Abstract: A system for solving nonlinear problems in implicit differential equations comprises hardware processors that transform differential equation systems into a unified canonical form enabling efficient numerical solving across multiple integration methods. The processors represent differential equations in a reduced canonical form G(x; v1, v2, ?, c)=v1+Mx??(h) f(x+v2, tn+ch) incorporating solution vectors, integrator parameters, mass matrices, and time parameters. The system generates model-specific mapping functions N(x)=y and N?1(y, ?, v1, v2)=x that transform between differential algebraic equation states and compressed nonlinear solver states, eliminating algebraically redundant variables through symbolic analysis. This compressed representation reduces computational complexity from O(n3) to O(m3) where m<n, while integrator-specific functions v1, v2, and ?(?h) encode method-specific discretization parameters.

Abstract: Methods for producing corn with increased transformability are provided. Markers for increased transformability are provided as well as their use to obtain corn plants with increased transformability. Locations on chromosomes that effect transformation efficiency of monocots are identified.

Abstract: A bicycle trailer hitch assembly including first and second complementary hitch bracket members adapted and arranged for attachment to opposites sides of the bicycle frame rear wheel drop out. Each bracket member includes a main body portion configured on one side for abutting relation with the bicycle rear wheel drop out and on the other side for receiving the trailer tongue tube to provide center pulling of the trailer. The bicycle quick release skewer which holds the rear wheel clamped to the drop out member likewise secures both brackets to the drop out member. Each of the brackets has a fastener arrangement for enabling securing the bracket to the trailer drawbar.

Abstract: Methods for using genetic marker genotype (e.g., gene sequence diversity information) to improve the process of developing plant varieties (e.g., single cross hybrids) with improved phenotypic performance are provided. Methods for predicting the value of a phenotypic trait in a plant are provided. The methods use genotypic, phenotypic, and optionally family relationship information for a first plant population to identify an association between at least one genetic marker and the phenotypic trait, and then use the association to predict the value of the phenotypic trait in one or more members of a second, target population of known marker genotype. Methods for identifying new allelic variants affecting the trait are also provided. Plants selected, provided, or produced by any of the methods herein, transgenic plants created by any of the methods herein, and digital systems for performing the methods herein are also provided.

Abstract: A method of making an electric motor which eliminates the need for a separate endplay adjustment wherein permanent magnets act on the armature laminations to urge the motor shaft in one direction so that the entire endplay appears at only one end of the shaft.