动态经济学数学建模及稳定化控制分析

通过考虑需求函数和供给函数受到不连续因素的影响以及引进切换型的控制策略,建立由右端不连续微分方程刻画的非线性价格调整模型.利用微分包含理论和Lyapunov稳定性方法分析不连续价格调整模型的有限时间稳定化控制问题,并给出数值模拟实例进行验证说明.最后,结合动态经济学数学建模提出数学建模教学改革的几点建议.     

FRAMELET BASED DECONVOLUTION

In this paper, two framelet based deconvolution algorithms are proposed. The basic idea of framelet based approach is to convert the deconvolution problem to the problem of inpainting in a frame domain by constructing a framelet system with one of the masks being the given （discrete） convolution kernel via the unitary extension principle of [26], as introduced in [6-9] . The first algorithm unifies our previous works in high resolution image reconstruction and infra-red chopped and nodded image restoration, and the second one is a combination of our previous frame-based deconvolution algorithm and the iterative thresholding algorithm given by [14, 16]. The strong convergence of the algorithms in infinite dimensional settings is given by employing proximal forward-backward splitting （PFBS） method. Consequently, it unifies iterative algorithms of infinite and finite dimensional setting and simplifies the proof of the convergence of the aluorithms of [6].     

Blind motion deblurring using multiple images

Recovery of degraded images due to motion blurring is a challenging problem in digital imaging. Most existing techniques on blind deblurring are not capable of removing complex motion blurring from the blurred images of complex structures. One promising approach is to recover the clear image using multiple images captured for the scene. However, in practice it is observed that such a multi-frame approach can recover a high-quality clear image of the scene only after multiple blurred image frames are accurately aligned during pre-processing, which is a very challenging task even with user interactions. In this paper, by exploring the sparsity of the motion blur kernel and the clear image under certain domains, we propose an alternative iteration approach to simultaneously identify the blur kernels of given blurred images and restore a clear image. Our proposed approach is not only robust to image formation noises, but is also robust to the alignment errors among multiple images. A modified version of linearized Bregman iteration is then developed to efficiently solve the resulting minimization problem. Experiments show that our proposed algorithm is capable of accurately estimating the blur kernels of complex camera motions with minimal requirements on the accuracy of image alignment. As a result, our method is capable of automatically recovering a high-quality clear image from multiple blurred images.     

Photoarylation of Iodocarboranes with Unactivated (Hetero)Arenes: Facile Synthesis of 1,2-[(Hetero)Aryl]n-o-Carboranes (n=1,2) and o-Carborane-Fused Cyclics

Photoarylation of iodocarboranes with unactivated arenes/heteroarenes at room temperature has been achieved, for the first time, thus leading to the facile synthesis of a large variety of cage carbon mono(hetero)arylated and di(hetero)arylated o-carboranes. This work represents a clean, efficient, transition-metal-free, and cheap synthesis of functionalized carboranes, which has significant advantages over the known methods.     

Direct Nucleophilic Substitution Reaction of Cage B−H Bonds by Grignard Reagents: A Route to Regioselective B4-Alkylation of o-Carboranes

Direct nucleophilic substitution reaction of cage B−H bonds of o-carboranes by Grignard reagents in the absence of any transition metals has been achieved for the first time, and leads to the regioselective synthesis of a series of 4-alkyl-1,2-diaryl-o-carboranes in very high yields. The presence of two electron-withdrawing aryl groups on the cage carbon atoms is crucial to realizing the reaction. The regioselectivity is controlled by both electronic and steric factors. This work represents a new strategy for the development of methods for carborane functionalization.     

ANALYTICAL STUDY ON GROUND VIBRATION INDUCED BY MOVING VEHICLE 1)

本文从汽车动力学出发,建立 1/4 汽车与半空间地基耦合振动的动力学模型,并采用弹性滚子接触模型来反映轮胎包容性. 模型中同时考虑轮-地之间的纵向和竖向作用力,构建系统动力控制方程,利用 Fourier 和 Laplace 积分变换进行求解,推导出地表振动位移的解析解. 在数值算例中,利用离散傅里叶逆变换和 Crump 法进行数值反演,得出地表振动位移的空间分布,由此讨论了轮胎着地长度和轮-地相互作用力的变化规律,并对地表振动位移的参数影响作出分析. 结果表明,地面不平度对轮-地之间作用力的影响最为显著,地面越不平顺则轮-地作用力和地表振动位移越大. 车速对轮-地作用力的大小影响有限,但对载荷激励频率影响较大,车速增大则激励频率增大,地表振动位移随之增大. 在较低车速时,轮胎包容性对轮-地作用力和地表振动产生一定影响,轮胎充气压力增大,轮-地作用力和地表振动位移增大,但随着车速升高,这种影响将逐渐消失.     

Facial Synthesis of o‐Carborane‐Substituted Alkenes and Allenes by a Regioselective Ene Reaction of 1,3‐Dehydro‐o‐carborane

1,3‐Dehydro‐o‐carborane is a useful synthon for selective cage boron functionalization of o‐carboranes. It reacts readily with alkenes or alkynes to give a variety of cage B(3)‐alkenyl/allenyl o‐carboranes by ene reactions in very high yields and excellent regioselectivity. This can be ascribed to the highly polarized cage C?B multiple bond, which lowers the activation barriers of the ene reaction.     

Nickel‐Catalyzed Cross‐Coupling Reactions of o‐Carboranyl with Aryl Iodides: Facile Synthesis of 1‐Aryl‐o‐Carboranes and 1,2‐Diaryl‐o‐Carboranes

A nickel‐catalyzed arylation at the carbon center of o‐carborane cages has been developed, thus leading to the preparation of a series of 1‐aryl‐o‐carboranes and 1,2‐diaryl‐o‐carboranes in high yields upon isolation. This method represents the first example of transition metal catalyzed C,C′‐diarylation by cross‐coupling reactions of o‐carboranyl with aryl iodides.     

Raman sensitivity enhancement for aqueous absorbing sample using Teflon-AF 2400 liquid core optical fibre cell

The compatibility Teflon-AF 2400 liquid core optical fibre with resonance Raman spectroscopy (RRS-LCOF) was used to detect aqueous biomolecules. The maximum sensitivity enhancement factor for concentrations greater than the detection limit in a conventional cell was 10, and detection limit reduction of about 1000-fold have been achieved for the measurement of aqueous absorbing sample using Teflon-AF 2400 fibre Raman cell compared to the conventional cell. We were able to collect spectra of 2.5 × 10⁻⁹ and 2.5 × 10⁻¹⁰ M aqueous β-carotene using 16.2 mW of laser power and 10 s integration time. This volume of a 2.5 × 10⁻¹⁰ M aqueous solution corresponds to only 1.5 fmol or 830 fg of β-carotene. The results of this preliminary study indicate that RRS-LCOF has potential in bioanalytical and biomedical applications.