From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

k元de Bruijn-Good图的1-因子图与分配多面体图

本文首先修正了文献[2]中的定义1.2,然后给出了由κ元(?)级 de Bruijn-Good图的1-因子构成的变换图的结构,得到了它与分配多面体图(graph of assign-ment polytope)的关系,从而得知它具有一些好的性质.     

扇形域上高阶Schwarz边值问题

本文主要讨论一类角度为θ=π/α,α≥1/2的扇形域上高阶多解析方程的Schwarz边值问题.通过构造适当的高阶-Schwarz算子和Pompeiu算子,我们给出了详细的解表达式.本文把边值问题进一步推广到高阶情形,丰富了扇形域上边值问题的发展.     

拉曼光谱的16种多环芳烃（PAHs）特征振动光谱辨识

借助密度泛函理论中B3LYP/6-311++G(d, p)方法对美国EPA优先控制污染物中的16种多环芳烃(PAHs)：萘、苊烯、苊、芴、菲、蒽、荧蒽、芘、苯并[a]蒽、稠二萘、苯并[b]荧蒽、苯并[k]荧蒽、苯并[a]芘、二苯并(a, h)蒽、二苯并[g, h, i]芘以及茚苯(1, 2, 3-cd)芘进行结构优化,并计算拉曼光谱振动频率和去偏振度,在此基础上辨识多环芳烃的拉曼特征光谱。研究显示,16种PAHs的拉曼振动主要分布在3个频区：200～1 000 cm-1（指纹区）、1 000～1 700和3 000～3 200 cm-1（基团频率区）,3个频区主要振动归属分别为环变形(ring def),碳碳伸缩(CCStr)、碳氢摇摆(CHw)及其耦合振动(CCStrCCw),碳氢伸缩(CHStr)。进一步分析显示,指纹区16种PAHs的去偏振度随苯环变形振动对称性增强而降低,在该频区去偏振度最小的频移处苯环呼吸振动的对称性最强,指纹区的峰强也在此处出现最大值。任意PAHs在指纹区的最强峰之间的波数差较大,在显微拉曼光谱的可分辨范围内,因而利用指纹区的去偏振度和最强峰可将16种PAHs逐一识别。烷烃、烯烃、炔烃、醇类和酚类、脂肪醚、芳基烷基醚、醛类、酮类、羧酸、酯类、胺类、腈类、酰胺类、酸酐、芳烃的振动频率和峰强分布不完全一致,利用PAHs与这几类物质拉曼频率和峰强分布的差异可以逐一排出干扰。     

反传热问题及其在深冷处理传热分析中的应用

深冷处理作为一种新的材料处理工艺,越来越受到人们的关注,目前深冷处理使材料性能提高的机理尤其是与升降温过程的耦合关系等还尚未完全清楚,需开展更深入的研究,而传热分析是此方面研究的基础。反传热分析方法是研究深冷处理传热问题的一种可行方法。较为详细地叙述了反传热问题的定义及其求解方法,介绍了反传热在深冷处理传热分析中的初步应用,并对深冷处理中应用反传热方法存在的问题进行了探讨。     

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an equilibrium one through particle collisions. The different mechanism in the flux evaluation deviates their numerical performance. Through this study, we may conclude scientifically that it may NOT be valid to use the Euler equations as governing equations to construct numerical fluxes in a discretized space with limited cell resolution. To adapt the Navier–Stokes (NS) equations is NOT valid either because the NS equations describe the flow behavior on the hydrodynamic scale and have no any corresponding physics starting from a discontinuity. This fact alludes to the consistency of the Euler and Navier–Stokes equations with the continuum assumption and the necessity of a direct modeling of the physical process in the discretized space in the construction of numerical scheme when modeling very high Mach number flows. The development of numerical algorithm is similar to the modeling process in deriving the governing equations, but the control volume here cannot be shrunk to zero.     

A novel pose and illumination robust face recognition with a single training image per person algorithm

In the real-world application of face recognition system, owing to the difficulties of collecting samples or storage space of systems, only one sample image per person is stored in the system, which is so-called one sample per person problem. Moreover, pose and illumination have impact on recognition performance. We propose a novel pose and illumination robust algorithm for face recognition with a single training image per person to solve the above limitations. Experimental results show that the proposed algorithm is an efficient and practical approach for face recognition.     

The kinetic boundary layer for the Klein-Kramers equation; A new numerical approach

We explore a numerical technique for determining the structure of the kinetic boundary layer of the Klein-Kramers equation for noninteracting Brownian particles in a fluid near a wall that absorbs the Brownian particles. The equation is of interest in the theory of diffusion-controlled reactions and of the coagulation of colloidal suspensions. By numerical simulation of the Langevin equation equivalent to the Klein-Kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities. The data can be used to construct the solutions of the standard problems at an absorbing wall, the Milne and the albedo problem. We confirm and extend earlier results by Burschka and Titulaer, obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion. We briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here.     

The absorption spectrum of water between 13 540 and 14 070 cm: ICLAS detection of weak lines and a complete line list

The absorption spectrum of water vapor has been investigated by Intracavity Laser Absorption Spectroscopy (ICLAS) between 13 540 and 14 070 cm⁻¹. This spectrum is dominated by relatively strong transitions of the 4δ polyad of vibrational states. The achieved sensitivity - on the order of α_min ∼ 10⁻⁹ cm⁻¹ - has allowed one to newly measure 222 very weak transitions with intensities down to 5 × 10⁻²⁸ cm/molecule at 296 K. Fifty new or corrected H₂¹⁶O energy levels belonging to a total of 13 vibrational states could be determined from the rovibrational analysis based on variational calculations by Schwenke and Partridge. The previous investigations in the region by Fourier Transform Spectroscopy were critically evaluated and used to construct the best to date set of energy levels accessed by transitions in the considered region. All the rovibrational transitions reaching these upper energy levels and having intensities larger than 4.0 × 10⁻²⁸ cm/mol were calculated. In the resulting line list, the positions at the level of experimental accuracy were augmented with variational intensities leading to the most complete line list for water in normal isotopic abundance in the 13 500-14 100 cm⁻¹ region.     

Principles of instrumentation and signal processing method of PLDA

It is shown in this paper that in geometrical space two polarization planes of thelinearly polarized light waves scattered by particles in measuring ellipsoid constitute anangle of π/2. while in sequence of time the signals sent out by two symmetricphotodetectors in PLDA ard separated by a phase angle π.This property of PLDAenables the improvement of SNR.The similarity between power spectrum of photoelectrical current of PLDA andprobability density function P_d(u_c)of investigated flow velocity has been provedtheoretically and checked by agreement of obtained results with classical theory andgenerally accepted experiments.