Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite set of points on the base curve.

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

dx(t) dt = v(x(t)), t≥ 0, x(0) = x0 ∈G, starting at a given point x(0) = x0 ∈ G and to develop statistical tests for the hypothesis that the integral curve reaches a specified set Γ ⊂ G. We develop an estimation procedure based on a Nadaraya– Watson type kernel regression estimator, show the asymptotic normality of the estimated integral curve and derive differential and integral equations for ...

The number of isolated intersections between a smooth curve in Eu-clidean space and an arbitrary hyperplane can be majorized by a weighted sum of integral Frenet curvatures of the curve. In the complex Hermitian space one can derive a similar result for holomorphic curves but with much better weights. The proof of this result is based on a generalizationof the Milnor{FF ary theorem for complex ...

This prospective study assessed whether respiratory variations in velocity time integral, peak blood flow velocity and non-invasive pleth variability index are useful measurements in infants undergoing congenital heart surgery and determined threshold values that may help guide fluid administration. In 27 infants receiving mechanical ventilation, of mean (SD) weight 10.4 (6.3) kg, 13 increased ...

Understanding vector fields resulting from large scientific simulations is an important and often difficult task. Integral curves, curves that are tangential to a vector field at each point, are a powerful visualization method in this context. Application of integral curve-based visualization to very large vector field data represents a significant challenge due to the non-local and data-depend...

We prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta divisor of an integral, nodal curve at an arbitrary point. We also suggest a general formula for the multiplicity of the theta divisor of a singular, integral curve at a point and present some evidence that this formu...