Abstract: Embodiments described herein include electronic packages and methods of forming such packages. An electronic package includes a package substrate, first conductive pads formed over the package substrate, where the first conductive pads have a first surface area, and second conductive pads over the package substrate, where the second conductive pads have a second surface area greater than the first surface area. The electronic package also includes a solder resist layer over the first and second conductive pads, and a plurality of solder resist openings that expose one of the first or second conductive pads. The solder resist openings of the electronic package may include conductive material that is substantially coplanar with a top surface of the solder resist layer. The electronic package further includes solder bumps over the conductive material in the solder resist openings, where the solder bumps have a low bump thickness variation (BTV).

Abstract: A computer-implemented method and system for representing and solving at least one of an algebraic problem, a proportions problem, and a linear growth problem. A graphical user interface has a symbolic section and a pictorial section. The symbolic section includes a symbolic representation of the mathematical problem and the pictorial section includes a pictorial representation of the mathematical problem. An input is received from a user. The input is associated with one of the symbolic section and the pictorial section. In response to the input, the other of the symbolic section and the pictorial section is modified such that the symbolic section and the pictorial section track each other. The user solves the mathematical problem by interacting with at least one of the symbolic section and the pictorial section.

Abstract: An instructional system and method for representing and solving algebraic problems. A computer-implemented method of representing and solving mathematical problems comprises providing a graphical user interface for displaying an instructional system. The instructional system comprises a primary cog having a plurality of primary cog teeth and a secondary cog having a plurality of secondary cog teeth. The secondary cog is linked to the primary cog such that a rotation of the secondary cog causes a rotation of the primary cog. The method comprises representing a mathematical problem on the graphical user interface using the instructional system. The method includes receiving an input from a user and rotating the secondary cog based on the input to cause the primary cog to also rotate. The mathematical problem is solved when a particular tooth of the plurality of primary cog teeth reaches a predefined location.

Abstract: An instructional system and method for representing and solving algebraic problems. A computer-implemented method of representing and solving mathematical problems comprises providing a graphical user interface for displaying an instructional system. The instructional system comprises a primary cog having a plurality of primary cog teeth and a secondary cog having a plurality of secondary cog teeth. The secondary cog is linked to the primary cog such that a rotation of the secondary cog causes a rotation of the primary cog. The method comprises representing a mathematical problem on the graphical user interface using the instructional system. The method includes receiving an input from a user and rotating the secondary cog based on the input to cause the primary cog to also rotate. The mathematical problem is solved when a particular tooth of the plurality of primary cog teeth reaches a predefined location.

Abstract: A tile instructional system for presenting a linear growth problem and for allowing the linear growth problem to be solved comprises an input tray having at least a first tile and a second tile. The first tile has a first marking and the second tile has a second marking. Each of the first tile and the second tile is configured to selectively expand in accordance with its respective marking. The system includes a tile bed comprising a plurality of tile slots. Each of the plurality of tile slots is configured to receive a tile. The linear growth problem is solvable by situating in the tile bed at least one of the first tile and the second tile and by causing each tile situated in the tile bed to expand in accordance with its respective marking to fill the tile bed.

Abstract: A liquid flow instructional system for presenting a proportions problem and for allowing the proportions problem to be solved comprises an input container and a plurality of output containers selectively and fluidly coupled to the input container. The system has an adjustable valve having a plurality of configurable regions. Each of the plurality of configurable regions corresponds to one of the plurality of output containers. An activable switch is provided for initiating flow of liquid from the input container to the plurality of output containers in accordance with a user configuration of the plurality of configurable regions. The proportions problem is solvable by filling each of the plurality of output containers to capacity without spillage. The correspondence between the plurality of configurable regions and the plurality of output containers is indicated by a visible indicator.

Abstract: A liquid flow instructional system for presenting a proportions problem and for allowing the proportions problem to be solved comprises an input container and a plurality of output containers selectively and fluidly coupled to the input container. The system has an adjustable valve having a plurality of configurable regions. Each of the plurality of configurable regions corresponds to one of the plurality of output containers. An activable switch is provided for initiating flow of liquid from the input container to the plurality of output containers in accordance with a user configuration of the plurality of configurable regions. The proportions problem is solvable by filling each of the plurality of output containers to capacity without spillage. The correspondence between the plurality of configurable regions and the plurality of output containers is indicated by a visible indicator.

Abstract: A tile instructional system for presenting a linear growth problem and for allowing the linear growth problem to be solved comprises an input tray having at least a first tile and a second tile. The first tile has a first marking and the second tile has a second marking. Each of the first tile and the second tile is configured to selectively expand in accordance with its respective marking. The system includes a tile bed comprising a plurality of tile slots. Each of the plurality of tile slots is configured to receive a tile. The linear growth problem is solvable by situating in the tile bed at least one of the first tile and the second tile and by causing each tile situated in the tile bed to expand in accordance with its respective marking to fill the tile bed.

Abstract: A method for adaptively teaching content to a user comprises providing a plurality of teaching topics. The method includes sequentially associating a lead problem and a plurality of secondary problems with each of the plurality of teaching topics. Each of the lead problems and the plurality of secondary problems is an open-ended puzzle having a range of solutions and a difficulty rank. The range of solutions for each of the lead problems and the plurality of secondary problems has an optimal solution and a plurality of secondary solutions. A teaching topic is selected and a corresponding lead problem is presented to a user. User provides answer data via a physical input device having enmeshed gears. The user is provided another secondary problem in the selected teaching topic if the answer data matches one of the secondary solutions. The user is provided another lead problem if the answer data matches the optimal solution.

Abstract: A method for adaptively teaching content to a user comprises providing a plurality of teaching topics. The method includes sequentially associating a lead problem and a plurality of secondary problems with each of the plurality of teaching topics. Each of the lead problems and the plurality of secondary problems is an open-ended puzzle having a range of solutions and a difficulty rank. The range of solutions for each of the lead problems and the plurality of secondary problems has an optimal solution and a plurality of secondary solutions. A teaching topic is selected and a corresponding lead problem is presented to a user. User provides answer data via a physical input device having enmeshed gears. The user is provided another secondary problem in the selected teaching topic if the answer data matches one of the secondary solutions. The user is provided another lead problem if the answer data matches the optimal solution.

Abstract: A lighting device such as an electronic ballast or LED driver includes a power factor correction (PFC) controller responsive to input power supply signals to generate control signals, a PFC boost converter responsive to said control signals to generate a boosted output voltage, and a fast start circuit with a power supply source and an energy storage device, a magnitude of the input power supply signal corresponding to energy stored in the energy storage device. During a first mode, the fast start circuit responds to a rectified mains input to enable the power supply source and charge the energy storage device. During a second mode, the fast start circuit responds to a magnitude of the power supply signal to disable the power supply source and discharge the energy storage device. The boost converter during the second operating mode maintains controller operation while the power supply source is disabled.

Abstract: An electronic ballast circuit includes a filament drive circuit that can adjust the pulse width of a pulsed heating signal in accordance with the lamp current to a gas-discharge lamp. A logic device, such as an SR flip-flop, is used to control a switch that is coupled to the primary winding of a filament drive transformer coupled to the lamp filaments. The logic device opens and closes the switch device to generate the pulses of the pulsed heating signal and thus controls the pulse width of the pulses. A clock signal triggers logic device to start a pulse while the end of the pulse is determined by a signal level across a resistor in series with the primary winding of filament drive transformer. Once this signal level is at or above a threshold level, logic device switches the switch device to end the pulse.

Abstract: A method of controlling a series-resonant, half-bridge inverter includes turning off the bottom switch and turning on the top switch the inverter when the current through the resonant inductor crosses the zero axis while the current is increasing, thereby insuring zero voltage switching of the inverter switches and increases the overall switching period so that the actual inverter frequency is closer to the resonant frequency of the series-resonant circuit. Using an on-time control circuit, the method further includes controlling the current delivered to the load (such as a gas discharge lamp) by varying the on-time of the top inverter switch.