GRAPH theoryREACTION-diffusion equationsLYAPUNOV functionsDYNAMICAL systemsThis paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spa...
Rate 51:23 Modular forms and their role in counting combinatorial and topological objects 58:25 The Geometric Structure of Possible Singularities for the Navier-Stokes and Eule 48:05 Wasserstein gradient flows for machine learning 1:02:17 Knot Floer homology of satellite knots 49:59 A survey on...
-norm with a rate of order one, and likewise we observe a first-order rate of convergence for the approximations of m in the \(l^2(l^2)\) -norm. these observed rates are the best possible to be expected since the discretization spaces \(\{\mathbb {v}_{k}^{\pm }\}_{k=1}^8...
1. Then we assume that the expression of V is autonomous, thus X satisfies a time-homogeneous Markov chain defined on Z∗. Assume that the mRNA synthesis rate at X (t) = n − 1, namely the transition rate from X = n − 1 to X = n, is fn ≥ 0. Assume that with n ...
Why is the rate determining step the slowest step? What is meant by the linear-response range of a detector? What do chemists mean by a precipitation reaction? Define the term titration. What is the slope ratio method and how is it used? What does it mean for a substance to be solub...
Define the term effective bandwidth of a filter. Explain how surface area affects the rate of a chemical reaction. Explain the difference between precision and accuracy. Explain why the maximum percent yield should never be above 100%. What rate of crystallization is preferred for ...
In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained. The mean value in short interval is also considered. Keywords: ...
When worms are exposed to pathogens, theskn-1gene is expressed via the activation of the PMK-1 pathway27. To determine whether the resistance of worms to pathogenic bacteria is enhanced,C. eleganswild type (N2) and theskn-1mutant were exposed toS. typhimurium, and the survival rate was mea...
The results of the two experiments indicate that English participants read at a similar rate but with much greater individual differences than the Italian participants. In a 3rd experiment, we extended these results to a vocal reaction time (vRT) task, examining the effect of word frequency. An...
Before writing down the new edge-based compartmental model it is worth introducing and explaining the structure of its equations. The message\(\varTheta \)is monotonically decreasing, and it depends on the density and age of infected neighbours,\(\phi _I(t,a)\), and the hazard rate\(\zet...