Variation analysis of uncertain stationary independent increment processes

A stationary independent increment process is an uncertain process with stationary and independent increments. This paper aims to calculate the variance of stationary independent increment processes, and gains that, for each fixed time, the variance is a constant multiplying the square of time. Based on this result, it is proved that the total variation of stationary independent increment process with finite variance is bounded almost surely. Besides, the quadratic variation of stationary independent increment process with finite variance is 0 almost surely and in mean.     

含有不可数个无界变差点的一维连续函数

在单位区间[0,1]上构造了图像长度为无穷的一维连续函数.该函数含有不可数个但Lebesgue测度为0的无界变差点.所有无界变差点组成的集合中每一点皆为该集合的聚点.     

Covariational reasoning among U.S. and South Korean secondary mathematics teachers

We investigated covariational reasoning among 487 secondary mathematics teachers in the United States and South Korea. We presented an animation showing values of two varying magnitudes (v and u) on axes in a Cartesian plane along with a request that they sketch a graph of the value of u in relation to the value of v. We classified teachers’ sketches on two independent criteria: (1) where they placed their initial point, and (2) their graph’s overall shape irrespective of initial point. There are distinct differences on both criteria between U.S. and South Korean teachers, suggesting that covariational reasoning is more prominent among South Korean secondary teachers than among U.S. secondary teachers. The results also suggest strongly that forming a multiplicative object that unites quantities’ values is necessary to express covariation graphically.     

Box-counting dimensions of fractal interpolation surfaces derived from fractal interpolation functions

A construction method of Fractal Interpolation Surfaces on a rectangular domain with arbitrary interpolation nodes is introduced. The variation properties of the binary functions corresponding to this type of fractal interpolation surfaces are discussed. Based on the relationship between Box-counting dimension and variation, some results about Box-counting dimension of the fractal interpolation surfaces are given.     

A Note on Gaussian BV Function and Its Heat Semigroup Characterization

In this note, we investigate the properties of Gaussian BV functions and give a heat semigroup characterization of BV functions in Gauss space. In particular, the latter is the nontrivial generalization of classical De Giorgi's heat kernel characterization of function of bounded variation on Euclidean space to the case of Gauss space.     

Optical and electrochemical properties of Cu-doped NiO films prepared by electrochemical deposition

Cu-doped nickel oxide (NiO) thin films were prepared by electrochemial deposition (cathodic deposition) technique onto the fluorine doped tin oxide (F: SnO₂; FTO) coated glass substrates from organic solutions. Effects of Cu content on the morphology, structure, optical and electrochromic properties of NiO films were investigated by means of scanning electron microscope (SEM), X-ray diffraction (XRD), ultraviolet-visible spectrophotometer (UV-vis) and cyclic voltammetry (CV), respectively. SEM images indicated the formation of nanorods after Cu was added. The films were formed with amorphous or short-range ordered NiO grains and a trace of face-centered cubic Ni_xCu_1−xO confirmed by XRD. The transmittances of both bleached state and colored state were significantly lowered when Cu was added. The NiO films doped with Cu (the molar ratio was 1/8) exhibited the optimum electrochromic behavior with a variation of transmittance (ΔT) up to ∼80% at the wavelength range of 350-600 nm. Cu doping reduces the response time for both the coloring and bleaching states, and the reversibility of the redox reaction was increased as well.     

On Spectral Integral Variations of Graphs

Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge.     

用变分法解Fokker—Planck方程计算核裂变几率

发展了一种用变分法解Fokker-Planck方程的方法,计算了一维核裂变几率,研究了F-P方程与Smoluchowski方程的关系,为推导多维的质量系数和粘滞系数随形变参量变化并具有交叉项的Smoluchowski方程和解位能形式比较复杂的多维的F-P方程打下了基础.     

Seasonal variations of volatile constituents of Hemizygia bracteosa (Benth.) Briq. aerial parts from Benin

Essential oils from fresh aerial parts of Hemizygia bracteosa (Benth.) Briq. were extracted by steam distillation. The oil yield from plants collected during the hot season (February) and during the cold season (August) were 0.12 ± 0.01% and 0.25 ± 0.02%, respectively. GC/FID and GC/MS analyses allowed us to identify a total of 65 compounds, representing 97% of the hydrodistillate. The main components of the oil from the hot period were (E)-β-farnesene (64 ± 0.04%), β-elemene (7.4 ± 0.05%), trans-nerolidol (6.2 ± 0.04%), and α-muurolene (2.7 ± 0.03%). The essential oil from the cold season was characterized by the presence, as major compounds, of (E)-β-farnesene (67 ± 0.04%) along with β-caryophyllene (3.6 ± 0.06%), β-elemene (3.3 ± 0.05%), 7-epi-α-selinene (3.1 ± 0.01%) and p-cymene (2.5 ± 0.04%). This is the first report of these components in the essential oil of Hemizygia bracteosa (Benth.) Briq.     

Operators related to truncated Hilbert transforms on <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript>

In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H ¹ to L ¹, and prove variation, oscillation and λ-jump operators related to smooth truncations are bounded from H ¹ to L ¹.