185 results about "Series expansion" patented technology

A DTMF signal generating circuit is provided with a frequency designating unit which designates frequencies to form a DTMF signal, a sinusoidal wave computing unit which computes sinusoidal waves by referring to frequencies designated by the frequency designating unit, and a sinusoidal wave synthesizing unit which synthesizes two sinusoidal waves computed by the sinusoidal wave computing unit. The sinusoidal wave computing unit is provided with operators such as an adder-subtracter and a multiplier and generates a sinusoidal wave by determining terms of a Taylor expansion of a sinusoidal function by arithmetic operation.

Methods and apparatus are provided for substantially reducing and/or canceling nonlinearities of any order in circuits, devices, and systems such as amplifiers and mixers. In particular, methods and apparatus are provided for substantially reducing and/or canceling third order nonlinearities in circuits, devices, and systems such as amplifiers and mixers. A first coupler is used to split an input signal into two equal-amplitude in-phase components, each component is processed by two nonlinear devices with different nonlinearities, and a final combiner, such as a 180-degree hybrid, recombines the processed signals 180 degrees out of phase and substantially reduces and/or cancels the undesired nonlinear distortion components arising due to nonlinearities in the nonlinear devices.

Embodiments of the present invention provide methods for optimizing a lithographic projection apparatus including optimizing projection optics therein, and preferably including optimizing a source, a mask, and the projection optics. The projection optics is sometimes broadly referred to as “lens”, and therefore the joint optimization process may be termed source mask lens optimization (SMLO). SMLO is desirable over existing source mask optimization process (SMO), partially because including the projection optics in the optimization can lead to a larger process window by introducing a plurality of adjustable characteristics of the projection optics. The projection optics can be used to shape wavefront in the lithographic projection apparatus, enabling aberration control of the overall imaging process. According to the embodiments herein, the optimization can be accelerated by iteratively using linear fitting algorithm or using Taylor series expansion using partial derivatives of transmission cross coefficients (TCCs).

According to some embodiments of the present invention, a nonlinear system may be modeled by obtaining a transfer function for the nonlinear system and generating a Taylor series expansion of the transfer function. The Taylor series expansion includes a plurality of moments respectively corresponding to a plurality of coefficients of the Taylor series terms. At least one Krylov subspace is derived that matches at least one of the plurality of moments. The nonlinear system is modeled using the at least one Krylov subspace.

Methods and systems are provided for determining the volume of epicardial fat of a heart, which include acquiring a plurality of volumetric image data representing the heart; morphologically characterizing a volume of interest represented by the volumetric image data, including identifying a predetermined number of reference contours of the heart; estimating the epicardial surface, Σ, according to a three-dimensional series expansion of vector spherical harmonic functions based on the reference contours; and determining the volume of epicardial fat based on the voxels which are located inside the estimated epicardial surface, Σ, and which have a grey level within a predetermined range, characteristic of fatty tissue.

The invention provides a random reactive optimization method for a power distribution network including a wind power plant, which is used for eliminating adverse effects caused by various undetermined factors of the power distribution network and keeping the power distribution network run in a qualified voltage state. The method comprises the following specific steps: firstly, establishing a probability calculation model considering various random factors; secondly, establishing determining trend including a fan equivalent circuit, establishing a random trend model for the power distribution network including the wind power plant in combination with a semi invariant and Gram-Charlier series expansion method, and solving the voltage of each node and the probability distribution of reactive output of a generator; and lastly, establishing a reactive optimization model including the wind power plant by taking the voltage of each node and the probability distribution of the reactive output of the generator as the chance constraints of reactive optimization, taking the reactive output limit of the wind power plant as a constraint condition and taking a minimum active consumption expected value as a target function, and solving by using a genetic algorithm.

The invention discloses a method for calculating the probability power flow of a power system containing a wind farm. The method comprises the following steps of: 1, calculating the power of the wind farm and probability distribution of load power; 2, calculating deterministic power flow of the power system containing the wind farm by a Newton method, and solving a sensitivity matrix S0; 3, calculating the each-order cumulant of each node injection vector; 4, solving the each-order cumulant of a state variable according to the each-order cumulant of the injection vector; and 5, solving a probability density function and a cumulative distribution function according to Gram-Charlier series expansion. By the method, errors caused by solving through a cumulant method when the wind farm is processed as a simplified PQ model with a constant power factor can be effectively reduced.

The invention discloses a dynamical probability load flow calculation method with consideration of wind power integration. A draught-fan output model is established on the basis of the Markov chain and a state scenario tree, draught-fan output historical data are normalized, states are partitioned, and a state transfer matrix is obtained according to the change relations between the states; according to the draught-fan output state at the current moment and the state transfer matrix, the most possible states of the draught-fan output at the next moment and the probabilities of the most possible states are predicted, repeated analysis is conducted, and the state scenario tree in a future period is generated; multi-period and multi-state distribution of the draught-fan output is obtained through the state scenario tree; probability load flow calculation based on the semi-invariant method and improved Von-Mises series expansion is conducted on each time section. Calculation results can reflect the relations between probability load flows of a power grid in different time periods, probability distribution of the draught-fan output states can be reasonably predicted, the change rule of the draught-fan output states is accurately described, and the method is used for comprehensively assessing safety and stability of a power system achieving wind power integration.

The objective is to obtain a respiratory induction apparatus and a particle beam therapy system in which respiration can appropriately be induced by accurately evaluating the respiration. There are provided a respiratory induction control unit (7cC) that generates a desired respiratory signal (R_tj(t)) for respiratory induction; a real respiration measurement unit (7a) that outputs a real respiratory signal (R_rl(t)) obtained by measuring real respiration of a patient; and a respiration evaluation unit (7cE) in which by, as a unit, utilizing data of a single period (T_res) of the desired respiratory signal (R_tj(t)), there is calculated a pair of coefficients (a₁ and b₁), of trigonometric functions, which correspond to the 1st-order terms by means of Fourier series expansion of data of the desired respiratory signal (R_tj(t)) and data of the real respiratory signal (R_rl(t)), which is acquired in synchronization with the data of the desired respiratory signal (R_tj(t)), and there are performed comparisons between the respective gains (G_tj and G_rl) and between the respective phases (φ_tj and φ_rl), which are obtained from the coefficients (a₁ and b₁), so that there is evaluated a misalignment of the real respiration from the desired respiratory signal.

The invention relates to a pupil center positioning method for iris recognition. The method includes the following steps that: (1) graying processing is carried out on an original iris image; (2) a gray image is preprocessed; (3) binarization processing is carried out on the gray iris image; (4) a binary image is preprocessed; (5) edge detection is carried out on the binary image; (6) star type scanning is carried out on edge points, so that a polar coordinate distribution diagram is obtained; (7) Fourier series expansion is carried out; (8) the radius of curvature of the edge of the image is calculated, and the edge points are filtered; and (9) filtering results are voted, and a pupil center or location failure is outputted. According to the pupil center positioning method for iris recognition of the invention adopted, according to the gray and shape characteristics of a pupil in the infrared iris image, binarization and edge shape analysis are carried out, and problems in pupil center determination can be solved.

A method is disclosed for processing seismic data. The method includes prestack depth migrating seismic measurements to compute common angle domain image gathers with an initial depth model. Residual moveout analysis is performed in the common angle domain, moveout corrections are derived in terms of the residual radii of curvature at zero reflection angle. Corrections for larger reflection angles are obtained from separate analyses for the coefficients of suitable series expansions. The residual radii of curvature at zero reflection angle can be used to improve the signal to noise ratio of the migrated data and to assess or improve the velocity model used for the prestack depth migration.

The invention relates to a dynamic probability load flow calculation method taking response correlation into account. The method comprises the following steps: (1) creating a probability model of dynamic random injection volume; (2) performing optimized analysis and calculation on imbalance power of a system, creating a dynamic load flow model for reference value distribution of the imbalance power of the system, and working out node voltage and a branch load flow reference value as well as a related sensitivity matrix; (3) performing random variable calculation taking interaction correlation into account, calculating each-order semi-invariant of a random variable, and working out each-order semi-invariants of the node voltage and the branch load flow random quantity by a linearization method based on sensitivity; (4) working out a distribution function to be calculated by a Gram-Charlier series expansion method. The dynamic probability load flow calculation method has the benefits that on one hand, a distribution method for imbalance power of dynamic load flow is used for improving the convergence of random load flow based on semi-invariant when the imbalance power of the system is relatively high, and on the other hand, the response correlation of the random variable can be taken into account.

The present invention discloses a preparation process of phosphonitrogen series expanded fire-retarding agent and fire-retarding agent prepared according to said preparation process. Said preparation process includes the following steps: making polybasic alcohol be reacted with phosphorus oxychloride, making the obtained product undergo the processes of hydrolysis and solution pH value regulation, then making said product be reacted with cyanurotriamide, the described polybasic alcohol includes pentaerythritol and dipentaerythritol, then using surfactant to make surface modification treatment so as to obtain the invented fire-retarding agent.

The invention relates to an airborne SAR image automatic target positioning method, which convert the coordinates of a target in the SAR image into an actual geographic coordinates of the target on the earth by utilizing the flight information (location, speed, etc.) of an aerial carrier and the SAR image information (resolution, center distance, central Doppler frequency, etc.). Based on a range-Doppler equation, the invention combines an earth model equation to carry out an target location, which not only can realize an absolute localization without a control point, but also considers the influence of the earth model on positioning accuracy; on the other hand, Taylor series expansion is used for carrying out the linearization of nonlinear equations; an iterative method is adopted to solve the equation, thus improving the positioning speed; meanwhile, the initial value point of an iterative computation is appropriately selected according to the operation mode of radar, thereby controlling a converging direction in the iteration and avoiding a target confusion. As a positioning method without the control point, the automatic target positioning method of the invention has the advantages of high accuracy and high speed, thereby being capable of carrying out a real-time processing and suitable to various airborne SAR systems.

The invention discloses a rapid probabilistic load flow calculation method considering the static power frequency characteristics of an electric power system. The rapid probabilistic load flow calculation method comprises the steps that electric power system parameters needed by conventional load flow calculation are extracted from the electric power system and are initialized; a frequency variable to be solved is added to a conventional load flow calculation model, an improved rapid decoupling load flow module is established, and the normal state of the node voltage, the system frequency and the branch power of the variable to be solved are worked out; cumulants of each order of the node voltage, the system frequency and the branch power are worked out; through Gram-Charlier series expansion, the cumulative probability distribution function and the probability density function of the node voltage, the system frequency and the branch power of the variable to be solved are worked out. According to the rapid probabilistic load flow calculation method, the influence of uncertain factors on the system frequency in the electric power system and the distribution characteristics of the system frequency are considered in the process of probabilistic load flow analysis, the calculation speed is high, and a complete comprehensive assessment can be provided for the safe and economical operation analysis and the stability analysis of the electric power system.

The present invention relates generally to separation of ions based on their transport properties. More particularly, the invention relates to separation of ionic mixtures and characterization of ions in gases using higher-order differential ion mobility spectrometry (HODIMS) enabled by asymmetric waveforms of fundamentally new types. The invention discloses a method and apparatus for separation of ionic mixtures and characterization, identification, or quantification of ions in a gas based substantially on the terms of third or higher order in a series expansion of ion mobility as a function of electric field intensity. This is achieved using a periodic, time-dependent electric field with novel waveform profiles that cancel or substantially reduce the contributions to time-averaged ion motion of the leading n (where n≧2) terms of that expansion, thereby achieving ion separations based substantially on the (n+1)th term. Separations using HODIMS with different n are expected to be highly orthogonal, enabling multidimensional separations employing HODIMS analyzers of different orders. The expected high orthogonality between HODIMS and mass spectrometry or ion mobility spectrometry would make HODIMS/MS and HODIMS/IMS combinations powerful analytical tools of broad utility.

The invention aims at providing a structural vibration analysis method based on a finite element method and a generalized Fourier series method, which comprises the following steps of: dividing a structure region to be subjected to vibration analysis to respectively and correspondingly form a finite element expression region and a generalized Fourier series expression region; dividing the finite element grids of the finite element expression region to form a corresponding quality stiffness matrix, and selecting a corresponding assumption displacement form according to the characteristics of the generalized Fourier series expression region to form a quality stiffness matrix; subsequently, establishing a virtual spring between the two regions, and converting the potential energy of the virtual spring into an overall coupling stiffness matrix by using an energy variation method; then, arranging the formed quality stiffness matrices according to displacement to form an overall structure quality stiffness matrix; and solving linear equations to obtain an unknown coefficient in corresponding node displacement and series expansion. When applied to a large complex structure, the method not only can obtain precision higher than the finite element method, but also can save a large amount of calculation cost.

As a feature, a local range image described in a log-polar coordinate system with a tangential plane set as an image plane is used. In a created image, ambiguity concerning an angular axis around the normal is normalized as a power spectrum using Fourier series expansion and changed to an amount invariable with respect to rotation. The power spectrum is dimensionally compressed by expanding the power spectrum in a peculiar space using a peculiar vector. Corresponding points are searched by nearest neighbor in a dimensionally compressed space to calculate a correspondence relation among the points. Wrong correspondence is removed by verification to determine a positional relation among range images. A reliable correspondence relation is narrowed down by verification by cross-correlation and a RANSAC to create a tree structure representing a link relation among the range images. A shape mode is created by applying a simultaneous registration method to plural range images of the tree structure using a result of this registration as an initial value.

Providing for reduced complexity or improved accuracy in de-mapping received wireless data streams for multi-channel wireless communication is described herein. By way of example, a low-complexity likelihood algorithm can be employed to de-map data bits from the wireless data streams. In one particular example, the likelihood algorithm can approximate a received bit with a subset of received wireless symbols correlated the bit, reducing algorithm complexity. In other examples, a limited set of received wireless symbols can be employed for the subset, further reducing algorithm complexity. According to at least one other example, logarithmic terms of the algorithm can be approximated with non-logarithmic functions, such as a look-up table, series expansion, polynomial approximation, or the like. These approximations can enhance symbol de-mapping accuracy while maintaining or improving processing overhead for a wireless receiver.

A method and apparatus determines an uncoded bit error rate p_b based on a target symbol error rate ε_s. The uncoded bit error rate p_b is determined based on a weighted series expansion of the target symbol error rate ε_s, comprising weights W that are a function of a maximum number of symbol errors that can be corrected t and a number of symbols in an information field K. The maximum number of symbol errors t and the number of symbols in the information field K is selected such that the uncoded bit error rate p_b that produces a symbol error rate that is less than or equal to the target symbol error rate ε_s is largest.

A method of estimating a thermophysical property of a fluid using a local model is disclosed herein. The method includes generating, for use within the local model, a series expansion of thermodynamic equations relating to the thermophysical property and one or more derivatives involving the thermophysical property. The method further includes evaluating, based upon a set of specified values of parameters of the fluid, a first order term of the series expansion and a second order term of the series expansion. The values of the first order term and the second order term are then compared. A value of the thermophysical property is then automatically updated when the values of the first order term and the second order term are found to differ by more than a predefined amount.

The invention discloses a method for producing sine and cosine signals, which comprises the steps that: an angle sequence is generated; the generated angle is treated with phase truncation; the angle after the phase truncation is parted into a high address bit including highest two address bits and a high address bit, the highest two address bits of which are wiped off, and a low address bit; the symbols of the sine and cosine signals corresponding to the angle are calculated by the highest two address bits; the corresponding sine and cosine values are obtained by inquiring a Pi/2 sine table and a Pi/2 cosine table with the high address bit, the highest two address bits of which are wiped off; the low address bit is corresponded to a trigonometric function for being equivalent to the value of the low address bit; a finite term Tylor series expansion of the trigonometric function is utilized for obtaining the sine and cosine values of the angle by the sine and cosine values and the value of the low address bit; the sine and cosine signals of the angle are obtained by the obtained symbols and the calculated sine and cosine values. The invention also discloses a numerical control oscillator. By utilizing the method, the space occupied by storage lists can be effectively compressed under the condition that phase-truncated word length is not increased.