Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$\mathrm{<font\; color="red">U</font>}\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$\mathrm{<font\; color="red">U</font>}\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

U6 is unsuitable for normalization of serum miRNA levels in patients with sepsis or liver fibrosis

MicroRNA (miRNA) levels in serum have recently emerged as potential novel biomarkers for various diseases. miRNAs are routinely measured by standard quantitative real-time PCR (qPCR); however, the high sensitivity of qPCR demands appropriate normalization to correct for nonbiological variation. Presently, RNU6B (U6) is used for data normalization of circulating miRNAs in many studies. However, it was suggested that serum levels of U6 themselves might differ between individuals. Therefore, no consensus has been reached on the best normalization strategy in ‘circulating miRNA''. We analyzed U6 levels as well as levels of spiked-in SV40-RNA in sera of 44 healthy volunteers, 203 intensive care unit patients and 64 patients with liver fibrosis. Levels of U6 demonstrated a high variability in sera of healthy donors, patients with critical illness and liver fibrosis. This high variability could also be confirmed in sera of mice after the cecal ligation and puncture procedure. Most importantly, levels of circulating U6 were significantly upregulated in sera of patients with critical illness and sepsis compared with controls and correlated with established markers of inflammation. In patients with liver fibrosis, U6 levels were significantly downregulated. In contrast, levels of spiked-in SV40 displayed a significantly higher stability both in human cohorts (healthy, critical illness, liver fibrosis) and in mice. Thus, we conclude that U6 levels in the serum are dysregulated in a disease-specific manner. Therefore, U6 should not be used for data normalization of circulating miRNAs in inflammatory diseases and previous studies using this approach should be interpreted with caution. Further studies are warranted to identify specific regulatory processes of U6 levels in sepsis and liver fibrosis.     

高中有机化学教学中提升核心素养并体味科学价值*——以“乙炔的化学性质”为例

介绍了“乙炔的化学性质”的教学设计思路,展现了如何利用创新实验、丰富素材和问题讨论,帮助学生理解有机物性质和结构之间的关系。主要涉及以下几个环节:(1)通过课前自主预习,从乙炔与乙烯的相似性入手,预测乙炔的性质,了解乙炔的实验室制法;(2)结合2个创新分组实验“基于井穴板的微型化气体连续制备和性质检验装置”“利用真空输液瓶、微型样品瓶和注射器的密闭气体微型反应装置”,教师和学生一起巩固了乙炔的实验室制法,验证了预测的化学性质,丰富了对乙炔性质的感性认知,发现了“乙炔不能使酸性K₂Cr₂O₇溶液褪色”的异常现象;(3)从尝试解释异常现象入手,教师和学生一起从键能、加成比例、聚合后主链结构等多个角度探讨了乙炔与乙烯性质和结构的差异,建立起有机物官能团与性质关系的认知模型;(4)通过尝试利用模型解释2000年诺贝尔化学奖“导电高分子”和2017年度国家自然科学成果一等奖“AIE聚集诱导发光材料” 的结构、性质与应用,教师和学生一起提升了对认知模型的理解建构,感悟了科学研究的乐趣,体会化学科学在促进人类文明发展和社会进步中的重要作用。     

Study on structure and properties of transition metal doped BiF3 by first-principles

Structure and physical properties of BiF₃ doped with M=Cr, Cu, Fe, Mn, Ni, Ti, V and Co are calculated by the DFT+U method. Effect of metal doping on the electronic structure and optical response of host materials BiF₃ is investigated systematically. New energy levels are formed and located within the band gap, which could decrease the recombination rate of e⁻/h⁺ pairs. Furthermore, transition metal doping extends the optical absorption of BiF₃ to the visible spectral region.     

Trace element determinations in shale oil products by neutron activation

Neutron activation offers some important advantages for the determination of selected trace elements in shale oil products. This paper gives techniques and results of a study of crude shale oil and naphtha, heavy distillate, and wax products of shale oil. The elements determined were Al, As, Au, Br, Ce, Cl, Co, Cr, Fe, Hg, I, K, Mn. Mo, Na, S, Sb, Se, V, and Zn. Some elements (Mn, Na, As) tend to accumulate in heavier fractions, whereas chlorine and iodine are concentrated in the more volatile fractions. The volatility of sulphur compounds in the shale oil products appears to be essentially uniform, with some tendency toward accumulation in distillation residues. The tendency for the trace elements to accumulate in the waxes that precipitated from cooled heavy distillates was very low.     

Image recovery via total variation minimization and related problems

Summary. We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails. Received December 21, 1995 / Revised version February 26, 1996     

Multi-modal calculations of prompt fission neutrons from 238U（n,f） at low induced energy

Properties of prompt fission neutrons from UP>238UP>U(n, f) are calculated for incident neutron energies below 6 MeV using the multi-modal model, including the prompt fission neutron spectrum, the average prompt fission neutron multiplicity, and the prompt fission neutron multiplicity as a function of the fission fragment mass υ(A) (usually named “sawtooth” data) The three most dominant fission modes are taken into account. The model parameters are determined on the basis of experimental fission fragment data. The predicted results are in good agreement with the experimental data.     

Strong commutativity preserving maps in prime rings with involution

Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:S→A is an additive map such that [f(x),f(y)]=[x,y] for all x,y∈S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ:S→Z(A) such that f(x)=x+μ(x) for all x∈S or f(x)=-x+μ(x) for all x∈S.     

Small polaron electron transport in reduced CeO2 single crystals

An investigation of the electrical properties of reduced ceria, CeO_2?x, carried out on single crystals, shows that CeO_2?x provides one of the clearest examples of hopping conduction and the small polaron mechanism. Included are conductivity and Seebeck coefficient measurements at constant x, obtained by sealing off the specimen chamber after reduction. The Seebeck coefficient is independent of temperature, suggesting that the number of carriers is constant. On the other hand, the mobility is activated, with activation energy E_h = 0.40 eV at small x and increasing to 0.52 eV at x = 0.25. The results for the mobility preexponential are consistent with the adiabatic theory of small polaron behavior. A puzzling feature of the Seebeck data as a function of x is that, for low x, the data fit the well-known Heikes formula, without a degeneracy factor of 2 for spin. Nevertheless, these data are interpreted to show that the proportion of mobile carriers decreases as x increases, presumably because of the presence of short-range ordered configurations which immobilize some carriers.     

U(1) symmetry in the current algebra and N-fermionic massless Thirring model

Local U(1) symmetry in current algebra constructed by fermions has been found. The symmetry is related to the simplest q-deformation of N-fermions. We give the physical interpretation through the N-fermionic massless Thirring model. The Bethe ansatz wavefunction is also given.