Baby Bhattacharya

On Bitopological γ-open sets

The purpose of this paper is to introduce and study the properties of (1,2) γopen set in bitopological space .In this paper we also study (1, 2) γ-locally closed set, (1,2) γ-t-set, (1,2) γ-B-set and relationship between (1,2) b-open set and (1,2) γ-open set . Keywords(1, 2) b-open set , (1,2) B-set, (1,2) t-set (1,2) locally closed , (1,2) γopen set .

Delayed State Feedback Controller Design for Inverted Pendulum Using T-S Fuzzy Modeling: An LMI Approach

Balancing inverted pendulum along a vertical position with or without cart is a benchmark control problem owing to the fact that out of two equilibrium points, inverted one is open-loop unstable. In this paper, an attempt has been made to stabilize the system with delayed state feedback control strategy using T-S fuzzy modeling in an linear matrix inequality (LMI) framework. Then, by Lyapunov–Krasovskii (L-K) theory, it is proved that the closed-loop system is locally asymptotically stable around its unstable equilibrium point. The result of the control design is validated through closed-loop simulation carried out in MATLAB Simulink.

On fuzzy γ∗-locally closed sets and their applications

This paper attempts to present the notion of fuzzy γ^∗-locally closed set as a stronger form of fuzzy γ^∗-locally closed set and also shows that fuzzy γ^∗-locally closed set is completely independent with the fuzzy locally closed set. Furthermore, we study the notion of fuzzy γ^∗-LC continuous function and fuzzy γ^∗-LC-irresolute function as an application of the newly defined concepts and establish the relationships with some other already existing functions. This study enables us to move one more step towards the learning of difference between topological space and fuzzy topological space.

Improved stability condition for fuzzy systems with interval time varying delay

In this paper, a new and improved stability condition is proposed for Takagi-Sugeno (T-S) fuzzy systems subject to interval time varying delay. The stability analysis is carried out by constructing a new Lyapunov-Krasovskii (L-K) functional along with the use of tighter bounding integral inequality to approximate the integral term coming out from the derivative of L-K functional. Two numerical examples are included to show the effectiveness of the proposed theoretical results over some existing approaches.

Chaos-based video steganography

In this paper a novel data hiding method has been proposed which is based on Non-Linear Feedback Shift Register and Tinkerbell 2D chaotic map. So far, the major work in Steganography using chaotic map has been confined to image steganography where significant restrictions are there to increase payload. In our work, 2D chaotic map and NLFSR are used to developed a video steganography mechanism where data will be embedded in the segregated frames. This will increase the data hiding limit exponentially. Also, embedding position of each frame will be different from others frames which will increase the overall security of the proposed mechanism. We have achieved this randomized data hiding points by using a chaotic map. Basically, Chaotic theory which is non-linear dynamics physics is using in this era in the field of Cryptography and Steganography and because of this theory, little bit changes in initial condition makes the output totally different. So, it is very hard to get embedding position of data without knowing the initial value of the chaotic map.

Quotology - Reading Between the Lines of Quotations

A quote is short eloquent sentence/s drawn from long experience. Quotes are full of poetry, abstraction in the form of restrained information, hidden significance and objective, and pragmatic twists. While a quote explanation always in elaborate form with more sentences than the quote, both of them convey the same concept or meaning. However, systematic study to understand linguistic structures and interpretation of quotes has not received much research attention till date. To this end we have developed a corpus of English quotes and their interpretations in elaborated forms. Finally, we proposed an automatic approach to recognize Textual Entailment (TE) between English quote and its explanation where quote has been considered as the text (T) and its explanation/interpretation has been considered as hypothesis (H). We have tested various linguistic features including lexical, syntactic, and semantic cues and also tried word-to-vector similarity measure using deep learning approach on quote-explanation to identify TE relation.

Generalizations of γ-open set in topological spaces

The main aim of this work is to study three generalized forms of γ-open set due to D. Andrijevic (D. Andrijevic, On the Topology Generated by pre-open sets, Presented at the Sixth Prague Topological Symposium, 39 (1987), 367-376)in a topological space. Out of which the dual appearance of one is the stronger form of b-locally closed set in the sense of Arafa A. Nasef (A. A Nasef,On b-locally closed sets and related topics, CHAOS SOLITONS & FRACTALS 12(2001) 1909-1915). Also, we introduce the concept of different types of continuity and study their basic properties by using these newly defined sets. Finally, we establish the interrelationships among themselves together with some already existing generalized forms of continuity.

Contra continuity and almost contra continuity in generalized fuzzy topological spaces

In this paper we introduce fuzzy contra continuity and almost contra continuity in generalized fuzzy topological space. Fuzzy almost contra continuity is weaker than fuzzy contra continuity in generalized fuzzy topological space. Then we investigate their characterizations and properties. We also established some equivalent relation on fuzzy contra continuity and fuzzy almost contra continuity in generalized fuzzy topological spaces.

On (1, 2)*-contra-γ-continuous functions

In this paper we apply the notion of (1, 2)*-γ-closed sets in bitopological space to present and study a new class of function called (1, 2)*-contra-γ-continuous functions. Relationships between this new class and other classes of function are established. Further we, introduce a new types of graphs, called (1, 2)*-γ-closed graphs via (1, 2)*-γ-open sets. Several characterizations and properties of such notions are investigated.

Some Properties of -Locally Closed Sets

A new kind of generalization of (1, 2)*-closed set, namely, (1, 2)*-locally closed set, is introduced and using (1, 2)*-locally closed sets we study the concept of (1, 2)*-LC-continuity in bitopological space. Also we study (1, 2)*-contracontinuity and lastly investigate its relationship with (1, 2)*-LC-continuity.