Abstract:
A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm, while previous FETI-DP methods only apply to discontinuous pressures. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved. This framework is also used to describe several previously developed FETI-DP algorithms and greatly simplifies their analysis. Numerical experiments of solving a two-dimensional incompressible Stokes problem demonstrate the performances of the discussed FETI-DP algorithms represented under the same framework.

Abstract:
The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp.~128--149] for solving incompressible Stokes equations, are extended to three-dimensional problems. A new analysis of the condition number bound for using the Dirichlet preconditioner is given. An advantage of this new analysis is that the numerous coarse level velocity components, required in the previous analysis to enforce the divergence free subdomain boundary velocity conditions, are no longer needed. This greatly reduces the size of the coarse level problem in the algorithm, especially for three-dimensional problems. The coarse level velocity space can be chosen as simple as for solving scalar elliptic problems corresponding to each velocity component. Both Dirichlet and lumped preconditioners are analyzed using a same framework in this new analysis. Their condition number bounds are proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments in both two and three dimensions demonstrate the convergence rate of the algorithms.

Abstract:
A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain domain boundary. The continuity of the pressure component is enforced in the primal form, i.e., neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no Lagrange multipliers are needed. After eliminating all velocity variables and the independent subdomain interior parts of the pressures, a symmetric positive semi-definite linear system for the subdomain boundary pressures and the Lagrange multipliers is formed and solved by a preconditioned conjugate gradient method. A lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments demonstrate the convergence rate of the proposed algorithm.

Abstract:
Protective effect of catalpol on myocardium was studied in relation to endothelial progenitor cells, Notch1 signaling pathway and angiogenesis in rats with isoprenaline (INN)-induced acute myocardial infarcts. To analyze the pathological status and impact of catalpol on the rats, 3 weeks after intragastric gavage, the animals were verified for myocardial infarcts with electrocardiogram and measured for enzyme activity of lactate dehydrogenase (LDH), malondialdehyde (MDA), creatine kinase (CK) and superoxide dismutase (SOD) in myocardium, and further analyzed using HE and TTC staining, as well as visual examination of infarct area. Flow cytometry study of endothelial progenitor cells (EPCs) indicated that the EPCs were mobilized during infarction. The roles of Notch1 signaling pathway in angiogenesis of the infracted animals were studied using immunohistochemistry analysis of RBPjκ and Western blot analysis of Notch1 and Jagged1. Our results obtained from the rats treated with catalpol, positive drug and control showed that catalpol could protect rats from infarction probably by mobilization of EPCs and activation of Notch1 signaling pathway.

Abstract:
A novel method for measuring the minute fluctuation of cell membrane is developed by modifying the super-resolution theory, increasing dimension in Fourier space, enhancing brightness gradient and utilizing maximum adaptive weighted averaging filter (MAWA) in obstructing noise. The application of the method in studying aspergillus flavus cell (AFC) and red blood cell and the new findings from the study show that it is a useful tool.

Abstract:
Porous Co(OH)2 film directly grown on nickel foam is prepared by a facile hydrothermal method. The as-prepared Co(OH)2 film possesses a structure consisting of randomly porous nanoflakes with thicknesses of 20–30 nm. The capacitive behavior of the Co(OH)2 film is investigated by cyclic voltammograms and galvanostatic charge-discharge tests in 2 mol/L KOH. The porous Co(OH)2 film exhibits a high discharge capacitance of 935 F g 1 at a current density of 2 A g 1 and excellent rate capability. The specific capacitance keeps a capacitance of 589 F g 1 when the current density increases to 40 A g 1. The specific capacitance of 82.6% is maintained after 1500 cycles at 2 A g 1.

Abstract:
A simple but powerful scheme exploiting the binning concept for asymmetric lossless distributed source coding is proposed. The novelty in the proposed scheme is the introduction of a syndrome former (SF) in the source encoder and an inverse syndrome former (ISF) in the source decoder to efficiently exploit an existing linear channel code without the need to modify the code structure or the decoding strategy. For most channel codes, the construction of SF-ISF pairs is a light task. For parallelly and serially concatenated codes and particularly parallel and serial turbo codes where this appear less obvious, an efficient way for constructing linear complexity SF-ISF pairs is demonstrated. It is shown that the proposed SF-ISF approach is simple, provenly optimal, and generally applicable to any linear channel code. Simulation using conventional and asymmetric turbo codes demonstrates a compression rate that is only 0.06 bit/symbol from the theoretical limit, which is among the best results reported so far.

Abstract:
An algorithm for carrier frequency offset estimation with narrowband interference in burst-mode transmissions is proposed. The algorithm is data-aided and has a feedforward structure that can be easily implemented digitally. The principle of the algorithm is based on a properly designed training sequence and an interpolation technique. Simulation results indicate that the estimation range is about ±20% of the symbol rate. The performance is satisfactory for a signal-to-noise ratio (SNR) as low as -13 dB and the mean square error (MSE) is approximately irrelevant to signal-to-interference ratio (SIR) values over -20 dB. An algorithm for carrier frequency offset estimation with narrowband interference in burst-mode transmissions is proposed. The algorithm is data-aided and has a feedforward structure that can be easily implemented digitally. The principle of the algorithm is based on a properly designed training sequence and an interpolation technique. Simulation results indicate that the estimation range is about ±20% of the symbol rate. The performance is satisfactory for a signal-to-noise ratio (SNR) as low as -13 dB and the mean square error (MSE) is approximately irrelevant to signal-to-interference ratio (SIR) values over -20 dB.

With
local realism quantum mechanics established, we can simply describe an
extranuclear electron as a large-scale elastic ring with an elastic phase
trajectory. Several small molecules can thus be strictly calculated through the
logical method of establishing an accurate mechanical equilibrium equation
describing the molecular structure, then solving the strict solutions of this
mechanical equation and the corresponding wave equation. The results (bond
length and dissociation energy) are in good agreement with observed results—i.e. if it is only coincidence, there
should not be such a high probability of agreement between calculated and
observed results. The method of local realism quantum mechanics is no longer
the semi-empirical method. The method to calculate the electron pairing energy
uses a linear regression of the ionization energy obtained through experiment.
Nonetheless, it is exciting that there are diatomic molecules such as Na_{2},
K_{2} and asymmetric HF molecules that possess a non-zero non-bonding
electron number in the calculation examples. Moreover, the molecular structures
are very intuitive, and the calculation method is much simpler than existing
methods.

Abstract:
The existing interpretation of quantum mechanics is contrary to common sense. The existing quantum mechanical interpretation schemes are puzzling. The confusing theory is unconvincing, and needs to be amended and completed. The successful interpretation program of quantum mechanics of local-realism and determinism is undoubtedly the most attractive. Preparing the interpretation program deserves to be chosen as a research goal. It is a very good premise to believe that an object particle consists of light-knot of monochromatic waves. According to this premise, the erroneous recognition about “superposition principle, wave-particle duality and uncertainty principle” can be corrected. Under this premise, above research goal is achieved by establishing, applying quantum mechanics inverse measurement theory, adhering to the principle that there must be a complete empirical chain in the derivation process of experimental conclusion, and using the side effect caused by accompanying-light to explain the diffraction experiment of object particles. Electron secondarily diffraction and other experiments directly prove that there is the measurement (observation) which may not destroy quantum coherence. The diffraction experiments of all kinds of particles show that the Keeping and playing of the coherence of moving particles in the vacuum have nothing to do with their previous experience. These are the existing experiments, to be found, that support the theory of quantum inverse measurements. The verification experiment of quantum inverse measurement is designed. The absolute superiorities of quantum inverse measurement and the new view of measurement of quantum mechanics are listed. These superiorities are that: it has the characteristics of local-realism and determinism; it is not contrary to common sense and there is no confusing place; it can predict several phenomena that cannot be predicted by other theories. A solid theoretical foundation has been laid for “correctly understanding the microscopic world” and establishment of local realism quantum mechanics.