Abstract: A method for performing symbolic computations on a mathematical expression. The mathematical expression may be converted to a tree structure having one or more parent nodes and one or more child nodes. Each parent node may be a mathematical operation. Each child node may be a mathematical expression on which the mathematical operation is performed in a specified order. Each child node may be in a hierarchical relationship to one of the parent nodes. The parent nodes, the child nodes or both may be manipulated to perform a first symbolic computation on the mathematical expression.

Abstract: A phase shift control method for a boost converter and circuit implementation comprises a master phase and at least one slave phase. A master-phase inductor current flowing through the master phase has a master-phase charge time interval and a master-phase discharge time interval; a slave-phase inductor current flowing through the slave phase has a slave-phase charge time interval and a slave-phase discharge time interval. The method comprises: calculating an ideal switching timing whereat the slave-phase inductor current descends to a zero-current judgment value; obtaining a physical switching timing whereat the slave-phase charge time interval starts; calculating a conduction timing error between the physical switching timing and the ideal switching timing; determining the time length of the slave-phase charge time interval in the same cycle according to the conduction timing error and the master-phase charge time interval.

Abstract: Techniques for providing arbitrary precision floating number (APFN) processing are disclosed. In some aspects, an APFN store may be used to store a large number (i.e., an APFN) having many significant digits, which in turn may enable a high degree of precision in mathematical operations. An APFN module may be used to create and define the APFN store. The APFN module may enable a user to define a precision (significant digits) for the large number that corresponds to the size of an array of bytes in the APFN store that are allocated for storing the large number. In further aspects, the APFN store may be used to store additional intermediary data and a resultant.

Abstract: A method for converting a polynomial expression to a data structure for symbolic computation. One or more variables in the polynomial expression may be determined. The variables may be stored in a first array. One or more terms in the polynomial expression may be determined. One or more exponents of the variables in each term may be determined. The exponents may be stored in a second array. One or more coefficients of the terms may be determined. The coefficients may be stored in a third array.

Abstract: Real-time rendering of realistic rain is described. In one aspect, image samples of real rain and associated information are automatically modeled in real-time to generate synthetic rain particles in view of respective scene radiances of target video content frames. The synthetic rain particles are rendered in real-time using pre-computed radiance transfer with uniform random distribution across respective frames of the target video content.

Abstract: The present invention relates to switched-mode power supply module and discloses a ferrite mosaic and a magnetic core structure for passive substrate for switched-mode power supply module. The ferrite mosaic includes a supporting plate and numbers of ferrite units stuck on the supporting plate, with each ferrite unit being rectangular. Wherein the ferrite mosaic comprises air-gaps defined between the ferrite units and ferrite glue polymer composites cured in air-gaps, and the magnetic core structure is finished after cutting, laminating and assembling said ferrite mosaics.

Abstract: An adjustment method of a plane of rotation possesses has a step (S62) of detecting a range of the first X-rays from the X-ray tube 125 positioned at a first position with an X-ray detector 70; a step of moving the X-ray tube from the first the position to a second position; a step of detecting a range of the second X-rays from the X-ray tube positioned at the second the position with the X-ray detector 70; a step (S64) of calculating quantity of adjustment of the X-ray tube 125 and the collimator 126 based on the detected ranges by the first X-rays and the second X-rays.

Abstract: Rendering of a partially translucent object is performed using a set of parameter maps derived from data measuring reflectance and transmittance of light received at the surface of the partially translucent object. Data is captured from an actual object being modeled, rather than estimated based on internal structure and composition. Parameter maps relating albedo, thickness variation, and specular intensity and roughness are stored as textures to facilitate rendering. In addition, realistic illumination from high energy sources such as sunlight is effected by separating light into low frequency and high frequency components. Low frequency components are rendered by precomputed radiance transfer. High frequency components, which are not modeled well by precomputed radiance transfer, are modeled using a light visibility convolution integral to generate light visibility maps for positions of the high frequency light source.

Abstract: A non-linear beam tracing technique that supports full non-linear beam tracing effects including multiple reflections and refractions for computer graphics applications. The technique introduces non-linear beam tracing to render non-linear ray tracing effects such as curved mirror reflection, refraction, caustics, and shadows. Beams are allowed to be non-linear where rays within the same beam are not parallel or do not intersect at a single point. Such is the case when a primary beam bounces off of a surface and spawns one or more secondary rays or beams. Secondary beams can be rendered in a similar manner to primary rays or beams via polygon streaming. Beyond smooth ray bundles, the technique can also be applied to incoherent ray bundles which is useful for rendering bump mapped surfaces.

Abstract: The invention relates to heterocyclic substituted amide derivatives that display selective binding to dopamine D3 receptors. In another aspect, the invention relates to a method for treating central nervous system disorders associated with the dopamine D3 receptor activity in a patient in need of such treatment comprising administering to the subject a therapeutically effective amount of said compounds for alleviation of such disorder. The central nervous system disorders that may be treated with these compounds include Psychotic Disorders, Substance Dependence, Substance Abuse, Dyskinetic Disorders (e.g. Parkinson's Disease, Parkinsonism, Neuroleptic-Induced Tardive Dyskinesia, Gilles de la Tourette Syndrome and Huntington's Disease), Dementia, Anxiety Disorders, Sleep Disorders, Circadian Rhythm Disorders and Mood Disorders.

Abstract: Data having express or implied relationships may be displayed by selecting a starting entity in a data structure, building a relationship tree, and building and optimizing a relationship matrix based on the relationship tree. The optimized relationship matrix may be used to layout and render a graphical image that positions various elements with respect to the starting entity based on the relationships. The distance matrix may be optimized by creating a first distance matrix based on the relationship tree, developing a dissimilarity matrix based on expressed or implied relationships, and multiplying the dissimilarity matrix by a weighting factor to determine a distance matrix that may be optimized by multi-dimensional scaling. An optimized weighting factor may be determined and used to select an optimized distance matrix.

Abstract: Disclosed herein is a roll profile for work rolls for both shape control and free ruled rolling. Each of the work rolls has a tapered end. Providing starting point of the tapered end of the rolls being origin of coordinates, the curve of respective tapered end is a quartic curve represented by a formula y(x)=a0+a1x+a2x2+a3x3+a4x4, x?[0,Le], y(x)?[0,He]. Because the transition between the tapered end and the roll body is smooth, asymmetric deformation due to the difference between abrasion of the upper and lower rolls is eliminated, which reducing wedged shape of strip and reducing unstable rolling due to asymmetrical strip stresses caused by the axial shifting of the roll.

Abstract: A composition for binding FKBP proteins is disclosed, along with a method of treating conditions associated with neuronal degeneration, wherein said composition comprises a compound of formula I, wherein, R, R1, R2, R3 and X are as defined herein.

Abstract: Comparing a sample image to a reference image. Differences between the color channel values of the pixels in the sample image and the corresponding color channel values for the corresponding pixels in the reference image are calculated and compared to predefined tolerances. Based on the comparisons, a pixel status for the pixels in the sample image is defined. An image status indicating whether the sample image differs from the reference image is defined based on the defined pixel status.

Abstract: Real-time rendering of realistic rain is described. In one aspect, image samples of real rain and associated information are automatically modeled in real-time to generate synthetic rain particles in view of respective scene radiances of target video content frames. The synthetic rain particles are rendered in real-time using pre-computed radiance transfer with uniform random distribution across respective frames of the target video content.

Abstract: An adjustment method of a plane of rotation possesses has a step (S62) of detecting a range of the first X-rays from the X-ray tube 125 positioned at a first position with an X-ray detector 70; a step of moving the X-ray tube from the first the position to a second position; a step of detecting a range of the second X-rays from the X-ray tube positioned at the second the position with the X-ray detector 70; a step (S64) of calculating quantity of adjustment of the X-ray tube 125 and the collimator 126 based on the detected ranges by the first X-rays and the second X-rays.

Abstract: The invention relates to heterocyclic substituted amide derivatives that display selective binding to dopamine D3 receptors. In another aspect, the invention relates to a method for treating central nervous system disorders associated with the dopamine D3 receptor activity in a patient in need of such treatment comprising administering to the subject a therapeutically effective amount of said compounds for alleviation of such disorder. The central nervous system disorders that may be treated with these compounds include Psychotic Disorders, Substance Dependence, Substance Abuse, Dyskinetic Disorders (e.g. Parkinson's Disease, Parkinsonism, Neuroleptic-Induced Tardive Dyskinesia, Gilles de la Tourette Syndrome and Huntington's Disease), Dementia, Anxiety Disorders, Sleep Disorders, Circadian Rhythm Disorders and Mood Disorders.

Abstract: Rendering of a partially translucent object is performed using a set of parameter maps derived from data measuring reflectance and transmittance of light received at the surface of the partially translucent object. Data is captured from an actual object being modeled, rather than estimated based on internal structure and composition. Parameter maps relating albedo, thickness variation, and specular intensity and roughness are stored as textures to facilitate rendering. In addition, realistic illumination from high energy sources such as sunlight is effected by separating light into low frequency and high frequency components. Low frequency components are rendered by precomputed radiance transfer. High frequency components, which are not modeled well by precomputed radiance transfer, are modeled using a light visibility convolution integral to generate light visibility maps for positions of the high frequency light source.

Abstract: The invention relates to heterocyclic substituted amide derivatives that display selective binding to dopamine D3 receptors. In another aspect, the invention relates to a method for treating central nervous system disorders associated with the dopamine D3 receptor activity in a patient in need of such treatment comprising administering to the subject a therapeutically effective amount of said compounds for alleviation of such disorder. The central nervous system disorders that may be treated with these compounds include Psychotic Disorders, Substance Dependence, Substance Abuse, Dyskinetic Disorders (e.g. Parkinson's Disease, Parkinsonism, Neuroleptic-Induced Tardive Dyskinesia, Gilles de la Tourette Syndrome and Huntington's Disease), Dementia, Anxiety Disorders, Sleep Disorders, Circadian Rhythm Disorders and Mood Disorders.

Abstract: The invention relates to heterocyclic substituted amide derivatives that display selective binding to dopamine D3 receptors. In another aspect, the invention relates to a method for treating central nervous system disorders associated with the dopamine D3 receptor activity in a patient in need of such treatment comprising administering to the subject a therapeutically effective amount of said compounds for alleviation of such disorder. The central nervous system disorders that may be treated with these compounds include Psychotic Disorders, Substance Dependence, Substance Abuse, Dyskinetic Disorders (e.g. Parkinson's Disease, Parkinsonism, Neuroleptic-Induced Tardive Dyskinesia, Gilles de la Tourette Syndrome and Huntington's Disease), Dementia, Anxiety Disorders, Sleep Disorders, Circadian Rhythm Disorders and Mood Disorders.