A full row-rank system matrix generated by the strip-based projection model in discrete tomography

Let Cu = k be an underdetermined linear system generated by the strip-based projection model in discrete tomography, where C is row-rank deficient. In the case of one scanning direction the linear dependency of the rows of C is studied in this paper. An index set H is specified such that if all rows of C with row indices in H are deleted then the rows of resultant matrix F are maximum linearly independent rows of C. Therefore, the corresponding system is equivalent to Cu = k and consequently, the cost of an image reconstruction from is reduced.     

Fully discrete linear approximation scheme for electric field diffusion in type-II superconductors

Superconductors are attracting physicists thanks to their ability to conduct electric current with virtually zero resistance. Their nonlinear behaviour opens, on the other hand, challenging problems for mathematicians. Our model of the diffusion of electric field in superconductors is based on three pillars: the eddy-current version of Maxwell’s equations, power law model of type-II superconductivity and linear dependence of magnetic induction on magnetic field. This leads to a time-dependent nonlinear degenerate partial differential equation. We propose a linear fully discrete approximation scheme to solve it. We have proven the convergence of the method and derived the error estimates describing the dependence of the error on the discretization parameters. These theoretical results were successfully confronted with numerical experiments.     

Relaxo-volumetric multispectral quantitative magnetic resonance imaging of the brain over the human lifespan: global and regional aging patterns

The objective of this study was to determine the T1, T2 and secular-T2 relaxo-volumetric brain aging patterns using multispectral quantitative magnetic resonance imaging, both globally and regionally, and covering an age range approaching the full human lifespan. Fifty-one subjects (28 males, 23 females; age range: 0.5–87 years) were studied consisting of 18 healthy volunteers and 33 patients. Patients were selected after carefully reviewing their radiology reports to have either normal-by-MRI findings (25 patient subjects) or small focal pathology less than 6 mm in size (eight patient subjects). All subjects were MR imaged at 1.5 T with the mixed turbo spin echo pulse sequence. The soft tissues inside the cranial vault, termed intracranial matter (ICM), were segmented using a dual-clustering segmentation algorithm. ICM segments were further divided into six subsegments: bilateral anterior cerebral, posterior cerebral and cerebellar subsegments. T1, T2 and secular-T2 relaxation time histograms of all segments were generated and modeled with Gaussian functions. For each segment, the volumes of white matter, gray matter and cerebrospinal fluid were calculated from the T1 histograms. The age-related tendencies of three quantitative MRI parameters (T1, T2 and secular-T2) and the fractional tissue volumes showed four distinct periods of life, specifically a maturation period (0–2 years), a development period (2–20 years), an adulthood period (20–60 years) and a senescence period (60 years and older). For all ages, the anterior cerebral subsegment exhibited consistently longer gray matter T1s and shorter white matter T1s than the posterior cerebral and cerebellar subsegments. Volumetric age-related changes of the cerebellar subsegment were more gradual than in the cerebral subsegments. This study shows that relaxometric and volumetric age-related changes are synchronized and define the same four periods of brain evolution both globally and regionally.     

Wavelets and Wavelet Packets Related to a Class of Dilation Matrices

The construction of wavelets generated from an orthogonal multiresolution analysis can be reduced to the unitary extension of a matrix, which is not easy in most cases. Jia and Micchelli gave a solution to the problem in the case where the dilation matrix is 21 and the dimension does not exceed 3. In this paper, by the method of unitary extension of a matrix, we obtain the construction of wavelets and wavelet oackets related to a class of dilation matrices.     

Production of biologically active peptides by hydrolysis of whey protein isolates using hydrodynamic cavitation

Whey protein isolate (WPI) hydrolysates have higher solubility in aqueous phase and enhanced biological properties. Hydrolysis of WPI was optimized using operating pressure (ΔP, bar), number of passes (N), and WPI concentration (C, %) as deciding parameters in hydrodynamic cavitation treatment. The optimum conditions for generation of WPI hydrolysate with full factorial design were 8 bar, 28 passes, and 4.5% WPI concentration yielding 32.69 ± 1.22 mg/mL soluble proteins. WPI hydrolysate showed alterations in binding capacity over WPI. SDS-PAGE and particle size analysis confirmed the hydrolysis of WPI. Spectroscopic, thermal and crystallinity analyses showed typical properties of proteins with slight variations after hydrodynamic cavitation treatment. ABTS, DPPH and FRAP assays of WPI hydrolysate showed 7–66, 9–149, and 0.038–0.272 µmol/mL GAE at 1–10, 0.25–4, and 3–30 mg/mL concentration, respectively. Further, a considerable enhancement in fresh weight, chlorophyll, carotenoids, reducing sugars, total soluble sugars, soluble proteins content and total phenolics content was noticed during in vitro growth of sugarcane in WPI hydrolysate supplemented medium at 50–200 mg/L concentration over the control. The process cost (INR/kg) to hydrolyze WPI was also calculated.     

镍族金属团簇在催化加氢过程中的应用

Nanoparticles of precious metals play an important role in many heterogeneous catalytic reactions due to their excellent catalytic performance. As an idealized model, gas phase metal clusters have been extensively utilized to understand catalytic mechanisms at a molecular level. Here we provide an overview of our recent studies on H₂ dissociative chemisorption on nickel family clusters. The structure evolution and the stability of the metal clusters were first compared. H₂ dissociation on the clusters was then carefully addressed to understand the capability of metal clusters to break the H-H bond. Two key parameters, the dissociative chemisorption energy (ΔE_CE) and the H sequential desorption energy (ΔE_DE), were employed to characterize the catalytic activity of metal clusters. Our results show that both ΔE_CE and ΔE_DE decline significantly as the H coverage increases. Since the catalyst is in general covered entirely by H atoms and H₂ molecules in a typical hydrogenation process, and maintained at a pre-determined pressure of H₂ gas, we can rationally use the calculated ΔE_CE and ΔE_DE values at full H saturation to address the activity of metal clusters. Our results suggest that at full H coverage, each Pt atom is essentially capable of adsorbing 4 H atoms, while each Ni or Pd atom can only accommodate 2 H atoms. Considering the similar values of H desorption energies on Pt and Pd clusters, the higher average H capacity per Pt atom could probably lead to a faster reaction rate because more active H atoms are produced on the Pt catalyst particles in the hydrogenation process. Finally, the charge sensitivity of the key catalytic properties of Pt clusters for hydrogenation was systematically evaluated. The results show that the dissociation of H₂ and H desorption are strongly correlated to the charge state of the Pt clusters at low H coverage. However, at high H-capacities, both ΔE_CE and ΔE_DE fall into a narrow range, suggesting that the charge can be readily dispersed and that the Pt-H bonds average the interaction between clusters and H atoms. As a result, the H-capacities on charged clusters were found to be similar as the cluster size increased; in case of sufficiently large clusters, the reactivity of a fully saturated cluster was no longer sensitive to its charge state.     

Poincaré invariants

We construct an obstruction theory for relative Hilbert schemes in the sense of [K. Behrend, B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1) (1997) 45-88] and compute it explicitly for relative Hilbert schemes of divisors on smooth projective varieties. In the special case of curves on a surface V, our obstruction theory determines a virtual fundamental class , which we use to define Poincaré invariants

     

The night driving behavior in a car-following model

In this paper, we have studied the night driving behaviors in the car-following model in periodic boundary conditions. The evolution of uniform traffic under both small and large perturbations is investigated. The simulations show that the traffic is always unstable when V^′<0$V^{\prime }<0$ with V the optimal velocity. The traffic clusters, the kink–antikink waves, and the unstable clusters are observed under different sensitivity parameters. Even more interesting phenomenon is observed when the randomness effect is considered. Under large perturbations, it is shown that the traffic will be unstable if its density is smaller than a threshold. The density corresponding to the threshold increases with the decrease of the sensitivity parameter values.     

熔融静电纺丝法制备单根聚合物微米纤维全可见光谱的放大自发发射特性研究

具有高能量转化效率的微纳尺度的激光光源的开发将极大地促进光电子系统的进一步集成。本文采用熔融静电纺丝方法成功制备了单根有机聚合物微米纤维,所制备的微米纤维表面光滑,成规范的圆柱形结构。我们通过在聚合物纤维中掺入不同的荧光染料,实现了在整个可见光范围内的光发射可调性。在光泵浦条件下,我们详细研究了单根聚合物微米纤维的放大自发发射特性,三种颜色的微米纤维均表现了较低的阈值和高增益的放大自发发射特性。采用时域有限差分法模拟微米纤维中的电场分布结果表明,纤维的柱状微结构有效地将光限制在圆柱体内,形成环形腔反馈,并沿着轴向传播,因而发射光表现了很好的方向性。这种可见光范围内可全色发射的单根的微米纤维的成功制备将为实现智能化、集成化、低成本和高可靠性的微纳激光光源器件提供可靠的技术支持。     

利用后向散射光空间谱强度分布探测尾流气泡的实验研究

利用自行设计制作的尾流模拟系统产生气泡,应用散射光空间频谱测量分析系统,对水中气泡群的后向散射光空间谱强度分布进行测量和分析,研究了不同探测距离的散射光衰减对其强度分布的影响.结果表明,在气泡密度、大小分布不变的情况下,扩束光照明时,由于参与光散射的气泡数目增加对散射光在水中传播衰减的补偿,散射空间谱强度分布的峰值和半宽值均不随探测距离变化;而细光束照明时,散射谱强度分布峰值随探测距离的增加而减小,半宽值则逐渐增大.所以在远距离探测时,细光束的探测效果好.