Abstract: Extending the work in 2D/3D graphical databases, the present invention discuss constraints in high dimensional spaces, its efficient storage; relational algebra. The relational algebra includes queries like finding polytopes disjoint or intersecting with the given polytope; or finding a subset or superset of the polytope. This invention also presents methods to generate new information equivalent constraints set from existing constraints sets, presents new kinds of joins and a rich relational algebra of the constraints. Different methods such as distortion, rotation and shape scaling transformations are employed to obtain the information equivalent different sets of constraints. Also, this invention discusses queries to obtain the information equivalent constraints set of the given constraints set along with a new query language, when the data is in memory.

Abstract: The present invention describes a system and method of high speed calculation of magnetic forces and collision detection between coin clusters in the graphical simulation of magnetic carom game, which has facilities of high speed calculation of magnetic forces, collision and dynamics in between the coins and coin clusters. Therefore, our invention is an interactive game simulation, which solves the problem of collision detection involving aggregates in an efficient manner.

Abstract: The present invention describes a system and method of high speed calculation of magnetic forces and collision detection between coin clusters in the graphical simulation of magnetic carom game, which has facilities of high speed calculation of magnetic forces, collision and dynamics in between the coins and coin clusters. Therefore, our invention is an interactive game simulation, which solves the problem of collision detection involving aggregates in an efficient manner.

Abstract: Extending the work in 2D/3D graphical databases, the present invention discuss constraints in high dimensional spaces, its efficient storage; relational algebra. The relational algebra includes queries like finding polytopes disjoint or intersecting with the given polytope; or finding a subset or superset of the polytope. This invention also presents methods to generate new information equivalent constraints set from existing constraints sets, presents new kinds of joins and a rich relational algebra of the constraints. Different methods such as distortion, rotation and shape scaling transformations are employed to obtain the information equivalent different sets of constraints. Also, this invention discusses queries to obtain the information equivalent constraints set of the given constraints set along with a new query language, when the data is in memory.

Abstract: A robust method for solving in a computer, optimization problems under uncertainty including the steps of: specifying the uncertainty as a hierarchical series of sets of constraints on parameters, with the parameters restricted to each constraint set forming an ensemble, and the hierarchy of constraints, represented as mathematical sets forming a hierarchy of ensembles, said hierarchy being based on subset, intersection or disjoint relationships amongst them; utilizing optimization techniques to create effective identify minimum and maximum bounds on the each objective function, said bounds depending on the constraints comprising each ensemble of parameters and being computed for each of the assumptions about the future; estimating a volume of candidate ensembles and relating the volume to one or more information theoretic measures; and utilizing information theoretic measures to analyze and improve the candidate iteratively refine the ensembles and associated by changing a specificity of the bounds on the ob

Abstract: In electrical mechanisms, a synthesis of electrical machines and mechanisms, irregularly shaped magnets are attached to different parts of the mechanism, and provide customizable tangential forces in different configurations. The presence of these tangential forces differentiates electrical mechanisms from other mechanisms. In this invention we present methods to design these magnets based on integral equations involving continuous and/or discrete variables, under a variety of constraints. We show that properly designed electrical mechanisms offer surprising properties—we can design slider-crank mechanisms which can present oscillatory forces to the load, even when driven by a constant force.

Abstract: This invention describes a game of inverse chess, with a pre-identified start position, and end position and arbitered moves chosen amongst a set of possible moves, played between two opponents on a chess board. This differs from normal chess in that it is played backwards in time where the objective is to reconstruct the pre-identified start position, from the pre-identified end position. While the pieces used in the game are essentially the same as that of regular chess, the moves they make are reversed. Since the state-space of this game is much larger in the potential moves, an arbiter is used to validate possible moves that one player might choose to make. Using either a regular or modified chess board, the pieces on the board move backwards. Three such moves are described in the I-castle, spawn and I-check moves. A variant of the game is the two-knight game wherein two knights play each other and the piece reaching the pre-identified start position, win.

Abstract: A robust method for solving in a computer, optimization problems under uncertainty including the steps of: specifying the uncertainty as a hierarchical series of sets of constraints on parameters, with the parameters restricted to each constraint set forming an ensemble, and the hierarchy of constraints, represented as mathematical sets forming a hierarchy of ensembles, said hierarchy being based on subset, intersection or disjoint relationships amongst them; utilizing optimization techniques to create effective identify minimum and maximum bounds on the each objective function, said bounds depending on the constraints comprising each ensemble of parameters and being computed for each of the assumptions about the future; estimating a volume of candidate ensembles and relating the volume to one or more information theoretic measures; and utilizing information theoretic measures to analyze and improve the candidate iteratively refine the ensembles and associated by changing a specificity of the bounds on the ob

Abstract: Modern decision support methods handle uncertainty or hypothesis about operating conditions, using one of two techniques viz. probabilistic formulation and constraints based method, which is the subject of the present invention. A large number of applications use linear constraints to specify uncertainty. These linear constraints are the set of linear inequalities, which are used to define the demand/supply in the area of supply chains. The set of linear inequalities forms a polytope, the volume of which represents the information content. The present invention deals with the application of computational geometrical methods to find the set theoretic relationship—subset, intersection and disjointness among the polytopes and then present a visualization technique to represent these relationships among polytopes. This invention proposes a decision support system and method to visualize the relationship among the polytopes to help with decision support.

Abstract: This invention describes a game of inverse chess, with a pre-identified start position, and end position and arbitered moves chosen amongst a set of possible moves, played between two opponents on a chess board. This differs from normal chess in that it is played backwards in time where the objective is to reconstruct the pre-identified start position, from the pre-identified end position. While the pieces used in the game are essentially the same as that of regular chess, the moves they make are reversed. Since the state-space of this game is much larger in the potential moves, an arbiter is used to validate possible moves that one player might choose to make. Using either a regular or modified chess board, the pieces on the board move backwards. Three such moves are described in the I-castle, spawn and I-check moves. A variant of the game is the two-knight game wherein two knights play each other and the piece reaching the pre-identified start position, win.