Abstract: A system for modeling the evolution of a system overtime using an advection-based process is provided. The system continuously evolves a probability density function (“PDF”) for a characteristic of a characteristic of the state of the system and its time-varying parameters. The PDF is evolved based on advection by solving an advection partial differential equation that is based on a system model of the system. The system model has time-varying parameters for modeling the characteristic of the state of the system. The system uses the continuously evolving PDF to make predictions about the characteristic of the state of the system.

Abstract: A system for modeling the evolution of a system over time using an advection-based process is provided. The system continuously evolves a probability density function (“PDF”) for a characteristic of a characteristic of the state of the system and its time-varying parameters. The PDF is evolved based on advection by solving an advection partial differential equation that is based on a system model of the system. The system model has time-varying parameters for modeling the characteristic of the state of the system. The system uses the continuously evolving PDF to make predictions about the characteristic of the state of the system.

Abstract: A system for modeling the evolution of a system over time using an advection-based process is provided. The system continuously evolves a probability density function (“PDF”) for a characteristic of a characteristic of the state of the system and its time-varying parameters. The PDF is evolved based on advection by solving an advection partial differential equation that is based on a system model of the system. The system model has time-varying parameters for modeling the characteristic of the state of the system. The system uses the continuously evolving PDF to make predictions about the characteristic of the state of the system.

Abstract: A tennis racket having string receiving holes in coaxial opposed pairs and having a slot in the throat between the bow and the handle through which the axes of holes pass so that strings can be pulled to the proper tension during stringing of the racket without frictional contact with the holes.

Abstract: A racket stringing apparatus having an open racket head frame holding fixture and means for tensioning a string drawn across the open area of the head frame wherein the fixture is formed as an annulus circumscribing the racket head frame and the latter is rigidly supported interiorly at its yoke and distal ends and exteriorly at its intermediate opposite sides. The conventional string holding clamp is rigidly supported by and in closely coupled relation to the racket head supporting member for minimizing deflection. The head holding fixture is combined with a rotating structure including a conveniently positioned tool supporting tray. A string guide roller ensures aligned passage of the string being tensioned through the racket head openings and proper automatic rotative orientation of the fixture during tensioning of the string. The apparatus further includes an improved string tensioning clamp.

Abstract: A device for aiding in the placement of cross strings in a racket head and having a plurality of transversely spaced substantially coplanar string-bearing surfaces adapted for mounting on a first set of alternate longitudinal strings in the racket head and a plurality of pin-like members mounted for rotation on the support about parallel transversely spaced axes substantially perpendicular to the string bearing surfaces thereon and being mounted for axial displacement. Each of the pin-like members has an offset end rotatable to positions parallel and perpendicular to the longitudinal strings and being positioned for engagement with a second set of longitudinal strings intermediate the first-mentioned strings.

Abstract: A racket stringing machine having a racket head holding fixture and a carriage mounted for reciprocation toward and away from the fixture and a string clamp mounted on the carriage for engaging a string drawn through a racket head mounted on the fixture for tensioning the string upon movement of the carriage away from the fixture; a first brake which is automatically set upon drawing of the string to an elevated tension greater than the desired final predetermined tension to effect a pre-stretching of the string to a length beyond its length at such predetermined tension while permitting a decrease in the string tension; and a second brake which is automatically set to lock the string at the desired final predetermined tension. The apparatus also includes means for providing a controlled restrained rate of increase in string tension and a controlled restrained rate of decreasing string tension at tensions between the predetermined tension and maximum tension.

Abstract: A racket stringing machine having a racket head holding fixture and a carriage and string clamp mounted for reciprocation toward and away from the fixture for engaging a string drawn through a racket head mounted on the fixture for tensioning of the string upon movement of the carriage away from the fixture; a brake for locking the position of the carriage relative to the fixture for maintaining the string at a predetermined tension, the carriage and brake being constructed to permit additional movement of the carriage away from the fixture for applying additional tension to and pre-stretching of the string; and means functioning on decrease of string tension to the desired predetermined tension to apply the brake.