Abstract: In one aspect, a method of preparing a composite wood panel is provided herein which includes: providing a flat core formed of cellulosic material having opposing top and bottom faces, wherein a density profile is defined across the core representing density of the core at different locations between the top and bottom faces, the density profile including a first density profile portion extending from the bottom face towards the top face and including a first maximum density, a second density profile portion extending from the top face towards the bottom face and including a second maximum density, and a third density profile portion extending between, and connecting, the first and second density profile portions; removing the top face, and an adjacent layer, of the core to remove the second maximum density and to define an exposed face; and, adhering, using an adhesive, a veneer to the exposed face.

Abstract: A tile that may be used as a covering on a floor, wall, or other surface comprises a top section, a protective section, and a core layer, and an exposed portion formed along at least one of its sides and structured to represent an imitation but highly realistic looking grout line. In a preferred embodiment, the top section comprises a wear layer, a decorative layer and a polyvinyl chloride layer, and the core layer comprises a densified foam material. The protective section is disposed between the top section and the core layer, and preferably comprises both a protective layer and another decorative layer. The exposed portion structured to represent an imitation grout line is formed within the protective section and is resistant to staining. In some embodiments, the exposed portion is also formed across a middle section of the tile, and may further include an interconnecting mechanism to facilitate installation.

Abstract: A building panel system is provided that includes a perimeter frame; a main beam attached to the perimeter frame; a carrier attached to the main beam, the carrier having a plurality of identical hook members, each of the hook members having a protruding hooking portion on only a first side of the hook member, and a non-hooking portion on a second side of the hook member, the second side being opposite the first side; and a plurality of panels removably attached to the carrier, each of the panels being attached to the carrier by engaging one of the hooking portions.

Abstract: Disclosed is a tile unit (10) that includes a resin net (20), a plurality of tiles (30) disposed on a front side of the resin net, and a magnet sheet (40) disposed on a back side of the resin net, with the tiles being bonded and fixed to the magnet sheet with the resin net interposed therebetween.

Abstract: A tile that may be used as a covering on a floor, wall, or ceiling surface comprises at least a top section and a core layer may be made from a densified foam material. In most embodiments, but not all, the top section comprises a polyvinyl chloride layer, and may also comprise a wear layer and/or a decorative layer. The tile includes a plurality of sides with an exposed portion(s) formed along at least one of the sides, but in some embodiments also across a middle section of the tile. The exposed portion(s) may be formed on the polyvinyl chloride layer below the tile's top surface at a depth to closely resemble an actual grout line. The tile may further comprise an interconnecting mechanism that at least partially enables an efficient tile installation. The interconnecting mechanism may further contribute to tile's visual appeal by at least partially concealing a connector(s).

Abstract: A tile system for use on a grid of a suspended ceiling comprises a plurality of tiles, each said tile having a main body having an exposed side and a concealed side, the exposed side defining a main surface, the concealed side defining a rear plane, and four side surfaces between the exposed side and the concealed side of the main body, wherein two of the four side surfaces have at least one tongue in the rear plane, and two other of the four side surfaces have at least one groove open to the rear plane. Fasteners, such as clips, are configured for attaching the tongues of one of the tiles to upside-down T channels of the grid, such that the rear plane of the tile is against a downwardly facing surface of the T channels of the grid.

Abstract: A surface coating structure adapted to be quickly installed and removed includes a plurality of parallel sections (1), a multiplicity of connecting members (2) and of slats (3) which engage the connecting members (2). Each connecting member (2) is provided with a pair of mutually opposite central angled hooks (4, 4) and a pair of side angled hooks (5, 5). Each slat has an undercut side groove (10) formed in each longitudinal edge (11) of the slat (3) to engage a central angled hook (4) and a bottom prismatic groove (12) in a part opposite to a part in sight near each longitudinal edge (11) of the slat (3). Each bottom prismatic groove (12) has, with respect to the longitudinal edge (11), a proximal side (14) provided with a series of parallel knurls (17) adapted to retain the side angled hook (5) of the connecting member.

Abstract: A board assembly for mounting to one or more support structures of a ceiling, deck, floor, or wall. The board assembly includes a board and a mounting member. The board has a length along a longitudinal direction, and first and second side channels that extend lengthwise along the board. The mounting member has first and second flanges biased inwardly toward one another. The first and second flanges are configured to be received inside the first and second side channels, respectively, of the board and to press inwardly on the board to limit movement and warping by the board. A plurality of the board assemblies may be included in a kit. Such a kit may also include a plurality of clip members configured to removably couple the board assemblies to the support structure(s). The mounting member may be constructed from aluminum or an aluminum alloy.

Abstract: A panel, which, at two opposite edges, is provided with coupling parts that allow joining by a downward movement, said coupling parts including a male part that fits in a female part, wherein vertically active locking portions are provided at opposite sides of the male part and female part, wherein these locking portions are located at different distances from an upper side of the panels.

Abstract: In one aspect, a component for an elastically averaged alignment system is provided. The component includes a body, an inner wall formed in the body and defining an alignment aperture, and an alignment member. The alignment member includes a pair of tabs extending from the body, and the alignment member is an elastically deformable material such that when the alignment member is inserted into another alignment aperture of another component, the alignment member elastically deforms to an elastically averaged configuration to facilitate aligning the component relative to the another component of the elastically averaged alignment system. The alignment aperture is configured to receive another alignment member of another component of the elastically averaged alignment system.

Abstract: Floorboards with a surface of flexible fibers for laying a mechanically joined floating floor, and methods for manufacturing and providing floorings containing such floorboards. For example, floorboards including a surface layer and a core, for making a floating flooring, which floorboards are mechanically lockable and which along their edge portions have pairs of opposing connectors for locking similar, adjoining floorboards to each other both vertically and horizontally, wherein the surface layer comprises flexible resilient fibers.

Abstract: Connectors for joining adjacent modular floor covering units. The connectors include a film and an adhesive layer coated on one side of the film. To install tiles using the connectors, a first tile is placed on the floor and a connector is positioned so that the adhesive layer faces upward and does not contact the floor. The connector is typically positioned so that only a portion of the adhesive layer adheres to the underside of the tile, leaving the remainder of the connector extending from the underside of the tile. Tiles are then positioned adjacent the first tile so that a portion of the connector adheres to the adjacent tiles. In this way, the connectors span adjacent tile edges. The tiles are assembled on a underlying flooring surface without the need to attach them to the floor surface. Rather, the tiles are linked to each other with the connectors, so that the tiles create a floor covering that “floats” on the underlying floor surface.

Abstract: A kit for connecting precast panels is disclosed herein. The kit includes at least two male member having a plate and a post projecting from the plate. The male member is operable to be embedded within a precast panel. The kit also includes at least two female members having a plate and a slot defined by the plate. Each female members is operable to be embedded within a precast panel. The post is received in the slot when the first precast panel and the second precast panel are slidably engaged with one another. Also disclosed is a precast panel formed using the kit and a method of connecting precast panels formed with the kit.

Abstract: Surface covering tiles made using synthetic materials employ junction strips which enable the tiles to be connected to one another. The connections can be made with or without adhesive. When the tiles are connected, a space is left between adjacent decorative surfaces to permit the application of grout or simulated grout therein. When the tiles are used as floor covering they can be used to make floating floors. As wall coverings, the tiles are adhered to the walls using conventional means.

Abstract: A modular flooring system is disclosed which is designed to support heavy loads while providing stability and ground protection. The invention contemplates a modular tile with fully integrated connector loops, receiver pins and optional metal cam locks located in the corners of the floor tile or along the tile edges. The tiles contain an overlap edge, which engages with an underlay edge on an adjacent tile. This arrangement allows the tiles to overlap at an angle other than 90 degrees, providing greater strength at the point where adjacent tiles meet. The underlay edge contains a liquid capture channel which traps liquids which may seep between the adjacent tiles. The tiles are also provided with longitudinal recesses which extend through the top and bottom surfaces to the surface below, allowing for ventilation that is critical for grass and turf surfaces. The modular flooring system provides increased strength and stability and protection of the subsurface.

Abstract: A modular plastic floor tile has a body of a first polymer compound and at least one upper feature overmolded onto an upper surface of the body from a second polymer compound which is injected from a gate adjacent the lower surface of the body. At least one through-hole communicates the gate to the upper feature. At least one vent hole, spaced from the through-hole, communicates the upper feature to the lower surface of the body. The vent hole allows any gas in the polymer flow path to be displaced from the upper feature, thereby preventing or minimizing defects that can affect adhesion and appearance.

Abstract: A modular fitted flooring system includes a plurality of bearing plates (2) and a plurality of panel elements (3) designed to be hooked onto the bearing plates (2), the bearing plates including a plurality of supporting elements (7), a panel hooking element (13), and elements (14) for bearing the load of the panel elements, and being complete with jointing elements (20, 21) for connecting one bearing plate (2) to the next, the panel hooking element (13) consisting of a plurality of teeth designed to engage in grooves (17) provided on at least two edges of the panel element (3), the teeth (13) being arranged on the plate so as to create a gap between one panel element and the next in a direction (Y) crosswise to the direction of installation (X) of the panel elements.

Abstract: Prior art rolled T-beams used in horizontal grids in suspended ceilings, serve as vertical studs in a grid that supports wallboard in a liner for a structural wall. A horizontal strut extends along, and is connected to, the studs, to unite the studs and the strut to form the vertical grid. The grid is braced from the structural wall.

Abstract: A pre-fabricated tile system includes modular backing boards comprising a plurality of tile backing board units including male/female edges for mating with an adjacent unit and a protruding bump serving as a grout spacer.

Abstract: A unique, three-dimensional wall or ceiling panel system has finished panels with randomly placed blocks protruding from the base board of each panel. These blocks are arranged in horizontal rows. Each block has the same thickness to form uniform rows but the lengths and heights of each block vary to form a random pattern on the base board. The ends of several rows of each finished panel are left open. When the finished panels are laid end to end, these open spaces may be filled with connecting blocks to create a seamless effect for the wall or ceiling system. Outside or inside corners are also provided for continuing the system around corners. The corners have one beveled edge to create a 90 degree corner. The other end of the corner connects to the finished pieces in the usual construction manner.

Abstract: A profile system for use with structures having a tiled base includes at least one elongate profile that has a base arm, two side arms of the same length projecting from the free ends of the base arm and arranged lying opposite one another, and two terminating arms which project from the free ends of the side arms and are aligned with one another, the side arms being arranged a distance apart from one another and the distance being at least 10 mm.

Abstract: Implementations of the present invention provide systems, methods, and apparatus for decorating and/or protecting a surface with one or more nonplanar panels. Particularly, the nonplanar panels can form a panel system that can conceal a support surface, structural components or elements, and can provide a decorative façade, and/or protect the underlying structure or components or elements thereof from elements.

Abstract: A tile floor system and apparatus, and manner of installation, uses ceramic and other rigid tiles, and a rubbery or polymeric mat or array of mats, providing a grid or pattern of receptacles that cooperatively receive and securely hold the tiles, with a removable grout securable between the tiles, so as to present a convincing appearance of a conventionally mortared and grouted tile floor, with the tiles and grout concealing the mats. The system and apparatus can be configured so as to be quickly and easily removed or replaced, Each mat can be configured for receiving one or multiple tiles, and the adjacent mats are joined together in the pattern or grid using suitable connectors, such as disk shaped biscuits receivable in slots along opposing sides of the individual mats.

Abstract: A modular plastic floor tile has a body of a first polymer compound and features overmolded onto the body from a second polymer compound. The compounds may be different from each other in hardness and/or color. The features may include skins on support member cores disposed below the tile lower surface. The skins adhere to the bottom and at least a portion of the sidewall of the support member core.

Abstract: The present invention relates to a decorative remaining formwork formed by combining a plurality of single frame plates defined by 3 or more edges comprising one edge arranged horizontally and at least one inclined edge inclined with respect to the horizontal edge; arranging the single frame plates so as to form a predetermined gap in a joint-shape between respective edges of the single frame plates adjacent each other; and having a back plate on a concrete casting surface, the back plate covering the predetermined gap in a longitudinal direction, and being fixed to the single frame plate to connect the single frame plates adjacent each other, and a cross-sectional shape in a width direction of the back plate being formed into a shape enlarged from a contact surface with respect to the single frame plate toward an opposed surface with respect to the contact surface.

Abstract: A do-it-yourself kit assembly and installation method for mounting a tile assembly to a predetermined support surface, such as a kitchen backsplash. The kit assembly includes the tile assembly comprised of one or more tile sheets as well as all of the installation materials and installation tools required to accomplish the do-it-yourself installation in a timely manner. Each tile sheet includes a plurality of fixed tile pieces, which may comprise glass mosaic tiles, and a self-adherent adhesive layer, which facilitates the mounting of the tile sheets to virtually any kind of surface. A ready-to-use grout supply makes it easy to apply the optimal quantity of grout onto the mounted tile sheet(s), wherein the installation materials and tools are cooperatively provided to facilitate the installation method.

Abstract: A method of making a mechanically-held tile is disclosed by providing a tile having a durable surface, an underside and an anchoring region, locating the tile in a mold, and injecting a polymer into the mold to form a substrate with an integral coupling region. Alternatively, a substrate can be provided in addition to the tile; the injected material mechanically anchors the substrate to the tile. A surrounding grout gasket can also be formed during injection. Injections can be consecutive or concurrent to tailor the properties of the substrate, grout gasket and other layers or regions. Also disclosed is a multi-part tile made by such a process, and a tile with intrinsic manufacturing deviations compensated by a grout gasket. The tile can be interconnected via the coupling regions with other surface-covering materials.

Abstract: A modular plastic floor tile has a body of a first polymer compound and features overmolded onto the body from a second polymer compound. The compounds may be different from each other in hardness and/or color. The features may include raised pads on the upper surface and/or skins on support member cores downwardly depending from the tile lower surface. The pads on the upper surface may be injection-molded from the lower surface through through-holes. Lateral edges of the tile are provided with latches which fit into loops with an interference fit. The loops flex in order to impose a compressive force on mating tile edges. The tile may have an overmolded peripheral seal.

Abstract: A veneer panel system is used with a wall or a retaining wall to provide a natural stone appearance and/or to improve the appearance of an existing wall. Panels can be interlocked to form a stable veneer structure. The structure is attached to a wall by various attachment devices.

Abstract: A do-it-yourself kit assembly and installation method for mounting a tile assembly to a predetermined support surface, such as a kitchen backsplash. The kit assembly includes the tile assembly comprised of one or more tile sheets as well as all of the installation materials and installation tools required to accomplish the do-it-yourself installation in a timely manner. Each tile sheet includes a plurality of fixed tile pieces, which may comprise glass mosaic tiles, and a self-adherent adhesive layer, which facilitates the mounting of the tile sheets to virtually any kind of surface. A ready-to-use grout supply makes it easy to apply the optimal quantity of grout onto the mounted tile sheet(s), wherein the installation materials and tools are cooperatively provided to facilitate the installation method.

Abstract: The installation system and method for installing an architectural covering material to a substrate surface utilizes an adhesive mat having layers of adhesive and release layers arranged to allow the covering material to be initially positioned, and later repositioned to be permanently set. The adhesive mat includes a planar carrier member, one or more adhesive layers on at least one planar side of the planar carrier member, and at least one release layer of material removably covering the one or more adhesive layers. In one form, the adhesive mat includes a carrier sheet, first and second adhesive layers on opposing planar sides of the carrier sheet, and first and second release layers of material removably covering the two adhesive layers.

Abstract: A prefabricated composite wall panel has a desired exterior finish defined by thin finish elements of brick, stone or any other suitable material and is adapted for mounting to the wall structure of a building framework by screws or other suitable fasteners. During panel manufacture thin wall finish elements are positioned at predetermined sites within the mold and aligned by alignment members in a pattern defining grout spaces. A grout placement screed having multiple holes arranged in a desired mortar pattern is positioned on the thin finish elements and pulverulent grout is deposited through the holes of the screed and into spaces between the finish elements.

Abstract: A method for forming a brick façade positioning assembly includes positioning a plurality of bricks in a specified wall pattern. A film is placed over the bricks, and the film is molded over the bricks to form a custom brick film tray. The custom brick film tray includes brick shaped tray recesses in the specified wall pattern. The plurality of bricks are positioned within the brick shaped tray recesses. Optionally, a liquid setting material is poured on the custom brick film tray and the plurality of bricks to form a brick façade wall. The brick façade wall includes the bricks in the specified wall pattern provided by the custom brick film tray.

Abstract: A system and method of attaching a natural stone to a wall surface includes attaching a piece of natural stone to a base plate so as to leave at least a portion of the base plate uncovered by the piece of natural stone and attaching the base plate to the wall surface with a fastener extending through the uncovered portion of the base plate.

Abstract: A formliner and master mold are disclosed. The master mold corresponds with the formliner, which includes a plurality of courses, each course having a plurality of pockets, each pocket sized and configured to receive a decorative brick, and a plurality of ridges arranged and disposed to separate the pockets. In the embodiment, the ridge lattice has a first ridge having a dimension that differs from a same dimension of a second ridge or a portion of the first ridge.

Abstract: The present invention provides a modular flooring system including a ramp to facilitate entry and exit from the flooring system. The ramp may be modular and interconnect with all or parts of a perimeter of the flooring system, and the ramp may also interconnect with adjacent ramp members.

Abstract: A polymeric interlocking tile for an adhesive-free assemblage with adjacent tiles having substantially similar, but inverted, edge interlocks thereon. The interlocks on each edge of a tile include a row of first and second sets of male-female types of alternating interlocks. The first interlock set includes a male lug projection having sidewalls forming one sidewall of a channel of U-shaped cross-section. The channel forms a female interlock cavity for the first set. The second interlock set is contiguous to the first set and includes a male projecting rib having two parallel sidewalls, one sidewall faces the edge and forms an opposite sidewall of the channel and an opposite, inwardly facing sidewall forms an enclosure for a second female cavity of the next set. At the opposite ends of each interlock row, the U-shaped channel sidewalls are wider to facilitate an initial interlock meshing between contiguous tiles of the assemblage.

Abstract: A wall lining is described, comprising wall panels (1) and holding profiles (2) which respectively comprise a downwardly open receiving groove (4) for a bottom wall panel (1), an upwardly open receiving groove (3) for an upper wall panel (1) and a suspension groove (5) for fixing hooks between the two receiving grooves (3, 4). In order to enable the insertion of wall panels (1) of different thickness it is proposed that the two receiving grooves (3, 4) of the holding profiles (2) which can be fixed to the wall, which grooves form a stop surface (9) for the outside of the wall panels (1) on the side facing away from the wall (6), form at least two sections (11) in the direction of the groove depth with different widths for holding wall panels (1) of different thickness.

Abstract: Disclosed is a surface covering panel including a first edge with a groove inclusive first coupling means, a second opposite edge with a tongue inclusive second coupling means, the coupling means enabling coupling of two panels, a mechanical locking means integrated into at least one of the coupling means which, when two panels are coupled, is configured to prevent these panels from moving apart, the coupling means being designed for coupling essentially without elastic deformation, wherein at least one part of the surface of at least one of the coupling means includes a repositionable adhesive configured to create bonds between the coupling means that are multiply breakable and re-bondable, wherein a breaking of the bonds on disassembly of the panels results in a chemical click designed to indicate decoupling to a user.

Abstract: The present invention provides a tile panel unit having a tile cap composed of at least one layer of crushed stone mixed with a resin and a catalyst and at least one layer of fiberglass strands mixed with a resin, and a base plate at least partially embedded in at least one layer of the tile cap material. The base plate provides a structure for supporting the tile cap, the structure having a matrix of supporting shapes and other reinforcing elements arranged within a peripheral support structure. The base plate further provides mounting features for securing the tile panel unit to an underlying support structure, and interlocking features for aligning and securing adjacent tile panel units in a wall and floor covering tile assembly system.

Abstract: A modular tile configured to interlock with multiple tiles to form a modular floor covering over a floor. The tile includes a top surface having a periphery defining side walls extending downward from the top surface, the side walls having a coupling portion configured to couple with other tiles adjacent thereto to form the modular floor covering. The tile also includes a bottom side, opposite the top surface, having a support grid including an array of downward extending polymeric post structures, at least some of the post structures including at least one resilient end portion with a radial end surface configured to be positioned against the floor to facilitate controlled deflection of the post structures. The post structures may comprise primary and secondary post structures, with the secondary post structures limiting the deflection of the primary post structures.

Abstract: The installation system and method for installing an architectural covering material to a substrate surface utilizes an adhesive mat having layers of adhesive and release layers arranged to allow the covering material to be initially positioned, and later repositioned to be permanently set. The adhesive mat includes a planar carrier member, one or more adhesive layers on at least one planar side of the planar carrier member, and at least one release layer of material removably covering the one or more adhesive layers. In one form, the adhesive mat includes a carrier sheet, first and second adhesive layers on opposing planar sides of the carrier sheet, and first and second release layers of material removably covering the two adhesive layers.

Abstract: Apparatus and processes that include tiles having an extending member that is disposed within a concavity on the bottom side of the tile and that extends a distance therefrom. The extending member may additionally be coupled to an anchor member disposed within the concavity on the bottom side of the tile. The extending member is set within a substrate such that it is held fast, thereby improving the bonding of the tile to the substrate.

Abstract: The invention relates to a system for laying and mechanically joining building panels, especially thin, hard, floating floors. Adjacent joint edges (3, 4) of two panels (1, 2) engage each other to provide a first mechanical connection locking the joint edges (3, 4) in a first direction (D1) perpendicular to the principal plane of the panels. In each joint, there is further provided a strip (6) which is integrated with one joint edge (3) and which projects behind the other joint edge (4). The strip (6) has an upwardly protruding locking element (8) engaging in a locking groove (14) in the rear side (16) of the other joint edge (4) to form a second mechanical connection locking the panels (1, 2) in a second direction (D2) parallel to the principal plane of the panels and at right angles to the joint. Both the first and the second mechanical connection allow mutual displacement of joined panels (1, 2) in the direction of the joint.

Abstract: A removable floor includes a support piece (1) having a floor tile (15) affixed to the upper surface thereof, with the support piece being equipped to be secured to other support pieces, in order to facilitate the installation and removal of the floor by the user and to enable the supports to be installed in an aligned and/or out of phase manner such as to produce different decorative patterns.

Abstract: Apparatus and processes that include a detectable warning tile having a top side with a plurality of protuberances forming a pattern or array and a second tile member disposed perpendicular to an edge of the detectable warning tile. The bottom side of both the detectable warning tile and the second tile member have at least one anchoring member embedded within a concavity in the bottom side, making the tile and tile member especially durable on platform edges.

Abstract: The invention relates to a multi-layer decoupling system, in particular for the laying of ceramic paving according to a thin-bed method. Said system comprises a layered construction containing, from the base upwards, an anchoring fleece made of non-woven material, an anchorage layer that is configured from a lattice-type structural element and that is used to hold a filler material, which is to be incorporated into the upper face of the decoupling system and which is plastic during processing and subsequently cures, in addition to a reinforcement layer, which is fixed, at least in some sections, to the anchorage layer. This improves the load-bearing capacity of the decoupling system and the bonding properties of ceramic paving that is laid in a conventional manner on the decoupling system.

Abstract: Floor covering, including hard floor panels which, at least at the edges of two opposite sides, are provided with coupling parts, cooperating which each other, substantially in the form of a tongue and a groove, wherein the coupling parts are provided with integrated mechanical locking elements which prevent the drifting apart of two coupled floor panels in a direction (R) perpendicular to the related edges and parallel to the underside of the coupled floor panels, and provide a snap-action coupling.

Abstract: A removable surface covering comprises a combination of lower supports with plastic support legs and upper ceramic parts which are joined to the supports by contact faces and with the aid of an adhesive material, such as to form covering modules which are interconnected using tongue-and-groove anchoring elements. The plastic supports and the ceramic parts are joined using a thick layer of adhesive which covers almost all of the contact surfaces thereof. In addition, the ceramic parts are equipped with channels and a peripheral notch which house respectively ribs and a frame belonging to the plastic support. The thickness of the adhesive extends over at least part of the thickness of the ribs and the frame of the plastic support. In another embodiment of the invention, the parts are joined at strategic points with a chemical-mechanical connection.

Abstract: The invention relates to a multi-layer decoupling and sealing system (1), in particular for the laying of ceramic paving (10) according to a thin-bed method (12). Said system comprises a layered construction containing, from the base upwards, a liquid-impermeable sealing layer (4), an anchorage layer (2, 3) that is configured from a lattice-type structural element and that is used to hold a filler material (12), which is to be incorporated into the upper face of the decoupling and sealing system (1) and which is plastic during processing and subsequently cures, in addition to a reinforcement layer (5), which is fixed, at least in some sections, to the anchorage layer (2, 3). This improves the load-bearing capacity of the decoupling and sealing system (1) and the bonding properties of ceramic paving (10) that is laid in a conventional manner on the decoupling and sealing system (1).