Moving least squares reconstruction for sharp interface immersed boundary methods

We propose a new approach for reconstructing velocity boundary conditions in sharp-inerface immersed boundary (IB) methods based on the moving least squares (MLS) interpolation method. The MLS is employed to not only reconstruct velocity boundary conditions but also to calculate the pressure and velocity gradients in the vicinity of the immersed body, which are required in fluid structure interaction problems to obtain the force exerted by the fluid on the structure. To extend the method to arbitrarily complex geometries with nonconvex shaped boundaries, the visibility method is combined with the MLS method. The performance of the proposed curvilinear IB MLS (CURVIB-MLS) is demonstrated by systematic grid-refinement studies for two- and three-dimensional tests and compared with the standard CURVIB method employing standard wall-normal interpolation for reconstructing boundary conditions. The test problems are flow in a lid-driven cavity with a sphere, uniform flow over a sphere, flow on a NACA0018 airfoil at incidence, and vortex-induced vibration of an elastically-mounted cylinder. We show that the CURVIB-MLS formulation yields a method that is easier to implement in complex geometries and exhibits higher accuracy and rate of convergence relative to the standard CURVIB method. The MLS approach is also shown to dramatically improve the accuracy of calculating the pressure and viscous forces imparted by the flow on the body and improve the overall accuracy of FSI simulations. Finally, the CURVIB-MLS approach is able to qualitatively capture on relatively coarse grids important features of complex separated flows that the standard CURVIB method is able to capture only on finer grids.     

Rapid Simultaneous Determination of Andrographolides in Andrographis paniculata by Near-Infrared Spectroscopy

The potential of near-infrared spectroscopy (NIRS) for the quality control of traditional Chinese medicine has been evaluated. Seven quantitative parameters, andrographolide, deoxyandrographolide, dehydroandrographolide, neoandrographolide, moisture, ash content, and alcohol-soluble extract of Andrographis paniculata, were evaluated by NIRS. The reference values of andrographolides were determined by high-performance liquid chromatography, and the others were obtained using the standard methods of the 2015 Chinese Pharmacopoeia. The predicted values were determined by a quantitative model using NIRS based on partial least square regression. Different spectral preprocessing methods, spectral ranges, and optimum number of factors were selected to optimize the models. All models were estimated by the combination of various parameters, including the correlation coefficient of calibration for andrographolide, deoxyandrographolide, dehydroandrographolide, neoandrographolide, moisture, ash content, alcohol-soluble extract (values of 0.980, 0.984, 0.989, 0.983, 0.987, 0.988, 0.979, respectively), root mean square error of calibration (values of 0.156, 0.038, 0.050, 0.029, 0.604, 0.431, 0.135, respectively), root mean square error of prediction (values of 0.169, 0.041, 0.050, 0.033, 0.280, 0.493, 0.140, respectively), root mean square error of cross-validation (values of 0.626, 0.114, 0.158, 0.046, 1.145, 0.774, 0.508, respectively), and ratio of standard deviation to standard error of prediction (values of 4.583, 4.690, 4.796, 4.899, 4.899, 4.690, 5.099, respectively). The results show that the calibration models by NIRS are reliable and can be applied for the quantification for seven parameters from A. paniculata for quality control in traditional Chinese medicine production and processing.     

Nondestructive Discrimination of Pharmaceutical Preparations Using Near-Infrared Spectroscopy and Partial Least-Squares Discriminant Analysis

Metronidazole is a widely used antibacterial and amoebicide drug. The feasibility of the classification of metronidazole samples with respect to their brands was investigated by near-infrared (NIR) spectroscopy along with chemometrics. A total of 92 samples of different lots and four brands were collected for measurements. First, principal component analysis was conducted to visualize the difference between metronidazole samples of different brands. Then, based on an effective classifier-independent method, i.e., joint mutual information, only the 30 most important variables were selected for modeling. From the independent test set, the partial least-squares discriminant analysis model based on the reduced variable set was compared with the corresponding full-spectrum model using all variables, which indicates the model based on the reduced variable set outperforms the full-spectrum model. It appears that the combination of NIR spectroscopy, joint mutual information, and partial least-squares discriminant analysis is a potential method for the classification of metronidazole from different brands and can, therefore, be used in the screening of counterfeit pharmaceutical products.     

Theorems of the Alternative and Duality

This paper investigates the relations between theorems of the alternative and the minimum norm duality theorem. A typical theorem of the alternative is associated with two systems of linear inequalities and/or equalities, a primal system and a dual one, asserting that either the primal system has a solution, or the dual system has a solution, but never both. On the other hand, the minimum norm duality theorem says that the minimum distance from a given point z to a convex set is equal to the maximum of the distances from z to the hyperplanes separating z and . We consider the theorems of Farkas, Gale, Gordan, and Motzkin, as well as new theorems that characterize the optimality conditions of discrete l ₁-approximation problems and multifacility location problems. It is shown that, with proper choices of , each of these theorems can be recast as a pair of dual problems: a primal steepest descent problem that resembles the original primal system, and a dual least–norm problem that resembles the original dual system. The norm that defines the least-norm problem is the dual norm with respect to that which defines the steepest descent problem. Moreover, let y solve the least norm problem and let r denote the corresponding residual vector. If r=0, which means that z , then y solves the dual system. Otherwise, when r0 and z , any dual vector of r solves both the steepest descent problem and the primal system. In other words, let x solve the steepest descent problem; then, r and x are aligned. These results hold for any norm on . If the norm is smooth and strictly convex, then there are explicit rules for retrieving x from r and vice versa.     

The Spectral Function and Principal Eigenvalues for Schrödinger Operators

Let m , 0 m₊ in Kato's class. We investigate the spectral function s( + m) where s( + m) denotes the upper bound of the spectrum of the Schrödinger operator + m. In particular, we determine its derivative at 0. If m_- is sufficiently large, we show that there exists a unique ₁ > 0 such that s( + ₁m) = 0. Under suitable conditions on m⁺ it follows that 0 is an eigenvalue of + ₁m with positive eigenfunction.     

Some properties of rational approximations of degree (k, 1) in the hardy spaceH 2(D)

We prove that the well-known interpolation conditions for rational approximations with free poles are not sufficient for finding a rational function of the least deviation. For rational approximations of degree (k, 1), we establish that these interpolation conditions are equivalent to the assertion that the interpolation pointc is a stationary point of the functionk(c) defined as the squared deviation off from the subspace of rational functions with numerator of degree k and with a given pole 1/¯c. For any positive integersk ands, we construct a functiong H₂(D) such thatR _k ,1(g)=R _k +s,1(g) > 0. whereR _k ,1(g) is the least deviation ofg from the class of rational function of degree (k, 1).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 251–259, August, 1998.The author is keenly grateful to N. S. Vyacheslavov, E. P. Dolzhenko, and V. G. Zinov for useful discussions.     

Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

Association Schemes with Multiple Q-polynomial Structures

It is well known that an association scheme with has at most two P-polynomial structures. The parametrical condition for an association scheme to have two P-polynomial structures is also known. In this paper, we give a similar result for Q-polynomial association schemes. In fact, if , then we obtain exactly the same parametrical conditions for the dual intersection numbers or Krein parameters.     

外推式高温测量的一种新方法

针对两点法、三点法、微分法、多点温度法、对点的对数法等［４］在动态高温测量中存在的不足,如：测量误差大、抗干拢能力弱、模型演算复杂、热惯性系数慢变性等对推算结果影响大,提出了一种在简化模型的基础上,利用最小二乘原则估计稳态温度值的方法．该方法由于引用了最小二乘估计理论,其算法使热惯性系数的慢变性原则上不影响估计精度;同时该算法模型简单,使用的数据量也不大,比较适合在实际中应用．仿真研究结果表明,在一定条件下,该方法估计精度较高．