Abstract: A jack lift device for lifting and positioning loads includes a tube, a pipe and a hoist. The tube is configured to insert into a hole in a top of a step ladder. The tube is configured to couple to the step ladder so that the tube is positioned substantially vertically. The pipe is complementary to and selectively slidably positionable within the tube. A plate is coupled to and extends perpendicularly from an upper end of the pipe. A hoist is coupled to the tube and operationally coupled to the pipe. The plate is configured to position a load, such as a metal conduit. The hoist is positioned to selectively compel the pipe vertically through the tube so that the load that is positioned on the plate is positioned at a desired height, such as proximate to a joist to which the metal conduit is to be is coupled.

Abstract: The invention is defined by an elongate member having a handle end and an opposite sock-engaging end. The member is longitudinally flexible and may be shaped into a generally frusto-conically shaped tube onto which a sock is applied. The sock-engaging lower portion includes longitudinally outwardly projecting shoulders, and preferably sock engaging structures, that engage the sock to retain the sock in place during use. Immediately adjacent to and contiguous with the sock-engaging lower portion is a heel portion that is flexible transversely to the longitudinal axis along the device and which defines a heel-receiving area where the user's heel is placed when being used. Immediately adjacent to and contiguous with the heel portion is an elongate portion and an extended handle portion that the user grasps to pull the entire device upwardly to cause the sock to be properly placed on the user's foot.

Abstract: The invention is defined by an elongate member having a handle end and an opposite sock-engaging end. The member is longitudinally flexible and may be shaped into a generally frusto-conically shaped tube onto which a sock is applied. The sock-engaging lower portion includes longitudinally outwardly projecting shoulders, and preferably sock engaging structures, that engage the sock to retain the sock in place during use. Immediately adjacent to and contiguous with the sock-engaging lower portion is a heel portion that is flexible transversely to the longitudinal axis along the device and which defines a heel-receiving area where the user's heel is placed when being used. Immediately adjacent to and contiguous with the heel portion is an elongate portion and an extended handle portion that the user grasps to pull the entire device upwardly to cause the sock to be properly placed on the user's foot.

Abstract: In performing a pattern search algorithm to find an optimal solution for an optimization, using a set of positive basis vectors that is non-maximal like a set of minimal positive basis vectors as search directions can sometimes causes the algorithm to converge at a non-optimal solution, like a horse saddle. The present invention provides a method to overcome this deficiency by rotating the vectors and hence increase the number of search directions.

Abstract: In performing a pattern search algorithm to find an optimal solution for an optimization, using a set of positive basis vectors that is non-maximal like a set of minimal positive basis vectors as search directions can sometimes causes the algorithm to converge at a non-optimal solution, like a horse saddle. The present invention provides a method to overcome this deficiency by rotating the vectors and hence increase the number of search directions.