Abstract: A rotating body of a printing press includes a barrel that has a base body and an outer body which at least partially surrounds the base body. The external body, or at least one channel which is located in the barrel is traversed by a temperature control medium. The outer body or the at least one channel is thermally insulated with respect to the base body.

Abstract: Aqueous printing inks for textile printing by the inkjet process, comprising one or more dyes of the formula (I) in which A, B, R1 to R6 and D are as defined in claim 1, processes for preparing them and their use for textile printing by the inkjet process.

Abstract: The velocity of detonation of an explosive such as detonating cord (18, 22) is controlled by the addition of a diluent to the explosive, e.g., to the core of the detonating cord (18, 22). An explosively inert diluent, or a diluent comprised of an explosive of lower brisance than the principal explosive comprising the core of the detonating cord, will serve to reduce the velocity of detonation. Such reduced velocity of detonation has beneficial effects in certain operations, including cleaving rock (10), wherein it is observed to significantly reduce radial cracks (24) and stickers (26) (long radial cracks) in the vicinity of the boreholes (12) in which the low-velocity detonating cord (18, 22) is functioned to cleave the rock (10). The low-velocity detonating cord also facilitates leaving behind a smoother face in cutting trenches and tunnels through rock.

Abstract: An explosive charge (3) can be equipped with two liners (4, 5) that can be attached to one another. The primary liner (4) is so devised that when choosing a first choice (11) of being able to work independently and by employing a symmetrical form achieving a forward-aimed Shaped Charge Warhead (SCW) effect upon explosive charge initiation by means of the material (7, 8) indicated for the primary liner. A secondary liner (5) is devised with a second choice (12) to be able to work together with the primary liner and together cause an asymmetric form that distributes the material (18, 19) from the liners at different velocities to thereby cause a forward-directed fragmentation effect. The ammunition unit (1) can, thus, be designed or prepared for two different combat cases in a technologically simple and unambiguous manner.

Abstract: A cartridge or ammunition casing is made of two components, one forming the outer casing sleeve and head end and the other comprising a plug seated within the head end to protect the outer casing material from propellant gases. The outer cylindrical sidewall and end panel of the casing may be made of a material selected from the group consisting of stainless steel, steel, pre-coated carbon steel, brass or brass-type alloys, aluminum, hardened aluminum alloys, and suitable polymeric plastic material such as nylon derivatives and VECTRA™. The inner plug may be made of a material selected from the group consisting of aluminum, brass, steel, stainless steel, and suitable polymeric materials.

Abstract: An electronic weapon impedes locomotion by a target by conducting a current through an electrode and through the target to produce contractions in skeletal muscles of the target that impede locomotion by the target. The weapon may include a deployment unit to deploy one or more electrodes away from the apparatus toward the target. The deployment unit may include an electrically fired primer, a first cavity, a second cavity, and a partition. The first cavity may include a pyrotechnic charge that produces a gas at an increasing pressure when ignited by the primer. The partition between the first cavity and the second cavity opens, in response to the pressure increasing to a threshold magnitude in the first cavity, to propel the electrode from the second cavity by a sudden release of the pressure.

Abstract: An apparatus (20) configured to effect personnel traverse though a pipeline (22) is presented. This apparatus (20) is suitable for pipelines (22) having an inner diameter (24) of not less than fifteen inches and not greater than thirty-six inches. The apparatus (20) is made up of a frame (26), a platform (28), a single drive wheel (40), and a pair of guidance wheels (72). An electric motor (48) is supported by a motor bracket (50) affixed to the frame (26). The motor (26) is coupled to the drive wheel (40) by a drive belt or chain (52). Each of the guidance wheels (72) has a plane of rotation (80), and is configured to contact an interior surface (36) of the pipeline (22) at a contact point (82) within that plane of rotation (80) when that plane of rotation (80) is substantially perpendicular to the interior surface (36) of the pipeline (22). This allows the apparatus (20) to automatically follow the curvature of the pipeline (22) during traverse.

Abstract: A mass transportation system deploys dual use vehicles that transfer between a primary track and streets via a secondary or switching track. The dual use vehicles have comparable size and weight to ordinary automobiles but are configured to engage the primary track via either the street tires or a co-axially disposed wheel. When engaging the primary track the vehicles travel clustered in pods or groups for higher speed travel than on ordinary roads. The vehicles transfer from the primary track without a significant change in speed by disengaging or engaging the switching track. The switching track selectively drops or removes single vehicles from the pods according to the position of a track engaging support member associated with each vehicle.

Abstract: A rail vehicle with at least two impact-absorbing posts (RS1, RS2) which are disposed in a front end region (END) and extend vertically to the floor (BOD) of the rail vehicle. A deformable area (KZO) is provided on the front side of the floor (BOD) and each impact-absorbing post (RS1, RS2) is connected to the roof section (DAB) of the rail vehicle via the upper-end region (OE1, OE2) thereof, each impact-absorbing post having, in the respective upper-end region thereof, a pre-determined collapsible region (OE1, OE2) where the buckling (SK1, SK2) of said post should occur in the event of a collision.

Abstract: An open-top rail car cover is defined by a frame having dimensions sufficient to fit an open-top freight car designed in accordance with the Association of American Railroads, a roof and a pair of end walls. A latch disposed about a side of the frame includes a first flange and a second flange that combine to define a means for receiving an engagement member of a rail car. Both the first and second flanges include a at least one first aperture and at least one second aperture designed to receive a means for securing the car cover to the rail car. The first and second apertures have dimensions sufficient to permit movement of the first and second flanges about the means for receiving.

Abstract: A side construction 302 has an outside sheathing 306 and outside sheathing reinforcement members 307A and 307B joined to the outside sheathing 306 interiorly of the outside sheathing 306. The reinforcement member 307A (307B) is shaped like a hat in section. The reinforcement members 307A provided in the vicinity of a window opening portion have a laser welding spacing L1 of 80 mm and each have a hat width of 50 mm, while the reinforcement members 307B provided on other part have a laser welding spacing L1 of 100 mm and each have a hat width of 70 mm. The reinforcement members 307A and 307B each have a height of 25 mm.

Abstract: A salt of a mono- and/or dialkyl ester of a sulfonated dicarboxylic acid is provided, where the dicarboxylic acid contains 4 to 8 carbon atoms and the alkyl groups are derived from 2-propylheptanol. A composition including (a) one or more salt(s) of a mono- and/or dialkyl ester(s) of a sulfonated dicarboxylic acid(s), where the dicarboxylic acid contains 4 to 8 carbon atoms and the alkyl groups are derived from 2-propylheptanol; and (b) one or more organic solvents liquid at 20° C. with a boiling point above 250° C. at 1 bar is also provided.

Abstract: The present invention relates to blends of encapsulated biocides with free biocides. In particular, the present invention relates to blends of encapsulated 4,5-dichloro-2-n-octyl-3(2H)-isothiazolone (“DCOIT”) with free biocides. The invention also relates to marine antifouling coatings and paints incorporating free biocides and encapsulated DCOIT, and using the free biocides and encapsulated DCOIT in marine antifouling coatings and paints.

Abstract: A medical instrument including a body member and an indicator component. The indicator component includes a mechanism for identifying when reprocessing of the medical instrument has occurred.

Abstract: An ink for ink-jet recording includes a solvent dye in which a xanthene structure and a phthalide structure are spiro bound to each other. When the ink is stored in an ink cartridge containing a polyurethane foam and ink-jet recording is performed, a stable printing density may be achieved and changes in hue may be avoided.

Abstract: A mixture is provided that includes an ink composition and a basic solid compound. There is also provided a method for storing an ink composition that includes a step of preparing an ink composition and a step of contacting the ink composition with a basic solid compound. There is also provided an ink container housing an ink composition and a basic solid compound, and a method for forming an image, the method including a step of recording an image on a recording medium using the ink composition contained in the mixture and a step of irradiating the recorded image with actinic radiation so as to carry out curing.

Abstract: There is provided a stain-proofing coating composition being capable of forming a uniform stain-proofing surface by blending a hydrophilic material in a low concentration irrespective of kind of a polymer for a coating. The stain-proofing coating composition comprises the hydrophilic material (A), the hydrophobic polymer (B) for a coating, the organic solvent (C) for the hydrophobic polymer for a coating and the other organic solvent (D); the other organic solvent (D) being a high boiling point organic solvent having a boiling point higher than that of the organic solvent (C) for the hydrophobic polymer for a coating by 5° C. or more, and a ratio of the hydrophilic material (A) to the hydrophobic polymer (B) being from 1/99 to 50/50 (% by mass ratio).

Abstract: A coated titanium dioxide pigment with good opacity and simultaneously good retention for use in decorative laminating paper characterized by a surface coating containing aluminium oxide phosphate and attached hollow bodies, e.g., hollow microbodies. A manufacturing method is characterized in that an aluminium containing component and a phosphorus containing component are first added to a TiO2 suspension, during which time the pH value does not drop below 10. The hollow bodies are subsequently added, followed by addition of at least one acidic component, as a result of which the pH value of the suspension is lowered to the range from about 4 to 9. In an alternative embodiment of the method, the suspension has a pH value of under 4 at the time of addition of the aluminium containing component and a phosphorus containing component.

Abstract: The present invention provides a photocatalyst which is excellent in absorbability to organic materials and the like and is inexpensive, a method for manufacturing the photocatalyst at low cost with simple procedures, and molded articles using the photocatalyst. The photocatalyst of the present invention contains at least a porous body containing a calcium hydroxy apatite having photocatalytic activity. The method for manufacturing a photocatalyst of the present invention is a method for manufacturing the photocatalyst of the present invention, and includes doping a metal atom necessary for obtaining photocatalytic activity in an apatite contained in a bone. The molded articles are formed by using the photocatalyst of the present invention.

Abstract: A method for the finishing treatment of organic pigments includes allowing an, optionally milled, organic raw pigment and one or more ionic liquids to interact.

Abstract: The invention concerns a pigment preparation based on C.I. Pigment Yellow 155, containing 0.1% to 50% by weight, based on the weight of C.I. Pigment Yellow 155, of at least one pigment dispersant from the group of monoazo or disazo pigments substituted with at least one sulfonic acid group, characterized in that it has a chroma C greater than 53 in the CIELAB system in a solventborne alkyd melamine varnish comprising a 6.7% by weight concentration of the pigment preparation, and/or in that it has a chroma C greater than 35 in the CIELAB system in an aqueous base varnish system in a white reduction comprising a 0.2% by weight concentration of the pigment preparation in white reduction.

Abstract: A metal oxide nanoporous material comprises two or more kinds of first metal oxides selected from the group consisting of alumina, zirconia, titania, iron oxide, rare-earth oxides, alkali metal oxides and alkaline-earth metal oxides. The metal oxide nanoporous material has nanopores, each with a diameter of 10 nm or smaller, in which the metal oxides are dispersed homogeneously in the wall forming the nanopores.

Abstract: The present invention relates to a binder composition comprising a) an ash, b) an additive composition, wherein the additive composition comprises one or more components from group (b1) and one or more components from group (b2), wherein group (b1) consists of metal chlorides and wherein group (b2) consists of silica, zeolite and apatite, and c) a cement. In addition to that the present application relates to a construction composition comprising the present binder composition and a basic component, and also to a method for preparing the construction composition and to uses thereof.

Abstract: A convertible folding table having a dry erasable upper table surface. The table has two complementary tabletop portions hinged together so as to form a carrying case when closed, and a table when opened. Attached to the underside of the tabletop portions are leg assemblies that may be stowed adjacent the underside of the tabletop portions when the table is in a closed position and extended for use perpendicular to the common plane of the tabletop portions when the table is in an open position for use. Also attached to the underside of the tabletop portions are storage assemblies.

Abstract: An expandable television stand including a top, an expandable back leg, and a pair of front legs adjustably connected to the top. The stand is reconfigurable between a smallest size, wherein the front legs are connectable to the top adjacent to the top, and a plurality of larger sizes, wherein the front legs are shifted away from each other and connected to the top a predetermined distance away from the top. Leg extension elements are used to fill the space between the front legs and the top created when the stand is expanded beyond its smallest size.

Abstract: A decoration assembly is provided. The decoration assembly includes a tree and a support member coupled to the tree. The support member includes an interior surface and an opposite exterior surface. The interior surface defines a cavity within the support member. The support member further includes an electrical distribution system positioned within a portion of the cavity. The decoration assembly further includes a secondary support member including at least three legs. The secondary support member substantially circumscribes the support member. A method of assembly is also provided.

Abstract: A plastic pallet has a baseplate and a bracket. The baseplate is square and has a lower surface, an upper surface, multiple cavities and a mounting protrusion. The cavities are formed in the lower surface of the baseplate. The mounting protrusion is formed on the upper surface at the center of the baseplate. The bracket is formed on the baseplate and has multiple pillars and a mounting hole. The pillars are elongated, are arranged on the lower surface of the baseplate away from the opposite edges. The mounting hole is formed in the pillar that corresponds to the mounting protrusion on the baseplate.

Abstract: Shipping and storage containers, racks, and pallets including automatic interlocking mechanisms are provided. An embodiment of the automatically locking pallet includes a pallet frame including a forklift tine opening, a pallet platform, a locking component movable into and out of a locking arrangement with an interface fitting of a storage assembly when the automatically locking pallet and the storage assembly are stacked, and an actuator operatively connected to the locking component. The actuator may be activated by a forklift tine entering the forklift tine opening to move the locking component out of the locking arrangement.

Abstract: A worktop assembly for use in a travel trailer including a first structural portion, a second structural portion and a plurality of bracket assemblies. The first structural portion has a first end and a second end and the second structural portion has a first end and a second end. The plurality of bracket assemblies include a first bracket assembly and a second bracket assembly. The first bracket assembly is connected to the first structural portion proximate to the first end and to the second structural portion proximate to the first end. The second bracket assembly is connected to the first structural portion proximate the second end and the to the second structural portion proximate to the second end. Each bracket assembly has a plurality of pivot points.

Abstract: A resiliently bendable planar panel has a side that when juxtaposed laterally with a video display screen traverses the width of the screen, and is supported by a plurality of legs. The panel includes sufficient area and form to partition the display into two vertically distinct sections from the visual perspectives of viewers of the screen whenever the side is laterally juxtaposed with the screen. Preferably each leg includes a device slidable up and down the leg for containing and supporting a marginal portion of the panel. Preferably the panel is fabric and includes a marginal bias urging the fabric to be taut, such as an expansion rod disposed in a marginal seam of the panel.

Abstract: A locking mechanism for thermal treatment systems (e.g., systems heating and/or cooling solutions prior to the solutions being administered to the patient) or other medical equipment according to the present invention embodiments secures medications being stored and/or thermally treated therein. The locking mechanism includes an integrated monitoring and display system to determine and indicate the status of the thermal treatment system. The monitoring and display system includes indicator lights that allow for a visual representation indicating the locked or open states of system access doors and/or an audio system or alarm for alerting medial or other personnel to the status of the locking mechanism.

Abstract: A method for recovery of metals or metal compounds from metal-bearing solid particles comprising volatile compounds comprises supplying the solid particles (50) through a flame (25) of a burner (20). The volatile compounds are then evaporated by means of heat from the flame (25) without melting the solid particles, thereby providing a raw material product (34). The raw material product (34) is then recovered. By feeding the solid particles directly to the flame, a compact and efficient plant is provided. The melting process can be controlled in a satisfying way, avoiding melting of the metal-bearing solid particles supplied through the burner. The use of a burner is also described.

Abstract: The subject invention relates generally to methods and apparatuses for calcining gypsum. The apparatuses and methods place a gypsum particle optimizer in close association with the impact mill so that all the gypsum supplied to the impact mill has to enter the gypsum particle optimizer prior to the gypsum entering the impact mill, and so that heat generated from the impact mill enters into the gypsum particle optimizer from the impact mill. The gypsum particle optimizer utilizes a rotor to disperse the gypsum throughout the gypsum particle optimizer so that the gypsum is exposed to the heat from the impact mill prior to entering the impact mill. The exposure to the heat removes free water from the gypsum prior to the gypsum entering the impact mill.

Abstract: To enable a burnpot for a corn burning stove to be continuously operated, the burnpot has either: (1) an openable bottom with at least a first and second position, one of the at least first and second positions being substantially closed to enable a body of combustible fuel to burn on its upper surface, the other of the at least first and second positions providing an opening, burnpot side wall portions and a top of the burnpot being shaped so as to permit a solid clinker to drop out of the opening in the openable bottom when the openable bottom is in its second position; or (2) a bottom formed as one of a series of sections of a rotatable member so that as the member rotates, it carries ash with it away from the bottom of the burnpot.

Abstract: Combustion of hydrocarbon liquids and solids is achieved with less formation of NOx by feeding a small amount of oxygen into the fuel stream.

Abstract: This invention improves gas mixing and combustion, gaseous fluid flow and control of the char bed in recovery boilers burning black liquor or soda liquor, requires fewer primary air ports than conventional methods and can reduce capital and operating costs. Some primary air is introduced as powerful principal jets, from two opposing so-called active furnace walls. All or most of the remainder of the primary air is introduced as smaller jets, called scavenging jets, which prevent char from accumulating in the furnace corners and, in some cases, between the principal jets and are in the same plane as the principal jets. The momentum flux of each of the principal jets is approximately double or more than double that of each scavenging jet. Some of the primary air may be introduced as central jets, from the remaining two furnace walls and located in the same plane as the other ports, or on a second, somewhat higher plane. The momentum flux of the central jets is less than that of the principal jets.

Abstract: This invention refers to a self-propelled multipurpose agricultural machine of a considerable power and great soil clearing with a mechanism for fitting and lifting tools for tilling, sowing and/or fertilizing, spraying, fumigating and/or any other labor according to the element being attached, for lands apt for cultivating between crop lines whatever the degree of growth of those crops, without damaging them.

Abstract: A workpiece cloth ruler is disclosed which is detachably attachable to an attaching part of a cloth presser holder or a walking foot to which a cloth presser is attached to press workpiece cloth. The ruler includes a bar-shaped support detachably attachable to the attaching part of the cloth presser holder so as to be directed in a right-left direction and so as to be substantially horizontal, a connecting part located on an end of the bar-shaped support, a cloth guide connected via a supporting part to the connecting part of the bar-shaped support so as to be vertically pivotable, and an elastic member biasing the cloth guide to the workpiece cloth side so that the cloth guide pivots.

Abstract: The present invention relates to a sewing machine comprising a needle bar mounted with a needle reciprocating within a predetermined sewing work section, and a needle bar driver to drive the needle bar to reciprocate, the sewing machine further comprising a lifting unit to lift up and down the needle bar to make the needle get out of the sewing work section and reach a predetermined auxiliary work position; and a lifting driver driving the lifting unit to be lifted up and down. Thus, the present invention provides a sewing machine capable of decreasing work inconvenience and enhancing work efficiency.

Abstract: The present invention is a view port suitable for installation under the water line of a vessel wherein the view port comprises a flange made from a corrosion resistant material and a body made from a heat resistant material. An alternative embodiment of the invention is an underwater light in which a high intensity discharge light is installed into the above mentioned view port. The light may be swiveled while installed in the view port in order to direct the light along a desired path.

Abstract: The invention relates to a rotatable fairing (1) for a marine riser (2) or other slender marine structure. The fairing (1) is arranged on the riser for reducing watercurrent-induced stresses on said riser (2), said fairing (1) having a tail portion (3) for trailing generally in the downstream direction behind said riser. The fairing (1) is provided with an attenuation unit (8) for counteracting the unstable rotation of said fairing (2) relative to said riser (2), in order to prevent undesired vibrations of said riser (2). The fairing is provided with one or more clamps (10) for attachment to and around a periphery of said riser (2), said clamps (10) arranged with a gear rim (12) for engagement with an actuating cogged wheel (14) of said attenuation unit (8).

Abstract: An entrapment tunnel watercraft vessel having three hulls consists of a main hull and two amas arranged outboard of the main hull with the keels of the three hulls being parallel. The main hull is a narrow, vee hull with variable, rearwardly decreasing deadrise. The amas have very fine bows and narrow, asymmetric deep-V hulls, with nearly vertical slab outboard sides above their keels and variable reverse deadrise on their inboard sides with the reverse deadrise angles decreasing from bow to stem. The tunnels on each side of the main hull are formed by three distinct surfaces, the sides of the main hull above its chine, the reverse deadrise inboard sides of each ama upward from their keels and a ceiling surface transversely spanning the aforementioned sides and having rearwardly increasing deadrise and rearwardly decreasing width. The tunnel ceilings slopes down from the bow to a section aft of midship where the ceiling height above the keel remains essentially constant.

Abstract: A submarine is equipped with an extending apparatus on whose free end a container (4) resistant to underwater pressure is arranged, in which an essentially recoil-free gun (5) lies. The container (4) in the submerged condition of the submarine may be brought to the water surface (15) by way of the extending apparatus, and pivoted out so that one may also shoot in the submerged condition.

Abstract: A marine windshield and cockpit cover attachment system, utilizing a slot longitudinally extending along an elongated windshield frame, and where the windshield frame extends longitudinally around the edge of a windshield glass, where a series of plastic cover snap anchors are mounted within the slot. With the slot having inward facing lips, so that the anchors, having a pair of protruding tabs, are pressured onto the underside of the lips when a metal screw holding a plastic washer and a metal cover snap retainer, is inserted into the anchors so to clamp the anchors and cover snap retainers together on the slot lips, where the cover snap retainers are oriented in a forward and outward direction along the slot, and making no metal contact with the windshield frame. An alternate method included is a flexible anchor for attachment under a windshield lip of a hidden windshield lower frame.

Abstract: Wheel and other bearing restraint jam nuts and early warning visual warning indicators for use with bearing hubs including driven and non-driven wheel bearing hubs wherein each jam nut is adapted to be received on either a threaded drive axle tube spindle or an axle spindle by use of a convention tool and such that the jam nut is of a size to obstruct wheel bearing hub separation in the event of a bearing failure and wherein a portion of the jam nut is engageable to force an indicator outwardly of the wheel bearing hub whenever the wheel bearing hub is not properly rotating about it's axis of rotation to thereby provide a visual indication of a potential problem with the bearings or other components within the wheel or other bearing hub.

Abstract: There is provided a group III nitride crystal growth method capable of obtaining a material which is a GaN substrate of low defect density capable of being used as a power semiconductor substrate and in which characteristics of n-type and p-type requested for formation of transistor or the like. A growth method of group III nitride crystals includes: forming a mixed melt containing at least group III element and a flux formed of at least one selected from the group consisting of-alkaline metal and alkaline earth metal, in a reaction vessel; and growing group III nitride crystals from the mixed melt and a substance containing at least nitrogen, wherein after immersing a plurality of seed crystal substrates placed in an upper part of the reaction vessel in which the mixed melt is formed, into the mixed melt to cause crystal growth, the plurality of seed crystal substrates are pulled up above the mixed melt.

Abstract: In a crystal preparing device, a crucible holds a mixed molten metal containing alkali metal and group III metal. A container has a container space contacting the mixed molten metal and holds a molten alkali metal between the container space and an outside of the container, the molten alkali metal contacting the container space. A gas supply device supplies nitrogen gas to the container space. A heating device heats the crucible to a crystal growth temperature. The crystal preparing device is provided so that a vapor pressure of the alkali metal which evaporates from the molten alkali metal is substantially equal to a vapor pressure of the alkali metal which evaporates from the mixed molten metal.

Abstract: The present invention provides a method for producing a compound single crystal that can improve a growth rate and grow a large single crystal with high crystal uniformity in a short time, and a production apparatus used for the method. The compound single crystal is grown while stirring a material solution to create a flow from a gas-liquid interface in contact with a source gas toward the inside of the material solution. With this stirring, the source gas can be dissolved easily in the material solution, and supersaturation can be achieved in a short time, thus improving the growth rate of the compound single crystal. Moreover, the flow formed by the stirring goes from the gas-liquid interface where a source gas concentration is high to the inside of the material solution where the source gas concentration is low, so that dissolution of the source gas becomes uniform.

Abstract: Space and time co-divided atomic layer deposition (ALD) apparatuses and methods are provided. Substrates are moved (e.g., rotated) among multiple reaction zones, each of which is exposed to only one ALD reactant. At the same time, reactants are pulsed in each reaction zone, with purging or other gas removal methods between pulses. Separate exhaust passages for each reactant and purging during wafer movement minimizes particle contamination. Additionally, preferred embodiments permit different pulsing times in each reaction space, thus permitting flexibility in pulsing.

Abstract: A light irradiation apparatus irradiates a target plane with light having a predetermined light intensity distribution. The apparatus includes a light modulation element having a light modulation pattern of a periodic structure represented by a primitive translation vector (a1, a2), an illumination system for illuminating the modulation element with the light, and an image forming optical system for forming the predetermined light intensity distribution obtained by the modulation pattern on the target plane. A shape of an exit pupil of the illumination system is similar to the Wigner-Seitz cell of a primitive reciprocal lattice vector (b1, b2) obtained from the primitive translation vector (a1, a2) by the following equations: b1=2?(a2×a3)/(a1·(a2×a3)) and b2=2?(a3×a1)/(a1·(a2×a3)) in which a3 is a vector having an arbitrary size in a normal direction of a flat surface of the modulation pattern of the modulation element, “·” is an inner product of the vector, and “×” is an outer product of the vector.