Szpiro’s Conjecture asserts the existence of an absolute constant K > 6 such that if E is an elliptic curve over Q, the minimal discriminant ∆(E) of E is bounded above in modulus by the K-th power of the conductor N(E) of E. An immediate consequence of this is the existence of an absolute upper bound upon min {vp(∆(E)) : p | ∆(E)}. In this paper, we will prove this local version of Szpiro’s Con...

In this paper, we study the minimization problem on the L∞-norm functional over the divergence-free fields with given boundary normal component. We focus on the computation of the minimum value and the classification of certain special minimizers including the so-called absolute minimizers. In particular, several alternative approaches for computing the minimum value are given using Lq -approxi...

There has been a long-standing debate about the mechanisms underlying the perception of stereoscopic depth and the computation of the relative disparities that it relies on. Relative disparities between visual objects could be computed in two ways: (a) using the difference in the object's absolute disparities (Hypothesis 1) or (b) using relative disparities based on the differences in the monoc...

The article considers the peculiarities of philosophical understanding and definition concept "absolute" in works Russian philosopher Y. Golosovker. We suggest a consistent analysis original creativity theory researcher place term "imaginative absolute". is considered as unique construct, which marked by synthesis culturological, aesthetic epistemological orientations author. imaginative absolu...

For a given quadratic equation with any number of unknowns in any free group F , with right-hand side an arbitrary element of F , an algorithm for solving the problem of the existence of a solution was given by Culler [8] using a surface method and generalizing a result of Wicks [46]. Based on different techniques, the problem has been studied by the authors [11; 12] for parametric families of ...

In conversations between native speakers, words such as ‘same’ and ‘identical’ do not usually cause much difficulty. We take it for granted that others use them with the same sense as we do. If it is unclear whether numerical or qualitative identity is intended, a brief gloss such as ‘one thing not two’ for the former or ‘exactly alike’ for the latter removes the unclarity. In this paper, numer...

During recent years, we have observed a rapidly growing interest in the design and fabrication of novel types of photonic-crystal structures possessing large absolute band gaps. The study of various geometries of three-dimensional photonic crystals and different ways to enlarge their absolute band gaps is a key issue in the physics of periodic dielectric structures, where different polarization...