The group reduction for bounded cosine functions on UMD spaces

It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)^1/2 generates a bounded C ₀-group. The proof uses a transference principle for cosine functions.      

Solving fractional integral equations by the Haar wavelet method

Haar wavelets for the solution of fractional integral equations are applied. Fractional Volterra and Fredholm integral equations are considered. The proposed method also is used for analysing fractional harmonic vibrations. The efficiency of the method is demonstrated by three numerical examples.     

Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in R^d${\mathbb{R}}^d$ (d≥1$d\ge 1$ and d≤3$d\le 3$, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation.     

Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative

The aim of this paper is to present the analytical solutions corresponding to two types of unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative between two parallel plates. The fractional calculus approach is used in solving the problems. The velocity distributions are determined by means of discrete Laplace transform and finite Fourier sine transform. The obtained results indicate that some well known solutions for the generalized second grade fluid, the generalized Maxwell fluid as well as the ordinary Oldroyd-B fluid appear as the limiting cases of the presented results.     

以反应机理为主线的芳烃亲电取代反应教学设计

在缩减大学课时而不降低教学效果的背景下,如何保证有机化学的教学质量是新时期亟需研究和解决的课题之一。在大学有机化学知识中,不同反应具备相似的反应机理的例子很多,如Friedel-Crafts（烷基化、酰基化）反应、卤化反应、磺化反应、硝化反应、Hoesch反应等都具有相似的亲电取代机理,论文展示了以反应机理为抓手,可运用较少课时讲授的该部分内容的教学设计。同时总结了芳烃亲电取代反应知识的学习方法。     

Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure

The forced vibration analysis of nonhomogeneous thermoelastic, isotropic, thin annular disk under periodic and exponential types of axisymmetric dynamic pressures applied on its inner boundary has been performed and analytical benchmark solution has been obtained. The material has been assumed to have inhomogeneity according to a simple power law in the radial coordinate. The present analysis has been worked out in the context of generalized theory of thermoelasticity with one relaxation time. The two coupled partial differential equations have been clubbed and solved by employing Laplace transform technique to obtain the solution for radial displacement and temperature change in the space domain. In order to obtain the solution in physical domain, the inversion of the transform has been carried out by using residue calculus. The radial displacement, radial stress, circumferential stress, and temperature change have been computed numerically for copper material annular disk. The numerically computed results have been presented graphically to demonstrate the effect of two different types of dynamic pressure in reference to homogeneous and nonhomogeneous material disk. The results for homogeneous material disk have been deduced and validated with that available in literature. The closed-form solution obtained here is interesting and allows further parametric studies of nonhomogeneous structures.     

新建本科院校仪器分析教学的改革与探索

仪器分析课程是化学、药学、食品等专业的一门专业基础课,对培养符合产业界和社会需要的专门人才起着非常重要的作用。基于新建本科院校的功能定位,对仪器分析课程教学改革的跟进具有重要的意义。以重庆第二师范学校为例,在加强与当地企业联合制定教学内容、引入新型“翻转课堂”教学模式,结合企业考核员工指标,注重过程评价方式等方面进行了初步的探讨。期望可以为培养实践能力较强的应用型人才开辟新的路径。     

An incentivized early remediation program in Calculus I

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea that a lack of prerequisite knowledge is a significant hurdle for students, but also that participation in the remediation program is correlated with student success. In addition, the program allows for the very early identification of students at high risk of failing. The program is easy to implement, and it would be adaptable to a variety of other courses for which prerequisite knowledge is essential for success including science courses, engineering courses and other mathematics courses.     

Differential quotients in elliptic scator algebra

The quotient of the function difference over the variable increment is evaluated in 1+n finite dimensional imaginary scator algebra. A distinctive property of the scator product is that it is commutative albeit not distributive over addition. In , a subset of where the product is defined, all the elements have inverse provided that zero is excluded. The quotient of scators and their differential limit can thus be defined in this subset, establishing the notion of scator differentiability. The necessary conditions that a scator holomorphic function must satisfy are then derived in terms of an extended set of partial differential equations. It is shown that affine transformations involving a scaling and a translation are scator holomorphic. These results are compared with holomorphy in quaternion and Cℓ_0,n Clifford algebras. Functions, such as the quadratic mapping, are shown not to satisfy the scator holomorphic conditions.     

Discretizing Malliavin calculus

Suppose $B$ is a Brownian motion and $B^n$ is an approximating sequence of rescaled random walks on the same probability space converging to $B$ pointwise in probability. We provide necessary and sufficient conditions for weak and strong $L^2$-convergence of a discretized Malliavin derivative, a discrete Skorokhod integral, and discrete analogues of the Clark–Ocone derivative to their continuous counterparts. Moreover, given a sequence $\left(X^n\right)$ of random variables which admit a chaos decomposition in terms of discrete multiple Wiener integrals with respect to $B^n$, we derive necessary and sufficient conditions for strong $L^2$-convergence to a $\sigma \left(B\right)$-measurable random variable $X$ via convergence of the discrete chaos coefficients of $X^n$ to the continuous chaos coefficients.