Simulation Patents (Class 706/920)
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Patent number: 12236184Abstract: A method of computerized presentation of a legend of object symbols on a document. The method includes receiving a document having object symbols. Each object symbol includes a graphical representation, an object symbol type and an object type numerical value. The method includes generating one or more groups of object symbols of the one or more object symbols based upon the object symbol type of each of the object symbols. The method includes deriving a group cumulative quantity for each group of object symbols based upon the object type numerical value of each object symbol in each group of object symbols. The method includes generating a legend including a one or more legend entries corresponding to each of the one or more groups of object symbols. Each legend entry includes a group type symbol, the object symbol type, and a group cumulative quantity. The method includes displaying the legend.Type: GrantFiled: November 19, 2021Date of Patent: February 25, 2025Assignee: Bluebeam, Inc.Inventors: Jack Kutilek, Elliot Chenault
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Patent number: 12235628Abstract: A computer-implemented resource management method for modular plants may include: receiving data identifying a required module type to be assembled into the modular plant as part of a module pipeline including one or more modules; and executing an optimization algorithm to select, from a plurality of modules having the required module type, a module for inclusion in the module pipeline on the basis of one or more predetermined optimization criteria.Type: GrantFiled: November 26, 2021Date of Patent: February 25, 2025Assignee: ABB Schweiz AGInventors: Marcel Dix, Katharina Stark, Roland Braun, Michael Vach, Sten Gruener, Mario Hoernicke, Nicolai Schoch
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Patent number: 12124356Abstract: Systems and methods for vehicle hardware coverage testing are provided. For instance, a vehicle includes a memory to store a vehicle compute software and a hardware coverage test software associated with the vehicle compute software. The vehicle includes a timer configured based on a timer period and one or more processing units to execute the vehicle compute software using hardware resources of the one or more processing units. Responsive to an expiration of the timer, the one or more processing units execute the hardware coverage test software to test only the hardware resources used by the vehicle compute software and determine whether there is a failure associated with the hardware resources used by the vehicle compute software.Type: GrantFiled: October 31, 2022Date of Patent: October 22, 2024Assignee: GM Cruise Holdings LLCInventor: Edmond Jordan
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Patent number: 11936558Abstract: Systems and methods are provided for evaluation of networks and changes thereto using automated analysis of network models. The automated analysis can be used to determine how to implement and mutate networks efficiently and effectively, to determine whether and why network resources are unable to communicate with each other, and the like. Automated analysis can allow users (e.g., network administrators) to define networks and pose changes to networks using high-level policies (e.g., written in a declarative language), have those polices automatically translated to lower-level implementation operations for analysis, and in some cases have results of the analysis presented back to the users in an easy-to-understand form.Type: GrantFiled: December 10, 2021Date of Patent: March 19, 2024Assignee: Amazon Technologies, Inc.Inventors: Baihu Qian, Bashuman Deb, Justin Lin Hsieh, Daniel William Dacosta, Nick Matthews, Anoop Dawani, Omer Hashmi, Thomas Nguyen Spendley, Viktor Heorhiadi
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Patent number: 11893589Abstract: Support queries are automatically provided. An error is identified during execution of an application. A support query for the error is produced using the source code for the application with the support query including context information for the error. The support query is displayed to a user.Type: GrantFiled: September 15, 2020Date of Patent: February 6, 2024Assignee: International Business Machines CorporationInventors: Grzegorz Piotr Szczepanik, Piotr Kalandyk, Pawel Tadeusz Januszek, Michal Maciej Zalas
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Patent number: 11687860Abstract: Tools and techniques are provided for assessing spill risk in a liquid container storage area of a facility. In one embodiment, a process includes identifying a largest capacity liquid storage container stored in the area; applying a computer-implemented algorithm for calculating a spill reach value for the largest capacity container, and calculating various kinds of risk facet values associated with the area; and generating a risk assessment summary associated with the calculated values. An improvement path can be determined in response to the calculated values, and the liquid storage area may be physically modified to reduce spill risks in the area.Type: GrantFiled: October 26, 2017Date of Patent: June 27, 2023Inventor: Andrew Ian James
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Patent number: 11684315Abstract: Gastric resident electronics, devices, systems, and related methods are generally provided. Some embodiments comprise administering (e.g., orally) an (electronic) resident structure to a subject (e.g., a patient) such that the (electronic) resident structure is retained at a location internal to the subject for a particular amount of time (e.g., at least about 24 hours) before exiting said location internal to the subject. In some embodiments, the resident structure is a gastric resident electronic. That is to say, in some embodiments, the resident structure is configured for relatively long gastric residence and comprises an electronic component. In some embodiments, the structures and components described herein may comprise one or more components configured for the delivery of an active substance(s) (e.g., a pharmaceutical agent) to the subject.Type: GrantFiled: November 28, 2018Date of Patent: June 27, 2023Assignees: Massachusetts Institute of Technology, The Brigham and Women's Hospital, Inc.Inventors: Robert S. Langer, Carlo Giovanni Traverso, Yong Lin Kong
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Patent number: 11507914Abstract: Examples of cognitive procurement are described. In an example embodiment, procurement-specific data sources associated with at least one of a process, an organization, and an industry relevant for procurement operations are monitored. From the monitored procurement-specific data, an operation behavioral pattern is identified. Subsequently, a behavior model of an order is constructed using the operation behavioral pattern and a pre-existing behavior model library. A procurement interaction indicating a query for processing the order is received from a user. The order is tracked by the cognitive order concierge. Using the behavior model, a potential event relating to the order is predicted, the potential event being indicative of an issue affecting the order. Accordingly, the issue affecting the order is proactively remediated to automatically troubleshoot the order. In an example, the user is notified as per the remediation requirement.Type: GrantFiled: March 27, 2019Date of Patent: November 22, 2022Assignee: ACCENTURE GLOBAL SOLUTIONS LIMITEDInventors: Chung-Sheng Li, Emmanuel Munguia Tapia, Jingyun Fan, Cynthia Michelle Barrera, Scott Gillette, Colin Connors, Kayhan Moharreri
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Patent number: 11494292Abstract: A testing engine and/or other machine learning and artificial intelligence evaluates one or more user activity logs associated with one or more users and/or one or more software applications or apps. The testing engine generates one or more testing scripts based on one or more sequences of activities in the one or more user activity logs. Such testing scripts may then be used to perform one or more tests, such as using a testing automation framework and/or engine. In various examples, evaluating the one or more user activity logs and/or generating one or more testing scripts may involve categorizing one or more users, activities, and/or user activity logs; consolidating one or more users, activities, and/or user activity logs; modifying one or more user activity logs; and so on.Type: GrantFiled: February 26, 2021Date of Patent: November 8, 2022Assignee: T-MOBILE USA, INC.Inventor: Michael Waldron
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Patent number: 10372350Abstract: A method for execution by one or more processing modules of one or more computing devices of a dispersed storage network (DSN), the method begins by determining an addressing range of a storage configuration of the DSN. The method continues by determining a storage performance level associated with the addressing range. The method continues by determining whether the storage performance level compares favorably to a storage performance threshold. The method continues, when the storage performance level does not compare favorably to a storage performance threshold, by determining an updated storage configuration associated with the addressing range and re-assigning storage resources in accordance with the updated storage configuration.Type: GrantFiled: October 5, 2016Date of Patent: August 6, 2019Assignee: PURE STORAGE, INC.Inventors: Timothy W. Markison, Jason K. Resch
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Patent number: 9471736Abstract: A computing system includes a memory device into which a design file for a predetermined intellectual property (IP) and a transactor generating tool are loaded, and a processor configured to execute the transactor generating tool loaded into the memory device. The transactor generating tool executed by the processor extracts port information of the IP from the design file, and generates at least one transactor corresponding to the IP based on the port information.Type: GrantFiled: February 26, 2015Date of Patent: October 18, 2016Assignee: Samsung Electronics Co., Ltd.Inventor: In-Gwang Chang
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Patent number: 9030475Abstract: A method for computer-aided design of a modeled object having several faces, comprising a steps of identifying, for each of said faces of the object, at least another of said faces related to said face according to geometrical criteria, and marking such faces as connected; computing a plurality of points forming a tessellated representation of each of said faces; based on this tessellation, defining critical regions by determining and storing data representative of intersection between a three-dimensional geometrical figure and the face related to said face; determining whether intersections occur for each point of the tessellated representation of a face and for each face of the object; computing frontiers between points according to their respectively stored data and determines zones according to the determined frontiers; and, re-computing surfaces according to the determined zones.Type: GrantFiled: April 7, 2006Date of Patent: May 12, 2015Assignee: Dassault SystemesInventors: Joran Maille, Remy Rorato
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Patent number: 8832019Abstract: A method and system to evaluate image-guided dental implant treatment plans with error simulation. Error sources contributing to the inaccuracy of implant cases come from impressions, stone models, radiographic guides, CT scan and its image processing, surgical guides, as well as the surgical procedures. They are translated into the deviations between the planned and actual implant positions and orientations. The error simulation is to continuously modify and update treatment plans with the possible deviations so that the treatment plans can be visually evaluated along with other evaluation tools.Type: GrantFiled: January 31, 2011Date of Patent: September 9, 2014Inventor: Fei Gao
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Patent number: 8222581Abstract: A process of using finite element analysis for determining the behavior of a system, submitted to predetermined load and displacement boundary conditions with a degree of freedom relative to a local coordinate system released at one system node. For a geometrically non-linear solution scheme, a plurality of incremental steps are carried, for which computing for a finite element of the system a displacement vector at the nodes of the finite element is performed by minimizing the energy of the system. For a geometrically linear solution scheme, a single solving step is carried. The step of minimizing is carried out, for a node having a released degree of freedom, in a local frame of reference, and the released degree of freedom at the node is expressed along one axis of such frame. Hybrid reference frames allow expressing and considering in the formulation the constraints of the non-released degrees of freedom simply.Type: GrantFiled: April 10, 2006Date of Patent: July 17, 2012Assignee: Dassault SystemesInventors: Charles-André De Hillerin, Sébastien Voegele
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Patent number: 8224486Abstract: There is provided a device for evaluating and correcting a robot operation program for evaluating an appropriateness for the robot operation program and correcting the robot operation program, comprising a computer including a simulation function for confirming a robot operation. The computer includes a load calculation section for calculating a load given to a motor for driving an operating portion of the robot by a simulation conducted by a computer; and an evaluation section for evaluating, by an evaluation function, whether or not the load exceeds a predetermined allowed value.Type: GrantFiled: December 16, 2010Date of Patent: July 17, 2012Assignee: Fanuc LtdInventors: Yoshiharu Nagatsuka, Toshiya Takeda
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Patent number: 8065022Abstract: Embodiments of the invention can include methods and systems for controlling clearances in a turbine. In one embodiment, a method can include applying at least one operating parameter as an input to at least one neural network model, modeling via the neural network model a thermal expansion of at least one turbine component, and taking a control action based at least in part on the modeled thermal expansion of the one or more turbine components. An example system can include a controller operable to determine and apply the operating parameters as inputs to the neural network model, model thermal expansion via the neural network model, and generate a control action based at least in part on the modeled thermal expansion.Type: GrantFiled: January 8, 2008Date of Patent: November 22, 2011Assignee: General Electric CompanyInventors: Karl Dean Minto, Jianbo Zhang, Erhan Karaca
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Patent number: 8049762Abstract: Architectural structure design methods, architectural structure design apparatuses, and articles of manufacture are described according to some aspects of the disclosure. In one aspect, an architectural structure design method includes responsive to user input, modifying a visual representation of an architectural structure, wherein the visual representation comprises an object of the architectural structure, first displaying the visual representation comprising the object at a first moment in time, wherein the object is positioned at a first location of a display screen, responsive to user input, selecting an attribute for the object from a second location of the display screen which is different than the first location of the display screen, responsive to user input, associating the attribute with the object after the selecting, and displaying the visual representation comprising the object having the attribute at a second moment in time after the associating.Type: GrantFiled: January 13, 2006Date of Patent: November 1, 2011Assignee: Chief Architect, Inc.Inventors: Gregory Wells, Jason Troye, Dermot Dempsey
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Patent number: 7853356Abstract: An apparatus and a method for optimizing robot performance includes a computer connected to the robot controller for receiving performance data of the robot as the controller executes a path program. The computer uses the performance data, user specified optimization objectives and constraints and a kinematic/dynamic simulator to generate a new set of control system parameters to replace the default set in the controller. The computer repeats the process until the new set of control system parameters is optimized.Type: GrantFiled: April 14, 2006Date of Patent: December 14, 2010Assignee: Fanuc Robotics America, Inc.Inventors: Jason Tsai, Yi Sun, Sai-Kai Cheng, Min Ren Jean, Hadi Akeel
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Patent number: 7555021Abstract: A Digital Multi-Source Multi-Destination Video Multiplexer and Crossbar Device and method which may be applied to a video imaging system, in which multiple input image sources including super-computer-generated digital image scenes, personal computer generated digital image scenes, or any machine with OC-48 fiber optically generated digital scenes are multiplexed, bit combined, and output as a selection of multiple digital video output formats.Type: GrantFiled: October 5, 2005Date of Patent: June 30, 2009Assignee: The United States of America as represented by the Secretary of the NavyInventor: Bryan J. Ogilvie
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Patent number: 7369976Abstract: A design of a tire can be facilitated. An optimization apparatus 30 inputs known design parameters of the shape, structure, and pattern of a tire, and performances thereof by an experimental data input unit 40 and learns, as a conversion system of a neural network, a correlation between design parameters of the shape, structure, and pattern of the tire, and performances thereof. Ranges which constrain performances of the tire and design parameters of the shape, structure, and pattern of the tire, which are to be optimized, are inputted in an optimization item input unit 42, and the performances of the tire are predicted in an optimization calculation unit 34 from the design parameters of the shape, structure, and pattern of the tire by using the optimization item and models of the calculation unit 32, and an objective function is optimized until the objective function which is the performances of the tire is converged.Type: GrantFiled: August 8, 1997Date of Patent: May 6, 2008Assignee: Bridgestone CorporationInventor: Yukio Nakajima
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Patent number: 7349838Abstract: Developing decision-making skills of a user through practice in a simulated environment comprises defining a simulated situation to be influenced by the user including a set of objects that are represented by an attribute-characteristic representation, presenting information concerning a current state of the simulation, obtaining decisions from the user that at least partially determine object designs to be evaluated, evaluating an object design using a value function having multiple optima, updating the simulation with the results from the evaluation, and permitting continued practice by selectively repeating several of these steps. A system executes simulation software that simulates such a situation on a processor, and includes evaluation software for selecting and evaluating design objects by applying a value function having multiple optima. At least one terminal and communication links are provided for information transfer and implementation of the simulated situation.Type: GrantFiled: June 30, 2004Date of Patent: March 25, 2008Inventor: Gary J. Summers
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Patent number: 7180411Abstract: A user of a computer aided design (CAD) system graphically places fire alarm appliances, such as smoke detectors and sirens, in a drawing area. After elements are placed and physical paths are determined, a series of electrical circuit connections between alarm source elements and alarm appliance elements are determined. Labels for alarm system device are automatically generated and automatically resequenced. Riser details may be generated in multiple formats. The system also allows standard CAD drawings to be imported into the alarm CAD system. This feature includes a gravitate command which automatically connects unconnected wire paths to the nearest alarm appliance. Circuit requirements can be listed with either a base unit, an appliance, or both. When both the base unit and the corresponding appliance have circuit requirements listed, the circuits are combined into a single listing.Type: GrantFiled: May 16, 2003Date of Patent: February 20, 2007Assignee: M.E.P. Cad, Inc.Inventors: Joseph Reghetti, Barry Kenneth Anspach, Russell Sandquist
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Patent number: 6883148Abstract: A system for using machine-learning to create a model for performing integrated circuit layout extraction is disclosed. The system of the present invention has two main phases: model creation and model application. The model creation phase comprises creating one or more extraction models using machine-learning techniques. First, a complex extraction problem is decomposed into smaller simpler extraction problems. Then, each smaller extraction problem is then analyzed to identify a set of physical parameters that fully define the smaller extraction problem. Next, models are created using machine learning techniques for all of the smaller simpler extraction problems. The machine learning is performed by first creating training data sets composed of the identified parameters from typical examples of the smaller extraction problem and the answers to those example extraction problems as solved using a highly accurate physics-based field solver.Type: GrantFiled: January 31, 2002Date of Patent: April 19, 2005Assignee: Cadence Design Systems, Inc.Inventors: Steven Teig, Arindam Chatterjee
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Publication number: 20040030414Abstract: A general automated method for synthesizing the design of both the topology and parameter values for controllers is described. The automated method automatically makes decisions concerning the total number of signal processing blocks to be employed in the controller, the type of each signal processing block, the topological interconnections between the signal processing blocks, the values of all parameters for the signal processing blocks, and the existence, if any, of internal feedback between the signal processing blocks within the controller. The general automated method can simultaneously optimize prespecified performance metrics (such as minimizing the time required to bring the plant outputs to the desired values as measured by the integral of the time-weighted absolute error or the integral of the squared error), satisfy time-domain constraints (such as overshoot, disturbance rejection, limits on control variables, and limits on state variables), and satisfy frequency domain constraints (bandwidth).Type: ApplicationFiled: January 30, 2003Publication date: February 12, 2004Inventors: John R. Koza, Martin A. Keane, Jessen Yu, Forrest H. Bennett, William Mydlowec
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Publication number: 20040017385Abstract: A system and method is provided for combining independent scene layers to form computer generated environments. The method includes the operation of constructing a terrain layer using stored terrain data. Another operation is generating a feature layer using feature layer data that is stored separately from the stored terrain data. The feature layer and the terrain layer can then be combined to form a composite scene.Type: ApplicationFiled: July 18, 2003Publication date: January 29, 2004Inventors: Michael A. Cosman, Robert C. Dawson, Heber B. Bennion
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Patent number: 6643555Abstract: An apparatus and method of generating an application for a control system. A control process is defined by a physical model and a topological model. An application generator utilizes the physical and topological models to generate an application for the control system.Type: GrantFiled: October 10, 2000Date of Patent: November 4, 2003Assignee: Schneider Automation Inc.Inventors: Thomas Eller, M. Remi Peyrou
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Patent number: 6445964Abstract: To train the sequential kinematic behavior of an automated telekinegenesis robot system, a virtual reality simulator is driven with kinematic parameter data derived from a teleoperational device, which models the sequential behavior to be exhibited by the target robot. Sensor outputs of the teleoperational device are processed by a geometry conversion algorithm, to generate data representative of the spatial kinematics of the robot's desired travel path. A kinematic machine simulator program within a robotic control simulation workstation simulates a virtual machine based upon the actual parameters of the robot. The virtual reality simulation program is interactive, allowing the workstation operator to selectively interrupt the operation of the machine, modify its control parameters, and then rerun the program, until the desired behavior of the target machine is achieved.Type: GrantFiled: January 18, 2000Date of Patent: September 3, 2002Assignee: Harris CorporationInventors: John E. White, Hollis Ambrose, Brent A. Stancil
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Patent number: 6445963Abstract: An advanced control block that implements multiple-input/multiple-output control, such as model predictive control, within a process control system is initiated by creating an initial control block having generic control logic and desired control inputs and control outputs communicatively connected to process outputs and process inputs within a process control routine. A waveform generator within the control block systematically upsets each of the process inputs via the control block outputs using excitation waveforms designed for use in developing a process model. At the same time, a data collection routine collects data indicating the response of each of the process outputs to the waveforms delivered at each of the process inputs. After sufficient data has been collected, a process modeling routine generates a process model from the collected data and a control logic parameter creation routine creates control logic parameters for the control logic from the process model.Type: GrantFiled: October 4, 1999Date of Patent: September 3, 2002Assignee: Fisher Rosemount Systems, Inc.Inventors: Terrence L. Blevins, Wilhelm K. Wojsznis, Vasiliki Tzovla, Dirk Thiele
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Patent number: 6427000Abstract: The present invention performs automated testing on service applications using automatically generated logs, so that new testing applications do not need to be created for each new release of a service application. The invention further provides for testing of all aspects of the service application by accounting for all data and processes performed, and does so without interfering with the processing of the service application. An Automated Regression Tester (ART) captures and records data generated by the execution of an initial version of a service application. This data is recorded to a first test log. When a new or ported version of that service application is developed, the first test log is used by the ART to generated output that emulates the operating environment, including caller and user input, of the service application. The processing of the new/ported version of the service application is captured and recorded to a second test log.Type: GrantFiled: September 24, 1999Date of Patent: July 30, 2002Assignee: WorldCom, Inc.Inventors: Gregory Mumford, Don Stock
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Patent number: 6378013Abstract: A system for assessing performance of a device, such as a hard drive, in a computer system. The system allows measurement of data transfer rates during read and write operations from and to the hard drive. The system comprises a virtual drive in random access memory (RAM) subsystem which acts as a destination and source for the data read from and written into the hard drive. The system determines the data transfer rate of the hard drive by monitoring the duration of the data transfer between the hard drive and virtual drive. This system is able to achieve consistent and reliable assessment of performance of the hard drive.Type: GrantFiled: September 17, 1998Date of Patent: April 23, 2002Assignee: Micron Technology, Inc.Inventor: James H. Hanson
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Patent number: 6366969Abstract: A method of assessing performance of a device, such as a hard drive, in a computer system. The method allows measurement of data transfer rates during read and write operations from and to the hard drive. The method establishes a virtual drive in random access memory (RAM) subsystem to act as a destination and source for the data read from and written into the hard drive. The method determines the data transfer rate of the hard drive by monitoring the duration of the data transfer between the hard drive and virtual drive. The method achieves consistent and reliable assessment of performance of the hard drive.Type: GrantFiled: September 17, 1998Date of Patent: April 2, 2002Assignee: Micron Technology, Inc.Inventor: James H. Hanson
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Patent number: 6195624Abstract: A system (10) and method (42,44,46,48,52,54) for generating an index (38,132,40,134) commensurate with the degree to which a tube array degrades over a period of time due to corrosion in a particular operating environment. A data array (62,114) is created defining the number of tubes in the tube array, a plurality of time points defining time intervals during which the degradation is to be assessed, and operating conditions that induce corrosion during each time interval. The expected degradation value of the array is computed over each of a plurality of time points using a deterministic failure model (88) having at least one parameter (102,104,106) that is assumed constant at each time point. For each time point and at least one parameter, a plurality of values of the parameter (108,110) that deviate from the assumed constant value, are generated.Type: GrantFiled: February 15, 1995Date of Patent: February 27, 2001Assignee: Combustion Engineering, Inc.Inventors: Brian Wilder Woodman, John F. Hall
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Patent number: 6086617Abstract: A directed heuristic search (DHS) has been developed for an optimization design system. The DHS an optimization simulation system has been developed. The DHS directs a design optimization process that implements a user's selections and directions, the order and directions in which the search for an optimal design is to be conducted, and how the search is to sequence through potential design solutions. In addition, DHS is tractable, in that it records a log of the sequence of design solutions that were evaluated during a particular design optimization search. The user may review this search log, to understand how and why the DHS made design optimization decisions. The user may change search parameter settings in a user defined dependency to change future search patterns for optimal designs.Type: GrantFiled: July 18, 1997Date of Patent: July 11, 2000Assignee: Engineous Software, Inc.Inventors: Scott Waldon, Dave Powell, Siu Tong
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Patent number: 6052677Abstract: A multi-dimensional Gauss distribution generating portion obtains one vector from a multi-dimensional Gauss probability distribution and outputs it as an initial momentum. An approximated energy function differential generating portion generates a gradient of an approximated energy function. A Hamilton equation integral portion integrates a Hamilton equation using a gradient of an approximated energy function for a predetermined integral period with initial conditions of an initial state and an initial momentum. The result of the integration as the state of the next alternative is output from a next alternative generating apparatus. The state is used with a high probability corresponding to the difference of approximated energy calculated by an approximated energy difference calculating portion and the difference between a value of an original energy in the present state and that in the next state.Type: GrantFiled: October 24, 1997Date of Patent: April 18, 2000Assignee: Fujitsu LimitedInventors: Ryusuke Masuoka, Hironobu Kitajima
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Patent number: 5844820Abstract: A simulation method and design systems are provided for simulating and analyzing the properties of a periodically structured material such as a semiconductor or a superconductor to develop a novel periodically structured material. In the simulation method of the present invention, an overlap integral between Bloch functions, .psi..sub.m (k.sub.A) and .psi..sub.i (k.sub.B), for two adjacent wave number vectors, k.sub.A and k.sub.B, in Brillouin zone is found as S.sub.im =<.psi..sub.i (k.sub.B).vertline..psi..sub.m (k.sub.A)> whereby a matching degree in terms of symmetrical nature of the Bloch functions, .psi..sub.m (k.sub.A) and .psi..sub.i (k.sub.B), can be quantitatively estimated. Accordingly, if the band array operation matrix, ##EQU1## is diagonalized to find an eigenvalue, .gamma..sub.p and an eigenvector, U.sub.np, then there can be found from .gamma..sub.p and U.sub.np the Bloch functions in a one-to-one relation with two adjacent wave number vectors, k.sub.A and k.sub.Type: GrantFiled: January 21, 1997Date of Patent: December 1, 1998Assignee: Mitsubishi Denki Kabushiki KaishaInventor: Hideharu Nobutoki