point problems for a single self-map with the help of a control function that alters the distance between two points in a metric space which they called an altering distance function. In this paper, we prove the results of existence of random common fixed point and its uniqueness for a pair of random mappings under weakly contractive condition for generalizing alter distance function in polish spaces using Random Common Fixed Point Theorem for Generalized Weakly Contractions.

Keywords: Polish space, random common fixed point theorem, weakly contractive mapping, altering function

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Authors: Bowen Ding, Yihao Kuang

Abstract:

In recent years, with the development of large-scale pre-trained lan-guage models, building vector representations of text through deep neural network models has become a standard practice for natural language processing tasks. From the performance on downstream tasks, we can know that the text representation constructed by these models contains linguistic information, but its encoding mode and extent are unclear. In this work, a structural probe is proposed to detect whether the vector representation produced by a deep neural network is embedded with a syntax tree. The probe is trained with the deep metric learning method, so that the distance between word vectors in the metric space it defines encodes the distance of words on the syntax tree, and the norm of word vectors encodes the depth of words on the syntax tree. The experiment results on ELMo and BERT show that the syntax tree is encoded in their parameters and the word representations they produce.

Keywords: deep metric learning, syntax tree probing, natural language processing, word representations

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Authors: K. M. Anusha, R. Krishnaveni

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Crossing a decade of the 21st century, the paradigm of human resources can be seen evolving with the strategic gene induced into it. There seems to be a radical shift descending as the corporate sector calls on its HR team to become strategic rather than administrative. This transferal eventually requires the metrics employed by these HR teams not to be just operationally reactive but to be aligned to an evidence-based strategic thinking. Realizing the growing need for a prescriptive metric model for effective HR analytics, this study has designed a conceptual framework for a basic metric model that can assist IT-HRM professionals to transition to a practice of evidence-based decision-making to enhance organizational performance.

Keywords: metric model, evidence based HR, HR analytics, strategic HR practices, IT sector

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Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

Abstract:

We study the molecular evolution of insulin from the metric geometry point of view. In mathematics, and particularly in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from the geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: metric geometry, evolution, insulin, C. elegans

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Authors: Kwan-u Kim, Jin-Sim, Ryong-Jin Jang, Sung-Duk Kim

Abstract:

106 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not solve correctly one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the exact physical laws obtained from the solution of the geodesic equations in Schwarzschild metric, so some former scholars mentioned that Einstein’s theoretical basis of general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, because general theory of relativity has not given a quantitative solution to the obscure and incorrect problems, generalization of gravitational theory although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore theobscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first sarytep for achieving the purpose, the correct solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results has been presented, the obscure and incorrect problems have been showed and an analysis of them has been made on the basis of the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

Abstract:

The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Prajwal Prakash Vasisht, Sharath Rajamurthy, Nishanth Dara

Abstract:

In a supervised machine learning approach, metrics such as precision, accuracy, and coverage can be calculated using ground truth labels to help in model tuning, evaluation, and selection. In an unsupervised setting, however, where the data has no ground truth, there are few interpretable metrics that can guide us to do the same. Our approach creates a framework to adapt the Intersection over Union metric, referred to as Adapted IoU, usually used to evaluate supervised learning models, into the unsupervised domain, which solves the problem by factoring in subject matter expertise and intuition about the ideal output from the model. This metric essentially provides a scale that allows us to compare the performance across numerous unsupervised models or tune hyper-parameters and compare different versions of the same model.

Keywords: general metric, unsupervised learning, classification, intersection over union

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Marina B. Cottrell

Abstract:

Tempo plays a significant role in the perception of metrical groupings, with faster tempi tending to increase the number of beats in a given metrical unit. Previous research has shown a correlation between the perception of metric grouping and native language, but little is currently known about other possible musical factors that contribute to metric grouping tendencies. This study aims to find the tempo boundaries at which the perceptual groupings of a melodic pattern changes and to correlate these regions with self-reported musical experience. Participants were presented with looping melodies (divided between major and minor keys). Using a slider bar that controlled the tempo, subjects were asked to locate the point at which they heard the metric grouping doubled or halved. This region was shown to primarily be affected by the mode and time signature of the stimulus. The results also suggest a correlation between the level of musical training and the region of perceived grouping change.

Keywords: meter, metric grouping, mode, tempo

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Authors: Hla Hla Khaing, Yit Jian Liang, Nant Nyein Moe Htay, Jiang Fan

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Partial shadowing is one of the problems that are always faced in terrestrial applications of solar photovoltaic (PV). The effects of partial shadow on the energy yield of conventional mono-crystalline and multi-crystalline PV modules have been researched for a long time. With deployment of new thin-film solar PV modules in the market, it is important to understand the performance of new PV modules operating under the partial shadow in the tropical zone. This paper addresses the impacts of different partial shadowing on the operating characteristics of four different types of solar PV modules that include multi-crystalline, amorphous thin-film, CdTe thin-film and CIGS thin-film PV modules.

Keywords: partial shade, CdTe, CIGS, multi-crystalline (mc-Si), amorphous silicon (a-Si), bypass diode

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Authors: P. Y. Tsyba, O. V. Razina, E. Güdekli, R. Myrzakulov

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In this paper, we consider the equation of motion for the F(R,T) gravity on their property of conformal invariance. It is shown that in the general case such a theory is not conformally invariant. Special cases for the functions v and u, in which the properties of the theory can appear, were studied.

Keywords: conformal invariance, gravity, space-time, metric

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Authors: Chander Kant, Arun Kumar

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Biometric systems automatically recognize an individual based on his/her physiological and behavioral characteristics. There are also some traits like weight, age, height etc. that may not provide reliable user recognition because of there common and temporary nature. These traits are called soft bio metric traits. Although soft bio metric traits are lack of permanence to uniquely and reliably identify an individual, yet they provide some beneficial evidence about the user identity and may improve the system performance. Here in this paper, we have proposed an approach for integrating the soft bio metrics with fingerprint and face to improve the performance of personal authentication system. In our approach we have proposed a combined architecture of three different sensors to elevate the system performance. The approach includes, soft bio metrics, fingerprint and face traits. We have also proven the efficiency of proposed system regarding FAR (False Acceptance Ratio) and total response time, with the help of MUBI (Multimodal Bio metrics Integration) software.

Keywords: FAR, minutiae point, multimodal bio metrics, primary bio metric, soft bio metric

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Authors: Rahma Amri, Narjès Bellamine Ben Saoud

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Sustainable development or sustainability is one of the most urgent issues in actual debate in almost domains. Particularly the significant way the software pervades our live should make it in the center of sustainability concerns. The social aspects of sustainability haven’t been well studied in the context of software systems and still immature research field that needs more interest among researchers’ community. This paper presents a Goal-Question-Metric based approach to assess social sustainability of software systems. The approach is based on a generic social sustainability model taken from Social sciences.

Keywords: software assessment approach, social sustainability, goal-question-metric paradigm, software project metrics

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Authors: Riccardo Patriarca, Giulio Di Gravio, Francesco Costantino, Massimo Tronci

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An accurate inventory management policy acquires a crucial role in the several high-availability sectors. In these sectors, due to the high-cost of spares and backorders, an (S-1, S) replenishment policy is necessary for high-availability items. The policy enables the shipment of a substitute efficient item anytime the inventory size decreases by one. This policy can be modelled following the Multi-Echelon Technique for Recoverable Item Control (METRIC). The METRIC is a system-based technique that allows defining the optimum stock level in a multi-echelon network, adopting measures in line with the decision-maker’s perspective. The METRIC defines an availability-cost function with inventory costs and required service levels, using as inputs data about the demand trend, the supplying and maintenance characteristics of the network and the budget/availability constraints. The traditional METRIC relies on the hypothesis that a Poisson distribution well represents the demand distribution in case of items with a low failure rate. However, in this research, we will explore the effects of using a Poisson distribution to model the demand of low failure rate items characterized by an irregular demand trend. This characteristic of a demand is not included in the traditional METRIC formulation leading to the need of revising its traditional formulation. Using the CV (Coefficient of Variation) and ADI (Average inter-Demand Interval) classification, we will define the inherent flaws of Poisson-based METRIC for irregular demand items, defining an innovative ad hoc distribution which can better fit the irregular demands. This distribution will allow defining proper stock levels to reduce stocking and backorder costs due to the high irregularities in the demand trend. A case study in the aviation domain will clarify the benefits of this innovative METRIC approach.

Keywords: METRIC, inventory management, irregular demand, spare parts

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Authors: Qasim Khan, Furkan Ahmad, Asfar A. Khan, M. Saad Alam, Faiz Ahmad

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In this paper, partial discharge analysis is performed in cavities artificially created in insulation. The setup is according with Cigre-II Method. Circular Samples created from Perspex Sheet with different configuration with changing number of cavities. Assessment of insulation health can be performed by Partial Discharge measurement as this has been found to be important means of condition monitoring. The experiments are done using MPD 540, which is a modern partial discharge measurement system. By analyzing the PD activity obtained for various voids/cavities, it is observed that the PD voltages show variation for cavity’s diameter, depth even for its ratios. This can be employed for scrutiny of insulation system.

Keywords: partial discharges, condition monitoring, insulation defects, degradation and corrosion, PMMA

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Authors: Ivan Ravlich, Ivan Linscott, Sigrid Close

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The experimental search for spin coupling in General Relativity via torsion has been inconclusive. In this work, further experimental avenues to test dynamic torsion are proposed and evaluated. In the extended theory, by relaxing the torsion free condition on the metric connection, general relativity is reformulated to relate the spin density of particles to a new quantity, the torsion tensor. In torsion theories, the spin tensor and torsion tensor are related in much the same way as the stress-energy tensor is related to the metric connection. Similarly, as the metric is the field associated with the metric connection, fields can be associated with the torsion tensor resulting in a field that is either propagating or static. Experimental searches for static torsion have thus far been inconclusive, and currently, there have been no experimental tests for propagating torsion. Experimental tests of propagating theories of torsion are proposed utilizing various spin densities of matter, such as interfaces in superconducting materials and plasmas. The experimental feasibility and observable bounds are estimated, and the most viable candidates are selected to pursue in detail in a future work.

Keywords: general relativity, gravitation, propagating torsion, spin density

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