Abstract: A method for converting a mathematical optimization problem into an object program for a mathematical programming problem. A processor stores, in an object, information on each of components from deblocking of a mathematical expression representing a mathematical model corresponding to a mathematical optimization problem, and holds objects in association with each other through a connecting node as a tree structure in which an object corresponding to the mathematical model is taken as a root node and an object pertaining to each component from the deblocked mathematical expression is taken as a leaf node.

Abstract: Light emitting diode (LED) lights are mixed with incandescent lights in a light string, e.g., for Christmas or other holiday season lighting. In an incandescent light string, such as a mini-light string, in which the incandescent lights are wired in series, LED lights are wired in parallel in one or more groups which are in turn wired in series with incandescent lights in described light string circuits. The LED lights may be provided in the form of an add-on LED light string, or “piggy-back” light string, that for its power supply connects with an empty bulb socket in an incandescent light string. An incandescent flasher bulb may be incorporated into the LED light string to provide surge protection as well as to enable flashing or twinkling of the LED lights. Surge protection may also be provided by an electrical shunt, e.g., a semiconductor shunt, incorporated into the LED light string, or incorporated with the associated empty bulb socket as part of the incandescent light string.

Abstract: Light emitting diode (LED) lights are mixed with incandescent lights in a light string, e.g., for Christmas or other holiday season lighting. In an incandescent light string, such as a mini-light string, in which the incandescent lights are wired in series, LED lights are wired in parallel in one or more groups which are in turn wired in series with incandescent lights in described light string circuits. The LED lights may be provided in the form of an add-on LED light string, or “piggy-back” light string, that for its power supply connects with an empty bulb socket in an incandescent light string. An incandescent flasher bulb may be incorporated into the LED light string to provide surge protection as well as to enable flashing or twinkling of the LED lights. Surge protection may also be provided by an electrical shunt, e.g., a semiconductor shunt, incorporated into the LED light string, or incorporated with the associated empty bulb socket as part of the incandescent light string.