**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**210

# Search results for: metric tensor

##### 210 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.

##### 209 On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields

**Authors:**
Nisha Goyal,
R.K. Gupta

**Abstract:**

**Keywords:**
Gravitational fields,
Lie Classical method,
Exact solutions.

##### 208 Green Function and Eshelby Tensor Based on Mindlin’s 2nd Gradient Model: An Explicit Study of Spherical Inclusion Case

**Authors:**
A. Selmi,
A. Bisharat

**Abstract:**

Using Fourier transform and based on the Mindlin's 2^{nd} gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

**Keywords:**
Eshelby tensor,
Eshelby-like tensor,
Green’s function,
Mindlin’s 2nd gradient model,
Spherical inclusion.

##### 207 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.

##### 206 Non Approximately Inner Tensor Product of C*—Algebras

**Authors:**
Rasoul Abazari

**Abstract:**

In this paper, we show that C*-tensor product of an arbitrary C*-algebra A, (not unital necessary) and C*-algebra B without ground state, have no approximately inner strongly continuous one-parameter group of *-automorphisms.

**Keywords:**
One–parameter group,
C*– tensor product,
Approximately inner,
Ground state.

##### 205 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.

##### 204 An Improved Algorithm for Calculation of the Third-order Orthogonal Tensor Product Expansion by Using Singular Value Decomposition

**Authors:**
Chiharu Okuma,
Naoki Yamamoto,
Jun Murakami

**Abstract:**

As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

**Keywords:**
Singular value decomposition (SVD),
higher-orderSVD (HOSVD),
outer product expansion,
power method.

##### 203 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.

##### 202 Riemannian Manifolds for Brain Extraction on Multi-modal Resonance Magnetic Images

**Authors:**
Mohamed Gouskir,
Belaid Bouikhalene,
Hicham Aissaoui,
Benachir Elhadadi

**Abstract:**

**Keywords:**
Riemannian manifolds,
Riemannian Tensor,
Brain
Segmentation,
Non-Euclidean data,
Brain Extraction.

##### 201 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.

##### 200 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.

##### 199 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.

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

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

**Abstract:**

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

##### 197 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.

##### 196 On CR-Structure and F-Structure Satisfying Polynomial Equation

**Authors:**
Manisha Kankarej

**Abstract:**

**Keywords:**
CR-submainfolds,
CR-structure,
Integrability condition & Nijenhuis tensor.

##### 195 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.

##### 194 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.

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

**Authors:**
Jehad Al Dallal

**Abstract:**

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

##### 192 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.

##### 191 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.

##### 190 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

##### 189 Blind Identification and Equalization of CDMA Signals Using the Levenvberg-Marquardt Algorithm

**Authors:**
Mohammed Boutalline,
Imad Badi,
Belaid Bouikhalene,
Said Safi

**Abstract:**

In this paper we describe the Levenvberg-Marquardt (LM) algorithm for identification and equalization of CDMA signals received by an antenna array in communication channels. The synthesis explains the digital separation and equalization of signals after propagation through multipath generating intersymbol interference (ISI). Exploiting discrete data transmitted and three diversities induced at the reception, the problem can be composed by the Block Component Decomposition (BCD) of a tensor of order 3 which is a new tensor decomposition generalizing the PARAFAC decomposition. We optimize the BCD decomposition by Levenvberg-Marquardt method gives encouraging results compared to classical alternating least squares algorithm (ALS). In the equalization part, we use the Minimum Mean Square Error (MMSE) to perform the presented method. The simulation results using the LM algorithm are important.

**Keywords:**
Identification and equalization,
communication
channel,
Levenvberg-Marquardt,
tensor decomposition

##### 188 Curvature of Almost Split Quaternion Kaehler Manifolds

**Authors:**
Erhan Ata,
H. Hilmi Hacisalihoğlu,
Yusuf Yayli

**Abstract:**

**Keywords:**
Almost split quaternion Kaehler manifold,
Riemann curvature,
Ricci curvature.

##### 187 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.

##### 186 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.

##### 185 Probabilistic Bhattacharya Based Active Contour Model in Structure Tensor Space

**Authors:**
Hiren Mewada,
Suprava Patnaik

**Abstract:**

Object identification and segmentation application requires extraction of object in foreground from the background. In this paper the Bhattacharya distance based probabilistic approach is utilized with an active contour model (ACM) to segment an object from the background. In the proposed approach, the Bhattacharya histogram is calculated on non-linear structure tensor space. Based on the histogram, new formulation of active contour model is proposed to segment images. The results are tested on both color and gray images from the Berkeley image database. The experimental results show that the proposed model is applicable to both color and gray images as well as both texture images and natural images. Again in comparing to the Bhattacharya based ACM in ICA space, the proposed model is able to segment multiple object too.

**Keywords:**
Active Contour,
Bhattacharya Histogram,
Structure tensor,
Image segmentation.

##### 184 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

##### 183 Region Segmentation based on Gaussian Dirichlet Process Mixture Model and its Application to 3D Geometric Stricture Detection

**Authors:**
Jonghyun Park,
Soonyoung Park,
Sanggyun Kim,
Wanhyun Cho,
Sunworl Kim

**Abstract:**

In general, image-based 3D scenes can now be found in many popular vision systems, computer games and virtual reality tours. So, It is important to segment ROI (region of interest) from input scenes as a preprocessing step for geometric stricture detection in 3D scene. In this paper, we propose a method for segmenting ROI based on tensor voting and Dirichlet process mixture model. In particular, to estimate geometric structure information for 3D scene from a single outdoor image, we apply the tensor voting and Dirichlet process mixture model to a image segmentation. The tensor voting is used based on the fact that homogeneous region in an image are usually close together on a smooth region and therefore the tokens corresponding to centers of these regions have high saliency values. The proposed approach is a novel nonparametric Bayesian segmentation method using Gaussian Dirichlet process mixture model to automatically segment various natural scenes. Finally, our method can label regions of the input image into coarse categories: “ground", “sky", and “vertical" for 3D application. The experimental results show that our method successfully segments coarse regions in many complex natural scene images for 3D.

**Keywords:**
Region segmentation,
tensor voting,
image-based 3D,
geometric structure,
Gaussian Dirichlet process mixture model

##### 182 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

##### 181 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.