Abstract: An electric power generator capable of using external vibrations in various directions to generate power. A fixed substrate having a surface with a plurality of electret electrodes and a movable substrate having a surface with a movable electrode are spaced from each other. The fixed substrate is fixed in the electric power generator. Spring driving bodies support the movable substrate so that the movable substrate elastically moves in any direction within an XY plane when receiving external vibrations.

Abstract: The present application is directed to novel electrostatic actuators and methods of making the electrostatic actuators. In one embodiment, the electrostatic actuator comprises a substrate, an electrode formed on the substrate and a deflectable member positioned in proximity to the electrode so as to provide a gap between the electrode and the deflectable member. The deflectable member is anchored on the substrate via one or more anchors. The gap comprises at least one first region having a first gap height positioned near the one or more anchors and at least one second region having a second gap height positioned farther from the anchors than the first region. The first gap height is smaller than the second gap height.

Abstract: A method of manipulating preferable thin wafers, preferably having a thickness of less than 200 ?m, wherein the wafers are placed prior to polishing or another processing step for reducing the thickness thereof on a transportable electrostatic carrier. The wafers remain on the transportable electrostatic carrier for the duration of and between at least two processing steps, during the manipulating steps and during any necessary intermediate storage.

Abstract: An electret actuator comprising a fixed substrate having driving electrodes of a plurality of phases arranged therein, a movable element arranged on the fixed substrate and made electret in similar polarity at predetermined pitches in portions which face the driving electrodes, and a driving control section configured to generate driving voltage patterns of a plurality of phases set at stages to move the movable element relative to the fixed substrate and a floating voltage pattern of a plurality of phases to float the movable element from the fixed substrate, and to apply the voltage patterns to the driving electrodes. The floating voltage pattern output from the driving control section has voltages similar to the electret charged polarity of the movable element.

Abstract: The micro-actuation element (X1) includes a movable unit (111), a frame (112) and a coupler (113) for connecting these, where the unit, the frame and the coupler are integrally formed in a material substrate having a multi-layer structure that consists of electroconductive layers (110a-110c), such as a core conduction layer (110b), and insulation layers (110d, 110e) intervening between the electroconductive layers (110a-110c). The movable unit (111) includes a first structure originating in the core conduction layer (110b). The frame (112) includes a second structure originating in the core conduction layer (110b). The coupler (113) includes a plurality of electrically separated torsion bars (113a, 113b) that originate in the core conduction layer (110b) and are connected continuously to the first structure and the second structure.

Abstract: Two similarly shaped, such as rectangular, shells are attached to one another such that they form a resulting thin airfoil-like structure. The resulting device has at least two stable equilibrium shapes. The device can be transformed from one shape to another with a snap-through action. One or more actuators can be used to effect the snap-through; i.e., transform the device from one stable shape to another. Power to the actuators is needed only to transform the device from one shape to another.

Abstract: An apparatus for driving an actuator includes a power unit, a sensing unit, and a first outer capacitor. The power unit provides first and second power in mutually reverse phases to first and second activating vibration plate, respectively. The sensing unit senses a displacement of a suspended vibration plate according to a result of sensing by a sensing plate. The first outer capacitor is disposed between a first power terminal connecting the power unit to the actuator and a sensing terminal connecting the sensing plate to the sensing unit.

Abstract: A micro-electro mechanical system (MEMS) device using in-plane motion is provided. The MEMS device includes a stage which is supported by an axle and an actuator which provides a push-pull exciting force to the axle at upper and lower eccentric positions of an axis of the axle. The actuator includes a plurality of fixed combs; a plurality of driving combs for engagement with the fixed combs, the driving combs being translationally vibrated between engaging and disengaging positions by an electrostatic attractive force periodically generated by the fixed combs; a driving frame which connects and supports the driving combs, the driving frame being vibrated together with the driving combs; and a motion transmitting member transmitting the translational vibration of the driving frame to the eccentric positions of the axle. With this MEMS device, the comb structure can be easily expanded to improve the dynamic performance and high-speed/long displacement characteristic.

Abstract: A micro-electro mechanical system (MEMS) device and a method of forming comb electrodes of the MEMS device are provided.

Abstract: An electrostatic motor includes a stator electrode member (1a) and a slider electrode member (1b). The stator electrode member (1a) and the slider electrode member (1b) are provided with drive electrode patterns (2), and the drive electrode patterns are covered by cover films (4). Surfaces of the stator electrode member (1a) and the slider electrode member (1b) contacting each other are provided with a plurality of minute projections (5). A clearance between the stator electrode member and the slider electrode member is maintained by the contact of the projections. The projections (5) may also be provided on only one of the stator electrode member (1a) and the slider electrode member (1b), with the other electrode member having a flat surface.

Abstract: Disclosed is a micro mirror having a structure improved to have an increased driving angle while being driven in high speed. The micro mirror comprises a rotatable mirror section that reflects light, a pair of spring sections for supporting the mirror section and serving as a rotational axis for the mirror section when the mirror section is rotationally driven, an oval adjoining section for connecting the mirror section and the pair of spring sections, and a driving section comprising mobile combs arranged on the adjoining section, and a fixed comb provided above and/or below the mobile combs to correspond to the mobile combs to generate electrostatic force. According to the present invention, by existence of the oval adjoining section, moment can be increased without increasing rotational inertia moment so largely. Therefore, a high-speed optical scanner with an increased driving angle can be provided, which is required for a high-resolution laser TV.

Abstract: An electrical energy generator with improved efficiency has a base on which is mounted an elastically deformable micromechanical element that has a section that is free to be displaced toward the base. An absorber of radioactively emitted particles is formed on the base or the displaceable section of the deformable element and a source is formed on the other of the displaceable section or the base facing the absorber across a small gap. The radioactive source emits charged particles such as electrons, resulting in a buildup of charge on the absorber, drawing the absorber and source together and storing mechanical energy as the deformable element is bent. When the force between the absorber and the source is sufficient to bring the absorber into effective electrical contact with the source, discharge of the charge between the source and absorber allows the deformable element to spring back, releasing the mechanical energy stored in the element.

Abstract: Methods and apparatuses for sensing and adjusting lateral motion in a comb drive actuated MEMS device are provided. If lateral motion is sensed by a lateral motion sensor coupled to the comb drive actuated MEMS device, and the lateral motion is greater than a reference value, a feedback controller adjusts the lateral motion by providing a drive signal to a comb drive electrode of a comb drive actuator.

Abstract: An electrostatic actuator includes a stator having an electrode substrate, a movable unit having a movable element and an electrode arranged opposite to the electrode substrate, a plurality of first operation modules each of which issues an operation command for realizing a first operation, a plurality of second operation modules each of which issues an operation command for realizing a second operation, a module selector which selectively enables one first operation module of the first operation modules and selectively enables one second operation module of the second operation modules, an actuator drive module which generates a waveform signal on the basis of the operation command from the enabled first operation module and the operation command from the enabled second operation module and a switching circuit which converts the waveform signal into a voltage to apply the voltage to the electrode substrate.

Abstract: A MEMS device which utilizes a capacitive sensor or actuator is enhancement by initially fabricating the capacitive assembly which comprises the sensor or actuator as two sets of interdigitated fingers in a noninterdigitated configuration. One of the two sets of fingers is coupled to a movable stage. The stage is moved from an initial position to a post-release position in which the two sets of interdigitated fingers are interdigitated with each other. The stage is carried by two pairs flexures which maintain the stability of motion of the stage and when in the post-release position provide stiffness which prevents deflection of the set of fingers coupled to the stage. The stage and hence the assembled sets of fingers are then locked into the post-release position.

Abstract: An oscillator is oscillatable in a predetermined direction. First and second driving electrodes are secured to the base and apply an electrostatic force to the oscillator to make drive oscillation of the oscillator in the predetermined direction. At the time of the drive oscillation of the oscillator, a predetermined electric charge is accumulated in the oscillator, and electric charges of opposite polarities are alternately and periodically accumulated in the first and second driving electrodes, respectively, to exert an attractive force between the oscillator and a corresponding one of the first and second driving electrodes and also to exert a repulsive force between the oscillator and the other one of the first and second driving electrodes, and vice versa.

Abstract: A compliant mechanism is provided for accurate and precision alignment of mechanical component parts, surfaces or assemblies and the like, where low-cost, accurate, and repeatable alignment are desired. The compliant mechanism may be used in applications that require high precision alignment and where the relative location of coupled components must be variable or adjustable. The compliant mechanism includes a stage coupled to a plurality of hinges, at least one tab coupled to one of the hinges, and a support coupled to the tab. The relative position of the stage and the support may be adjusted by actuating (i.e., displacing) the tab(s) or other parts of the structure, to enable controlled movement in six degrees of freedom therebetween.

Abstract: Methods and systems of assembling and making laminated electro-mechanical systems and structures are described. A plurality of structural layers are formed that include at least one structural layer having a movable element formed therein. The plurality of structural layers are stacked and aligned into a stack. Each structural layer in the stack is attached to an adjacent structural layer of the stack.

Abstract: MEMS devices (100) and methods for forming the devices have now been provided. In one exemplary embodiment, the MEMS device (100) comprises a substrate (106) having a surface, an electrode (128) having a first portion coupled to the substrate surface, and a second portion movably suspended above the substrate surface, and a stress-release mechanism (204) disposed on the electrode second portion, the stress-release mechanism (204) including a first slot (208) integrally formed in the electrode. In another exemplary embodiment, the substrate (106) includes an anchor (134, 136) and the stress-release mechanism 222 is formed adjacent the anchor (134, 136).

Abstract: An embodiment of the present invention provides a stepping actuator, comprising a suspended membrane comprising a plurality of movable electrodes connected by plurality of spring hinges to a payload platform; and anchors connecting said membrane to a substrate, said substrate comprising a plurality of fixed electrodes; wherein said movable electrodes of said suspended membrane and said fixed electrodes from said substrate form parallel-plate electrostatic sub-actuators.

Abstract: A microscopic translation device for a microelectromechanical system includes a pair of linear stator assemblies disposed in spaced relation to define an elongate channel. Each assembly is formed by a plurality of stators arranged in a row along the channel. A shuttle member is disposed between the stator assemblies for translating movement along the channel. The shuttle member includes a plurality of rotors extending outwardly from opposite sides. The shuttle is grounded through the stator assemblies and includes a mounting area for an object to be translated. Electrical lines are individually connected to alternate stators of a plurality of groups of the stators. A current supply sequentially supplies current through the electrical lines to the alternate stators so as to effect charging of the stators in a predetermined sequence. This produces a tangential capacitive force that causes translation of the shuttle.

Abstract: A micro-oscillation element includes an oscillation section and a frame. The oscillation section is provided with a mirror surface and is connected to the frame via trapezoidal first and second springs. The oscillation section is located between the first spring and the second spring. Each of the first spring and the second spring is deformable along with the oscillation of the oscillation section.

Abstract: A semiconductor integrated circuit comprises an electrostatic actuator, an estimation circuit, a storage circuit and a bias circuit. The electrostatic actuator has a top electrode, a bottom electrode, and an insulating film disposed between the top electrode and the bottom electrode. The estimation circuit estimates the amount of a charge accumulated in the insulating film of the electrostatic actuator. The storage circuit stores a result of the estimation of the charge amount by the estimation circuit. The bias circuit changes, on the basis of the estimation result stored in the storage circuit, a drive voltage to drive the electrostatic actuator.

Abstract: Multiple drives are coupled together to cause rotation about a single axis by an arrangement in which two moveable electrode plates flank a fixed electrode plate such that the opposite direction rotations of the two moveable electrode plates are combined. To this end, at least one arm from at least one of the moveable electrode plates is connected to at least one arm of a moveable electrode plate on the opposite side of the fixed electrode plate, e.g., by a spring. The electrode plates may have comb projections. A post may be coupled at one of its ends to the top of one of the moveable electrode plates, and the post's other end is coupled to a plate, e.g., a mirror or other structure to be moved.

Abstract: Provided is a two-axis actuator having a large stage area. The two-axis actuator includes a stage moving in two directions and connected to an upper part of an inertial part. The two-axis actuator is configured to maximize a stage area relative to the overall area of the actuator, thereby increasing the data storage capacity of the stage.

Abstract: The invention relates to a microbeam oscillator. Tuning of the oscillator is carried out by addition or subtraction of material to an oscillator member in order to change the mass of the oscillator member.

Abstract: Disclosed is an axial fan motor for air-cooling a heat sink of a heating element and thermally connected to the heat sink. The casing of the axial fan motor is formed of a plurality of laminated metal plates. The plurality of metal plates include a single first metal plate and a plurality of second metal plates. The single first metal plate, which is an outermost layer located at the air exhaust side of the fan, has a peripheral portion, a central portion, and a plurality of arm portions for connecting the peripheral portion and the central portion. A bearing holder for supporting a rotary shaft of the fan is attached to the central portion.

Abstract: Provided is a microelectromechanical system (MEMS) actuator in which a cantilever piezoelectric actuator and a comb actuator are combined to perform dual shaft drive. The MEMS includes: a stationary comb fixed on a substrate; a movable comb disposed separately from the substrate; and a spring connected to the movable comb and the substrate to resiliently support the movable comb, wherein the movable comb includes a piezoelectric material layer in a laminated manner to be perpendicularly moved by a piezoelectric phenomenon and laterally moved by an electrostatic force to the stationary comb, whereby the MEMS actuator can be used in a driving apparatus of an ultra-slim optical disk drive since the movable comb is made of a piezoelectric material to simultaneously perform focusing actuation to a Z-axis as well as planar actuation.

Abstract: A high-power electrostatic actuator comprising rotor and stator layers with fault-tolerant electrode structures, a housing to contain the electrodes and dielectric fluid, and electronic circuitry driving a plurality of high-voltage phases. The actuator is constructed from multiple rotor and stator films separated by spacing elements. The electrode structure provides self-alignment for precise assembly. The actuator assembly includes built-in fine-position sensors to allow optimal timing in powering phases, and a coarse position sensor for feedback control. The electrode structure has a large region of linear force to provide low torque-ripple allowing simple high/low voltage pulsing instead of analog high voltage waveforms. Single or double sided flexible circuit manufacturing techniques are used to fabricate the rotor and stator films at low cost.

Abstract: The present invention provides a digital optical switch apparatus and process for manufacturing the apparatus. The apparatus includes a mirror assembly coupled to a top cap and to a bottom cap. The top and bottom caps each include one or more electrodes that, when energized with electrical energy, move a mirrored surface to one of a plurality of discrete positions. Mirror assemblies can be cascaded to create a packaged assembly having any multiple of discrete positions. The process includes planar micro-machining techniques to create isolated islands for electrical feed through. The process enables mechanical bonding of multiple tiers via a single bond region and through a bond-pad window.

Abstract: Stator and slider film electrodes (1, 2) are integrally provided with spacer members (10; 10?; 10?; 15; 15?; 15?; 20). The spacer member is bonded to one end of a base film (4a) on which different phase electrode elements (3a, 3b, 3c) are disposed. After this, cover films (4b) are bonded to the two surfaces of the base film on which the spacer member is bonded to obtain a spacer-equipped film electrode.

Abstract: A plurality of mechanically coupled MEMS resonators that are arranged in an N×M MEMS array structure. Each MEMS resonators includes a plurality of straight (or substantially straight) elongated beam sections that are connected by curved/rounded sections. Each elongated beam section is connected to another elongated beam section at a distal end via the curved/rounded sections thereby forming a geometric shape (e.g., a rounded square). Further, each resonator is mechanically coupled to at least one other adjacent resonator of the array via a resonator coupling section. The resonator coupling sections may be disposed between elongated beam sections of adjacent resonators. The resonators, when induced, oscillate at the same or substantially the same frequency. The resonators oscillate in a combined elongating (or breathing) mode and bending mode; that is, the beam sections exhibit an elongating-like (or breathing-like) motion and a bending-like motion.

Abstract: The present invention relates to an ultrasonic transducer that has a diaphragm in which an electrode layer is formed thereon. A fixed electrode having a plurality of asperities on the surface facing the diaphragm is provided. An alternating current signal is applied between the electrode layer formed on the diaphragm and the fixed electrode to generate ultrasonic waves. A groove is formed on the upper surface of the projections of the asperities of the fixed electrode to prevent the diaphragm from sticking to the fixed electrode.

Abstract: The present invention relates to transducers, their use and fabrication. The transducers convert between mechanical and electrical energy. Some transducers of the present invention include a pre-strained polymer. The pre-strain improves the conversion between electrical and mechanical energy. The present invention also relates to devices including an electroactive polymer to convert between electrical and mechanical energy. The present invention further relates to compliant electrodes that conform to the shape of a polymer included in a transducer. The present invention provides methods for fabricating electromechanical devices including one or more electroactive polymers.

Abstract: A comb shaped actuator having off centered electrodes to the fixed electrode and the movable electrode comprise a plurality of electrode finger units containing two fixed electrode fingers next to each other and the movable electrode finger interposed between the two fixed electrode fingers, at least two of the electrode finger units comprising off-centered electrode finger units having the movable electrode finger being off-centered with respect to a central position between the two fixed electrode fingers, the off-centered electrode finger units being located on both sides of a central line dividing the fixed electrode and the movable electrode along the opening into two parts, and directions of off-centering of the both sides being inverse to each other.

Abstract: Exemplary embodiments of the invention provide a micromechanical electrostatic resonator which designs high frequency, increases a ratio of output voltage to input voltage, and designs low drive voltage or reduced power consumption. A micromechanical electrostatic resonator of exemplary embodiments includes a plate-shaped vibration body, a pair of electrodes arranged oppositely to each other at both sides of the vibration body with a gap from an outer circumferential portion of the vibration body, a feeding device to apply in-phase alternating-current power to the pair of electrodes, and a detecting device to obtain an output corresponding to a change in capacitance between the vibration body and the electrodes. The planar shape of the vibration body takes a shape having a curved outline which comprises a neck portion.

Abstract: An electrostatic actuator includes a waveform output register which generates waveform data having a drive time and a drive pattern on the basis of an operation request from the outside and has queues 0 and 1 to 3 holding the waveform data, a waveform data management unit which erases the waveform data held in the queue 0 of the waveform output register after the drive time has elapsed and moves the waveform data held in the queues 1 to 3 to the queue 0, an output waveform generation unit which generates a corresponding waveform signal on the basis of the drive pattern held in the queue 0 of the waveform output register, and a switching circuit which converts the inputted drive pattern into voltage to electrode substrate.

Abstract: Disclosed is an oscillator that relies on redundancy of similar resonators integrated on chip in order to fulfill the requirement of one single quartz resonator. The immediate benefit of that approach compared to quartz technology is the monolithic integration of the reference signal function, implying smaller devices as well as cost and power savings.

Abstract: A power system includes a member with two or more sections and at least one pair of electrodes. Each of the two or more sections has a stored static charge. Each of the pair of electrodes is spaced from and on substantially opposing sides of the member from the other electrode and is at least partially in alignment with the other electode. At least one of the member and the at least one pair of electrodes is moveable with respect to the other. When at least one of the sections is at least partially between the pair of electrodes, the at least one of the sections has the stored static electric charge closer to one of the pair of electrodes. When at least one of the other sections is at least partially between the pair of electrodes, the other section has the stored static electric charge closer to the other one of the pair of electrodes.

Abstract: A plurality of stator-side electrodes disposed in a stator is vertically disposed so as to face a plurality of mover-side electrodes disposed on a mover in a protruding manner. Wide areas facing each other can be secured between the electrodes on the stator and the mover-side electrodes even at a narrow space in three dimensions. Great electrostatic attraction force can be generated between both electrodes, and the mover 30 can be driven with greater driving force.

Abstract: A method and system of calibrating a drive includes changing an electrode voltage between a first set of electrodes and a second set of electrodes in the drive divided by an electrode gap, determining a threshold voltage for the electrode voltage at which an electrostatic attractive force causes the first set of electrodes to be drawn to the second set of electrodes and calculating an operational electrode voltage between the first set of electrodes and the second set of electrodes using the threshold voltage that allows the drive to operate while one or more external accelerations are acting upon the drive.

Abstract: A micromechanical resonator structure including a plurality of straight or substantially straight beam sections that are connected by curved or rounded sections. Each elongated beam section is connected to another elongated beam section at a distal end via the curved or rounded sections thereby forming a geometric shape having at least two elongated beam sections that are interconnected via curved or rounded sections (for example, a rounded triangle shape, rounded square or rectangle shape). The structure includes one or more nodal points or areas (i.e., portions of the resonator structure that are stationary, experience little movement, and/or are substantially stationary during oscillation of the resonator structure) in one or more portions or areas of the curved sections of the structure. The nodal points are suitable and/or preferable locations to anchor the resonator structure to the substrate.

Abstract: The present invention relates to transducers, their use and fabrication. The transducers convert between mechanical and electrical energy. Some transducers of the present invention include a pre-strained polymer. The pre-strain improves the conversion between electrical and mechanical energy. The present invention also relates to devices including an electroactive polymer to convert between electrical and mechanical energy. The present invention further relates to compliant electrodes that conform to the shape of a polymer included in a transducer. The present invention provides methods for fabricating electromechanical devices including one or more electroactive polymers.

Abstract: A two-axis device is provided. The two-axis device includes a first substrate having a plurality of electrodes, a first connecting layer located on the first substrate, an actuating layer, a second connecting layer and a cover. The actuating layer is connected to the first substrate via the first connecting layer and includes a circular portion, an actuating portion, a first shaft and a second shaft. The second connecting layer is connected to the actuating layer and the cover is connected to the actuating layer via the second connecting layer. In addition, a vacuum concavity is formed by the first substrate, the first connecting layer, the actuating layer, the second connecting layer and the cover. The actuating portion and the first shaft are located in the vacuum concavity, and the second shaft extends outside of the vacuum concavity.

Abstract: Electromechanical systems utilizing suspended conducting nanometer-scale beams are provided and may be used in applications, such as, motors, generators, pumps, fans, compressors, propulsion systems, transmitters, receivers, heat engines, heat pumps, magnetic field sensors, kinetic energy storage devices and accelerometers. Such nanometer-scale beams may be provided as, for example, single molecules, single crystal filaments, or nanotubes. When suspended by both ends, these nanometer-scale beams may be caused to rotate about their line of suspension, similar to the motion of a jumprope (or a rotating whip), via electromagnetic or electrostatic forces. This motion may be used, for example, to accelerate molecules of a working substance in a preferred direction, generate electricity from the motion of a working substance molecules, or generate electromagnetic signals. Means of transmitting and controlling currents through these beams are also described.

Abstract: An electromechanical resonator includes a monocrystalline-silicon substrate (S) provided with an active zone (ZA) delimited by an insulating region, a vibrating beam (10) anchored by at least one of its free ends on the insulating region and including a monocrystalline-silicon vibrating central part (12), and a control electrode (E) arranged above the beam and bearing on the active zone. The central part (12) of the beam is separated from the active zone (ZA) and from the control electrode (E).

Abstract: A mirror apparatus has a reflecting surface to reflect an incident luminous flux. A fixed member has a plurality of driving electrodes on a surface of the fixed member. A movable member is formed with the reflecting surface on one side, and capable of escaping out of the optical path of the incident luminous flux along the fixed member. A driving circuit is capable of applying a voltage to the driving electrodes to generate an electrostatic force between the driving electrodes and movable members. A control circuit supplies a control signal to the driving circuit to change the electrostatic force acted on the movable member.

Abstract: A micro-electro-mechanical system (MEMS) mirror device includes an mirror, bonding pads, springs, and beams connected to the mirror. The mirror has a width greater than 1000 and less than 1200 microns, a length greater than 4000 and less than 5500 microns, and a thickness greater than 240 microns. Each beam includes a plurality of rotational comb teeth and is connected by multiple springs to the bonding pads.

Abstract: First and second stationary members are arranged to face each other, and a movable member is arranged between these first and second stationary members so as to be movable in a predetermined direction. An electrode groups including a plurality of stationary electrodes having the same width and sequentially arranged at substantially the same pitch in a predetermined direction is formed on each of these stationary electrodes. Also, a movable electrode having a width in the predetermined direction, which is larger than the width of each of the stationary electrodes constituting the electrode group, is arranged on the movable member. First and second voltage signal patterns differing from each other in the timing are applied to the stationary electrodes constituting the electrode group. When the movable member is driven in the predetermined direction by one of the first and second voltage signal patterns, the voltage signal pattern serving to drive the movable member is determined as the driving signal.

Abstract: A fixed voltage and a movable electrode are placed face to face with each other, and an insulating film is formed on the surface of the fixed electrode. The insulating film is made of a nitride film (SiN) as a main material, with oxide films (SiO2) being formed on the front and rear surfaces of the nitride film. Moreover, a plurality of protrusions are formed on an area facing the movable electrode of the upper face of the insulating film. The charge quantity in the insulating film is mainly determined by a film thickness of the oxide film, and the nitride film is used for maintaining a sufficient film thickness required for the voltage proof characteristic.