Abstract: An air/oil separator for use in a gas turbine engine includes a centrifugal separation stage in fluid communication with a downstream electrostatic separation stage. The centrifugal separation stage rotationally drives an electric generator to power the electrostatic separation stage.

Abstract: An air conditioning system includes an air flow pathway extending through a housing from an inlet to an outlet. Air conditioning apparatus is disposed in the airflow pathway between the inlet and the outlet conditioning an air stream passing through the air flow pathway from the inlet to the outlet. A modular electrically stimulated air filter apparatus is carried by opposed, parallel frameworks mounted in series in the air flow pathway between the inlet and the air conditioning apparatus filtering entrapping contaminants in the air stream flowing through the housing from the inlet to the outlet. The opposed parallel frameworks are mounted to opposed supports affixed to the housing.

Abstract: Disclosed is a device for purifying a process gas in a reflow soldering system. Said device comprises a receptacle that contains at least one packing bed. The process gas is fed to the receptacle via a gas inlet while being discharged from the receptacle after penetrating the packing bed. The inventive device further comprises an apparatus for delivering a liquid fluid to the receptacle. Secondary materials of the soldering process in the reflow soldering system can be absorbed by the liquid fluid and thus be eliminated from the process gas. Secondary materials and/or droplets and vapors of the fluid can additionally be absorbed and adsorbed on the surface of the packing.

Abstract: The invention refers to a device and a method for cleaning a gas containing particulate impurities. The device includes a main separator having an inlet for the gas, an outlet for the gas and a rotating member provided between the inlet and the outlet. The rotating member is adapted to bring the gas to rotate for separating by means of centrifugal forces a main amount of the particulate impurities from the gas, wherein a rest amount of the particulate impurities remains in the gas. The device also includes an additional separator adapted to separate substantially the whole rest amount. The additional separator includes an electrostatic filter.

Abstract: A composite filter media for a vacuum cleaner comprising a first filtration layer comprising a slit film having a plurality of continuous electrostatically-charged polyolefin filaments disposed substantially parallel to each other along their lengths; and a second filtration layer comprising a high-efficiency filtration media selected from wet-laid filter paper, dry-laid filter paper, and nonwoven filter media; wherein said first filtration layer is disposed in series with said second filtration layer, with respect to an air flow direction through said vacuum cleaner, to form a composite.

Abstract: An air/oil separator for use in a gas turbine engine comprises a centrifugal separation stage in fluid communication with a downstream electrostatic separation stage. The centrifugal separation stage rotationally drives an electric generator to power the electrostatic separation stage.

Abstract: An air cleaner is provided according to an embodiment of the invention. The air cleaner includes an air duct including an inlet end and an outlet end, a pre-filter positioned at the inlet end, an electrostatic precipitator positioned in the air duct downstream of the pre-filter, a post-filter positioned in the air duct downstream of the electrostatic precipitator, and a fan unit positioned in the air duct downstream of the post-filter. Airflow travels from the inlet end to the outlet end. The airflow first encounters the pre-filter, encounters the electrostatic precipitator after encountering the pre-filter, encounters the post-filter after encountering the electrostatic precipitator, and encounters the fan unit after encountering the post-filter. Each of the pre-filter, the electrostatic precipitator, and the post-filter can be separately installed and removed from the air duct.

Abstract: A battery (16) drives an electric motor (17) which in turn drives a fan (18). A circuit board (20) controls the operation of the motor and fan to maintain the flow rate. Air is drawn through an inlet (22) and out through a vent (24). Foam discs (32) and (34) may extract particles from the air and an electrostatic filter may attract aerosols in the air.

Abstract: Contaminant laden gas streams from wood product dryer operations, and other sources, are purified. The gas stream first is saturated with moisture by contacting the gas stream with fine liquid droplets which entrain particulates. The gas stream then is subjected to a plurality of separate particulate and liquid droplet removal steps before a droplet-free gas stream having substantially reduced particulate contaminant levels is passed to a burner for removal of volatile organic compounds from the gas stream.

Abstract: A high performance, high efficiency filter is provided by a multi-stage filter having combinations of tribologically different fibers, nanofibers, and layering.

Abstract: A method and apparatus for preventing contamination of a substrate or a substrate surface, and particularly relates to prevention of contamination of raw materials, semi-finished products, base materials of products and substrate surface in a high-tech industry such as an in the production of semiconductors and liquid crystals. A gas coming into contact with a base material or substrate is purified by dust removing apparatus and adsorption and/or absorption apparatus so that the concentration of fine particles in the gas is below class 1,000 and a non-methane hydrocarbon concentration is below 0.2 ppm. Thereafter, the base material or the substrate surface is exposed to this gas.

Abstract: Air-treatment apparatus and methods are disclosed that are especially suitable for treating the air in a room or other dwelling or working space. An apparatus embodiment of the subject apparatus includes a housing having air-intake and air-output openings. A gas-filter assembly inside the housing receives air entering the air-intake opening and includes a dual-media filter element having a matrix of fibers to which particles of activated carbon are adhered at mutual points of contact without using an extraneous binder. As air passes through the gas-filter assembly, the carbon particles adsorb odor compounds from the air. At least one electrostatic 3-dimensional (E3D) filter assembly downstream of the gas-filter assembly includes a respective charging element sandwiched between dielectric-fiber filters sandwiched between two respective electrically conductive screens. The screens are electrically grounded while the charging element (which is conductive) is connected to a source of high-voltage DC power.

Abstract: An air cleaning apparatus is disclosed which, in one embodiment, has: an inlet for ambient air; an outlet for purified air; a mechanism for the uptake of a scrubbing liquor and for the removal of impurities dissolved or dispersed in the ambient air by contact with said scrubbing liquor; an inlet for feeding a scrubbing liquor from a scrubbing liquor feeding tank; an outlet for discharging used scrubbing liquor; and a blower for drawing ambient air into the apparatus, flowing the air through the apparatus and discharging the purified air from the apparatus. A kit including an apparatus as described above and a refill of scrubbing liquor ingredients, or of a scrubbing liquor concentrate or of a ready-to-use scrubbing liquor is also disclosed.

Abstract: The present invention includes a filtered mask enclosure having an exterior portion and interior regions within the exterior portion such that the interior regions have a filtering region and a purging region connected to the filtering region. The present invention further includes a method of removing a first contaminant in a gas phase, a second contaminant in a solid phase, and a third contaminant having an electrical charge from a purge gas and flowing the purge gas through a vicinity of a mask while exposing a wafer with light through the mask.

Abstract: There is provided a process for trapping particulate matter in a gas stream exiting a combustion equipment comprising providing a combustion equipment with one or more exits for exhaust gases, each exit connected to one or more ducts, and placing at least one particulate trap in each duct, wherein the particulate trap is removable and/or replaceable while the combustion equipment is online.

Abstract: A device for filtering a dirty air stream in a vacuum cleaner to obtain a clean air stream includes subjecting the dirty air stream to a first cyclonic separation stage to obtain a partially cleaned air stream and subjecting the partially cleaned air stream to an electronic filtration stage and optionally a second cyclonic separation stage to obtain the clean air stream. The electronic filtration stage is optionally removable with a cyclonic cleaning stage from the vacuum cleaner. The electronic filtration stage is optionally an electrostatic precipitator which utilizes air flow through the vacuum cleaner to generate the voltage used by the electrostatic precipitator.

Abstract: It is disclosed a combined system for the elimination of pollutants from gaseous effluents of the type that comprises means for carrying out at least one electronic bombardment operation and means for carrying out at least one electrostatic interaction operation, in which a heat diffusion and molecular destabilization operation is performed as a previous treatment in order to restrict the flow of gases in such a way that it causes the gas molecules and suspended particles to tend to split up and electronically destabilize at the time that the temperature of the same gases is reduced; and/or a magnetic molecular rearrangement operation is carried out prior to each electrostatic interaction operation, consisting of subjecting the gases to a magnetic field having such a force that achieve a rearrangement of the sub-particles and heavier molecules thus achieving a selective separation that prepares the gaseous stream for the electrostatic interaction operation.

Abstract: A housing for purifying an air flow moving through it provides a reception space for receiving the air flow. The air is treated with mechanical filtration of particles larger than approximately 2 micron, ionizing with energetic ions, exposure to ultraviolet light radiation, and electrostatic precipitation of particles in the air inflow. The ionizing and UV bombardment of the air inflow occur simultaneously.

Abstract: The present invention includes a filtered mask enclosure having an exterior portion and interior regions within the exterior portion such that the interior regions have a filtering region and a purging region connected to the filtering region. The present invention further includes a method of removing a first contaminant in a gas phase, a second contaminant in a solid phase, and a third contaminant having an electrical charge from a purge gas and flowing the purge gas through a vicinity of a mask while exposing a wafer with light through the mask.

Abstract: A size preferential electrostatic agglomerator is provided for agglomerating small particles with larger “carrier” particles. The agglomerator includes an inlet for receiving a gas flow, a separator for separating the gas flow into flow streams based on the size of the particles therein, an ionization region for imparting an opposite electrical charge to each of the flow streams, an agglomeration region receiving the flow streams to facilitate the agglomeration of the oppositely charged particles, and an outlet for exhausting the gas flow containing agglomerated particles to facilitate collection, processing or other activity on the agglomerated particles. The present invention provides an efficient system for gathering large amounts of small particles in a gas flow.

Abstract: A device and method for controlling particulate air pollutants of the present invention combines filtration and electrostatic collection devices. The invention includes a chamber housing a plurality of rows of filter elements. Between the rows of filter elements are rows of high voltage discharge electrodes. Between the rows of discharge electrodes and the rows of filter elements are grounded perforated plates for creating electrostatic precipitation zones.

Abstract: An apparatus for filtering a dirty air stream in a vacuum cleaner to obtain a clean air stream includes subjecting the dirty air stream to a first cyclonic separation stage to obtain a partially cleaned air stream and subjecting the partially cleaned air stream to an electronic filtration stage and optionally a second cyclonic separation stage to obtain the clean air stream. The electronic filtration stage is optionally removable with a cyclonic cleaning stage from the vacuum cleaner. The electronic filtration stage is optionally an electrostatic precipitator which utilizes air flow through the vacuum cleaner to generate the voltage used by the electrostatic precipitator.

Abstract: A low density ash particle separation and collection method and device for separating low density particles, primarily frothy-solid particles with internal and external porosity and thick walled hollow particles, from the overall mixture of higher density particles including raw fly ash as produced by coal fired power plants. Specifically, the invention relates to a device and method for separating and collecting the low density fly ash fraction composed of thick walled hollow fly ash particles and frothy generally solid particles with both internal and external porosity and a relatively small amount of cenospheres from the overall mixture of ash particles composing raw ash as produced by coal fired power plants by de-energizing one or more fields of large electrostatic precipitators during electrostatic precipitation of the ash resulting in the dropping out of the lower density particles in the hoppers located below the de-energized field(s) of the electrostatic precipitator.

Abstract: A filter apparatus for use in removing mist, smoke and particles generated by a machine tool includes a mechanical first filtration stage and a second filtration stage consisting of an electrostatic precipitator. A blower device creates a stream of air for entraining and moving mist, smoke and other particles upwardly through the first and second filtration stages. Circuitry is provided selectively opening the circuit to the collector of the electrostatic precipitator. The collector is energized by a lower voltage from the ionizing field when current to the collector is interrupted. By energizing the collector of the electrostatic filter at a low voltage and by operating the blower unit at a low velocity, mist, smoke and other particles are efficiently collected without shorting the collector plates when water based metal working fluids are used.

Abstract: A method of separating a low density fly ash fraction from an overall group of fly ash entrained in a gas stream including the steps of passing the gas through a duct having a first area; passing the gas stream from the duct through an expansion nozzle; passing the gas stream through the expansion nozzle and into a hollow body having a second area, whereby the second area is larger than the first area; decelerating the gas stream as it enters the expansion nozzle to separate out low density ash particles; and collecting the low density ash particles from a hopper positioned adjacent the expansion nozzle.

Abstract: An apparatus for filtering a dirty air stream in a vacuum cleaner to obtain a clean air stream includes subjecting the dirty air stream to a first cyclonic separation stage to obtain a partially cleaned air stream and subjecting the partially cleaned air stream to an electronic filtration stage and optionally a second cyclonic separation stage to obtain the clean air stream. The electronic filtration stage is optionally removable with a cyclonic cleaning stage from the vacuum cleaner. The electronic filtration stage is optionally an electrostatic precipitator which utilizes air flow through the vacuum cleaner to generate the voltage used by the electrostatic precipitator.

Abstract: An alcohol separator is provided with an atomizer which supplies a mist of atomized alcohol solution to one region of a flow path, and an electrostatic collection device which uses an electrostatic field corona discharge to capture, liquefy, and recover alcohol solution mist generated by the atomizer.

Abstract: A kitchen hood filtration system having improved odor removal properties includes an electrostatic precipitator having negative corona which generates ozone. The ozone interacts with odor-producing moieties to help eliminate the odors. The filtration system also includes a grease remover, an odor remover which utilizes the ozone, and a fan which drives kitchen effluent through the hood filtration system.

Abstract: The process serves for removing carbon monoxide and/or hydrogen from an air stream by catalytic oxidation. Dusts and/or aerosols of a particle size of less than 20 &mgr;m are removed from the air stream upstream of the catalytic oxidation.

Abstract: A vacuum cleaner exhaust filter assembly includes a main HEPA exhaust filter, and an ion generation stage to add ions to the air. The ion generation stage preferably is a polypropylene mesh which generates ions through static electric interaction with the moving air as the result of friction. The exhaust filter assembly preferably also includes a pre-filter impregnated with carbon, preferably in the form of activated charcoal, to absorb odors from the exhaust air. The filter components, arranged in the preferred order, are the carbon pre-filter, the main HEPA exhaust filter, and the ion generation mesh.

Abstract: Apparatus and method for removing particulates and corrosive gases from a gas stream includes the serial use of a condensing wet electrostatic precipitator section for removing smaller particulates, in the submicron range, in conjunction with a vertically aligned preliminary scrubber section which removes larger particulates, in the micron range, and corrosive gases, in an integrated unit in which the temperature and moisture conditions in the gas stream are controlled for assuring effective and efficient operation of the condensing wet electrostatic precipitator section. Discharge electrodes of the electrostatic precipitator are supported by insulators which are protected against deleterious deposits of particulates by discharge electrode elements and collector electrode elements placed between the gas stream and the insulators.

Abstract: A submicron filter assembly (24) is added to an exhaust gas controlled destruction and oxidation unit (10). Controlled destruction and oxidation unit (10) treats exhaust gas from at least one semiconductor wafer fabricating reactor. The submicron filter (24) filters submicron particles out of the treated exhaust gas to prevent visible plumes from forming in wafer fab exhaust systems (stacks). The controlled destruction and oxidation unit (10) and submicron filter assembly (24) are ideally suited for use at the point of generation of the exhaust gases. In one embodiment of the invention, the submicron filter assembly comprises an electrostatic filter (26). The electrostatic filter (26) includes a positively charged first grid (28) and a grounded second grid (30). The second grid may include a mist screen for removing particulate build-up. In another embodiment of the invention, the submicron filter assembly (36) comprises a mist eliminator (38) and a HEPA filter (40).

Abstract: Apparatus and method for separating carbon particles from flyash includes one of increasing a relative humidity of the flyash or decreasing the relative humidity of the flyash to within an optimum humidity range, and introducing the flyash within the optimum humidity range into a triboelectric separator so as to triboelectrically charge the carbon particles and the flyash and so as to electrostatically separate the charged carbon particles from the charged flyash.

Abstract: An apparatus and method for reducing the amount of unburned carbon in raw flyash, wherein raw flyash containing unburned carbon is introduced into the tribocharger, the tribocharger producing positive and negative surface charges on the respective particles of carbon and flyash, introducing the charged particles into an electrical field containing positively and negatively charged plates, the positively and negatively charged particles being collected on the negatively and positively charged plates, and selectively vibrating the plates to selectively recover the unburned carbon and flyash.

Abstract: A combined furnace limestone injection and dry scrubber flue gas desulfurization (FGD) system collects solids from the flue gas stream in first particulate collection device located downstream of an outlet of a convection pass of the furnace and upstream of the dry scrubber. The collected solids are diverted to the dry scrubber feed slurry preparation system to increase sulfur oxide species removal efficiency and sorbent utilization. The level of lime in the feed slurry provided to the dry scrubber is thus increased, which enhances removal of sulfur oxide species in the dry scrubber. The decreased particulate loading to the dry scrubber helps maintain a desired degree of free moisture in the flue gas stream entering the dry scrubber, which enhances sulfur oxide species removal both in the dry scrubber and downstream particulate collector, normally a baghouse.

Abstract: Method to remove organic halogenated molecules from gaseous currents arriving as a residue of industrial working processes or not, the gaseous current being delivered into a reactor (16) containing a fluid bed consisting of at least one solid adsorbent element after having undergone at least one filtration followed by a cooling, the gaseous current cooperating with the solid particles with exchange by adsorption between the gaseous current and the solid particles, the reactor (16) achieving a time of contact between the gaseous current and the solid particles at least longer than 3 seconds, the gaseous current which enters the reactor (16) having a temperature lower than 80.degree. C., but advantageously between 30.degree. and 70.degree. C., the cooling of the gaseous current upstream of the reactor (16) being followed by a gas/water or gas/air heat exchanger (13).

Abstract: A dust neutralizing and flocculating system used in an air cleaning system for removing contaminants contained in indoor air including a radio frequency generating electrode and an ion generating electrode. Fine particles passing through a moderately efficient filter equipped in the air cleaning system sequentially pass through the radio frequency generating electrode and ion generating electrode. The fine particles are dipolarly magnetized while passing through the radio frequency generating electrode, thereby exhibiting an increased inter-particles attraction. The ion generating electrode adds cations and anions to the fine particles, thereby promoting the flocculation of the fine particles circulating in the room installed with the air cleaning system. By virtue of the promoted flocculations, the particle size of the particles circulating in the room increases. The particles with an increased size are secondarily removed by the filter.

Abstract: An exhaust gas purifying apparatus capable of exhibiting an excellent exhaust gas purifying capability and restoring the capability to an initial level even after running for a long period of time. An electrification mesh section electrostatically negatively charges useless particulates contained in exhaust gas and a purification filter section adsorbs thereon the particulates thus charged, resulting in the particulates being separated from the exhaust gas. Also, when the purification filter is made of carbon fiber or carbon particles or the denitration filter section is additionally provided, a reduction in concentration of nitrogen oxides in the exhaust gas is accomplished as well. In a reactivation unit, cleaning liquid cleans the purification filter section to remove useless particulates therefrom, so that an exhaust gas purification capacity of the exhaust gas purifying apparatus may be restored to a level substantially equal to an initial level thereof.

Abstract: A clog-resistant filter and method for extracting fine particulate contaminants, such as smoke, from a gaseous fluid stream, such as air, uses an induced voltage electrode to efficiently capture the contaminant particles in a filter material whose pores are many times larger than the diameter of the particles to be captured. The filter material is physically so configured to further enhance that interaction and is disposed between at least a pair of electrodes of opposite polarity.

Abstract: A self contained air movement system for air purification and infection control includes an elongated upright enclosed housing including a base module, sidewalls, and an upper module. A fan intermediate the base module and the upper module draws unclean air from a room containing the system through the base module, then discharges a purified air stream from the upper module. The base module includes a downward facing air intake opening spaced from the floor. A pair of pre-filters are disposed on the base module in stacked relationship for trapping relatively large particulate matter from the entering air stream. The upper module includes a discharge grille opening to the environment with angled louvers for guiding and re-directing the purified air stream from a downstream HEPA-type filter into an inclined stream, flowing proximate to and along the ceiling of the room in which the system is located.

Abstract: A vacuum cleaner having a reduced velocity chamber with a high velocity air inlet, an electric motor, a rotary mechanism driven by the motor for creating a vacuum in the chamber, an outlet for exhausting air from the chamber, which air flows in a selected path from the air inlet, through the chamber and out the air exhaust outlet and a disposable porous sheet filter layer in the chamber for removing solids particles from the air. The vacuum cleaner also has a fiber filter between the filter layer and the motor where the fiber filter has an electrically charged non-woven material for removing very fine air particles in the chamber, intersecting the air path and generally coterminous with the disposable filter layer.

Abstract: A horse riding simulating exerciser includes a rod for securing a foot support and a seat post pivotally coupled to a middle portion of a frame at a pivot axle and coupled to the rod. A track is secured on the seat post for carrying a slide. A handle is pivotally coupled to the frame and a lever couples the handle to the slide. When the slide is moved to one side of the pivot axle, the seat cushion may be elevated by pulling the handle. When the slide is moved to the other side of the pivot axle, the seat cushion may be elevated by pushing the handle upward.

Abstract: An air treatment system includes a housing having a from cylindrical chamber and a rear rectangular chamber, the front and rear chambers being separated by an internal wall. The front chamber is provided with a series of outlet vents, the rear chamber is provided with a series of inlet vents, and the internal wall is provided with a series of interchamber vents. A pair of electrically-powered cylindrical fan blades are disposed within the front chamber and are used to draw air into the rear chamber through the inlet vents, to move the air from the rear chamber to the front chamber through the interchamber vents and to exhaust the air from the front chamber through the outlet vents. A plurality of ionizer needles are also disposed within the front chamber. The rear chamber is shaped to include a generally rectangular reservoir. The air treatment system also includes a water tank removably mounted within the rear chamber for use in supplying water to the reservoir.

Abstract: An electrostatic filter of a combination of a layer of filter material having electrostatic properties and a layer of filter medium without electrostatic properties. The medium is a lofted material arranged to retain particles in the sub-micron and lower micron ranges, and in use, is located upstream of the material. The invention also includes a method of filtering dust from the atmosphere utilizing the electrostatic filter.

Abstract: An apparatus for the selective control of the sulfur trioxide concentration in flue gases, to enhance the ash removal efficiency of electrostatic precipitators, which includes: catalytically converting a portion of the sulfur dioxide contained within the flue gas to sulfur trioxide, by passing a portion of such flue gas through at least one catalyst containing converter module which is positioned within such a flue gas stream; and selectively varying the quantity of flue gas passing through such module by providing an aspirating force to cause flue gas to be drawn through such a converter module.

Abstract: The invention relates to apparatus for biological purification and filtration of air. The apparatus includes a coarse filter (1), an ionizer (5), an additional plate (9) and a fine filter (10), which are installed in this order along the path of the gas flow, and a power source (23). The coarse filter (1) is essentially an electrostatic precipitator consisting of three plates (2,3,4) adjacent to each other, the outer-most (2,3) of which are made of a cellular metal and are connected electrically to the opposite-in-sign terminals of the power source (23), whereas the central plate (4) is made of polyurethane foam. The coarse filter (1) abuts closely on the cylindrical nondischarge electrode (6) of the ionizer (5).

Abstract: Disclosed is an apparatus for removing emissions, originated in the manufacturing industry, especially from polymerization operations and thermoplastic polymer processing operations which has a duct system for collecting the air, containing emissions, with an entrance and an exit, a first heat exchanger, which is connected to the entrance of the duct system, a liquid removal system which is connected to the first heat exchanger, a second heat exchanger, which is connected to the liquid removal system and a fan which is connected to the second heat exchanger and the exit of the duct system.

Abstract: An air purifier has discharge electrodes which generate a corona emission. These discharge electrodes are disposed within a flow passage provided in the air purifier along with a blower. Also included in the air purifier is a filter which scavenges contaminant particles in the air charged by the discharge electrodes. A control unit detects a discharge current of the discharge electrodes to control a rotational speed of the blower in accordance with the detected emission current.

Abstract: For the separation of dioxins and furans from exhaust gases from combustion plants, particularly from refuse incinerating plants, a process is described in which the dust and the gaseous pollutants HF, HCl, SO.sub.2, and SO.sub.3 are first substantially entirely separated from the exhaust gases in known manner, the thus prepurified exhaust gas is then supplied to a wet-process electrostatic precipitator, and 10 to 500 mg activated carbon powder per sm.sup.3 are added to the prepurified exhaust gas immediately before it enters the wet-process electrostatic precipitator.

Abstract: Disclosed is an apparatus for removing emissions, originated in the manufacturing industry, especially from polymerization operations and thermoplastic polymer processing operations which has a plurality of ducts, an entrance for collecting air, containing the emissions and an exit for exiting exhaust air, a first heat exchanger which has a hot side with an entrance and an exit and a cold side with an entrance and an exit, a second heat exchanger, which has a hot side with an entrance and an exit and a cold side, a liquid removal system, and a fan, whereby the first heat exchanger is connected with the entrance of the hot side to the entrance of the duct system and with the exit of the hot side to the entrance of the hot side of the second heat exchanger by a duct; the exit of the hot side of the second heat exchanger is connected to the entrance of the cool side of the first heat exchanger by a duct; the precipitator is connected to the exit of the cool side of the first heat exchanger by a duct and to the f