**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1573

# Search results for: metric space.

##### 1573 Method of Moments Applied to a Cuboidal Cavity Resonator: Effect of Gravitational Field Produced by a Black Hole

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.

**Keywords:**
Method of moments,
General theory of relativity,
Electromagnetism,
Metric tensor,
schwarzchild metric,
Wave Equation.

##### 1572 An Iterated Function System for Reich Contraction in Complete b Metric Space

**Authors:**
R. Uthayakumar,
G. Arockia Prabakar

**Abstract:**

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

**Keywords:**
Fractals,
Iterated Function System,
Compact set,
Reich
Contraction,
Well posedness.

##### 1571 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

**Authors:**
Ismat Beg,
Asma Rashid Butt

**Abstract:**

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

**Keywords:**
Fixed point,
partially ordered set,
metric space,
set
valued mapping.

##### 1570 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractal Analysis,
Fixed Point,
Contraction,
Iterated Function System,
Intuitionistic Fuzzy Metric Space.

##### 1569 IFS on the Multi-Fuzzy Fractal Space

**Authors:**
Nadia M. G. AL-Sa'idi,
Muhammad Rushdan Md. Sd.,
Adil M. Ahmed

**Abstract:**

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

**Keywords:**
Fuzzy metric space,
Fuzzy fractal space,
Multi fuzzy
fractal space.

##### 1568 Hutchinson-Barnsley Operator in Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractals,
Iterated Function System,
Hutchinson- Barnsley Operator,
Fuzzy Metric Space,
Hausdorff Fuzzy Metric.

##### 1567 Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

**Keywords:**
Contraction,
Iterated Function System,
Hutchinson- Barnsley Operator,
Intuitionistic Fuzzy Metric Space,
Hausdorff Intuitionistic Fuzzy Metric.

##### 1566 Tensorial Transformations of Double Gai Sequence Spaces

**Authors:**
N.Subramanian,
U.K.Misra

**Abstract:**

The precise form of tensorial transformations acting on a given collection of infinite matrices into another ; for such classical ideas connected with the summability field of double gai sequence spaces. In this paper the results are impose conditions on the tensor g so that it becomes a tensorial transformations from the metric space χ2 to the metric space C

**Keywords:**
tensorial transformations,
double gai sequences ,
double analytic,
dual.

##### 1565 A New Class F2 (M, 0, N)L„ p)F of The Double Difference Sequences of Fuzzy Numbers

**Authors:**
N. Subramanian,
C. Murugesan

**Abstract:**

The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.

**Keywords:**
Orlicz function,
solid space,
metric space,
completeness

##### 1564 Best Proximity Point Theorems for MT-K and MT-C Rational Cyclic Contractions in Metric Spaces

**Authors:**
M. R. Yadav,
A. K. Sharma,
B. S. Thakur

**Abstract:**

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

**Keywords:**
Cyclic contraction,
rational cyclic contraction,
best proximity point and complete metric space.

##### 1563 New Class of Chaotic Mappings in Symbol Space

**Authors:**
Inese Bula

**Abstract:**

Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.

**Keywords:**
Infinite symbol space,
prefix metric,
chaotic mapping,
generator function,
jump mapping.

##### 1562 Graphs with Metric Dimension Two-A Characterization

**Authors:**
Sudhakara G,
Hemanth Kumar A.R

**Abstract:**

In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. β (G) = 2 ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H .

**Keywords:**
Metric basis,
Distance partition,
Metric dimension.

##### 1561 Action Functional of the Electomagnetic Field: Effect of Gravitation

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

**Keywords:**
General theory of relativity,
electromagnetism,
metric tensor,
Maxwells equations,
test functions,
finite element method.

##### 1560 Metric Dimension on Line Graph of Honeycomb Networks

**Authors:**
M. Hussain,
Aqsa Farooq

**Abstract:**

**Keywords:**
Resolving set,
metric dimension,
honeycomb network,
line graph.

##### 1559 Cognitive Weighted Polymorphism Factor: A Comprehension Augmented Complexity Metric

**Authors:**
T. Francis Thamburaj,
A. Aloysius

**Abstract:**

**Keywords:**
Cognitive complexity metric,
cognitive weighted
polymorphism factor,
object-oriented metrics,
polymorphism factor,
software metrics.

##### 1558 The Validity Range of LSDP Robust Controller by Exploiting the Gap Metric Theory

**Authors:**
Ali Ameur Haj Salah,
Tarek Garna,
Hassani Messaoud

**Abstract:**

This paper attempts to define the validity domain of LSDP (Loop Shaping Design Procedure) controller system, by determining the suitable uncertainty region, so that linear system be stable. Indeed the LSDP controller cannot provide stability for any perturbed system. For this, we will use the gap metric tool that is introduced into the control literature for studying robustness properties of feedback systems with uncertainty. A 2nd order electric linear system example is given to define the validity domain of LSDP controller and effectiveness gap metric.

**Keywords:**
LSDP,
Gap metric,
Robust Control.

##### 1557 A Geometrical Perspective on the Insulin Evolution

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

**Abstract:**

We study the molecular evolution of insulin from metric geometry point of view. In mathematics, and in particular 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 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.

##### 1556 A Design-Based Cohesion Metric for Object-Oriented Classes

**Authors:**
Jehad Al Dallal

**Abstract:**

**Keywords:**
Object-oriented software quality,
object-orienteddesign,
class cohesion.

##### 1555 A P2P File Sharing Technique by Indexed-Priority Metric

**Authors:**
Toshinori Takabatake,
Yoshikazu Komano

**Abstract:**

**Keywords:**
peer-to-peer,
file-sharing system,
load-balancing,
dependability

##### 1554 A New Class χ2 (M, A,) of the Double Difference Sequences of Fuzzy Numbers

**Authors:**
N.Subramanian,
U.K.Misra

**Abstract:**

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

**Keywords:**
Modulus function,
fuzzy number,
metric space.

##### 1553 Identification of Reusable Software Modules in Function Oriented Software Systems using Neural Network Based Technique

**Authors:**
Sonia Manhas,
Parvinder S. Sandhu,
Vinay Chopra,
Nirvair Neeru

**Abstract:**

**Keywords:**
Software reusability,
Neural Networks,
MAE,
RMSE,
Accuracy.

##### 1552 Knowledge Impact on Measurement: A Conceptual Metric for Evaluating Performance Improvement (PI) at the Kuwait Institute for Scientific Research (KISR)

**Authors:**
AlMatrouk H. S.,
Juszczak M. D.

**Abstract:**

**Keywords:**
Knowledge Creation,
Performance Improvement
(PI),
Conceptual Metric,
Knowledge Management (KM) addedvalue.

##### 1551 PIL Theory

**Authors:**
A. Peveri

**Abstract:**

The curvature space-time by the presence of material, this deformation must present a pattern of deformation, not random. Space is uniform, elastic and any modification that occurs in one part, causes a change in another.

This deformation exists, must be a constant value and is independent of the observer, and relates the amount of matter, the force caused by the curvature of space and surface space. This unit of space is defined in this study as PIL and represents a constant area of space, deformable in the direction and sense of the center of mass of the body. The PIL is curved and connected to the center of mass of the Earth, to get to that point, through all matter, thus forming part of any place between particles at atomic and subatomic levels. At these levels the space between each particle is flat, unlike the macro where the space curves.

**Keywords:**
Space flat,
Space curved,
Unit of space,
Deformation.

##### 1550 A Robust Salient Region Extraction Based on Color and Texture Features

**Authors:**
Mingxin Zhang,
Zhaogan Lu,
Junyi Shen

**Abstract:**

**Keywords:**
salient regions,
color and texture features,
image
segmentation,
saliency metric

##### 1549 Attribute Weighted Class Complexity: A New Metric for Measuring Cognitive Complexity of OO Systems

**Authors:**
Dr. L. Arockiam,
A. Aloysius

**Abstract:**

**Keywords:**
Software Complexity,
Attribute Weighted Class Complexity,
Weighted Class Complexity,
Data Type

##### 1548 Application of Scientific Metrics to Evaluate Academic Reputation in Different Research Areas

**Authors:**
Cristiano R. Cervi,
Renata Galante,
José Palazzo M. de Oliveira

**Abstract:**

In this paper, we address the problem of identifying academic reputation of researchers using scientific metrics in different research areas. Due to the characteristics of each area, researchers can present different behaviors. In previous work, we define Rep-Index that makes use of a profile template to individually identify the reputation of researchers. The Rep-Index is comprehensive and adaptive because involves hole trajectory of the researcher built throughout his career and can be used in different areas and in different contexts. Now, we compare our metric (Rep-Index) with the h-index and the g-index through experiments with researchers in the fields of Economics, Dentistry and Computer Science. We analyze the trajectory of 830 Brazilian researchers from the National Council of Technological and Scientific Development (CNPq), which receive grants research productivity. The grants are aimed at productivity researchers that stand out among their peers, enhancing their scientific normative criteria established by CNPq. Of the 830 researchers, 210 are in the area of Economics, 216 of Dentistry e 404 of Computer Science. The experiments show that our metric is strongly correlated with h-index, g-index and CNPq ranking. We also show good results for our hypothesis that our metric can be used to evaluate research in several areas. We apply our metric (Rep-Index) to compare the behavior of researchers in relation to their h-index and g-index through extensive experiments. The experiments showed that our metric is strongly correlated with h-index, g-index and CNPq ranking.

**Keywords:**
Researcher reputation,
profile model,
scientific metrics.

##### 1547 A Distance Function for Data with Missing Values and Its Application

**Authors:**
Loai AbdAllah,
Ilan Shimshoni

**Abstract:**

Missing values in data are common in real world applications. Since the performance of many data mining algorithms depend critically on it being given a good metric over the input space, we decided in this paper to define a distance function for unlabeled datasets with missing values. We use the Bhattacharyya distance, which measures the similarity of two probability distributions, to define our new distance function. According to this distance, the distance between two points without missing attributes values is simply the Mahalanobis distance. When on the other hand there is a missing value of one of the coordinates, the distance is computed according to the distribution of the missing coordinate. Our distance is general and can be used as part of any algorithm that computes the distance between data points. Because its performance depends strongly on the chosen distance measure, we opted for the k nearest neighbor classifier to evaluate its ability to accurately reflect object similarity. We experimented on standard numerical datasets from the UCI repository from different fields. On these datasets we simulated missing values and compared the performance of the kNN classifier using our distance to other three basic methods. Our experiments show that kNN using our distance function outperforms the kNN using other methods. Moreover, the runtime performance of our method is only slightly higher than the other methods.

**Keywords:**
Missing values,
Distance metric,
Bhattacharyya distance.

##### 1546 Application of l1-Norm Minimization Technique to Image Retrieval

**Authors:**
C. S. Sastry,
Saurabh Jain,
Ashish Mishra

**Abstract:**

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

**Keywords:**
l1-norm minimization,
content based retrieval,
modified Gabor function.

##### 1545 Adaptive Few-Shot Deep Metric Learning

**Authors:**
Wentian Shi,
Daming Shi,
Maysam Orouskhani,
Feng Tian

**Abstract:**

Currently the most prevalent deep learning methods require a large amount of data for training, whereas few-shot learning tries to learn a model from limited data without extensive retraining. In this paper, we present a loss function based on triplet loss for solving few-shot problem using metric based learning. Instead of setting the margin distance in triplet loss as a constant number empirically, we propose an adaptive margin distance strategy to obtain the appropriate margin distance automatically. We implement the strategy in the deep siamese network for deep metric embedding, by utilizing an optimization approach by penalizing the worst case and rewarding the best. Our experiments on image recognition and co-segmentation model demonstrate that using our proposed triplet loss with adaptive margin distance can significantly improve the performance.

**Keywords:**
Few-shot learning,
triplet network,
adaptive margin,
deep learning.

##### 1544 Image Indexing Using a Color Similarity Metric based on the Human Visual System

**Authors:**
Angelo Nodari,
Ignazio Gallo

**Abstract:**

The novelty proposed in this study is twofold and consists in the developing of a new color similarity metric based on the human visual system and a new color indexing based on a textual approach. The new color similarity metric proposed is based on the color perception of the human visual system. Consequently the results returned by the indexing system can fulfill as much as possibile the user expectations. We developed a web application to collect the users judgments about the similarities between colors, whose results are used to estimate the metric proposed in this study. In order to index the image's colors, we used a text indexing engine to facilitate the integration of visual features in a database of text documents. The textual signature is build by weighting the image's colors in according to their occurrence in the image. The use of a textual indexing engine, provide us a simple, fast and robust solution to index images. A typical usage of the system proposed in this study, is the development of applications whose data type is both visual and textual. In order to evaluate the proposed method we chose a price comparison engine as a case of study, collecting a series of commercial offers containing the textual description and the image representing a specific commercial offer.

**Keywords:**
Color Extraction,
Content-Based Image Retrieval,
Indexing