We introduce the volume function for C-hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef C-hermitian invertible sheaf. We also give another applications, for example, a generalized Hodge ...

The atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are two well-studied topological indices, which are useful tools in QSPR and QSAR investigations. In this paper, we first obtain explicit formulae for the expected values of ABC and GA indices in random spiro chains, which are graphs of a class of unbranched polycyclic aromatic hydrocarbons. Based on these formulae, we t...

The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties, like very dry initial conditions, a steep pressure gradient and great variation of hydraulic conductivity occur across the wetting front during the infiltration of water.  So, the averaging method applied to compute hydraul...

K e y w o r d s S e c o n d o r d e r impulsive differential system, Singular boundary value problem, Semilinear elliptic problem, Positive solution, Radial solution, Upper solution, Lower solution, Fixed-point index. 1. I N T R O D U C T I O N In this paper , we prove the existence of mul t ip le posi t ive solut ions for a s ingular Gel fand type b o u n d a r y value p rob lem of the followi...

This paper studies the existence of positive solutions for a class of second-order semipositone differential equations with a negatively perturbed term and integral boundary conditions. By using a well-known fixed-point index theorem, some new existence results are derived for the case where nonlinearity is allowed to be sign changing. Several examples are presented to demonstrate the applicati...

In parameter estimation, it is often desirable to supplement the estimates with an assessment of their quality. A new family of methods proposed by Campi et al. for this purpose is particularly attractive, as it makes it possible to obtain exact, nonasymptotic confidence regions under relatively mild assumptions on the noise distribution. A bottleneck of this approach, however, is the numerical...