Abstract: Provided is an X-ray generator including an electron passage in an electron-passage forming member; and a target on an insulative substrate. The transmission X-ray generator irradiates the target with electrons that have passed through the electron passage to generate X-rays. The target is provided at a central region of the substrate; the electron passage accommodates a secondary-X-ray generating section that generates X-rays by irradiation with electrons reflected from the target; the secondary-X-ray generating section and the target are disposed so that both of X-rays generated by direct irradiation of the target with the electrons and X-rays generated by irradiation of the secondary-X-ray generating section with the electrons reflected from the target are radiated to the outside; and at least part of the peripheral region of the substrate has higher transmittance for the X-rays generated at the secondary-X-ray generating section than the central region of the substrate.

Abstract: Provided is an X-ray generator including an electron passage in an electron-passage forming member; and a target on an insulative substrate. The transmission X-ray generator irradiates the target with electrons that have passed through the electron passage to generate X-rays. The target is provided at a central region of the substrate; the electron passage accommodates a secondary-X-ray generating section that generates X-rays by irradiation with electrons reflected from the target; the secondary-X-ray generating section and the target are disposed so that both of X-rays generated by direct irradiation of the target with the electrons and X-rays generated by irradiation of the secondary-X-ray generating section with the electrons reflected from the target are radiated to the outside; and at least part of the peripheral region of the substrate has higher transmittance for the X-rays generated at the secondary-X-ray generating section than the central region of the substrate.

Abstract: In an X-ray generation apparatus of transmission type including an electron emission source, and a target generating an X-ray with collision of electrons emitted from the electron emission source against the target, the X-ray generation apparatus further includes a secondary X-ray generation portion generating an X-ray with collision of electrons reflected by the target against the secondary X-ray generation portion, and the secondary X-ray generation portion and the target are arranged such that the X-ray generated with the direct collision of the electrons against the target and the X-ray generated with the collision of the electrons reflected by the target against the secondary X-ray generation portion are both radiated to an outside. X-ray generation efficiency is increased by effectively utilizing the electrons reflected by the target.

Abstract: Provided is an X-ray generator including an electron passage in an electron-passage forming member; and a target on an insulative substrate. The transmission X-ray generator irradiates the target with electrons that have passed through the electron passage to generate X-rays. The target is provided at a central region of the substrate; the electron passage accommodates a secondary-X-ray generating section that generates X-rays by irradiation with electrons reflected from the target; the secondary-X-ray generating section and the target are disposed so that both of X-rays generated by direct irradiation of the target with the electrons and X-rays generated by irradiation of the secondary-X-ray generating section with the electrons reflected from the target are radiated to the outside; and at least part of the peripheral region of the substrate has higher transmittance for the X-rays generated at the secondary-X-ray generating section than the central region of the substrate.

Abstract: In an X-ray generation apparatus of transmission type including an electron emission source, and a target generating an X-ray with collision of electrons emitted from the electron emission source against the target, the X-ray generation apparatus further includes a secondary X-ray generation portion generating an X-ray with collision of electrons reflected by the target against the secondary X-ray generation portion, and the secondary X-ray generation portion and the target are arranged such that the X-ray generated with the direct collision of the electrons against the target and the X-ray generated with the collision of the electrons reflected by the target against the secondary X-ray generation portion are both radiated to an outside. X-ray generation efficiency is increased by effectively utilizing the electrons reflected by the target.

Abstract: The solution of a constrained optimization problem is easily solved by linearly approximating a point of interest to a first hypersurface given as a constraint and finding the extreme value of the objective function by moving a point r along a curved line having second-order osculation with the geodetic line of a hypersurface S(r)=c and passing through the point r.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: An input coordinate sequence is acquired by sampling a handwritten input pattern at predetermined intervals, and a pattern expressed by this input coordinate sequence is approximated by coupling a plurality of line segments to attain line segment conversion. Adjacent angle data ?[i] is generated based on the directions of the respective line segments. At this time, the segment line length along line segments of all the line segments is divided by a predetermined value at equal intervals, and the angles obtained from the directions of the line segments at respective division positions are defined as ?[i]. This ?[i] is compared with a standard pattern (adjacent angle distribution data) prepared in advance to obtain a matching level. In this way, more accurate pattern matching for a handwritten input, which is approximately invariant to affine transformation and can reduce the influence of discretization errors can be implemented.

Abstract: Hierarchical lattice generating method, apparatus, and program are capable of representing figures of areas in the neighborhood of boundary surfaces on a hierarchical lattice at reduced computation costs and with desired resolutions, using form data for computer simulation. A hierarchical lattice is generated by dividing a group of cells that are composed of vertices and line segments present in a predetermined area, in accordance with a resolution. A boundary surface provided in the area, is represented in the hierarchical lattice by hierarchically dividing cells in a vicinity of a boundary surface. A first value is assigned as an initial value to all of the vertices in the area in an initial state. A second value is assigned to each of vertices in focus, out of the vertices, that has the first value or the second value if any cell to which each of the vertices in focus belongs includes the boundary surface, and otherwise assigning a third value to each of the vertices in focus.

Abstract: The solution of a constrained optimization problem is easily solved by linearly approximating a point of interest to a first hypersurface given as a constraint and finding the extreme value of the objective function by moving a point r along a curved line having second-order osculation with the geodetic line of a hypersurface S(r)=c and passing through the point r.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: There is provided a hierarchical lattice generating method which is capable of representing figures of areas in the neighborhood of boundary surfaces on a hierarchical lattice at reduced computation costs and with desired resolutions, using form data for computer simulation. A hierarchical lattice is generated by dividing a group of cells that are composed of vertices and line segments present in a predetermined area, in accordance with a resolution. A boundary surface provided in the area, is represented in the hierarchical lattice by hierarchically dividing cells in a vicinity of a boundary surface. A first value is assigned to all of the vertices in the area in an initial state. A second value is assigned to each of vertices in focus out of vertices that have the first value or the second value, if any cell to which each of the vertices in focus belongs includes the boundary surface and otherwise assigning a third value to each of the vertices in focus.

Abstract: An input coordinate sequence is acquired by sampling a handwritten input pattern at predetermined intervals, and a pattern expressed by this input coordinate sequence is approximated by coupling a plurality of line segments to attain line segment conversion. Adjacent angle data &phgr;[i] is generated based on the directions of the respective line segments. At this time, the segment line length along line segments of all the line segments is divided by a predetermined value at equal intervals, and the angles obtained from the directions of the line segments at respective division positions are defined as &phgr;[i]. This &phgr;[i] is compared with a standard pattern (adjacent angle distribution data) prepared in advance to obtain a matching level. In this way, more accurate pattern matching for a handwritten input, which is approximately invariant to affine transformation and can reduce the influence of discretization errors can be implemented.

Abstract: An electron-emitting apparatus according to the present invention comprises (A) a substrate, which has a first major surface and a second major surface that are positioned opposite each other, (B) an electron-emitting device, which includes a first electrode, to which a first voltage is applied, and a second electrode, to which a voltage Vf is applied, that are mounted, with an intervening interval, on the first major surface, (C) an anode electrode, which is located opposite and at a distance H from the first major surface, (D) first voltage application means, for applying to the second electrode the voltage Vf that is higher than the first voltage, and (E) second voltage application means, for applying to the anode electrode a voltage Va that is higher than the voltage Vf, wherein a space defined between the anode electrode and the electron-emitting device is maintained in a reduced-pressure condition, and wherein, when a value Xs=H*Vf/(&pgr;*Va) is established for a plane that is substantially per

Abstract: 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.

Abstract: 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.