We have all possible parameter of 2-class association schemes having the property that suitable (1,-1)-linear combinations of their association matrices yield the blocks of a Hadamard matrix (H-matrix) of certain classical form of Paley and Williamson. Some 2-class association schemes with the above parameters are identified. The known Hadamard Coherent Configurations or 2-Class Association Schemes (CC's or 2-AS's) listed in Table 2 do not yield H-matrices of new order. However we have forwarded new methods of constructing H-matrices of the forms II and III. The developed technique gives several easy constructions of H-matrix from any 2-AS, whose parameters are given.
In the present paper, we introduce and investigate two new subclasses Q Σ (n, γ, k) and B Σ (n, β , k) of bi-valent functions in the unit disk U. For functions belonging to the classes Q Σ (n, γ, k) and B Σ (n, β , k), we obtain estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |.Mathematics Subject Classification 2010: 30C45, 30C50
We define a new subclass (, , ,) by using an integral operator (). We find a coefficient inequality and using that we derive many sharp results. These results generalize many results which are existing in the literature.
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