Multiple Coverings of the Plane with Triangles

We prove that any 43-fold covering of the plane with translates of a triangle can be decomposed into two coverings.     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

γ-LiAlO2晶体生长、改性和热学性质研究

采用快速提拉法生长出了透明、完整的γ-LiAlO2晶体,但是晶体的高熔点和易挥发性限制了γ-LiAlO2晶体质量.采用气相传输平衡法(vapor transport equilibration technique,VTE)工艺对晶体改性,半高宽(FWHM)值从116.9arcsec降至44.2arcsec,继续升高VTE处理温度至1300℃,FWHM值反而升高至55.2arcsec.快速提拉法生长出来晶体,[100]方向和[001]方向的热膨胀系数分别为17.2398×10-6/K,10.7664×10-6/K.经过三步VTE处理后[100]和[001]方向热膨胀系数降至16.6539×10-6/K和10.1784×10-6/K.     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

How many black holes fit on the head of a pin?

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations. Fourth Award in the 2007 Essay Competition of the Gravity Research Foundation.     

DSC analysis of strengthening precipitates in ultrafine Al–Mg–Si alloys

Equal channel angular pressing (ECAP) was carried out on solution annealed samples of Al–Mg–Si–Zr and Al–Mg–Si–Zr–Sc alloys to achieve a substantial grain refinement of the materials. Post ECAP aging was then investigated on the ultrafine grained alloys by DSC and TEM analyses. DSC scans were carried out with heating rates ranging from 5 to 30°C min^–1. Peak identification was performed by the support of literature information and TEM analyses. Precipitation kinetics revealed to be similar for both alloys but the Sc-free alloy showed a recrystallization peak at temperatures ranging from 310 to 340°C, depending on the strain accumulated during ECAP. On the contrary, the Sc-containing alloy showed a greater grain stability. Analyses of peak positions and of activation energies as a function of ECAP passes experienced by the samples revealed large modifications of precipitation kinetics in the ultrafine-grained alloys with respect to the coarse-grained materials.     

Algebro-Geometric Approach in the Theory of Integrable Hydrodynamic Type Systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. The class of symmetric hydrodynamic type systems is defined and the calculation of the associated Riemann surfaces is greatly simplified for this class. Many interesting and physically motivated examples are investigated.