Let X be a variety of logarithmic general type, defined over a number field K. Let S be a finite set of places in K and let OK,S be the ring of S-integers. Suppose that X is a model of X over Spec OK,S . As a natural generalizasion of theorems of Siegel and Faltings, It was conjectured by S. Lang and P. Vojta ([Vojta], conjecture 4.4) that the set of S-integral points X (OK,S) is not Zariski de...

On the basis of a fully discrete trigonometric Galerkin method and two grid iterations we propose solvers for integral and pseudodifferential equations on closed curves which solve the problem with an optimal convergence order ‖uN − u‖λ ≤ cλ,μNλ−μ‖u‖μ, λ ≤ μ (Sobolev norms of periodic functions) in O(N log N) arithmetical operations.

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...

We construct a stacky curve of genus 1 / 2 1/2 </inline-for...

We present two new methods for visualizing cross-sections of 3D diffusion tensor magnetic resonance imaging (DTI) volumes. For each of the methods we show examples of visualizations of the corpus callosum in the midsagittal plane of several normal volunteers. In both methods, we start from points sampled on a regular grid on the cross-section and, from each point, generate integral curves in bo...