Interpolation method, apparatus for carrying out the method, and control program for implementing the method
    2.
    发明授权
    Interpolation method, apparatus for carrying out the method, and control program for implementing the method 失效
    插值方法,执行方法的装置以及用于实现该方法的控制程序

    公开(公告)号:US07349936B2

    公开(公告)日:2008-03-25

    申请号:US10632136

    申请日:2003-07-31

    IPC分类号: G06F7/38

    CPC分类号: G06F17/175

    摘要: There is provided an interpolation method for the Volume-of-Fluid (VOF) applied to a two-phase incompressible fluid, in particular, which makes it possible to cause time evolution of a shape-describing function based on the Volume-of-Fluid (VOF) method while preserving a sharpness of a shape described by the function. The method defines a function F on a one-dimensional structured grid formed on a one-dimensional real region, the function being defined through definition of a value thereof at a center of each cell within the one-dimensional structured grid, as an interpolation function H. With respect to a cell of interest on the one-dimensional structured grid, a slope is set to zero if a forward difference and a backward difference of the function f have different signs, and to a value twice as large as a smaller one of absolute values of the forward difference and the backward difference if the forward difference and the backward difference have the same sign. The function F on a partial region of the one-dimensional real region determined by the cell of interest is defined by a linear function having a value of F0 at a center of the cell of interest and the slope.

    摘要翻译: 提供了一种应用于两相不可压缩流体的流体流体(VOF)的插值方法,特别地,这可以使基于流体体积的形状描述函数的时间演化 (VOF)方法,同时保持由该功能描述的形状的清晰度。 该方法定义了在一维实体区域上形成的一维结构网格上的函数F,该函数通过在一维结构化网格内的每个单元的中心定义其值作为内插函数来定义 对于一维结构化网格上的感兴趣的单元格,如果函数f的前向差和后向差具有不同的符号,则将斜率设置为零,并且将其设置为与小的两倍大的值 如果正向差和后向差具有相同的符号,则前向差和后向差的绝对值。 由感兴趣单元确定的一维实际区域的部分区域上的函数F由在关注单元格的中心处具有值F0的线性函数和斜率来定义。

    Optimization method with constraints and apparatus therefor
    3.
    发明授权
    Optimization method with constraints and apparatus therefor 失效
    具有限制和优化方法的优化方法

    公开(公告)号:US07197486B2

    公开(公告)日:2007-03-27

    申请号:US10192158

    申请日:2002-07-11

    IPC分类号: G06F7/10

    CPC分类号: G06Q10/04 Y10S706/919

    摘要: In a method for determining a minimum value of an optimization function under constraints given by equations, a set of points which satisfy the constraints is regarded as a Riemannian manifold within a finite-dimensional real-vector space, the Riemannian manifold is approached from an initial position within the real-vector space. An exponential map regarding a geodesic line equation with respect to a tangent vector on the Riemannian manifold ends at a finite order, an approximate geodesic line is generated as a one-dimensional orbit. An approximate parallel-translation is performed on the tangent vector on the Riemannian manifold and on the orbit generated in the orbit generating step by finite-order approximation of the exponential map regarding the parallel translation of the tangent vector. By repeating the above-described procedure from the position at which a minimum value is given until the minimum value on the orbit converges, the solution of the optimization problem with constraints is determined using a simple calculation procedure.

    摘要翻译: 在用等式确定的约束条件下确定优化函数的最小值的方法中,满足约束的一组点被认为是有限维实空间中的黎曼流形,黎曼流形从初始 在实数向量空间内的位置。 关于黎曼流形上的切线向量的测地线方程的指数图以有限的顺序结束,生成近似测线,作为一维轨道。 对黎曼流形上的切线向量和在轨道生成步骤中产生的轨道上的切线矢量进行近似平行平移,通过有限次逼近关于切线矢量的并行平移的指数图。 通过从给出最小值的位置重复上述过程直到轨道上的最小值收敛,使用简单的计算过程来确定具有约束的优化问题的解。

    Electron-emission device and apparatus and image-formation using same
    4.
    发明授权
    Electron-emission device and apparatus and image-formation using same 失效
    电子发射装置和装置以及使用它们的图像形成

    公开(公告)号:US06262701B1

    公开(公告)日:2001-07-17

    申请号:US08565871

    申请日:1995-12-01

    IPC分类号: G09G322

    摘要: An electron-emitting device having an electron-emitting portion between a lower potential side electrode and a higher potential side electrode which are opposite to each other, the electron-emitting device including a field correction electrode disposed adjacent to the lower potential side electrode or the higher potential side electrode and capable of independently supplying a potential.

    摘要翻译: 一种电子发射器件,其具有彼此相对的下电位侧电极和较高电位侧电极之间的电子发射部分,该电子发射器件包括邻近下电位侧电极设置的场校正电极或 高电位侧电极,能够独立地提供电位。

    Finite element method library, finite element method program, and storage medium
    6.
    发明授权
    Finite element method library, finite element method program, and storage medium 失效
    有限元方法库,有限元法程序和存储介质

    公开(公告)号:US07197440B2

    公开(公告)日:2007-03-27

    申请号:US10192159

    申请日:2002-07-11

    IPC分类号: G06F17/10 G06F9/44

    CPC分类号: G06F17/5018

    摘要: It provides a finite element method library which improves the reliability of a program using the finite element method as a library, and avoids calculation errors and an increase in convergence time due to programming errors. To this end, a library that describes a program process based on the finite element method is characterized in that a vector of a vector space spanned by basis functions of the finite element method, and a dual vector of a dual vector space defined by a metric derived from an inner product which is determined by the square integrations of the basis functions, are defined as different abstract data types.

    摘要翻译: 它提供了一种有限元方法库,它使用有限元方法作为库来提高程序的可靠性,并避免计算错误和由于编程错误引起的收敛时间的增加。 为此,描述基于有限元方法的程序过程的库的特征在于,由有限元方法的基函数跨越的向量空间的向量和由度量定义的双向量空间的双向量 从由基函数的平方积分确定的内积产生的,被定义为不同的抽象数据类型。

    Electron-emitting apparatus having a periodical electron-emitting region
    7.
    发明授权
    Electron-emitting apparatus having a periodical electron-emitting region 有权
    具有周期性电子发射区的电子发射装置

    公开(公告)号:US06259191B1

    公开(公告)日:2001-07-10

    申请号:US09437746

    申请日:1999-11-10

    IPC分类号: H01J130

    CPC分类号: H01J9/027 H01J1/316

    摘要: An electron-emitting apparatus is constituted by an electron-emitting device having an electroconductive film including electron-emitting portions, and an electrode for attracting electrons. An electrically insulated elongated region is formed in the electroconductive film to divide the film into a higher potential side and a lower potential side. The insulated region has a substantially periodical shape formed of portions projecting to the higher potential side and portions projecting to the lower potential side. Continuous electron-emitting portions are present at at least part of the portion projecting to the higher potential side in one period of the insulated region.

    摘要翻译: 电子发射设备由具有包括电子发射部分的导电膜和用于吸引电子的电极的电子发射器件构成。 在导电膜中形成电绝缘的细长区域,以将膜分成较高的电势侧和较低的电位侧。 绝缘区域具有基本上周期性的形状,其形成为突出到较高电位侧的部分和向下电位侧突出的部分。 连续的电子发射部分存在于在绝缘区域的一个周期内突出到较高电位侧的部分的至少一部分。

    Electron-emitting apparatus having a periodical electron-emitting region
    8.
    发明授权
    Electron-emitting apparatus having a periodical electron-emitting region 失效
    具有周期性电子发射区的电子发射装置

    公开(公告)号:US6005334A

    公开(公告)日:1999-12-21

    申请号:US845770

    申请日:1997-04-28

    IPC分类号: H01J1/316 H01J9/02 H01J1/30

    CPC分类号: H01J9/027 H01J1/316

    摘要: An electron-emitting apparatus is constituted by an electron-emitting device having an electroconductive film including electron-emitting portions, and an electrode for attracting electrons. An electrically insulated elongated region is formed in the electroconductive film to divide the film into a higher potential side and a lower potential side. The insulated region has a substantially periodical shape formed of portions projecting to the higher potential side and portions projecting to the lower potential side. Continuous electron-emitting portions are present at at least part of the portion projecting to the higher potential side in one period of the insulated region.

    摘要翻译: 电子发射设备由具有包括电子发射部分的导电膜和用于吸引电子的电极的电子发射器件构成。 在导电膜中形成电绝缘的细长区域,以将膜分成较高的电势侧和较低的电位侧。 绝缘区域具有基本上周期性的形状,其形成为突出到较高电位侧的部分和向下电位侧突出的部分。 连续的电子发射部分存在于在绝缘区域的一个周期内突出到较高电位侧的部分的至少一部分。

    OPTIMUM DESIGN METHOD AND APPARATUS, AND PROGRAM FOR THE SAME
    10.
    发明申请
    OPTIMUM DESIGN METHOD AND APPARATUS, AND PROGRAM FOR THE SAME 失效
    最佳设计方法和设备及其相关程序

    公开(公告)号:US20080015828A1

    公开(公告)日:2008-01-17

    申请号:US11778367

    申请日:2007-07-16

    IPC分类号: G06F17/10

    CPC分类号: G06F17/11

    摘要: In an optimum design method comprising a first solution determining step of solving an optimization problem of a first evaluation function for a state variable vector with a design variable vector being as a parameter, and a second solution determining step of solving an optimization problem of a second evaluation function for the design variable vector and the state variable vector thus obtained, the second solution determining step includes the steps of computing a gradient vector of the second evaluation function for the design variable vector, computing a first coefficient based on a value of a norm of the gradient vector, computing a search vector based on the first coefficient, computing a second coefficient, and updating the design variable vector based on the second coefficient. The second coefficient computing step includes the first solution determining step, the first solution determining step is executed as an iterative method based on the gradient vector, and the state variable vector is not initialized during iteration. The optimum design method is precisely adaptable for structural changes.

    摘要翻译: 一种最优设计方法,包括:第一解决方案确定步骤,用于以设计变量向量作为参数来求解用于状态变量向量的第一评估函数的优化问题;以及第二解决方案确定步骤,用于求解第二 第二解决方案确定步骤包括以下步骤:计算用于设计变量向量的第二评估函数的梯度向量,基于规范的值计算第一系数;对于设计变量向量和状态变量向量的评估函数, 的梯度向量,基于第一系数计算搜索向量,计算第二系数,并且基于第二系数更新设计变量向量。 第二系数计算步骤包括第一解决方案确定步骤,基于梯度向量作为迭代方法执行第一解决方案确定步骤,并且在迭代期间不初始化状态变量向量。 最佳设计方法适用于结构变化。