For any gentle algebra $Lambda=KQ/langle Irangle$, following Kalck, we describe the quiver and the relations for its Cohen-Macaulay Auslander algebra $mathrm{Aus}(mathrm{Gproj}Lambda)$ explicitly, and obtain some properties, such as $Lambda$ is repre
sentation-finite if and only if $mathrm{Aus}(mathrm{Gproj}Lambda)$ is; if $Q$ has no loop and any indecomposable $Lambda$-module is uniquely determined by its dimension vector, then any indecomposable $mathrm{Aus}(mathrm{Gproj}Lambda)$-module is uniquely determined by its dimension vector.
Let $K$ be an algebraically closed field. Let $(Q,Sp,I)$ be a skewed-gentle triple, $(Q^{sg},I^{sg})$ and $(Q^g,I^{g})$ be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra $KQ^{sg}
/< I^{sg}>$ is singularity equivalent to $KQ/< I>$. Moreover, we use $(Q,Sp,I)$ to describe the singularity category of $KQ^g/< I^g>$. As a corollary, we get that $mathrm{gldim} KQ^{sg}/< I^{sg}><infty$ if and only if $mathrm{gldim} KQ/< I><infty$ if and only if $mathrm{gldim} KQ^{g}/< I^{g}><infty$.
Helium bubbles nucleation and growth in metals or metal tritide is a long-standing problem attracting considerable attention in nuclear industry but the mechanism remains indistinct and predicting the growth rate of helium bubble is inexistence still
up to new. Here, the rate of helium bubbles nucleation and growth in metal tritide is developed based on a dynamical model, which describes the diameter of helium bubbles increasing linearly as t**(1/3) in titanium tritide at room temperature, agreeing quite well with the experimental phenomenon. The way of reducing storage temperature from 300 to 225 K or increasing the helium atoms diffusion barrier from 0.81 to 1.1 eV can effectively restrain bubbles growth and prolong lifetime of titanium tritide more than 4 times, which provides a useful reference to relevant experiment exploration and applications. This model also can be used to predict lifetime of new tritium-storage materials and plasma facing materials in nuclear industry.
The thermal stability of $alpha$-, $beta$-, 6,6,12-graphyne and graphdiyne was studied by a statistic model, which was seriously tested by classical molecular dynamics simulations. By first-principles calculations of related potential energy curves,
the model predicts that all the lifetime of free-standing single layer graphynes considered is more than 10$^{44}$ years at room temperature. When the temperature gets up to 1000 K, they are still very stable, but quickly turn into graphene if the temperature is about 2000 K
We propose a scheme for realizing the continuously tunable spectrum based on monatomic carbon chains. By hybrid density functional calculations, we first show that the direct band gap of monatomic carbon chains change continuously from 1.58 to 3.8 eV
as strain is applied from -5 to 10% to the chain, with separated Van Hove singularity peaks enhanced. To realize this tunability, a realistic stretching device is proposed by contacting the chain with graphene sheets, which can apply up to 9% elongation to the chain, yielding tunable light-emitting wavelengths from 345 to 561 nm.
A new set of nonlocal boundary conditions are proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive eq
uations are performed on a nested set of domains, and the results are discussed.
In this paper, we demonstrate the LHC discovery potential of new charged vector boson $W_1^{pm}$ predicted by the Minimal Higgsless model in the process $ppto W_1^{pm}qq^{prime}to W^{pm}Z^0qq^primeto ell^{pm}ell^+ell^- u qq^{prime}(ell=e,mu)$ by anal
yzing the generator level events of the signal and backgrounds. The generator for the signal $pp to {W_1}^{pm}qq^primeto W^{pm}Z^0qq^prime$ at tree level is developed with the Minimal Higgsless model and then interfaced with PYTHIA for the parton showers and hadronization. The backgrounds are produced with PYTHIA and ACERMC. We give integrated luminosities required to discover 5$sigma$ signal as a function of $W_1^{pm}$ mass.
We have investigated the tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals, based on the Pockels effect. The positive and negative lateral shifts could be easily controlled by adjusting
the permittivity tensor, which is modulated by the external applied electric field. An alternative way to realize the polarization beam splitter was also proposed by the polarization-dependent lateral shifts. Numerical simulations for Gaussian-shaped incident beam have demonstrated the above theoretical results obtained by stationary phase method. All these phenomena have potential applications in optical devices.
We established a physically utilizable Bell inequality based on the Peres-Horodecki criterion. The new quadratic probabilistic Bell inequality naturally provides us a necessary and sufficient way to test all entangled two-qubit or qubit-qutrit states
including the Werner states and the maximally entangled mixed states.
