Poisson过程作为更新过程的若干新的特征刻画

本文将给出Poisson过程作为更新过程的一系列新的特征刻画．这些刻画是借助于更新过程中所有关键量的条件概率分布或条件期望来表述的．所给的条件是至任一指定时刻发生的抵达敷为已知．     

Reversed‐phase liquid chromatography with electrospray mass detection and 1H and 13C NMR characterization of new process‐related impurities,including forced degradants of Efavirenz: Related substances correlated to the synthetic pathway

In this study, a stability‐indicating reversed‐phase liquid chromatographic electrospray mass spectrometric method was developed and validated for the determination of process‐related impurities and forced degradants of Efavirenz in bulk drugs. Efavirenz was subjected to acid, alkaline hydrolysis, H₂O₂ oxidation, photolysis, and thermal stress. Significant degradation was observed during alkaline hydrolysis, and the degradants were isolated on a mass‐based purification system and characterized by high‐resolution mass spectrometry, positive electrospray ionization tandem mass spectrometry, and ¹H and ¹³C NMR spectroscopy. Accurate mass measurement and NMR spectroscopy revealed the possible structure of process‐related impurities and degradant under stress conditions. The acceptable separation was accomplished on Waters bondapak C₁₈ column (250 mm × 4.6 mm; 5 μm), using 5 mM ammonium acetate and acetonitrile as a mobile phase in a gradient elution mode at a flow rate of 1.0 mL/min. The eluents were monitored by diode array detector at 247 nm and quantitation limits were obtained in the range of 0.1–2.5 μg/mL for Efavirenz, degradants, and process‐related impurities. The liquid chromatography method was validated with respect to accuracy, precision, linearity, robustness, and limits of detection and quantification as per International Conference on Harmonization guidelines.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Fuzzy logic modifications of the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a measurement methodology based on pair-wise comparisons that relies on judgment to derive priority scales. During its implementation, one constructs hierarchies, then makes judgments or performs measurements on pairs of elements with respect to a criterion to derive preference scales, which are then synthesized throughout the structure to select the preferred alternative.One of the areas where the AHP finds application is in the subjective phases of risk assessment (RA), where it is used to structure and prioritize diverse risk factors, including the judgments of experts. Since fuzzy logic (FL) has been shown to be an effective tool for accommodating human experts and their communication of linguistic variables, there has been research aimed at modeling the fuzziness in the AHP (FAHP), and recently the focus of some of that modeling has been with respect to RA.The literature discusses more than one FAHP model, which raises the question as to which are the prominent models and what are their characteristics. In response to this question, we examine three of the most influential FAHP models. The article proceeds as follows. It begins with a brief overview of the AHP and its limitations when confronted with a fuzzy environment. This is followed by a discussion of FL modifications of the AHP. A RA-based likelihood score example is used throughout. The article ends with a commentary on the findings.     

Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis

In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017     

On aspects of damping for a vertical beam with a tuned mass damper at the top

In this paper, the wind-induced, horizontal vibrations of a vertical Euler–Bernoulli beam will be considered. At the top of the beam, a tuned mass damper (TMD) has been installed. The horizontal vibrations can be described by an initial-boundary value problem. Perturbation methods will be applied to construct approximations of the solutions of the initial-boundary value problem, and it will be shown that the TMD uniformly damps the oscillation modes of the beam. In the analysis, it will be assumed that damping, wind-force, and gravity effects are small but not negligible.     

Infinite-Dimensional Hyperbolic Sets and Spatio-Temporal Chaos in Reaction Diffusion Systems in $${\mathbb{R}^{n}}$$

The paper is devoted to a rigorous construction of a parabolic system of partial differential equations which displays space–time chaotic behavior in its global attractor. The construction starts from a periodic array of identical copies of a temporally chaotic reaction-diffusion system (RDS) on a bounded domain with Dirichlet boundary conditions. We start with the case without coupling where space–time chaos, defined via embedding of multi- dimensional Bernoulli schemes, is easily obtained. We introduce small coupling by replacing the Dirichlet boundary conditions by strong absorption between the active islands. Using hyperbolicity and delicate PDE estimates we prove persistence of the embedded Bernoulli scheme. Furthermore we smoothen the nonlinearity and obtain a RDS which has polynomial interaction terms with space and time-periodic coefficients and which has a hyperbolic invariant set on which the dynamics displays spatio-temporal chaos. Finally we show that such a system can be embedded in a bigger system which is autonomous and homogeneous and still contains space–time chaos. Obviously, hyperbolicity is lost in this step. Research partially supported by the INTAS project Attractors for Equations of Mathematical Physics, by CRDF and by the Alexander von Humboldt–Stiftung.     

First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

维布妥昔单抗关键中间体的合成工艺优化

本研究对维布妥昔单抗关键中间体(1)的合成工艺进行了改进与优化。以芴甲氧羰基-L-缬氨酸琥珀酰亚胺酯(2)为起始原料,先后经酯的氨解反应、酰胺化、Fmoc脱保护、酰胺化与酯交换反应制得目标产品1,总收率11.6%,纯度99.2%,产物结构经1H NMR, 13C NMR和HRMS表征。优化后的工艺路线具有反应条件温和、可操作性强、生产过程更安全的特点。在初步放大试验中,首步投料量达百克级别,并已完成三批工艺验证,适合于工业化生产。     

NIR analysis of pharmaceutical samples without reference data: improving the calibration

Using an appropriate set of samples to construct the calibration set is crucial with a view to ensuring accurate multivariate calibration of NIR spectroscopic data. In this work, we developed and optimized a new methodology for incorporating physical variability in pharmaceutical production based on the NIR spectrum for the process. Such a spectrum contains the spectral changes caused by each treatment applied to the component mixture during the production process. The proposed methodology involves adding a set of process spectra (viz. difference spectra between those for production tablets and a laboratory mixture of identical nominal composition) to the set of laboratory samples, which span the wanted concentration range, in order to construct a calibration set incorporating all physical changes undergone by the samples in each step of the production process. The best calibration model among those tested was selected by establishing the influence of spectral pretreatments used to obtain the process spectrum and construct the calibration models, and also by determining the multiplying factor m to be applied to the process spectra in order to ensure incorporation of all variability sources into the calibration model. The specific samples to be included in the calibration set were selected by principal component analysis (PCA). To this end, the new methodology for constructing calibration sets for determining the Active Principle Ingredients (API) and excipients was applied to Irbesartan tablets and validated by application to the API and excipients of paracetamol tablets. The proposed methodology provides simple, robust calibration models for determining the different components of a pharmaceutical formulation.