**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**184

# Search results for: Lorentz metric.

##### 184 Lorentz Forces in the Container

**Authors:**
K. Horáková,
K. Fraňa

**Abstract:**

**Keywords:**
Lorentz forces,
magnetohydrodynamics,
rotatingmagnetic field,
computing program NS-FEM3D

##### 183 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.

##### 182 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.

##### 181 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.

##### 180 Planning Rigid Body Motions and Optimal Control Problem on Lie Group SO(2, 1)

**Authors:**
Nemat Abazari,
Ilgin Sager

**Abstract:**

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

**Keywords:**
Optimal control,
Hamiltonian vector field,
Darboux vector,
maximum principle,
lie group,
rigid body motion,
Lorentz metric.

##### 179 HPM Solution of Momentum Equation for Darcy-Brinkman Model in a Parallel Plates Channel Subjected to Lorentz Force

**Authors:**
Asghar Shirazpour,
Seyed Moein Rassoulinejad Mousavi,
Hamid Reza Seyf

**Abstract:**

In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.

**Keywords:**
Lorentz Force,
Porous Media,
Homotopy Perturbation method

##### 178 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.

##### 177 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.

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

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

**Abstract:**

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

##### 175 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.

##### 174 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.

##### 173 Phenomenological and Theoretical Analysis of Relativistic Temperature Transformation and Relativistic Entropy

**Authors:**
Marko Popovic

**Abstract:**

**Keywords:**
STR,
relativistic temperature transformation,
Boyle'slaw,
equilibrium constant,
Gibbs energy.

##### 172 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.

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

**Authors:**
Jehad Al Dallal

**Abstract:**

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

##### 170 Description of Unsteady Flows in the Cuboid Container

**Authors:**
K. Horáková,
K. Fraňa,
V. Honzejk

**Abstract:**

This part of study deals with description of unsteady isothermal melt flow in the container with cuboid shape. This melt flow is driven by rotating magnetic field. Input data (instantaneous velocities, grid coordinates and Lorentz forces) were obtained from in-house CFD code (called NS-FEM3D) which uses DDES method of computing. Description of the flow was performed by contours of Lorentz forces and caused velocity field. Taylor magnetic numbers of the flow were used 1.10^6, 5.10^6 and 1.10^7, flow was in 3D turbulent flow regime.

**Keywords:**
In-house computing code,
Lorentz forces,
magnetohydrodynamics,
rotating magnetic field.

##### 169 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.

##### 168 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.

##### 167 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

##### 166 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.

##### 165 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.

##### 164 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.

##### 163 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

##### 162 An Optimal Control Problem for Rigid Body Motions on Lie Group SO(2, 1)

**Authors:**
Nemat Abazari,
Ilgin Sager

**Abstract:**

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

**Keywords:**
Optimal control,
Hamiltonian vector field,
Darboux vector,
maximum principle,
lie group,
Rigid body motion,
Lorentz metric.

##### 161 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

##### 160 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.

##### 159 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.

##### 158 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.

##### 157 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

##### 156 A New Concept for Deriving the Expected Value of Fuzzy Random Variables

**Authors:**
Liang-Hsuan Chen,
Chia-Jung Chang

**Abstract:**

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

**Keywords:**
Fuzzy random variables,
Distance measure,
Expected value.

##### 155 3D CAD Models and its Feature Similarity

**Authors:**
Elmi Abu Bakar,
Tetsuo Miyake,
Zhong Zhang,
Takashi Imamura

**Abstract:**

Knowing the geometrical object pose of products in manufacturing line before robot manipulation is required and less time consuming for overall shape measurement. In order to perform it, the information of shape representation and matching of objects is become required. Objects are compared with its descriptor that conceptually subtracted from each other to form scalar metric. When the metric value is smaller, the object is considered closed to each other. Rotating the object from static pose in some direction introduce the change of value in scalar metric value of boundary information after feature extraction of related object. In this paper, a proposal method for indexing technique for retrieval of 3D geometrical models based on similarity between boundaries shapes in order to measure 3D CAD object pose using object shape feature matching for Computer Aided Testing (CAT) system in production line is proposed. In experimental results shows the effectiveness of proposed method.

**Keywords:**
CAD,
rendering,
feature extraction,
feature classification.