关于对称函数的一些恒等式

本文则利用分部分式方法结合形式幂级数技巧给出了推广的Matrix定理一个自然的证明，并由此得到了另外一些关于对称函数的恒等式。

European Option Pricing under a Class of Fractional Market

In order to price European contingent claim in a class of fractional Black-Scholes market, where the prices of assets follow a Wick-Ito stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions, the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of tile fractional Brownian motion. A result about fractional Clark derivative was also obtained.

Three-dimensional analysis of natural convection in nanofluid-filled parallelogrammic enclosure opened from top and heated with square heater

A numerical study based on the finite volume method has been performed to study the three-dimension natural convection in a parallelogrammic top side opened cavity filled nanofluid with partially heated square at the bottom side.Results are obtained for different governing parameters such as nanoparticle concentration (φ) from 0 to 0.05,inclination angle of the back and front walls (α) from 5° to 75°,Rayleigh number from 10^3 to 10^5,and length of heater changer from 0.1 to 1.The main finding from the obtained result showed that the inclination angle and nanoparticle volume fraction affect the flow structure and enhance the heat transfer.

Fault detection method with PCA and LDA and its application to induction motor

A feature extraction and fusion algorithm was constructed by combining principal component analysis(PCA) and linear discriminant analysis(LDA) to detect a fault state of the induction motor.After yielding a feature vector with PCA and LDA from current signal that was measured by an experiment,the reference data were used to produce matching values.In a diagnostic step,two matching values that were obtained by PCA and LDA,respectively,were combined by probability model,and a faulted signal was finally diagnosed.As the proposed diagnosis algorithm brings only merits of PCA and LDA into relief,it shows excellent performance under the noisy environment.The simulation was executed under various noisy conditions in order to demonstrate the suitability of the proposed algorithm and showed more excellent performance than the case just using conventional PCA or LDA.

Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs

In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson （C-N） scheme for solving decoupled FBSDEs. Based on the Taylor and ItS-Taylor expansions, the Malliavin calculus theory （e.g., the multiple Malliavin integration-by-parts formula）, and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.

Rupture segmentation and slip partitioning of the mid-eastern part of the Kunlun Fault,north Tibetan Plateau

The Kunlun Fault, an active fault on the border between the Bayan Har and Kunlun-Qaidam blocks, is one of the major left lateral strike-slip faults in the Tibetan Plateau. Previous research has not reached a consensus on agreeable slip rates along much of its length and the slip rate gradient along the eastern part, both of which play critical roles in a range of models for the eastward extrusion and thickened crust of the Tibetan Plateau. New slip rates have been determined at sites along the eastern part of the Kunlun Fault by dating deposits and measuring atop displaced fluvial terrace risers. Field investigations and interpretation of satellite images reveal geometrical features of the fault and the late Quaternary offset, new earthquake ruptures and surface-rupturing segmentation, from which long-term slip rates and earthquake recurrence intervals on the fault are estimated. The tectonic geomorphology method has determined that the long-term horizontal slip rates on the Tuosuohu, Maqin and Ma- qu segments from west to east are 11.2±1, 9.3±2, and 4.9±1.3 mm/a while their vertical slip rates are 1.2±0.2, 0.7±0.1, and 0.3 mm/a in the late Quaternary. Results indicate that the slip rates regularly decrease along the eastern -300 km of the fault from 〉10 to 〈5 mm/a. This is consistent with the decrease in the gradient such that at the slip rate break point is at the triple point intersection with the transverse fault, which in turn is transformed to the Awancang Fault. The vector decomposition for this tectonic transformation shows that the western and eastern branches of the Awancang Fault fit the slip-partitioning mode. The slip rate of the southwestern wall is 4.6 mm/a relative to the northeastern wall and the slip direction is 112.1°. The mid-eastern part of the Kunlun Fault can be divided into three independent segments by the A＇nyemaqen double restraining bend and the Xigongzhou intersection zone, which compose the surface rupture segmentation indicators for themselves as well as the ending point of the 1937 M7.5 Tuosuohu earthquake. The average recurrence interval of the characteristic earthquakes are estimated to be 500-1000 a, respectively. The latest earthquake ruptures occurred in AD 1937 on the western Tuosuohu segment, as compared to -514-534 a BP on the Maqin segment, and -1055 to 1524 a BP on the Maqu segment. This may indicate a unidirectional migration for surface rupturing earthquakes along the mid-eastern Kunlun Fault related to stress triggered between these segments. Meanwhile, the long-term slip rate is obtained through the single event offset and the recurrence interval, which turn out to be the same results as those determined by the offset tectonic geomorphology method, i.e., the decreasing gradient corresponds to the geometrical bending and the fault＇s intersection with the transverse fault. Therefore, the falling slip rate gradient of the mid-eastern Kunlun Fault is mainly caused by eastward extension of the fault and its intersection with the transverse fault.

Polynomial solutions of quasi-homogeneous partial differential equations

By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite