On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic

The Transverse Momentum and Total Cross Section of E+ E- Pairs in the Z-Boson Region from P Anti-P Collisions at s**(1/2) = 1.8-Tev

The transverse momentum and total cross section of e^+e^- pairs in the Z-boson region of 66<M_{ee}<116 GeV$/c^2$ from $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV are measured using 110 pb^{-1} of collisions taken by the Collider Detector at Fermilab during 1992-1995. The total cross section is measured to be $248 \pm 11$ pb. The differential transverse momentum cross section is compared with calculations that match quantum chromodynamics perturbation theory at high transverse momentum with the gluon resummation formalism at low transverse momentum.Comment: Accepted for Publication in Phys. Rev. Letters, 7 page

Augmented reality for learning mathematics: A pilot study with webxr as an accessible tool

One of the concerns in service mathematics courses, such as calculus for engineering, is students’ interest in these studies. Research suggests that engineering undergraduates’ lack of awareness about the importance of mathematics for their study success and for their careers contributes to their low motivation for mathematics. An approach to increasing student motivation is to take advantage of technological tools to provide students with more engaging learning experiences. Recent studies showed that augmented reality (AR) enhances student engagement, motivation, and knowledge retention. However, implementing AR can be challenging since it can be quite costly and technically complex. The current paper describes a case study in which an AR application was designed and developed using WebXR, in the context of a service mathematics course for teaching calculus. The AR content involves drawing of level curves and the visualization of a volcano and the flow of lava to support students’ learning of directional derivatives. A pilot study was conducted to examine engineering undergraduates’ perceptions of using AR for learning mathematics. Results show that students perceived using AR for learning math as enjoyable and motivating. Students reported that AR content adds value to their classes by making the mathematical concepts clearer and helping them apply what they have learned to real life. However, the AR content did not work well on all mobile phones and all versions of web browsers. Lessons learned from the design and development of AR using WebXR as well as recommendations for future studies are discussed in this paper

Gene-engineered rigidification of membrane lipid enhance the cold inducibility of gene expression in Synechocystis

The exposure of Synechocystis sp.PCC 6803 (hereafter Synechocystis) cells to low temperature induces the expression of a specific set of genes that includes the desA, desD and desB genes for acyl-lipid desaturases. Previously we produced a series of mutants of Synechocystis in which the extent of unsaturation of fatty acids is modified in a step-wise manner. One of these mutants, desA-/desD-, synthesizes only a saturated C16 fatty acid and a monounsaturated C18 fatty acid regardless of the growth temperature, while the wild type synthesizes di-unsaturated and tri-unsaturated C18 fatty acids in addition to the monounsaturated C18 fatty acid (Tasaka et al, 1996). Thys system is suitable to examine the contribution of membrane fluidity/rigidity to the cold-inducible gene expression