A viscoelastic frictionless contact problem with adhesion

We consider a model for the quasistatic, bilateral, adhesive and frictionless contact between a viscoelastic body and a rigid foundation. The adhesion process on the contact surface is modeled by a surface internal variable, the bonding field, and the tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and an integro-differential equation for the bonding field. The existence of a unique weak solution for the problem is established by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space. We also consider the problem describing the bilateral contact between two viscoelastic bodies, and establish similar results.     

Bilateral Obstacle Optimal Control for a Quasilinear Elliptic Variational Inequality

ABSTRACT

In this paper, we consider an obstacle control problem where the state satisfies a quasilinear elliptic bilateral variational inequality and the control functions are the upper and the lower obstacles. Existence and necessary conditions for the optimal control are established.     

Bilateral vocal fold paralysis: an unsual treatment with botulinum toxin

We presented a patient with bilateral vocal fold paralysis treated with intralaryngeal Botox injection to improve the glottal airway. The use of Botox in this manner has not been previously reported and highlights the value and role of intralaryngeal Botox in changing the configuration of the glottis. The concept and various approaches for using Botox to alter pathologic vocal fold position is reviewed and discussed.     

Sarcoidosis Presenting as Bilateral Vocal Fold Paralysis

Sarcoidosis with cranial polyneuritis and mediastinal granulomatous compression as a cause of unilateral left vocal fold paralysis has been reported infrequently. No case of sarcoidosis causing bilateral vocal fold paralysis in the abducted position has been reported in the Otolaryngology/Voice literature. Vocal fold function can be impacted in sarcoidosis by direct laryngeal involvement or by neural pathways. In the patient described in this case, sarcoid cranial polyneuritis coupled with bilateral paratracheal and mediastinal adenopathy resulted in bilateral vocal fold paralysis. This patient had a dramatic response to treatment with steroids. Sarcoidosis should be included in the differential diagnosis of unilateral or bilateral vocal fold paralysis.     

基于双边拟合的高稳定性共焦拉曼光谱定焦方法

共焦拉曼光谱技术可实现定量、无损、无需标记的样品微区“分子结构特征和物质组成信息”成像,被广泛应用于生物医学、物理化学以及材料科学等领域。由于共焦拉曼系统采用“点”激发和“点”探测的探测机制,且拉曼散射光谱信号微弱,导致成像所需时间可长达数小时甚至数十小时;测量过程中系统极易受环境变化、空气扰动等因素影响产生漂移,造成被测样品离焦,从而导致成像质量不稳定。针对现有共焦拉曼系统对样品定焦能力不足、样品易产生离焦误差、系统漂移大等问题,本文提出了一种基于双边拟合的高稳定性共焦拉曼光谱定焦方法。该方法首先对共焦拉曼光谱强度轴向响应曲线两侧对样品离焦敏感的数据区间分别进行线性拟合,得到两条拟合直线方程;然后,将所得的两条直线方程相减得到新的差分直线;最后,通过差分直线的过零点位置确定系统焦平面位置,实现了被测样品的高精度定焦,消除了离焦对系统测量结果的影响。以单晶硅表面同一位置,轴向扫描步距100 nm,进行60次重复定焦实验,实验获得的重复定焦极差为80.2 nm,说明系统具有良好的抗漂移能力。对周期5 μm的竖条栅格标准原子力台阶样品进行拉曼mapping成像测试,结果表明在长时间的成像过程中,和无定焦功能的图像相比,该方法获得的竖条栅格图像更清晰、边缘更锐利、信噪比较好。仿真分析和实验结果表明：提出的基于双边拟合共焦拉曼光谱探测方法可以提高系统的定焦准确度,抑制干扰因素导致的系统离焦对成像质量的影响,进而确保了系统探测的稳定性和成像分辨力,是一种自动定焦、抗漂移的拉曼光谱成像方法。     

Small target detection using bilateral filter and temporal cross product in infrared images

We introduce a spatial and temporal target detection method using spatial bilateral filter (BF) and temporal cross product (TCP) of temporal pixels in infrared (IR) image sequences. At first, the TCP is presented to extract the characteristics of temporal pixels by using temporal profile in respective spatial coordinates of pixels. The TCP represents the cross product values by the gray level distance vector of a current temporal pixel and the adjacent temporal pixel, as well as the horizontal distance vector of the current temporal pixel and a temporal pixel corresponding to potential target center. The summation of TCP values of temporal pixels in spatial coordinates makes the temporal target image (TTI), which represents the temporal target information of temporal pixels in spatial coordinates. And then the proposed BF filter is used to extract the spatial target information. In order to predict background without targets, the proposed BF filter uses standard deviations obtained by an exponential mapping of the TCP value corresponding to the coordinate of a pixel processed spatially. The spatial target image (STI) is made by subtracting the predicted image from the original image. Thus, the spatial and temporal target image (STTI) is achieved by multiplying the STI and the TTI, and then targets finally are detected in STTI. In experimental result, the receiver operating characteristics (ROC) curves were computed experimentally to compare the objective performance. From the results, the proposed algorithm shows better discrimination of target and clutters and lower false alarm rates than the existing target detection methods.     

Scene-based nonuniformity correction based on bilateral filter with reduced ghosting

In order to correct the nonuniformity noise of the IR imaging system, a nonuniformity correction deghosting algorithm based on high-brightness region detection was proposed. Firstly, the bilateral filter was used to filter the image. The high-brightness regions in the result image were detected, and the correction factors corresponding to the regions were reduced. And then, the positions were detected which are high-brightness pixels in former frame but are not in current frame, and the correction factors corresponding to the regions were enlarged. Thus, the wrong update of the correction factor caused by high-brightness region of both the current frame and the previous frame was reduced. The correction method was validated using a real image sequence. The experimental results showed that the suppression effect of the proposed algorithm on the ‘ghost’ effect caused by the high-brightness region is better than the other two algorithms named SLTH-NUC and BFTH-NUC, respectively. Moreover, the proposed algorithm can also suppress the ‘ghost’ effect caused by the sharp edge of the scene.     

Bilateral inversions and terminating basic hypergeometric series identities

The q-analogue of Legendre inversions is established and generalized to bilateral sequences. They are employed to investigate the dual relations of three basic formulae due to Jackson and Bailey, on balanced ₃?₂-series, well-poised ₈?₇-series and bilateral ₆ψ₆-series. Several terminating well-poised series identities are consequently derived, including the q-Dixon formulae on terminating ₃ψ₃-series and two terminating well-poised ₅ψ₅-series identities due to [F.H. Jackson, Certain q-identities, Quart. J. Math. (Oxford) 12 (1941) 167-172; W.N. Bailey, On the analogue of Dixon’s theorem for bilateral basic hypergeometric series, Quart. J. Math. (Oxford) 1 (1950) 318-320].     

A simple proof of Bailey's very-well-poised summation

We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauß' summation and elementary series manipulations to give a simple proof of Dougall's summation. Similarly, we apply Rogers' nonterminating summation and elementary series manipulations to give a simple proof of Bailey's very-well-poised summation. Our method of proof extends M. Jackson's first elementary proof of Ramanujan's summation.

     

Non-sequential weak supercyclicity and hypercyclicity

A bounded linear operator T acting on a Banach space B is called weakly hypercyclic if there exists x∈B such that the orbit is weakly dense in B and T is called weakly supercyclic if there is x∈B for which the projective orbit is weakly dense in B. If weak density is replaced by weak sequential density, then T is said to be weakly sequentially hypercyclic or supercyclic, respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic. This is achieved by constructing a Borel probability measure μ on the unit circle for which the Fourier coefficients vanish at infinity and the multiplication operator Mf(z)=zf(z) acting on L₂(μ) is weakly supercyclic. It is not weakly sequentially supercyclic, since the projective orbit under M of each element in L₂(μ) is weakly sequentially closed. This answers a question posed by Bayart and Matheron. It is proved that the bilateral shift on ?p(Z), 1?p<∞, is weakly supercyclic if and only if 2<p<∞ and that any weakly supercyclic weighted bilateral shift on ?p(Z) for 1?p?2 is norm supercyclic. It is also shown that any weakly hypercyclic weighted bilateral shift on ?p(Z) for 1?p<2 is norm hypercyclic, which answers a question of Chan and Sanders.