A semiconductor mounting apparatus includes a storing unit that stores a liquid or a gas, a contact unit that comes into contact with a semiconductor chip when the storing unit is filled with the liquid or the gas, and a sucking unit that sucks up the semiconductor chip to bring the semiconductor chip into close contact with the contact unit.

A semiconductor device includes a substrate comprising a trench; a gate dielectric layer formed over a surface of the trench; a gate electrode positioned at a level lower than a top surface of the substrate, and comprising a lower buried portion embedded in a lower portion of the trench over the gate dielectric layer and an upper buried portion positioned over the lower buried portion; and a dielectric work function adjusting liner positioned between the lower buried portion and the gate dielectric layer; and a dipole formed between the dielectric work function adjusting liner and the gate dielectric layer.

Embodiments of the inventive concepts provide a method for manufacturing a semiconductor device. The method includes forming a stack structure including insulating layers and sacrificial layers which are alternately and repeatedly stacked on a substrate. A first photoresist pattern is formed on the stack structure. A first part of the stack structure is etched to form a stepwise structure using the first photoresist pattern as an etch mask. The first photoresist pattern includes a copolymer including a plurality of units represented by at least one of the following chemical formulas 1 to 3, wherein “R1”, “R2”, “R3”, “p”, “q” and “r” are the same as defined in the description.

A performance of a semiconductor device is improved. A film, which is made of silicon, is formed in a resistance element formation region on a semiconductor substrate, and an impurity, which is at least one type of elements selected from a group including a group 14 element and a group 18 element, is ion-implanted into the film, and a film portion which is formed of the film of a portion into which the impurity is ion-implanted is formed. Next, an insulating film with a charge storage portion therein is formed in a memory formation region on the semiconductor substrate, and a conductive film is formed on the insulating film.

A method of manufacturing a semiconductor device according to one embodiment includes forming a first film including a first metal above a processing target member. The method includes forming a second film including two or more types of element out of a second metal, carbon, and boron above the first film. The method includes forming a third film including the first metal above the second film. The method includes forming a mask film by providing an opening part to a stacked film including the first film, the second film and the third film. The method includes processing the processing target member by performing etching using the mask film as a mask.

Embodiments of the inventive concept provide a method for manufacturing a semiconductor device. The method includes forming a stack structure by alternately and repeatedly stacking insulating layers and sacrificial layers on a substrate, sequentially forming a first lower layer and a first photoresist pattern on the stack structure, etching the first lower layer using the first photoresist pattern as an etch mask to form a first lower pattern. A first part of the stack structure is etched to form a stepwise structure using the first lower pattern as an etch mask. The first lower layer includes a novolac-based organic polymer, and the first photoresist pattern includes a polymer including silicon.

The present invention provides a method for manufacturing the N-type TFT, which includes subjecting a light shielding layer to a grating like patternization treatment for controlling different zones of a poly-silicon layer to induce difference of crystallization so as to have different zones of the poly-silicon layer forming crystalline grains having different sizes, whereby through just one operation of ion doping, different zones of the poly-silicon layer have differences in electrical resistivity due to difference of grain size generated under the condition of identical doping concentration to provide an effect equivalent to an LDD structure for providing the TFT with a relatively low leakage current and improved reliability. Further, since only one operation of ion injection is involved, the manufacturing time and manufacturing cost can be saved, damages of the poly-silicon layer can be reduced, the activation time can be shortened, thereby facilitating the manufacture of flexible display devices.

A method of manufacturing a thin film transistor is disclosed. The method of manufacturing the thin film transistor includes: manufacturing a substrate; forming an oxide semiconductor layer on the substrate; forming a pattern including an active layer through a patterning process; forming a source and drain metal layer on the active layer; and forming a pattern including a source electrode and a drain electrode through a patterning process, an opening being formed between the source electrode and the drain electrode at a position corresponding to a region of the active layer used as a channel, wherein the step of forming the pattern including the source electrode and the drain electrode through a patterning process includes: removing a portion of the source and drain metal layer corresponding to the position of the opening through dry etching. The method may also be used to manufacturing a thin film transistor.

A first photoresist pattern and a second photoresist pattern are formed over a substrate. The first photoresist pattern is separated from the second photoresist pattern by a gap. A chemical mixture is coated on the first and second photoresist patterns. The chemical mixture contains a chemical material and surfactant particles mixed into the chemical material. The chemical mixture fills the gap. A baking process is performed on the first and second photoresist patterns, the baking process causing the gap to shrink. At least some surfactant particles are disposed at sidewall boundaries of the gap. A developing process is performed on the first and second photoresist patterns. The developing process removes the chemical mixture in the gap and over the photoresist patterns. The surfactant particles disposed at sidewall boundaries of the gap reduce a capillary effect during the developing process.

A TFT and manufacturing method thereof, an array substrate and manufacturing method thereof, an X-ray detector and a display device are disclosed. The manufacturing method includes: forming a gate-insulating-layer thin film (3'), a semiconductor-layer thin film (4') and a passivation-shielding-layer thin film (5') successively; forming a pattern (5') that includes a passivation shielding layer through one patterning process, so that a portion, sheltered by the passivation shielding layer, of the semiconductor-layer thin film forms a pattern of an active layer (4a'); and performing an ion doping process to a portion, not sheltered by the passivation shielding layer, of the semiconductor-layer thin film to form a pattern comprising a source electrode (4c') and a drain electrode (4b'). The source electrode (4c') and the drain electrode (4b') are disposed on two sides of the active layer (4a') respectively and in a same layer as the active layer (4a'). The manufacturing method can reduce the number of patterning processes and improve the performance of the thin film transistor in the array substrate.

Manufacturing methods of JFET-type compact three-dimensional memory (3D-MC) are disclosed. In a memory level stacked above the substrate, an x-line extends from a memory array to an above-substrate decoding stage. A JFET-type transistor is formed on the x-line as a decoding device for the above-substrate decoding stage, where the overlap portion of the x-line with the control-line (c-line) is semi-conductive.

To provide a semiconductor device having improved reliability. After formation of an n+ type semiconductor region for source/drain, a first insulating film is formed on a semiconductor substrate so as to cover a gate electrode and a sidewall spacer. After heat treatment, a second insulating film is formed on the first insulating film and a resist pattern is formed on the second insulating film. Then, these insulating films are etched with the resist pattern as an etching mask. The resist pattern is removed, followed by wet washing treatment. A metal silicide layer is then formed by the salicide process.

A method for manufacturing an LDMOS device includes: providing a semiconductor substrate (200), forming a drift region (201) in the semiconductor substrate (200), forming a gate material layer on the semiconductor substrate (200), and forming a negative photoresist layer (204) on the gate material layer; patterning the negative photoresist layer (204), and etching the gate material layer by using the patterned negative photoresist layer (204) as a mask so as to form a gate (203); forming a photoresist layer having an opening on the semiconductor substrate (200) and the patterned negative photoresist layer (204), the opening corresponding to a predetermined position for forming a body region (206); and injecting the body region (206) by using the gate (203) and the negative photoresist layer (204) located above the gate (203) as a self-alignment layer, so as to form a channel region.

An organic layer deposition assembly for depositing a deposition material on a substrate includes a deposition source configured to spray the deposition material, a deposition source nozzle arranged in one side of the deposition source and including deposition source nozzles arranged in a first direction, a patterning slit sheet arranged to face the deposition source nozzle and having patterning slits in a second direction that crosses the first direction, and a correction sheet arranged between the deposition source nozzle and the patterning slit sheet and configured to block at least a part of the deposition material sprayed from the deposition source.

A method of forming microelectronic systems on a flexible substrate includes depositing a plurality of layers on one side of the flexible substrate. Each of the plurality of layers is deposited from one of a plurality of sources. A vertical projection of a perimeter of each one of the plurality of sources does not intersect the flexible substrate. The flexible substrate is in motion during the depositing the plurality of layers via a roll to roll feed and retrieval system.

A fastening strap and a manufacturing method thereof are provided. The fastening strap includes a first band and a second band. The first band has a first surface and a second surface. The first surface has a plurality of hooks of special configuration. The second band has a third surface and a fourth surface. The third surface is directly adhered to the second surface of the first band, and the fourth surface has a plurality of loops for being mechanically latched by the hooks on the first surface. The second surface and/or the third surface is printed with at least one pattern. After the first band and the second band are adhered together, the pattern can be seen from the first surface of the first band.

Embodiments of a loop clip used with a golf bag and methods to manufacture a golf bag are generally described herein. Other embodiments of the loop clip may be described and claimed.

A method is used to prepare a body for burial. The method includes placing the body inside a vessel. The body includes bones and tissue. The method further includes subjecting the body to a flow of steam until the bones are free of tissue. In one implementation, the flow of steam has a temperature of about 212 degrees Fahrenheit and a mass flow rate of at least 1000 pounds per hour. The method may further include removing the bones from the vessel.

A modular casket made of lightweight materials is structurally reinforced using a structural sealant along at least the inner surfaces of the side panels, and optionally along at least side edge portions of a base panel to which the side panels are coupled, to stiffen and rigidize the casket against flexion along longitudinal and lateral axes, as well as torsional flexion. The structurally reinforced casket is sealed or more readily sealed against leakage and provides other benefits of structural stiffness and rigidity with relatively small cost and weight penalties.

Disclosed is a hinge having a rigid portion integral with a flexible portion suitable to be bent with respect to the rigid portion, wherein the rigid portion has a substrate in a rigid composite material and the flexible portion has a first flexible sheet, wherein a first portion of the first flexible sheet is joined at least partially to the substrate by means of at least one first layer of resin for composite materials, wherein the flexible portion also has a second flexible sheet joined at least partially by means of at least one second layer of resin for composite materials both to the first portion of the first flexible sheet and to at least one second portion of the first flexible sheet which is not joined to the substrate.

A piston manufacturing device includes a first forming device (42) configured to form an annular groove (61) in a piston (11), and a second forming device (52) configured to press an edge (15) of an opening (14) of the piston (11) toward other end side in an axial direction of the piston (11) and to form a thick section (65) extruded from an inner circumferential surface (12b) arranged between the edge (15) and the groove (61) toward an axial center side of the piston (11), wherein a recessed section (53) is formed at a portion of the second forming device (52) that is arranged to abut the edge (15) so that an inner circumferential side of the edge (15) is plastically deformed toward the other end side in an axial direction of the piston (11).

Solid carboniferous fuels contain varying quantities of moisture, mercury, chlorine, nitrogen, sulfur, heavy metals and other materials that attain vapor pressure at elevated temperatures. The cost effective removal of these degrading and sometimes hazardous materials is important to the further use of the fuel for combustion as a solid, liquid, or gas. The solid fuel is cut, shredded, ground or sieved to appropriate size, and heated in a chamber that can exclude oxygen and air thus preventing ignition. The unwanted materials are driven in the gaseous state and extracted for disposal. The solid fuel cleaned of pollutants exits the chamber and is cooled below ignition temperature prior to contact with oxygen. The solid fuel thus purified is more appropriate for combustion, liquefaction or gasification due to the reduced costs in use as a fuel or in the post combustion clean up.

The present invention provides a reformer tube apparatus, including: an axially aligned tubular structure including a flange section, a top section, a middle section, and a bottom section; wherein the top section of the axially aligned tubular structure includes a first portion having a first wall thickness; wherein the top section of the axially aligned tubular structure includes a second portion having a second wall thickness; and wherein the top section of the axially aligned tubular structure includes a third portion having a transitioning wall thickness that joins the first portion to the second portion. The flange section includes a concentric flange disposed about a top portion thereof. The bottom section of the tubular structure includes a plurality of concentric wedge structures disposed about the interior thereof. The bottom section of the tubular structure also includes a recess disposed about the exterior thereof. The axially aligned tubular structure further includes a secondary flange section coupled to the flange section, wherein the secondary flange section includes a concentric flange disposed about a top portion thereof. Optionally, the reformer tube apparatus is disposed within a reformer used in a direct reduction process.

Provided is an electronic device that is highly resistant to a water-soluble grinding oil and a method for manufacturing the same. An electronic device includes a main body and a cable including a lead wire, an insulating portion, and an outer coat, a first sealing portion that covers the insulating portion, and a second sealing portion that seals the first sealing portion, the insulating portion is made of a material that is more resistant to a water-soluble grinding oil than the outer coat is, and the first sealing portion is made of a material that has higher adherence to the insulating portion than that of the second sealing portion does.

An abrasive article includes a polymer matrix and abrasive grains dispersed in the polymer matrix, wherein the abrasive article has a void volume of at least 50%. The polymer matrix is polymerized from a monomer including at least one double bond.

An abrasive element comprises a body of crystalline abrasive material. The body has an array of cutting elements formed of crystalline abrasive material which projects from a surface of the body. The shape, size and form of the projections is controlled in the production process. The body may be a natural or synthetic crystal. The body may be a film formed by deposition. The body may be diamond or cubic boron nitride. The body may be monocrystalline or polycrystalline. The projections may be aligned along a crystallographic plane or planes.

Provided are a polishing pad which remedies the problem of scratches occurring when a conventional hard (dry) polishing pad is used, which is excellent in polishing rate and polishing uniformity, and which can be used for not only primary polishing but also finish polishing, and a manufacturing method therefor. The polishing pad is a polishing pad for polishing a semiconductor device, comprising a polishing layer having a polyurethane-polyurea resin foam containing substantially spherical cells, wherein the polyurethane-polyurea resin foam has a Young's modulus E in a range from 450 to 30000 kPa, and a density D in a range from 0.30 to 0.60 g/cm3.

The present invention provides a shearing die having longer life and a method for manufacturing the same. The shearing die includes a pair of substrates, at least one of which has a hard film formed by an arc ion plating method and located at least on a region of a curved surface and on an adjacent region from the end part of the curved surface on the side facing to the surface of the sheet or plate material to 300 μm along the surface of the substrate. The hard film comprises Al and one or more of Ti and Cr, and has a thickness of 1 to 5 μm, such that a number of metal particles having a diameter of 20 μm or more, which are present on a line segment having a length of 10 mm on a surface of the hard film, is 2 or less.

A method of manufacturing grooved polishing layers for use in chemical mechanical polishing pads is provided, wherein the formation of defects in the polishing layers are minimized.

A process writes phase shift error correction values into a phased-array antenna to normalize a range of manufacturing variances. An axial ratio is determined for an antenna weight vector (AWV) by making multiple measurements with the horn of a test antenna mechanically rotating from 0 to 180 degree or with dual polarization test antenna. For calibration of the whole array, each subarray is treated in the same fashion as equivalent to an antenna element in the subarray calibration. The subarray is electronically rotated as a whole (all elements rotated by the same phase shift value) from 0 to 360 degree during the full array calibration. Due to small power variation among AWVs, calibration solely by REV results fail to consistently converge to resolution. Accordingly, the apparatus measures and compares axial ratios. During final fabrication, the apparatus programs an AWV with best axial ratio into each non-transitory array element.

A planter for holding a plant includes a container having an open upper end. The container has side walls extending downward from the upper end and tapering inward to a lower end. A base at the lower end of the container has a diameter smaller than the diameter of the upper end. A circumferential ring surrounds the lower end of the container. The circumferential ring has an upper edge that extends outward from the container by a distance such that removal of the container and ring from a mold as a single unit would be inhibited. Accordingly, the container and the circumferential ring are molded from a thermoplastic material as separate components. The circumferential ring fits around the lower end of the container and is held in place by a mechanical interlock between the container and the ring.

This tool, which is in particular a hammer, comprises a gripping handle, a striking head, and an intermediate shaft extending the handle and supporting the head, whereas the handle comprises a tube in which the shaft partially extends, this tube and this shaft being made from a rigid material presenting a first hardness. This shaft has a radial area bearing against the tube, with interposition of a link part, for absorbing vibrations, made from flexible material presenting a second hardness that is much lower than the first hardness, and a free terminal area, not covered by the link part, radially separated from the walls of the tube so as to be able to vibrate freely in an internal volume of the tube.

Provided is a hardcoat film having a film thickness of 25 μm or less in which a polymerized substance of a compound having an energy ray-curable group and a resin are mixed across an entire region in a film thickness direction, in which a percentage of a mass concentration of the resin which is represented by the Expression (1) as defined herein has a distribution in which the percentage is maximized on at least one of two opposed surfaces, in the film thickness direction, of the hardcoat film or at a central part, in the film thickness direction, of the hardcoat film.

Method for the manufacture of a formulation comprising the steps of: i) providing a metal in liquid form; ii) spraying the metal or metal alloy of step i) through a stream of gas under pressure to obtain substantially spherical solid metal particles; iii) mixing the solid metal particles of step ii) and at least a fluoropolymer to obtain said formulation; iv) optionally applying the formulation of step iii) to a surface to obtain a coating, or optionally shaping said formulation to obtain a shaped material. The present invention further relates to a formulation, a coating or a shaped material, preferably obtained through the method described.

An aromatic printed object containing a film-like substrate and a printing section formed on the film-like substrate using a perfume microcapsule-containing toner. The aromatic printed object is an adhesive sheet wherein the printing section is adherend surface. A protective layer is pressed with the adherend surface. A fragrance diverges by peeling off the protective layer of the film-like substrates.

A lightweight construction element (1) comprises at least one lightweight panel (2) and a layer of insulating material (4) associated with the lightweight panel (2), wherein the at least one lightweight panel (2) comprises boards (6), which, on at least one of the main surfaces (8) thereof, have a group of grooves (9) running parallel and which boards (6) are arranged in at least one layer (5) and are connected to one another via adhesive bonds. The layer of insulating material (4) comprises wood chips (19), which are removed from starting boards during the manufacture of boards (6) for the lightweight panels (2). These lightweight construction elements have good load and thermal insulation properties. The material used originates from one source and achieves a large overall volume after processing.

The invention provides a high strength stone plastic floor and manufacturing method thereof. The stone plastic floor comprises a PVC substrate and a surface layer on a surface of the PVC substrate. Compositions of PVC substrate comprise: PVC powder from 20 to 35 weight percent, calcium carbonate from 60 to 70 weight percent, stabilizer from 1 to 3 weight percent, flexibilizer from 1 to 3 weight percent, lubricants from 0.4 to 1 weight percent, and colorant from 0.4 to 1 weight percent. The high strength stone plastic floor does not contain plasticizer so environmental risks are completely avoided. The contractility is good. The high strength stone plastic floor is resistant to high temperature and direct sunlight. Compared with conventional stone plastic floor, lifespan of the present invention is prolonged. The PVC substrate of the floor can be combined with different layers and can integrate different advantages of other floors.

In nanoimprinting processes, photo-cured products often separate from the substrate and stick to the mold due to insufficient adhesion between the photo-cured product and the substrate. This causes a defect of pattern separation. An adhesion layer composition used for forming an adhesion layer between a substrate and a photocurable composition includes a compound (A) having at least two functional groups, and a solvent (B). The functional groups include at least one functional group capable of being bound to the substrate, selected from the group consisting of hydroxy, carboxy, thiol, amino, epoxy, and (blocked) isocyanate, and at least one hydrogen donating group as a functional group capable of being bound to the photocurable composition.

The magnetic tape has a nonmagnetic layer containing nonmagnetic powder and binder on a nonmagnetic support and a magnetic layer containing ferromagnetic powder and binder on the nonmagnetic layer, wherein a fatty acid ester is contained in at least the magnetic layer, the ferromagnetic powder is ferromagnetic hexagonal ferrite powder, the ferromagnetic hexagonal ferrite powder has a crystallite volume as determined by X-ray diffraction analysis ranges from 1,000 nm3 to 2,400 nm3, and a ratio of the crystallite size Dx(107) obtained from a diffraction peak of a (107) plane to a particle size in a direction of an easy axis of magnetization DTEM as determined by observation with a transmission electron microscope, Dx(107)/DTEM, is greater than or equal to 1.1, and ΔSFD in a longitudinal direction of the magnetic tape as calculated with Equation 1: ΔSFD=SFD25° C.−SFD−190° C., ranges from 0.50 to 1.60.

The present invention relates to an electrode having a multilayer nanomesh structure using single-crystalline copper and a method for manufacturing same, the electrode comprising: a substrate; a single-crystalline copper electrode layer formed on the substrate and having a hive-shaped pattern with a nano-sized line width; and a metal oxide layer formed on the single-crystalline copper electrode layer, this providing an electrode having excellent optical transmittance, low electrical sheet resistance, and excellent mechanical stability. The present invention is technically characterized by an electrode having a multilayer nanomesh structure using single-crystalline copper, the electrode comprising: a substrate; a single-crystalline copper electrode layer formed on the substrate and having a hive-shaped pattern with a nano-sized line width; and a metal oxide layer formed on the single-crystalline copper electrode layer.

Provided is a method for manufacturing magnetic particles, in which an oxidation treatment, a reduction treatment, and a nitriding treatment are performed in that order on raw material particles with a core-shell structure in which a silicon oxide layer is formed on the surfaces of iron microparticles, thereby nitriding the iron microparticles while maintaining the core-shell structure. Due to this configuration, granular magnetic particles with a core-shell structure in which a silicon oxide layer is formed on the surfaces of iron nitride microparticles can be obtained.

The present invention provides shuffled playing cards which eliminate the need for a game host to shuffle cards before games by taking a lot of time as well as eliminate the possibility of cheating. A shuffled playing cards (1) obtained by shuffling a predetermined number of decks of playing cards (12) using a shuffling machine is packaged as an individual pack. The shuffled playing cards (1) is individually packaged and sealed with an adhesive label (13). A bar code (13a) which represents a unique shuffled card ID has been printed on the adhesive label (13). The shuffled card ID is registered in a database by being associated with information which allows identification of a shuffling machine used to shuffle the playing card set.

The present invention relates to a process for the preparation of articles of manufacture made of or based on sulphur, which comprises cooling of liquid sulphur in a volume of containment until the sulphur mass solidifies and forming of the product, characterized in that elastic pressure waves are applied to the cooling mass of liquid sulphur to produce a crystalline suspension of solid sulphur in liquid sulphur.

A device for taking up a silicon melt comprises at least one block of a refractory with a capillary structure.

An acoustic resonator and a method of manufacturing the same are provided. An acoustic resonator includes a resonating part disposed on a substrate, a cap accommodating the resonating part and bonded to the substrate, and a bonded part bonding the cap and the substrate to each other, the bonding part including at least one block disposed between a bonding surface of the cap and a bonding surface of the substrate to block a leakage of a bonding material that forms the bonded part during a bonding operation.

An acoustic resonator and a method of manufacturing the same are provided. The acoustic resonator includes a resonating part including a first electrode, a second electrode, and a piezoelectric layer; and a plurality of seed layers disposed on one side of the resonating part.

In a method of manufacturing a piezoelectric device in which a piezoelectric thin film on which functional conductors are formed is fixed to a support substrate by a fixing layer, an alignment mark is formed on one main surface of a light-transmitting piezoelectric substrate. A sacrificial layer is formed on a main surface of the piezoelectric substrate with reference to the alignment mark and the fixing layer is formed so as to cover the sacrificial layer and is bonded to the support substrate. The piezoelectric thin film is formed by being separated from the piezoelectric substrate and the functional conductors are formed on the surface of the piezoelectric thin film with reference to the alignment mark. The piezoelectric device is able to be manufactured while positions of formation regions of conductors are adjusted efficiently.

A MEMS piezoelectric device includes a monolithic semiconductor body having first and second main surfaces extending parallel to a horizontal plane formed by first and second horizontal axes. A housing cavity is arranged within the monolithic semiconductor body. A membrane is suspended above the housing cavity at the first main surface. A piezoelectric material layer is arranged above a first surface of the membrane with a proof mass coupled to a second surface, opposite to the first surface, along the vertical axis. An electrode arrangement is provided in contact with the piezoelectric material layer. The proof mass causes deformation of the piezoelectric material layer in response to environmental mechanical vibrations. The proof mass is coupled to the membrane by a connection element arranged, in a central position, between the membrane and the proof mass in the direction of the vertical axis.

An electric machine of a motor vehicle, in particular of an adjustment drive or of a radiator fan, has a rotor which is mounted so as to be rotatable about a machine axis. The rotor has a number of permanent magnets which are arranged in the radial direction. Each permanent magnet has one side with a strong magnetic flux and one side with a weak magnetic flux in the tangential direction. When the permanent magnets are adjacent in the tangential direction, different sides are directed towards one another.

Raw material magnet is milled to magnet powder, and the magnet powder thus milled is mixed with a binder to form a compound 12. Then, the compound 12 thus formed is molded to a green sheet 14 having a sheet shape. Thereafter, a magnetic field orientation is carried out by applying a magnetic field to the green sheet 14 thus molded, and then, the green sheet 14 having been subjected to the magnetic field orientation is shaped to a product shape by deforming thereof. Thereafter, the permanent magnet 1 is produced by sintering thereof. The permanent magnet 1 has a ring shape, and is constituted such that an axis of easy magnetization may be orientated at a slant so as to converge in a direction along a converging axis P which is set to a radius direction as well as to a center direction of the ring shape.