A novel electrochemical aptasensor for highly sensitive detection of thrombin based on the autonomous assembly of hemin/G-quadruplex horseradish peroxidase-mimicking DNAzyme nanowires

In this work, a new signal amplified strategy was constructed based on isothermal exponential amplification reaction (EXPAR) and hybridization chain reaction (HCR) generating the hemin/G-quadruplex horseradish peroxidase-mimicking DNAzyme (HRP-mimicking DNAzyme) nanowires as signal output component for the sensitive detection of thrombin (TB). We employed EXPAR’s ultra-high amplification efficiency to produce a large amount of two hairpin helper DNAs within a minutes. And then the resultant two hairpin helper DNAs could autonomously assemble the hemin/G-quadruplex HRP-mimicking DNAzymes nanowires as the redox-active reporter units on the electrode surface via hybridization chain reaction (HCR). The hemin/G-quadruplex structures simultaneously served as electron transfer medium and electrocatalyst to amplify the signal in the presence of H₂O₂. Specifically, only when the EXPAR reaction process has occurred, the HCR could be achieved and the hemin/G-quadruplex complexes could be formed on the surface of an electrode to give a detectable signal. The proposed strategy combines the amplification power of the EXPAR, HCR, and the inherent high sensitivity of the electrochemical detection. With such design, the proposed assay showed a good linear relationship within the range of 0.1 pM–50 nM with a detection limit of 33 fM (defined as S/N = 3) for TB.     

带加法白噪声的随机Boussinesq方程组的解的渐近行为

考虑速度和温度同时在加法白噪声扰动下的随机Boussinesq方程组的解的渐近特征.可以接轨道得到该随机方程组的唯一解,并可以验证该解生成随机动力系统,进而证明了该随机动力系统存在随机吸引子.     

Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows

In this article, we shall explore the state of art of stochastic flows to derive an exponential affine form of the bond price when the short rate process is governed by a Markovian regime-switching jump-diffusion version of the Vasicek model. We provide the flexibility that the market parameters, including the mean-reversion level, the volatility rate and the intensity of the jump component switch over time according to a continuous-time, finite-state Markov chain. The states of the chain may be interpreted as different states of an economy or different stages of a business cycle. We shall provide a representation for the exponential affine form of the bond price in terms of fundamental matrix solutions of linear matrix differential equations.     

指数分布场合下步进应力加速寿命试验的Bayes分析

当寿命分布为指数分布时，本文给出了步进应力加速寿命试验的一种新的Ｂａｙｅｓ估计，为计算上的方便，本文还给出一种近似方法，数值例子表明，此方法简便可行。     

A Feigenbaum sequence of bifurcations in the Lorenz model

For some high values of the Rayleigh numberr, the Lorenz model exhibits laminar behavior due to the presence of a stable periodic orbit. A detailed numerical study shows that, forr decreasing, the turbulent behavior is reached via an infinite sequence of bifurcations, whereas forr increasing, this is due to a collapse of the stable orbit to a hyperbolic one. The infinite sequence of bifurcations is found to be compatible with Feigenbaum's conjecture.     

Statistics of strange attractors by generalized cell mapping

It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.     

Application of trilinear SLICING to analyse a single relaxation curve

Determining the time constants and amplitudes of exponential decays from relaxation data is a common task in LF-NMR. In this communication, we present an application of the SLICING algorithm to evaluate its possibilities for solving this problem. The method, originally introduced to compare different samples, is applied here to analyse a single relaxation curve, using the embedding technique. To test this procedure, we acquired data sets from samples of liquids properly separated, and characterized by different relaxation times. The results show a good estimation of parameters, comparable with those obtained applying Marquardt's algorithm, when the components have sufficiently different relaxation times.     

The decay rate for a fractional differential equation

We consider the fractional differential equation

     

Exponential sums on , II

We prove a vanishing theorem for the -adic cohomology of exponential sums on . In particular, we obtain new classes of exponential sums on that have a single nonvanishing -adic cohomology group. The dimension of this cohomology group equals a sum of Milnor numbers.