we consider the number of zeros of the integral $i(h) = oint_{gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. we prove that the number of zeros of $i(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

A consistent loss function for multiclass classification is one such that for any source of labeled examples, any tuple of scoring functions that minimizes the expected loss will have classification accuracy close to that of the Bayes optimal classifier. While consistency has been proposed as a desirable property for multiclass loss functions, we give experimental and theoretical results exhibi...

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

The fuzzy structured element (FSE) theory is a very useful toolfor dealing with fuzzy multi-criteria decision making (MCDM)problems by transforming the criterion value vectors of eachalternative into the corresponding criterion function vectors. Inthis paper, some concepts related to function vectors are firstdefined, such as the inner product of two function vectors, thecosine of the included ...