Abstract: Flange technologies are described for a flange comprising a first and second side. Each side may include a knife edge surface disposed circumferentially around a base surface and a periphery section disposed around the knife edge surface. The knife edge surface and the periphery section are effective to define grooves therebetween. The flange may include an alloy with a relatively high thermal conductivity and yield strength. The flange may include water channels to remove heat.

Abstract: Flange technologies are described for a flange comprising a first and second side. Each side may include a knife edge surface disposed circumferentially around a base surface and a periphery section disposed around the knife edge surface. The knife edge surface and the periphery section are effective to define grooves therebetween. The flange may include an alloy with a relatively high thermal conductivity and yield strength. The flange may include water channels to remove heat.

Abstract: A computer program product, system and method are disclosed for aggregating expenses incurred by members of a group of commonly acquainted parties (the parties comprising individuals, entities, or organizations), and for collecting pro rated funds from each member. The parties are brought into communication by a computerized central managing forum, communicating via a network, which acts as a fiduciary of the parties and uses a uniquely configured data processing device which prompts the interconnected parties to remit pro rated payments of digitized bills stored and made digitally available by the central managing forum to the parties. Members network and generate pictures that are pertinent to products or services that benefit the collective. Merchants analyze personal information of members, and networking activity between members to provide discount offers accordingly.

Abstract: Query results and statistics regarding them are generated using a novel representation of an n-attribute relation as an order n relational tensor. Orders of the relational tensor respectively correspond to each of the attributes, and each coordinate along an order relates to a key value of the corresponding attribute. Numeric values are stored in the relational tensor, each numeric value representing a count of tuples having the attribute key values that correspond to the coordinate of the numeric value along the orders of the relational tensor. This storage representation is useful in a variety of contexts for enhancing the performance of a RDBMS system. Specifically, a data-representing relational tensor can be used to produce results for operations such as SQL restriction operations using IN and EXISTS criteria.

Abstract: Query results and statistics regarding them are generated using a novel representation of an n-attribute relation as an order n relational tensor. Orders of the relational tensor respectively correspond to each of the attributes, and each coordinate along an order relates to a key value of the corresponding attribute. Numeric values are stored in the relational tensor, each numeric value representing a count of tuples having the attribute key values that correspond to the coordinate of the numeric value along the orders of the relational tensor. This storage representation is useful in a variety of contexts for enhancing the performance of a RDBMS system. Specifically, a data-representing relational tensor can be used to produce results for join operations such as the SQL operations JOIN, LEFT OUTER JOIN, RIGHT OUTER JOIN and FULL OUTER JOIN.

Abstract: Query results and statistics regarding them are generated using a novel representation of an n-attribute relation as an order n relational tensor. Orders of the relational tensor respectively correspond to each of the attributes, and each coordinate along an order relates to a key value of the corresponding attribute. Numeric values are stored in the relational tensor, each numeric value representing a count of tuples having the attribute key values that correspond to the coordinate of the numeric value along the orders of the relational tensor. This storage representation is useful in a variety of contexts for enhancing the performance of a RDBMS system. Specifically, a data-representing relational tensor can be used to produce results for tuple grouping operations such as the SQL operations COUNT . . . GROUP BY, SUM . . . GROUP BY, AVG . . . GROUP BY, MIN . . . GROUP BY and MAX . . . GROUP BY.

Abstract: Query results and statistics regarding them are generated using a novel representation of an n-attribute relation as an order n relational tensor. Orders of the relational tensor respectively correspond to each of the attributes, and each coordinate along an order relates to a key value of the corresponding attribute. Numeric values are stored in the relational tensor, each numeric value representing a count of tuples having the attribute key values that correspond to the coordinate of the numeric value along the orders of the relational tensor. This storage representation is useful in a variety of contexts for enhancing the performance of a RDBMS system. Specifically, in a first aspect of the invention, a tensor representation can be used to generate statistics for a user query so that the relational database system can determine, from among two candidate approaches, an approach to use in processing the user query based on the statistic.

Abstract: Query results and statistics regarding them are generated using a novel representation of an n-attribute relation as an order n relational tensor. Orders of the relational tensor respectively correspond to each of the attributes, and each coordinate along an order relates to a key value of the corresponding attribute. Numeric values are stored in the relational tensor, each numeric value representing a count of tuples having the attribute key values that correspond to the coordinate of the numeric value along the orders of the relational tensor. This storage representation is useful in a variety of contexts for enhancing the performance of a RDBMS system. Specifically, a data-representing relational tensor can be used to produce results for tuple grouping operations such as the SQL operations COUNT . . . GROUP BY, SUM . . . GROUP BY, AVG . . . GROUP BY, MIN . . . GROUP BY and MAX . . . GROUP BY.

Abstract: Query results and statistics regarding them are generated using a novel representation of an n-attribute relation as an order n relational tensor. Orders of the relational tensor respectively correspond to each of the attributes, and each coordinate along an order relates to a key value of the corresponding attribute. Numeric values are stored in the relational tensor, each numeric value representing a count of tuples having the attribute key values that correspond to the coordinate of the numeric value along the orders of the relational tensor. This storage representation is useful in a variety of contexts for enhancing the performance of a RDBMS system. Specifically, in a first aspect of the invention, a tensor representation can be used to generate statistics for a user query so that the relational database system can determine, from among two candidate approaches, an approach to use in processing the user query based on the statistic.