Tautological rings of stable map spaces

We find a set of generators and relations for the system of extended tautological rings associated to the moduli spaces of stable maps in genus zero, admitting a simple geometrical interpretation. In particular, when the target is Pn, these give a complete presentation for the cohomology and Chow rings in the cases with/without marked points.     

The effect of hydrogen bubbles on the thymol blue velocity measurement technique

This note describes an experimental study of the damaging effect of hydrogen bubbles on the effectiveness of the thymol blue velocity measurement method. Specifically, we document the effect of flow velocity, cathode voltage, and cathode diameter on bubble formation and the quality of the thymol blue pattern. The time of bubble damage, i.e., the interval preceding the destruction of the blue pattern, was measured and reported as a function of flow velocity, cathode voltage, and cathode diameter.     

CPT violation does not lead to violation of Lorentz invariance and vice versa

We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncommutative space–time, which in place of the broken Lorentz symmetry possesses the twisted Poincaré invariance. With such a CPT-violating interaction and the addition of a C-violating (e.g., electroweak) interaction, the quantum corrections due to the combined interactions could lead to different properties for the particle and antiparticle, including their masses.     

Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry

The aim of this paper is to study two problems in the framework of paracontact geometry of dimension \(3\) , namely, the class of parallel symmetric tensor fields of \((0, 2)\) -type and possible Lorentz Ricci solitons. We search for two types of Ricci solitons: the first when its potential vector field is exactly the characteristic vector field \(\xi \) of the paracontact structure and the second when the potential vector field is a paracontact-holomorphic one. For the former case we find all variants of Ricci solitons, expanding, steady and shrinking, and the fact that \(\xi \) is a conformal Killing vector field. A class of examples is completely discussed.     

Corrigendum to “Convexity and concavity constants in Lorentz and Marcinkiewicz spaces” [J. Math. Anal. Appl. 343 (2008) 337-351]

In this note we state the accurate formulas of convexity and concavity constants in Lorentz spaces, correcting the formulas from Kamińska and Parrish (2008) [2].     

The Prandtl number effect near the onset of Bénard convection in a porous medium

This note focuses on Kladias and Prasad's claim that the critical Rayleigh number for the onset of Bénard convection in an infinite horizontal porous layer increases as the Prandtl number decreases, and argues that the critical Rayleigh number (Ra_c) depends only on the Darcy number (Da), as linear stability analysis indicates. The two-dimensional steady-convection problem is then solved numerically to document the convection heat transfer effect of the Rayleigh number, Darcy number, Prandtl number, and porosity. The note concludes with an empirical correlation for the overall Nusselt number, which shows the effect of Prandtl number at above-critical Rayleigh numbers. The correlation is consistent with the corresponding correlation known for Bénard convection in a pure fluid.     

Morphology,structure, and photoactivity of two types of graphene oxide-TiO<Subscript>2</Subscript> composites

Two types of graphene oxide-TiO₂ composites were prepared: one by including graphene oxide flakes in the TiO₂ sol, followed by thermal treatment (GI composite) at 300°C, and the second by including graphene oxide flakes in the calcined (at 500°C) TiO₂ xerogel (GII composite). The composites were characterized by SEM, TEM-EDS, TEM-SADP, STEM-HAADF, HRTEM coupled with FT, XRD, and XPS. Photocatalysis results were fitted to different kinetic models (pseudo-first and pseudo-second kinetics, intraparticle Weber-Morris diffusion, film diffusion, and external mass transfer). The results showed that by introducing graphene oxide flakes in the TiO₂ sol, followed by thermal treatment at 300°C (GI composite), an efficient graphene oxide-TiO₂ catalyst with high specific surface area, heterogeneity, and many graphitized areas can be obtained. Complete crystallization of the composite is not the key issue for the best photoactivity achievement. The rate limiting step in the photocatalytic process is the photooxidation of SA molecules on the TiO₂ surface.