Dark Energy with Phantom Crossing and the H0 Tension

We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.     

Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

MECHANICAL ANALYSIS OF TOROFLUX

流动环是一款魔术玩具,具有丰富的力学行为。制作流动环时应用了预应力储存技术,使得环内部储存了弹性弯曲变形能。一经外界扰动,流动环会迅速张开,进入一种新的稳定平衡状态;若给张开的流体环输入某种形式的能量,环会合拢,恢复原有的稳定平衡状态。本文从能量的角度对流动环张开与合拢等现象进行力学分析。     

Magnesium-Based Clusters as Building Blocks of Electrolytes in Lithium-Ion Batteries

Superhalogens, owing to their large electron affinity (EA, exceeding those of any halogen atom), play an essential role in physical chemistry as well as new material design. They have applications in hydrogen storage and lithium-ion batteries. Owing to the unique geometries and electronic features of magnesium-based clusters, their potential to form a new class of lithium salts has been investigated here theoretically. The idea is assessed by conducting ab initio computations on Li⁺/Mg_nF_2n+1-2mO_m⁻ compounds (n=2, 3; m=0-3) and analyzing their performance as potential Li-ion battery electrolytes. The Mg₃F₇⁻ cluster, with large electron binding energy (EA of 7.93 eV), has been proven to serve as a building block for lithium salts. It is shown that, apart from high electronic stability, the new superhalogen-based electrolytes exhibit a set of desirable properties, including a large band gap, high electrolyte stability window, easy mobility of the Li⁺, and favorable insensitivity to water.     

Ab initio structure and vibration-rotation dynamics of germylene,GeH2

Accurate structure and potential energy surface of germylene, GeH₂, in its ground electronic state ¹A₁ were determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to sextuple-zeta quality. The Born-Oppenheimer equilibrium structural parameters for the ¹A₁ state are estimated to be r_e(GeH) = 1.5793 Å and ∠_e(HGeH) = 91.19^∘. The term value T_e for the lowest excited electronic state ã³B₁ of GeH₂ is predicted to be 9140 cm^–1. The vibration-rotation energy levels for the ¹A₁ state of the ⁷⁴GeH₂, ⁷⁴GeD₂, ⁷²GeH₂, and ⁷⁰GeH₂ isotopologues were determined using a variational approach and compared with the experimental data. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, spin-orbit, and adiabatic effects for prediction of the structure and vibration-rotation dynamics of the GeH₂ molecule is discussed. © 2019 Wiley Periodicals, Inc.     

Resonance Energy Transfer in a Genetically Engineered Polypeptide Results in Unanticipated Fluorescence Intensity

The fluorescence intensity of a C-terminal acceptor chromophore, N-(7-dimethylamino-4-methyl coumarin (DACM), increased proportionally with 280 nm irradiation of an increasing number of donor tryptophan residues located on a β-sheet forming polypeptide. The fluorescence intensity of the acceptor chromophore increased even as the length of the β-sheet edge approached 256 Å, well beyond the Förster radius for the tryptophan–acceptor chromophore pair. The folding of the peptides under investigation was verified by circular dichroism (CD) and deep UV resonance Raman experiments. Control experiments showed that the enhancement of DACM fluorescence occurred concomitantly with peptide folding. In other control experiments, the DACM fluorescence intensity of the solutions of tryptophan and DACM did not show any enhancement of DACM fluorescence with increasing tryptophan concentrations. Formation of fibrillar aggregates of the substrate peptides prepared for the fluorescence studies was undetectable by thioflavin T (ThT) fluorescence.