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In this paper, we have discussed quotient structures of KU-algebras by using the concept of intersection soft ideals. In general, the soft sets are parameterized families of sets that are used to dealt with uncertainty. In particular, We... more
In this paper, we have discussed quotient structures of KU-algebras by using the concept of intersection soft ideals. In general, the soft sets are parameterized families of sets that are used to dealt with uncertainty. In particular, We have given the fundamental homomorphism theorem of quotient KU-algebras. A characterization of commutative quotient KU-algebras, implicative quotient KU-algebras and positive implicative quotient KU-algebras are also presented.
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Herein, we report the fluoride anion sensing properties of a commercially available and inexpensive organic compound, isatin, which is found to be a highly selective and sensitive sensor. In naked-eye experiments, by addition of fluoride... more
Herein, we report the fluoride anion sensing properties of a commercially available and inexpensive organic compound, isatin, which is found to be a highly selective and sensitive sensor. In naked-eye experiments, by addition of fluoride anions, isatin shows a dramatic color change from pale yellow to violet at room temperature, while the addition of other anions, i.e. $\mathrm{Cl}^-,$$\mathrm{Br}^-,\mathrm I^-,\mathrm{ClO}_4^-,{\mathrm H}_2\mathrm{PO}_4^-\,\mathrm{and}\,\mathrm{PF}_6^-,$did not induce any colour change. Additionally, recognition and titration studies have also been done through UV/Vis spectroscopy. Isatin displayed a new absorption band at 533 nm after the addition of fluoride anions, which is presumably due to acid-base interaction between isatin and fluoride anions, while other anions did not trigger noticeable spectral changes. The detection limit was observed to be 0.367 ppm. DFT calculations were also performed to further explain the behavior of receptor 1 tow...
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We establish an interpolation theorem for entire functions, in the case of an unbounded set of interpolation, which generalizes a series known results.
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The counting polynomials are useful in topological description of benzenoid structures. It also helps to describe its topological indices by virtue of quasi-orthogonal cuts of the edge strips in the polycyclic graphs. In this article we... more
The counting polynomials are useful in topological description of benzenoid structures. It also helps to describe its topological indices by virtue of quasi-orthogonal cuts of the edge strips in the polycyclic graphs. In this article we give a complete description of the Omega and the Sadhana polynomial of the nanotube C 4 C 6 C 8 and provide its mathematical proof.
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In this paper, we connect $(\alpha, \beta)$ union soft sets and their ideal related properties with $KU$-algebras. In particular, we will study $(\alpha, \beta)$-union soft sets, $(\alpha, \beta)$-union soft ideals, $(\alpha,... more
In this paper, we connect $(\alpha, \beta)$ union soft sets and their ideal related properties with $KU$-algebras. In particular, we will study $(\alpha, \beta)$-union soft sets, $(\alpha, \beta)$-union soft ideals, $(\alpha, \beta)$-union soft commutative ideals and ideal relations in $KU$-algebras. Finally, a characterization of ideals in $KU$-algebras in terms of $(\alpha, \beta)$-union soft sets have been provided.
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In this article we define an extension of KU-algebra and call it an extended KU-algebra. We study basic properties of this extended KU-algebra and its ideals. We also discuss the relations between extended KU-algebras and KU-algebras.
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In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤ n-2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that... more
In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤ n-2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.
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In this paper, we introduce inclusion ideals I(H) associated to a special class of non uniform hypergraphs H(gC; ɛ; d), namely, the uniformly increasing hypergraphs. We discuss some algebraic properties of the inclusion ideals. In... more
In this paper, we introduce inclusion ideals I(H) associated to a special class of non uniform hypergraphs H(gC; ɛ; d), namely, the uniformly increasing hypergraphs. We discuss some algebraic properties of the inclusion ideals. In particular, we give an upper bound of the Castelnouvo-Mumford regularity of the special dual ideal I[*](H).
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In this paper, we have defined ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings by defining the relation “≤” in ordered Γ semiring S as a≤b if a+x=b for any a,b,x∈S. By using this relation we have shown that ordered... more
In this paper, we have defined ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings by defining the relation “≤” in ordered Γ semiring S as a≤b if a+x=b for any a,b,x∈S. By using this relation we have shown that ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings are generalization of quasi-ideals and bi-ideals in ordered semirings. Properties of many types of ordered Γ-ideals including (semi)prime, (strongly) irreducible, and maximal ordered quasi-Γ-ideals and ordered bi-Γ-ideals in ordered Γ-semirings S have been studied.