1460752849-c54a82bd-1361-470f-b0a0-e4e465aea2e5

1. An apparatus for collecting debris including a stand having a plurality of support legs pivotally mounted to an upper support frame, a chute having an upper end portion and a lower free end, said upper end portion of said chute being pivotally mounted relative to said upper support frame such that said chute extends outwardly and downwardly relative to said upper support frame to said lower free end when in use, said plurality of support legs and said chute being pivoted to a collapsed storage position in generally parallel relationship with said upper support frame, whereby debris urged upwardly along said chute from said lower free end to said upper end portion will pass by gravity through said upper support frame into a collection receptacle.
2. The apparatus of claim 1 in which a pair of said plurality of support legs are inclined outwardly from first pivot connections said support frame to lower ends, and said chute being secured to said inclined legs whereby said chute is pivotably mounted relative to said upper support frame.
3. The apparatus of claim 2 including stop means for limiting the pivotal movement of at least two of said plurality of support legs relative to said upper support frame.
4. The apparatus of claim 2 wherein said chute includes a pair of spaced upwardly extending side members extending along a substantial length of said chute for purposes of preventing debris from falling from opposite sides of said chute as debris is moved toward said upper support frame.
5. The apparatus of claim 4 including means for hingely mounting said side members relative to a bottom of said chute, and means for maintaining said side members in a raised position extending generally transversely with respect to a primary plane defined by said bottom of said chute.
6. The apparatus of claim 5 wherein said chute includes a flexible material mounted to said pair of included support legs and said side members, and means for releasably securing said flexible material to said pair of inclined support legs.
7. An apparatus for collecting debris including a stand having a plurality of support legs pivotally mounted to an upper support frame, a chute having an upper end portion and a lower free end, said upper end portion being mounted to said upper support frame such that said chute extends outwardly and downwardly relative to said upper support frame to said lower free end, such that debris may be urged upwardly along said chute from said lower free end to said upper end portion and will pass by gravity through said upper support frame into a collection receptacle, a pair of said plurality of support legs being inclined outwardly from first pivot connections at said upper support frame to lower ends, and said chute being mounted to said inclined legs whereby said chute is pivotally mounted relative to said upper support frame.
8. The apparatus of claim 7 including stop means for limiting the pivotal movement of at least two of said plurality of support legs relative to said upper support frame.
9. The apparatus of claim 7 wherein said plurality of support legs and said chute are movable relative to said upper support frame such that said chute and said support legs are generally parallel with respect to one another in a collapsed configuration.
10. The apparatus of claim 9 wherein said chute includes a pair of spaced upwardly extending side members extending along a substantial length of said chute for purposes of preventing debris from falling from opposite sides of said chute as debris is moved toward said upper support frame.
11. The apparatus of claim 10 including means for hingely mounting said side members relative to a bottom of said chute, and means for maintaining said side members in a raised position extending generally transversely with respect to a primary plane defined by said bottom of said chute.
12. The apparatus of claim 11 wherein said chute includes a flexible material mounted to said pair of inclined support legs and said side members, and means for releasably securing said flexible material to said pair of inclined support legs.
13. An apparatus for collecting debris including a stand having a plurality of support legs pivotally mounted to an upper support frame, a chute mounted to a pair of said plurality of support legs, a pair of said plurality of support legs being inclined outwardly and downwardly from said upper support frame such that said chute extends outwardly and downwardly relative to said upper support frame, said chute including a pair of side members pivotally mounted relative to said pair of said plurality of support legs so as to be movable from a first position overlaying said pair of said plurality of support legs to a second position extending transversely with respect to said pair of said plurality of support legs.
14. The apparatus of claim 13 wherein said plurality of support legs and said pair of side members, are movable relative to said upper support frame such that said chute and said support legs are generally parallel with respect to one another in a collapsed configuration.
15. The apparatus of claim 14 in which said chute is formed of a flexible material which is removably mounted to said pair of said plurality of support legs.
16. The apparatus of claim 15 including means for reinforcing at least a portion of said flexible material.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A controller for actuating a door, the controller electrically coupled with a motor and a first door switch and a second door switch, the controller comprising:
a detection circuit that stops the motor if movement of the door is obstructed;
a position circuit that determines a relative position of the door; and
an override circuit that permits the first door switch to override the second door switch.
2. The controller of claim 1 further comprising:
a door position sensor connected with respect to the position circuit.
3. The controller of claim 1 further comprising:
a safety circuit that actuates or stops the door following an emergency input; and
a cessation circuit that stops the motor if door operation exceeds a maximum time threshold.
4. The controller of claim 3 further comprising:
a safety switch connected along the door and electrically coupled with respect to the safety circuit.
5. The controller of claim 1 further comprising
a local power source connected between the motor and the protection circuit, the local power source further connected to a primary energy supply.
6. The controller of claim 5 wherein the primary energy supply is a vehicle battery.
7. The controller of claim 6 wherein the charging circuit further selectively draws power from the vehicle battery to ensure that the vehicle battery is not drained by the local battery.
8. The controller of claim 1 further comprising:
a status display that indicates at least one of battery capacity, battery charging, safety switch activation, door switch activation and door position.
9. The controller of claim 1 further comprising:
a memory that retains one or more user-programmable door stopping positions.
10. A method of operation of a controller for actuating a door having a motor assist and a first door switch and a second door switch, the method comprising the steps of:
operating the controller, the controller uses one or more user-programmable presets that respectively correspond to door operation;
activating the motor assist based at least in part on the one or more user-programmable presets to move the door between a closed door position and an open door position;
maintaining a desirable current supply to the motor assist when moving the door between the closed door position and the open door position; and
determining a relative position of the door when moving the door between the closed door position and the open door position.
11. The method of claim 10 wherein the first door switch is an inner door switch and the second door switch is an outer door switch and wherein the inner door switch and outer door switch initiate opening of the door when actuated, the method further comprising the steps of:
engaging a lockout switch; and
overriding the outer door switch in favor of the inner door switch such that the door cannot be opened via the outer door switch when the lockout switch is engaged.
12. The method of claim 10 further comprising:
programming the controller using at least one of the first door switch and the second door switch.
13. The method of claim 10 further comprising:
programming the controller using at least one of the first door switch, the second door switch, a safety sensor, a door position sensor, a motor current draw, a battery voltage level or an alternator output.
14. The method of claim 10 further comprising:
activating the motor assist responsive to manual activation of an inside door handle.
15. The method of claim 14 further comprising:
reversing actuation of the door for a preset amount following activation of a safety switch wherein the safety switch uses pressure sensing to sense the presence of an obstruction between the door and a door frame.
16. The method of claim 10 further comprising:
activating at least one door switch for a preset period of time; and
activating the motor assist until the door is in a fully open or fully closed position.
17. The method of claim 16 further comprising:
sensing a current position of the door; and
moving the door to a position opposite the current position.
18. The method of claim 10 further comprising:
programming at least one preset for a door stopping position; and
retaining the at least one preset within the controller.
19. The method of claim 10 further comprising:
programming at least one preset for a mode of operation; and
retaining the at least one preset within the controller.
20. The method of claim 10 further comprising:
programming at least one preset for a speed of the motor assist; and
retaining the at least one preset within the controller.
21. The method of claim 10 further comprising:
programming at least one preset for a current draw of the motor assist; and
retaining the at least one preset within the controller.
22. The method of claim 10 further comprising:
determining a nominal current required to operate the door on a level surface under ordinary load; and
adjusting the desirable current supply if the nominal current is exceeded.
23. A vehicle door having a motor assist comprising:
a dedicated power supply connected with respect to the motor assist;
a controller connected between the motor assist and the dedicated power supply, the controller maintains a desirable current supply to a motor from the dedicated power supply and determines a relative position of the door, the controller further stops the motor if movement of the door is obstructed or exceeds operation for a preset time threshold; and
a memory associated with the controller, the memory stores one or more presets of respective door stopping positions wherein the one or more presets are stored using at least one of an operable handle or a switch associated with the vehicle door.
24. The vehicle door of claim 23 further comprising:
an override switch that deactivates external controls of the vehicle door.
25. The vehicle door of claim 23 wherein the controller is connected between the dedicated power supply and a vehicle battery.
26. The vehicle door of claim 23 wherein the controller reverses the operation of the door upon obstruction of the door.
27. The vehicle door of claim 23 wherein the controller modulates the desirable current supply provided to the motor if the vehicle door is open or closed on an incline.
28. The vehicle door of claim 23 wherein the controller modulates the desirable current supply provided to the motor if the vehicle door is open or closed while overloaded.
29. A system for motorizing at least one door of a vehicle relative to a door frame of the vehicle, the vehicle having a vehicle power supply to provide vehicle power, the system comprising:
an electric drive system coupled at least in part to the door frame and one of the doors of the vehicle, wherein the electric drive system moves the door between a closed door position and an open door position;
a local power source different from the vehicle power supply that is coupled at least in part with the electric drive system to allow for door operation independent of the vehicle power supply; and
wherein the local power source has priority over the vehicle power supply to provide power to the electric drive system when moving the door between the closed door position and the open door position.
30. The system of claim 29 further comprising a controller coupled at least in part with the electric drive system, the controller is coupled at least in part with the local power source such that the controller manages the local power source.
31. The system of claim 30 wherein the controller is adapted to determine when a predetermined amount of vehicle power is available to recharge the local power source.
32. The system of claim 31 wherein the local power source includes a local battery coupled at least in part with the controller and the electric drive system includes a motor coupled at least in part with the controller.
33. The system of claim 30 wherein the controller is adapted to monitor system inputs to determine when to stop supplying power to the drive system.
34. The system of claim 33 wherein the controller is adapted to prevent a continuous drain on at least one of: (a) the local power source, and (b) the vehicle power.
35. The system of claim 33 wherein a separate local power source and a separate controller are associated with each door of the vehicle.
36. The system of claim 33 further comprising a battery charger coupled at least in part with the controller and the local power source to recharge the local power source from the vehicle power supply as determined by the controller.
37. The system of claim 30 wherein the controller is adapted to use vehicle power as the primary power for the drive system and use the local power source as a back-up power source.
38. The system of claim 30 wherein the local power source is positioned on at least one of: (a) the door of the vehicle, and (b) a body of the vehicle.
39. The system of claim 30 further comprising at least one safety sensor adapted to send a door stop signal to the controller upon sensing an obstruction between the sensor and the door frame wherein the safety sensor uses pressure sensing to sense the presence of an obstruction between the door and the door frame.
40. The system of claim 39 in which the at least one safety sensor is disposed around an outer perimeter of an internal side of the door.
41. The system of claim 30 wherein the controller is adapted to determine when an obstruction prevents the door from opening or closing for a preset period of time and wherein the controller is adapted to stop a motor of the electric drive system when the preset period of time is reached.
42. The system of claim 30 further comprising a door open sensor adapted to signal the controller to initiate movement of the door toward the open door position upon manual actuation of at least one of: (a) an external latch actuator, and (b) an internal latch actuator.
43. The system of claim 30 wherein the controller is manually programmable to set at least one of: (a) a door open endpoint, (b) a door opening speed, (c) a door closing speed, and (d) a deceleration rate when approaching a door open endpoint or a door closed position.
44. The system of claim 30 wherein the controller is adapted to prevent the drawing of vehicle power when the vehicle is not running.
45. The system of claim 30 wherein the controller is adapted to initiate recharging of the local power source upon a determination that a vehicle engine is operational and alternator output is at or above a preselected level.
46. A system for motorizing at least one door of a vehicle relative to a door frame of the vehicle, the system comprising:
a drive system coupled at least in part to the door and the door frame of the vehicle, the drive system moves the door between a closed door position and an open door position;
a controller coupled at least in part with the drive system to control door operation of the door; and
a safety mechanism coupled at least in part with the controller, the safety mechanism uses pressure sensing to sense the presence of an obstruction between the door and door frame and to signal the controller upon sensing the obstruction.
47. The system of claim 46 in which the safety mechanism comprises at least one safety sensor adapted to send a door stop signal to the controller upon sensing an obstruction between the sensor and the door frame.
48. The system of claim 47 in which the at least one safety sensor is disposed around an outer perimeter of an internal side of the door.
49. The system of claim 48 wherein the safety sensor comprises a multi-segmented single pole switch having a plurality of sensor segments coupled by electrical connections, wherein the sensor segments are positioned to sense obstructions to door closings.
50. The system of claim 49 wherein the door stop signal is sent to the controller in response to any one of the sensor segments being contacted when the door is closing.
51. The system of claim 46 wherein the controller is adapted to open the door of the vehicle a preselected amount upon sensing of the obstruction to prevent entrapment of the obstruction.
52. The system of claim 46 wherein the controller is adapted to determine the presence of an obstruction located between the door and door frame.
53. The system of claim 52 wherein the controller is adapted to stop a motor of the drive system if the controller determines the presence of the obstruction.
54. The system of claim 47 further comprising a door position sensor adapted to detect movement and position of the door and to relay this information to the controller.
55. The system of claim 54 wherein the door position sensor is mounted proximate a door hinge with one portion attached to the door and another portion attached the door frame.
56. The system of claim 54 further comprising a door open sensor coupled at least in part with the controller to signal the controller to activate the drive system and open the door upon determining that a latch actuator has been actuated.
57. The system of claim 56 further comprising an external close switch mounted to an external side of one of the door or the vehicle, wherein the external close switch is in communication with the controller and, when activated, signals the controller to move the door toward the closed door position; and
an internal close switch mounted to an internal side of one of the door or the vehicle, wherein the internal close switch is in communication with the controller and, when activated, signals the controller to move the door toward the closed door position.
58. The system of claim 47 further comprising a door stop switch, the door stop switch when actuated initiates the deactivation of door movement such that the door stops moving either towards the door open position or the door closed position.
59. The system of claim 58 in which no further door movement takes place upon release of the door stop switch.
60. The system of claim 58 in which actuation of the door stop switch prompts the controller to open the door that moved towards the closed door position a preselected amount after movement of the door has been stopped.
61. A method of controlling operation of a door of a vehicle relative to a door frame of the vehicle, comprising:
coupling a drive system at least in part to the door and door frame of the vehicle, the drive system adapted to move the door between a closed door position and an open door position;
coupling a controller at least in part with the drive system;
sensing a position of the door;
receiving a door open command or a door close command at the controller;
initiating opening or closing of the door at preselected speeds based on the command received;
determining the length of time that the open command or close command is continuously received; and
directing the drive system to move the door at a relatively slow speed for a predetermined initial time period and to move the door at a relatively faster speed after the predetermined initial time period has ended.
62. The method of claim 61 wherein the relatively faster speed is a full speed for movement of the door until the door reaches a stop position.
63. The method of claim 61 further comprising moving the door to a fully open or closed position if the length that the open command or close command is continuously received exceeds a predetermined time period.
64. The method of claim 61 further comprising mounting a door open sensor to an internal latch actuator or an external latch actuator of the door, wherein the door open sensor is in communication with the controller.
65. The method of claim 61 further comprising sensing the presence of an obstruction between the door and the door frame and sending a door stop signal to the controller upon sensing the obstruction.
66. The method of claim 65 further comprising signaling the drive system to open the door of the vehicle a preselected amount upon the controller receiving the door stop signal.
67. The method of claim 61 further comprising providing the controller with control algorithms for door control operation based on received system inputs and user-programmable settings.
68. The controller of claim 1 wherein
the first door switch is an inner door switch and the second door switch is an outer door switch; and
operation of the door from the outside of the vehicle is prevented when the inner door switch overrides the outer door switch.
69. The controller of claim 1 further comprising a charging circuit that maintains a desirable power level of a power supply.
70. The method of claim 10 further comprising:
determining whether movement of the door is obstructed; and
reversing actuation of the door in response to a determination that movement of the door is obstructed.
71. The method of claim 10 further comprising:
determining whether door operation exceeds a maximum time threshold; and
deactivating the motor assist once the door operation exceeds the maximum time threshold.
72. The method of claim 10 further comprising:
activating the door to a user-programmable door stopping position; and
deactivating the motor assist once the door reaches the door stopping position.

1460752841-345769c0-089c-45e1-bd55-63434896bff4

1. An electronic device, comprising:
an element formed in a wafer;
a frame member, composed of a first resin and installed over said wafer to surround a functional unit of said element; and
a resin layer, composed of a second resin, and provided around a perimeter of said frame member so that a gap is present between said frame member and said resin layer,
wherein the frame member does not overlap with the resin layer when viewed from a direction normal to a topmost surface of the wafer,
wherein the gap is a void space having no material therein, and
wherein said functional unit of said element is exposed in a space surrounded by said frame member, said space extending to at least an upper surface of said frame member.
2. The electronic device as set forth in claim 1, further comprising a low adhesion layer disposed in at least side surface of said frame member, said low adhesion layer having higher adhesion for said second resin than said first resin.
3. The electronic device as set forth in claim 1, wherein said low adhesion layer is an oxide film created by oxidizing a surface layer of said frame member.
4. The electronic device as set forth in claim 1, wherein
a dimensional area of an upper surface of said frame member is larger than a dimensional area of a lower surface of said frame member.
5. The electronic device as set forth in claim 4, wherein a width in a cross-sectional geometry of said frame member is decreased toward the lower section.
6. The electronic device as set forth in claim 1, wherein all portions of the resin layer are disposed outside the perimeter of said frame member.
7. The electronic device as set forth in claim 1, wherein the resin layer does not overlap with the functional unit when viewed from a direction normal to the topmost surface of the wafer.
8. The electronic device as set forth in claim 1, wherein the frame member does not overlap with the functional unit when viewed from a direction normal to the topmost surface of the wafer.
9. The electronic device as set forth in claim 1, wherein a linear expansion coefficient of the frame member is different from a linear expansion coefficient of the resin layer.
10. The electronic device as set forth in claim 1, wherein the gap is configured to allow thermal expansion and thermal shrinkage of the frame member and the resin layer.
11. The electronic device as set forth in claim 1, wherein the gap is configured to substantially eliminate stress exerted by the resin layer to the frame member due to thermal expansion and thermal shrinkage of the frame member and the resin layer.
12. The electronic device as set forth in claim 1, wherein an topmost surface of the frame member is not more than 0.05 mm higher than an topmost surface of the resin layer in a direction normal to the topmost surface of the wafer.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A method for visualizing shear wave propagation in a medium, the method comprising:
(a) introducing a shear wave from a shear wave source into the medium, the shear wave having a shear wave frequency and a shear wave phase velocity;
(b) detecting a propagation of the shear wave through the medium by using an ultrasound probe to produce an ultrasound signal;
(c) introducing a vibration into the ultrasound signal at a second frequency;
(d) from the ultrasound signal having the vibration, deriving a modulation wave which represents a propagation of the shear wave relative to the ultrasound probe, the modulation wave having a modulation wave phase velocity which varies as a difference between the shear wave frequency and the second frequency; and
(e) producing an image representing the shear wave propagation from the modulation wave derived in step (d).
2. The method of claim 1, wherein step (e) comprises producing an image in real time of the modulation wave.
3. The method of claim 2, wherein step (e) further comprises estimating, from the image of the modulation wave, a local vibration phase at each pixel of the image of the modulation wave.
4. The method of claim 3, wherein a plurality of said images in real time of the modulation wave are produced, and wherein the local vibration phase is estimated from a Fourier transform carried out at a time trace of each pixel from the plurality of images of the modulation wave.
5. The method of claim 3, wherein step (e) further comprises performing a phase unwrapping on the local vibration phase to produce a smooth phase surface.
6. The method of claim 5, wherein step (e) further comprises performing a noise reduction on the smooth phase surface.
7. The method of claim 5, wherein step (e) further comprises converting the smooth phase surface to a wave pattern with an artificially increased spatial density.
8. The method of claim 1, wherein step (c) comprises physically vibrating the ultrasound probe at the second frequency.
9. The method of claim 8, wherein step (b) comprises applying a layer of ultrasound gel between the medium and the ultrasound probe such that the ultrasound probe is acoustically coupled to the medium through the ultrasound gel as the ultrasound probe vibrates.
10. The method of claim 1, wherein step (c) comprises electronically producing an equivalent virtual vibration in the ultrasound signal.
11. The method of claim 1, wherein step (a) comprises introducing multiple shear waves into the medium.
12. A system for visualizing shear wave propagation in a medium, the system comprising:
a shear wave source for introducing a shear wave into the medium, the shear wave having a shear wave frequency and a shear wave phase velocity;
an ultrasound probe for detecting a propagation of the shear wave through the medium to produce an ultrasound signal, a vibration at a second frequency being introduced into the ultrasound signal;
an image processing device, in communication with the ultrasound probe, for deriving, from the ultrasound signal having the vibration, a modulation wave which represents a propagation of the shear wave relative to the ultrasound probe, the modulation wave having a modulation wave phase velocity which varies as a difference between the shear wave frequency and the second frequency, and producing an image representing the shear wave propagation from the modulation wave; and
an image output device for outputting the image.
13. The system of claim 12, wherein the image output device comprises a display.
14. The system of claim 12, wherein the image processing device produces an image in real time of the modulation wave.
15. The system of claim 14, wherein the image processing device estimates, from the image of the modulation wave, a local vibration phase at each pixel of the image of the modulation wave.
16. The system of claim 15, wherein a plurality of said images in real time of the modulation wave are produced, and wherein the local vibration phase is estimated from a Fourier transform carried out at a time trace of each pixel from the plurality of images of the modulation wave.
17. The system of claim 15, wherein the image processing device estimates the local vibration phase by performing a phase unwrapping on the local vibration phase to produce a smooth phase surface.
18. The system of claim 16, wherein the image processing device performs a noise reduction on the smooth phase surface.
19. The system of claim 17, wherein the image processing device converts the smooth phase surface to a wave pattern with an artificially increased spatial density.
20. The system of claim 12, wherein the ultrasound probe is physically vibrated at the second frequency.
21. The system of claim 12, wherein an equivalent virtual vibration is electronically produced in the ultrasound signal.
22. The system of claim 12, wherein the shear wave source introduces multiple shear waves into the medium.
23. A method for visualizing shear wave propagation in a medium, the method comprising:
(a) introducing a shear wave from a shear wave source into the medium, the shear wave having a shear wave frequency and a shear wave phase velocity;
(b) detecting a propagation of the shear wave through the medium by using an ultrasound probe to produce an ultrasound signal;
(c) introducing, at a second frequency, at least one of (i) a vibration into the ultrasound signal and (ii) a second shear wave into the medium;
(d) from the ultrasound signal, deriving a modulation wave which represents a propagation of the shear wave relative to the ultrasound probe, the modulation wave having a modulation wave phase velocity which varies as a difference between the shear wave frequency and the second frequency; and
(e) producing an image representing the shear wave propagation from the modulation wave derived in step (d), wherein step (e) comprises:
(i) producing an image in real time of the modulation wave; and
(ii) estimating, from the image of the modulation wave, a local vibration phase at each pixel of the image of the modulation wave.
24. The method of claim 23, wherein the local vibration phase is estimated from a Fourier transform carried out at each pixel of the image of the modulation wave.
25. The method of claim 23, wherein step (e) further comprises performing a phase unwrapping on the local vibration phase to produce a smooth phase surface.
26. The method of claim 25, wherein step (e) further comprises performing a noise reduction on the smooth phase surface.
27. The method of claim 25, wherein step (e) further comprises converting the smooth phase surface to a wave pattern with an artificially increased spatial density.
28. A system for visualizing shear wave propagation in a medium, the system comprising:
a shear wave source for introducing a shear wave into the medium, the shear wave having a shear wave frequency and a shear wave phase velocity;
an ultrasound probe for detecting a propagation of the shear wave through the medium to produce an ultrasound signal;
means for introducing, at a second frequency, at least one of (i) a vibration into the ultrasound signal and (ii) a second shear wave into the medium;
an image processing device, in communication with the ultrasound probe, for deriving, from the ultrasound signal having the vibration, a modulation wave which represents a propagation of the shear wave relative to the ultrasound probe, the modulation wave having a modulation wave phase velocity which varies as a difference between the shear wave frequency and the second frequency, and producing an image representing the shear wave propagation from the modulation wave; and
an image output device for outputting the image, wherein the image processing device produces an image in real time of the modulation wave and estimates, from the image of the modulation wave, a local vibration phase at each pixel of the image of the modulation wave.
29. The system of claim 28, wherein the local vibration phase is estimated from a Fourier transform carried out at each pixel of the image of the modulation wave.
30. The system of claim 28, wherein the image processing device estimates the local vibration phase by performing a phase unwrapping on the local vibration phase to produce a smooth phase surface.
31. The system of claim 30, wherein the image processing device performs a noise reduction on the smooth phase surface.
32. The system of claim 31, wherein the image processing device converts the smooth phase surface to a wave pattern with an artificially increased spatial density.