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 $2[frac{n-1}{2}]+1$.

For an incidence geometry $${\mathcal G}= ({\mathcal P}, {\mathcal L}, {\text {I}})$$ with a linear representation T}_2^*({\mathcal K})$$ , we apply WQH switching to construct non-geometric graph $$\Gamma '$$ cospectral the line $$ of G}$$ . As application, show that for $$h \ge 2$$ and $$0< m < h$$ there are strongly regular graphs parameters $$(v, k, \lambda \mu ) = (2^{2\,h} (2^{m+h}+2^m-2^h...

We present two examples of SUSY mechanics related with Kähler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kähler manifold. The relation of these models with antisymplectic geometry is discussed.