A family of minimax rates for density estimators in continuous time

In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes of processes including the Gaussian ones     

Specific Deuteration in Patuletin and Related Flavonoids via Keto–Enol Tautomerism: Solvent‐ and Temperature‐Dependent 1H‐NMR Studies

An H/D exchange process in patuletin ( 1 ) and its derivatives in D‐donor solvents (e.g., CF₃COOD), which occurs regioselectively at C(8) was observed for the first time during NMR studies. The effect of substituents and temperature on the deuteration of various flavonoids (see Fig. 1) which include apigenin, chrysin, galangin, kaempferol, luteolin, morin, myricetin, patuletin, patulitrin, and quercetin, as well as derivatives of patuletin was examined extensively under NMR conditions. The rate constant of deuteration at C(8) of patuletin ( 1 ) and two flavones, luteolin ( 3 ) and apigenin ( 12 ), was also determined in CF₃COOD. The D‐atom was introduced into the flavonoids via a keto–enol tautomerism (Scheme 1). During these studies, monodeuterated patuletin was also obtained as a new compound. The examined flavonoids have been reported to possess significant pharmacological activities, and their deuterated derivatives would be of importance for the identification and quantification of these compounds in biological matrices.     

X-ray calculations for a NLTE Ar plasma

A model is developed to calculate emission spectrum of non-local thermodynamic equilibrium(NLTE) plasmas. The Collisional-Radiative model is adopted for non-LTE population calculations. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree-Fock-Slater self-consistent-field method is used to calculate electron wave functions. The present model is applied to the calculation of emissivity from a Ar plasma. The features of the spectra are in good agreement with those calculated by other theoretical models, but the data of the integrated emissivity differ by a factor 2～8.     

The ‘Temperature Integral’ — Its use and abuse

This paper first reviews the history of the temperature dependence of reaction rate in reaction kinetics. The various equations which are in use today for expressing this dependence were delineated by van't Hoff almost one hundred years ago. Since an exponential form best describes this dependence for most thermal analysis reactions and, due to the fact that the simple Arrhenius equation (with a temperature-independent preexponential factor) has traditionally been used for this purpose, the mathematically intractable temperature integral often has become a necessary evil in the analysis of thermal analysis kinetics. Methods which avoid the temperature integral in kinetics analysis are discussed. The merits of various evaluations and approximations for the temperature integral are described and assessed in this paper.     

The rate of convergence of q-Bernstein polynomials for

In the note, we obtain the estimates for the rate of convergence for a sequence of q-Bernstein polynomials {B_n,q(f)} for 0<q<1 by the modulus of continuity of f, and the estimates are sharp with respect to the order for Lipschitz continuous functions. We also get the exact orders of convergence for a family of functions , and the orders do not depend on α, unlike the classical case.     

On the rate of convergence to equilibrium in the Becker-Döring equations

We provide an explicit rate of convergence to equilibrium for solutions of the Becker-Döring equations using the energy/energy-dissipation relation. The main difficulty is the structure of equilibria of the Becker-Döring equations, which do not correspond to a Gaussian measure, such that a logarithmic Sobolev-inequality is not available. We prove a weaker inequality which still implies for fast decaying data that the solution converges to equilibrium as e^−ct1/3.     

Simultaneous approximation for Bézier variant of Szász-Mirakyan-Durrmeyer operators

We study the rate of convergence in simultaneous approximation for the Bézier variant of Szász-Mirakyan-Durrmeyer operators by using the decomposition technique of functions of bounded variation.     

树上秘密共享体制的信息率

研究以树G为通道结构的秘密共享体制的最优信息率ρ（G）。得到了ρ（G）＝2／3的要条件。证明了ρ（G）不会介于实数区间（3／5，2／3）中，给出了以树G的阶数表示的ρ（G）的下界，求出两类具有某种结构的树的最优信息率。     

Rate enhancement of PFP sulfonate ester aminolysis by chloride salts in organic and aqueous media

We report here, a method of accelerating the rate of aminolysis of PFP sulfonates to yield sulfonamides using tetrabutylammonium salts. We have previously explored the utility of employing PFP sulfonates in the formation of sulfonamides; however we demonstrate here the advantages of combining the existing methodology with a revised protocol which allows the diversity within both the sulfonate ester and the amine to be extended.     

Rate analysis of ZF receiver for uplink cell-free massive MIMO systems with D2D communications

This paper proposes a transmission structure of zero forcing (ZF) receiver for uplink cell-free massive multiple-input multiple-output (MIMO) systems with device-to-device (D2D) communications, followed by a rate analysis. We assumed that D2D users (DUEs) can utilize orthogonal radio resources to improve the efficiency of the scarce utilization or repurpose the time–frequency-spectrum resources currently used by the cell-free users (CFUEs). Assuming that the imperfect channel state information (CSI) is realizable, after that, the use-and-forget bounding technique is then used to respectively obtain the closed-form expressions of the CFUEs and DUEs, which provide the lower bounds on the ergodic approximate realizable rate of both communication links. First, we calculate the minimum-mean-square error (MMSE) estimation for all channels. Then, the derived results of the achievable uplink sum rate provide us with a tool that enables us to explain how some important parameters, such as the number of access points (APs)/CFUEs, each AP/CFUE/antenna, and the density of DUEs, affect system performance, highlighting the significance of cooperation between cell-free massive MIMO and D2D communication.