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In this paper, we discuss the notion of fuzzy strong ß -I -open sets. We introduce fuzzy almost I -open, fuzzy almost strong I -open sets, fuzzy SßI -set, fuzzy DI -sets closely related with fuzzy strong ß -I -open sets. Additionally, we investigate some characterizations and properties of these sets. With the help of fuzzy strong ß -I -open set and fuzzy DI -set to obtain a new decomposition of fuzzy continuity viaidealization. K. Malarvizhi | R. SriKirithiga | N. Arulselvam"Some new sets and a new decomposition of fuzzycontinuity, fuzzy almost strongI-continuity via idealization" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd10726.pdf  http://www.ijtsrd.com/mathemetics/topology/10726/some-new-sets-and-a-new-decomposition-of-fuzzycontinuity-fuzzy-almost-strongi-continuity-via-idealization/k-malarvizhi

In this paper we discuss new type of continuous functions called almost slightly semi−continuous, slightly semi-open and slightly semi-closed functions; its properties and interrelation with other such functions are studied.

We consider one-frequency analytic SL(2,R) cocycles. Our main result establishes the Almost Reducibility Conjecture in the case of exponentially Liouville frequencies. Together with our earlier work, this implies that all cocycles close to constant are almost reducible, independent of the frequency. In our forthcoming work, we discuss applications to the analysis of the absolutely continuous spectrum of one-frequency Schrodinger operators.

bang bang continuity from year 2010 or 2011.

In this paper, we discuss the notion of fuzzy strong ß -I -open sets. We introduce fuzzy almost I -open, fuzzy almost strong I -open sets, fuzzy SßI -set, fuzzy DI -sets closely related with fuzzy strong ß -I -open sets. Additionally, we investigate some characterizations and properties of these sets. With the help of fuzzy strong ß -I -open set and fuzzy DI -set to obtain a new decomposition of fuzzy continuity viaidealization. K. Malarvizhi | R. SriKirithiga | N. Arulselvam"Some new sets and a new decomposition of fuzzycontinuity, fuzzy almost strongI-continuity via idealization" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd10726.pdf Article URL: http://www.ijtsrd.com/mathemetics/topology/10726/some-new-sets-and-a-new-decomposition-of-fuzzycontinuity-fuzzy-almost-strongi-continuity-via-idealization/k-malarvizhi

In this paper, we discuss the notion of fuzzy strong ß -I -open sets. We introduce fuzzy almost I -open, fuzzy almost strong I -open sets, fuzzy SßI -set, fuzzy DI -sets closely related with fuzzy strong ß -I -open sets. Additionally, we investigate some characterizations and properties of these sets. With the help of fuzzy strong ß -I -open set and fuzzy DI -set to obtain a new decomposition of fuzzy continuity viaidealization. K. Malarvizhi | R. SriKirithiga | N. Arulselvam"Some new sets and a new decomposition of fuzzycontinuity, fuzzy almost strongI-continuity via idealization" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd10726.pdf Article URL: http://www.ijtsrd.com/mathemetics/topology/10726/some-new-sets-and-a-new-decomposition-of-fuzzycontinuity-fuzzy-almost-strongi-continuity-via-idealization/k-malarvizhi

For a compact Hausdorff space $X$, the space $SC(X\times X)$ of separately continuous complex valued functions on $X$ can be viewed as a $C^*$-subalgebra of $C(X)^{**}\overline\otimes C(X)^{**}$, namely those elements which slice into $C(X)$. The analogous definition for a non-commutative $C^*$-algebra does not necessarily give an algebra, but we show that there is always a greatest $C^*$-subalgebra. This thus gives a non-commutative notion of separate continuity. The tools involved are multiplier algebras and row/column spaces, familiar from the theory of Operator Spaces. We make some study of morphisms and inclusions. There is a tight connection between separate continuity and the theory of weakly almost periodic functions on (semi)groups. We use our non-commutative tools to show that the collection of weakly almost periodic elements of a Hopf von Neumann algebra, while itself perhaps not a $C^*$-algebra, does always contain a greatest $C^*$-subalgebra. This allows us to give a notion of non-commutative, or quantum, semitopological semigroup, and to briefly develop a compactification theory in this context.

If $X$ is an almost complex manifold, with an almost complex structure $J$ of class $\CC^\alpha$, for some $\alpha >0$, for every point $p\in X$ and every tangent vector $V$ at $p$, there exists a germ of $J$-holomorphic disc through $p$ with this prescribed tangent vector. This existence result goes back to Nijenhuis-Woolf. All the $J$ holomorphic curves are of class $\CC^{1,\alpha}$ in this case. Then, exactly as for complex manifolds one can define the Royden-Kobayashi pseudo-norm of tangent vectors. The question arises whether this pseudo-norm is an upper semi-continuous function on the tangent bundle. For complex manifolds it is the crucial point in Royden's proof of the equivalence of the two standard definitions of the Kobayashi pseudo-metric. The upper semi-continuity of the Royden-Kobayashi pseudo-norm has been established by Kruglikov for structures that are smooth enough. In [I-R], it is shown that $\CC^{1,\alpha}$ regularity of $J$ is enough. Here we show the following: Theorem. There exists an almost complex structure $J$ of class $\CC^{1\over 2}$ on the unit bidisc $\D^2\subset \C^2$, such that the Royden-Kobayashi seudo-norm is not an upper semi-continuous function on the tangent bundle.

We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.

The aim of this paper is to provide characterizations of the Lebesgue-almost everywhere continuity of a function f : [a, b] $\rightarrow$ R. These characterizations permit to obtain necessary and sufficient conditions for the Riemann integrability of f .

We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, settling the measure-theoretical case of Problem 6 of Barry Simon's list of Schr\"odinger operator problems for the twenty-first century.

The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in \cite{amfifrgi}, together with some application to the semiclassical limit of the Schr\"odinger equation.

Recently, Saleh claimed to have solved `a long standing open question' in Topology; namely, he proved that every almost continuous function is closure continuous (= $\theta$-continuous). Unfortunately, this problem was settled long time ago and even a better result is known.