The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a method for turning any knot into the regular planar polygon using only thickness non-decreasing moves. This approach ensures that the algorithm h...

Changes in volume play a significant but often under-emphasized role in governing the stability of proteins in the cell.1!6 When proteins fold from extended unfolded state to a compact or folded native state, there is a concomitant decrease in the characteristic volume occupied by the protein as probed by osmolyte particles, and thus an increase in the volume available to osmolytes or crowding ...

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper we propose a new approach of the fuzzy ranking of generalized trapezoidal fuzzy numbers based on radius of gyration point of centroids. The main advantage of the proposed approach is that the proposed approac...

We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of polymerization), including the leading scaling corrections. Using the expected large-concentration behavior, we extrapolate these low-density expansions outside the ...

Flory Fox, Kurata-Stockmayer, Berry, Inagaki-Suzuki-Kurata, Stockmayer-Fixman and Ahmad-Baloch methods based on the excluded volume theory have been applied to poly(vinyl chloride)-cyclohexanone system to obtain Kq and the radius of gyration. A discussion on the reliability of these methods is given. The Stockmayer-Fixman and Ahmad-Baloch methods are found to be...

Using small angle x-ray scattering from solutions of yeast phosphoglycerate kinase, we have measured the radius of gyration of the enzyme both in the presence and in the abscence of ligands. We find that the radius of gyration decreases by 1.09 +/- 0.34 A upon binding both substrates MgATP and 3-phosphoglycerate to form the ternary complex. Smaller decreases, at the limit of the precision of th...

X-ray diffraction (XRD) technique due to it's strength for providing visualized atomic model of molecules, stands as first in the field of characterization of new synthesized molecules. Here, the analysis of diffraction data on discrete units of new, not yet fairly known structure of molecule $rm C_{52} H_{60} N_4 S_8 Zn_2$ is performed to obtain a quantitative view of the structure of the syst...

We consider the problem of an ideal polymer confined in a droplet. When the droplet radius is smaller than the (unconfined) polymer radius of gyration, the polymer entropy will depend on the droplet shape. We compute the resulting surface free