134 research outputs found
Third Order Trace Formula
In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the
existence of higher order spectral shift functions when the unperturbed
self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In
this article, we give a different proof for the existence of spectral shift
function for the third order when the unperturbed operator is self-adjoint
(bounded or unbounded, but bounded below).Comment: 26 page
Bipolar quadripartitioned single valued neutrosophic rough set
Here bipolar quadripartitioned single valued neutrosophic rough (BQSVNR) set is introduced. Some
basic set theoretic terminologies like constant BQSVNR set, subsethood of two BQSVNR sets are shown.
Algebraic operations like union, intersection and complement have also been dened. Dierent types of measure
like similarity measure, quasi similarity measure and distance measures between two BQSVNR sets have been
discussed with their properties. Again various measures of similarity namely distance based similarity measure,
cosine similarity measure, membership function based similarity measure are introduced in this paper. A
medical diagonasis problem has been solved using similarity measure at the end
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