1 Characteristic 0 We start with a basic question: given a polynomial f ∈ C[z1, · · · , zn] with a singularity at 0, how can we measure the “singularness” of this polynomial in a precise way? In other words: we can look at various singularities and see intuitively that some singularities are worse than others. For instance, it feels like a transverse self-intersection is probably not as bad as ...

Several experimental and numerical studies have shown that turbulent motions in circular pipe flow near transitional Reynolds numbers may not persist forever, but may decay. We study the properties of these decaying states within direct numerical simulations for Reynolds numbers up to 2200 and in pipes with lengths equal to 5, 9, and 15 times the diameter. We show that the choice of the ensembl...

We prove a new isoperimetric inequality which relates the area of a multiply connected curved surface, its Euler characteristic, the length of its boundary, and its Gaussian curvature.

The electron microscope has been used to determine the characteristic dimensions and the distribution of the dry mass in bull spermatozoa. The most important result is that all characteristic data are occurring in logarithmic distributions. Furthermore, no correlation between such parameters as head weight and tail weight or head length and tail length was found. The occurrence in logarithmic d...

The entropic force exerted by the Brownian fluctuations of a grafted semiflexible polymer upon a rigid smooth wall are calculated both analytically and by Monte Carlo simulations. Such forces are thought to play an important role for several cellular phenomena, in particular, the physics of actin-polymerization-driven cell motility and movement of bacteria like Listeria. In the stiff limit, whe...

190 Russian texts – letters and poems by three different authors – are analyzed as to their word length. The basic question concerns the quantitative classification of these texts as to authorship or as to text sort. By way of multivariate analyses it is shown that word length is a characteristic of genre, rather than of authorship. 1 Word Length and the Quantitative Description of Text(s) and ...

This study focuses on the length estimation of ballistic targets based on the full-polarization range profiles measured by the wideband full-polarization radar system. Firstly, the mathematical model of full-polarization range profiles is introduced, and the full-polarization range profiles characteristics of typical ballistic targets are analyzed by using the microwave anechoic chamber measure...

We study the effect of confinement on glassy liquids using random first order transition theory as a framework. We show that the characteristic length scale above which confinement effects become negligible is related to the point-to-set length scale introduced to measure the spatial extent of amorphous order in supercooled liquids. By confining below this characteristic size, the system become...

The near-critical interfacial entropy profile is calculated in the one-loop approximation of renormalized field theory. shape broadened by fluctuations and goes beyond mean-field coupling between order parameter. excess heat capacity are using profile. interface creates corrections to χ/L, where $\xi$ correlation length, L a characteristic length system. These results discussed relation finite-...

The study of clustering processes is fundamentally significant in hydraulic engineering to comprehend the interactions between turbulence and particles. Previous studies on bubble clustering were carried out in plunging jets, hydraulic jumps and dropshafts. The present paper focuses on the bubble clustering process in a large-size dropshaft, and three criteria for cluster identification were ap...