Magnetic, magnetocaloric, and magnetotransport properties of RCo1.8Mn0.2 (R=Er, Ho, Dy, and Tb) compounds

The magnetic, magnetocaloric, and magnetotransport properties of RCo_1.8Mn_0.2 (R=Er, Ho, Dy, and Tb) were studied by room temperature X-ray diffraction, magnetization, and resistivity measurements at a temperature interval of 5-400 K and magnetic fields up to 5 T. The Curie temperature of RCo₂ was found to increase significantly when 10% Mn was substituted for Co. The effective paramagnetic moments were found to be in reasonable agreement with their theoretical values. A large magnetoresistance (MR) of Δρ/ρ_o≈−13.5% for R=Ho at T≈153 K for ΔH=5 T has been observed. The maximum relative cooling capacities vary from 467 J/kg at low temperature for R=Er to 202 J/kg at the near room temperature for R=Tb.     

A simple proof for persistence of snap-back repellers

In this article, we show that if f has a snap-back repeller then any small C¹ perturbation of f has a snap-back repeller, and hence has Li-Yorke chaos and positive topological entropy, by simply using the implicit function theorem. We also give some examples.     

Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups

We consider stochastic equations in Hilbert spaces with singular drift in the framework of [G. Da Prato, M. Röckner, Singular dissipative stochastic equations in Hilbert spaces, Probab. Theory Related Fields 124 (2) (2002) 261-303]. We prove a Harnack inequality (in the sense of [F.-Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemannian manifolds, Probab. Theory Related Fields 109 (1997) 417-424]) for its transition semigroup and exploit its consequences. In particular, we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure μ (satisfying some mild integrability conditions). Finally, we prove existence of such a measure μ for noncontinuous drifts.     

Topological free entropy dimension in unital C-algebras

The notion of topological free entropy dimension of n-tuple of elements in a unital C^∗ algebra was introduced by Voiculescu. In the paper, we compute topological free entropy dimension of one self-adjoint element and topological free orbit dimension of one self-adjoint element in a unital C^∗ algebra. We also calculate the values of topological free entropy dimensions of any families of self-adjoint generators of some unital C^∗ algebras, including irrational rotation C^∗ algebra, UHF algebra, and minimal tensor product of two reduced C^∗ algebras of free groups.     

THE CARBUNCLE PHENOMENON IS INCURABLE

Numerical approximations of multi-dimensional shock waves sometimes ex- hibit an instability called the carbuncle phenomenon. Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfactory. It is not known which numerical schemes are affected in which circumstances, what causes carbuncles to appear and whether carbuncles are purely mimerical artifacts or rather features of a continuum equation or model. This article presents evidence towards the latter： we propose that carbuncles are a special class of entropy solutions which can be physically correct in some circumstances. Using ＂filaments＂, we trigger a single carbuncle in a new and more reliable way, and compute the structure in detail in similarity coordinates. We argue that carbuncles can, in some circumstances, be valid vanishing viscosity limits. Trying to suppress them is making a physical assumption that may be false.     

Some controllability results for the 2D Kolmogorov equation

In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the right-hand side of the equation, located on a subdomain, that acts linearly on the state. In the first case, it is the complementary of a strip with axis x and in the second one, it is a strip with axis x.The proof relies on two ingredients. The first one is an explicit decay rate for the Fourier components of the solution in the free system. The second one is an explicit bound for the cost of the null controllability of the heat equation with potential that the Fourier components solve. This bound is derived by means of a new Carleman inequality.     

基于粗糙集理论的多维定性变量约简方法

基于粗糙集理论中的属性约简方法,提出了一种基于信息熵进行多维定性变量的约简方法,并进行了实证分析.     

基于近似熵的随机数检验方法的设计与实现

把近似熵用于密码技术中,设计一种实用的随机数检验方法.该方法可以检测随机序列发生器产生序列的随机性,也可以用于检验密码算法的安全性.通过实验,发现该方法能更全面检验序列的随机特性.     

生物质快速热解油水相溶液超声乳化特性

使用生物油水相溶液与0# 柴油乳化,筛选了四种常用乳化剂和一种助乳化剂进行复配乳化实验,考察了复配乳化剂型号、乳化剂用量、超声作用时间对乳化效果的影响。结果表明,六种乳化液超过30d不破乳,与0# 柴油相比,密度和热值相差不大,含水量3%以下,黏度增大约40%,pH值降低一半。因素分析法表明,水相溶液与柴油质量比和不同的水相溶液对乳化效果影响较大。探讨了乳化机理,认为生物油水相溶液中水、醛、酸、酮等极性组分化合物稳定地被乳化剂包裹在W/O型乳化液液滴中,生物油水相溶液中少量的乙酸乙酯、芳香类化合物等则增溶于非离子乳化剂胶束中。热力学分析表明,超声乳化作用比静置作用具有更大的熵增,乳化液更趋于稳定平衡状态。     

Is breaking of ensemble equivalence monotone in the number of constraints?

Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy between the two ensembles. In Garlaschelli et al. (2017) and Garlaschelli et al. (0000) it was shown that breaking occurs when the constraint is put on the degree sequence (configuration model). It is not known what is the effect on the relative entropy when the number of constraints is reduced, i.e., when only part of the nodes are constrained in their degree (and the remaining nodes are left unconstrained). Intuitively, the relative entropy is expected to decrease. However, this is not a trivial issue because when constraints are removed both the microcanonical ensemble and the canonical ensemble change. In this paper a formula for the relative entropy valid for generic discrete random structures, recently formulated by Squartini and Garlaschelli, is used to prove that the relative entropy is monotone in the number of constraints when the constraint is on the degrees of the nodes. It is further shown that the expression for the relative entropy corresponds, in the dense regime, to the degrees in the microcanonical ensemble being asymptotically multivariate Dirac and in the canonical ensemble being asymptotically Gaussian.