LINEAR TO NON-LINEAR TOPOLOGY VIA γ-OPEN SETS IN THE ENVIRONMENT OF BITOPOLOGICAL SPACES

Generalizations of open sets always gives a linear structure in an ordinary topological space. This paper proposes that there exists a non-linear structure in a given bitopological space via $\gamma$-open sets of the context. The new structure is also studied in the light of hyperconnectedness to show that it is completely independent with the original one. Also, the relationships between extremally disconnectedness, connectedness and hyperconnectedness are presented in the same environment by means of $\gamma$-open set. Moreover, the idea of maximal $\gamma$-hyperconnectedness is initiated in this work and some important results related to filter, ultrafilter, door space are established. Finally, some functions concerned with $(1, 2) \gamma$-open sets are introduced and interrelationships among them are produced. Some suitable examples and counter examples are properly placed to make the paper self sufficient

Generalized fuzzy closed sets in generalized fuzzy topological spaces

This paper aims to put forward one more difference between generalized topological space and generalized fuzzy topological space via generalized closed set in the respective fields. Also we claim and prove that to a certain extent, the role of generalized closed set in a fuzzy topological space is not similar in nature with that of generalized closed set in a generalized fuzzy topological space. Generalized closed sets coincide with closed sets under some appropriate restrictions though the implication does not hold in general in a generalized fuzzy topological space

Further results on stability analysis of Takagi–Sugeno fuzzy time-delay systems via improved Lyapunov–Krasovskii functional

The problem of delay-range-dependent (DRD) stability analysis for continuous time Takagi–Sugeno (T–S) fuzzy time-delay systems (TDSs) is addressed in this paper. An improved DRD stability criterion is proposed in an linear matrix inequality (LMI) framework by constructing an appropriate delay-product-type (DPT) Lyapunov–Krasovskii functional (LKF) to make use of Bessel-Legendre polynomial based relaxed integral inequality. The modification in the proposed LKF along with the judicious choice of integral inequalities helps to obtain a less conservative delay upper bound for a given lower bound. The efficacy of the obtained stability conditions is validated through the solution of three numerical examples

Efficacy and safety of Tinospora cordifolia (Tc) as an add-on therapy in patients with type-2 diabetes

Background: Type 2 diabetes has become a global epidemic. Tinospora cordifolia is being used in the treatment of type 2 diabetes since ancient times. It is a common misconception that Ayurvedic medicines are always safe. In fact, they also pose serious health risks either in the form of adverse reactions or in the form of drug interactions. Hence this study was undertaken to study the efficacy and safety of Tc on human subjects.Methods: We recruited 40 type 2 diabetic patients who were on oral hypoglycaemic agents. These patients were then randomly divided into two groups, A and B. Patients in group A continued with their anti-diabetic medications while in group B Tc was given at a dose of 500 mg three times daily along with their conventional medications. The fasting and post prandial blood glucose levels, renal function tests and liver function tests were recorded at baseline, 3 months and 6 months.Results: During the course of study we observed a decrease in the fasting and post prandial blood glucose levels of the patients. No significant change was observed in the renal function tests and liver function tests and no other event of any adverse drug reactions were recorded.Conclusion: Tinospora cordifolia (Tc) is effective as an add-on therapy in patients with type-2 diabetes. There is no negative impact of Tc on the renal as well as liver function tests.

On γ - locally closed sets in fuzzy bitopological space

The main objective of this paper is to introduce the notion of (i, j)-fuzzy γ -locally closed set in fuzzy bitopological space and to obtain various basic properties of the new notion. Also, we define the dual form of γ -locally closed set which is termed as (i, j)-fuzzy γ -locally open set and show that it is a stronger form of -fuzzy b-locally open set. Finally, we study the notion of (i, j)-fuzzy γ -LC-continuous function and (i, j)-fuzzy γ -LC-irresolute function as an application of the newly defined concept and establish the relationships with some already existing functions