Heatable seat for a sports or event venue

Abstract

A seat (1), in particular for a stadium, having a seat shell (2) made of plastic, in which at least one electric heater (3) is integrated, said electric heater (3) having at least one heating element (4) which is made with an electrically conductive plastic for generating heat.

Description

[0001] Heated seat for a sports or event venue

[0002] The invention relates to a system for operating seats with climate control. This system can be used, for example, in sports venues (such as stadiums) and event venues (such as concert halls or theaters). The system provides an air conditioning function for the audience seats. This air conditioning function is, in particular, a heating function.

[0003] In general, especially in venues where the spectator area is outdoors, there is an interest in offering visitors a high level of comfort. For example, it is often very cold in football stadiums during the winter. Heated seats would therefore be highly desirable.

[0004] However, the cost is a significant argument against offering such a function.

[0005] For example, seats in football stadiums are typically simple shell seats, often made of plastic. The unit cost of such seats is relatively low. Seats with built-in heating would incur significantly higher costs. Another problem is that the more complex the design of seats, the more susceptible they become to damage and potentially vandalism.

[0006] Furthermore, a heating function would incur considerable energy costs during operation. For example, if a typical football stadium has 20,000 seats and were equipped with heated seats, with each heated seat activated, this would result in a significant electrical power requirement. This would be particularly true if the seats in the football stadium are located outdoors and directly exposed to the elements. Against this background, the object of the present invention is to at least partially solve the problems described with reference to the prior art. In particular, a particularly advantageous system for providing seats with climate control for sports and event venues is proposed.

[0007] This problem is solved by the invention according to the features of the independent claims. Further advantageous embodiments are specified in the dependent claims, as well as in the description and, in particular, in the description of the figures. It should be noted that the person skilled in the art can combine the individual features presented in a technologically meaningful way and thereby arrive at further embodiments of the invention.

[0008] This describes a seat, particularly for a sports or event venue, comprising a seat shell made of plastic, into which at least one electric heater is integrated, wherein the electric heater has at least one heating element which is made of an electrically conductive plastic for heat generation.

[0009] The electrically conductive plastic can, for example, be an intrinsically conductive polymer (or an intrinsically conductive plastic). In other words, this means, in particular, that the electrically conductive polymer material is one that is itself electrically conductive. Alternatively or cumulatively, the electrically conductive polymer material can be made electrically conductive by at least one electrically conductive additive or filler, such as aluminum flakes or carbon black, which is contained or embedded in a (not necessarily self-conductive) polymer. The electrically conductive plastic preferably has a matrix of polyethylene or a similar material. Preferably, the electrically conductive plastic is soft compared to the material of the shielding wall.Preferably, at a switching temperature, a change occurs in the structure of the electrically conductive plastic, which leads to the deactivation of electrically conductive paths in the electrically conductive plastic and thus to a significant decrease in conductivity in the range of the switching temperature.

[0010] If a material's resistance increases with rising temperature, then the material's resistance has a positive temperature coefficient. Materials with metal-like conductivity generally exhibit a positive temperature coefficient with respect to their electrical resistance (PTC properties or PTC resistance properties). With metal-like conductivity, the resistance increases almost linearly with rising temperature. In contrast, electrically conductive polymer materials typically show a sharp increase in resistance within a very narrow temperature range. These polymer materials are commonly abbreviated as PPTC, which stands for Polymer Positive Temperature Coefficients.

[0011] In other words, the electrically conductive polymer material with PTC resistance properties can also be described as a so-called (polymer) cold conductor. A cold conductor, PTC resistor, or PTC thermistor is a temperature-dependent resistor that belongs to the group of thermistors. One of its defining characteristics is a positive temperature coefficient, meaning it conducts electricity better at low temperatures than at high temperatures.

[0012] The electrically conductive plastic is particularly preferably injected into at least one receiving area in the seat shell.

[0013] Particularly preferred is at least one heating element encased in a plastic material of the seat shell. The seat shell is preferably made of a different plastic material than the electrically conductive plastic material. This other electrically conductive plastic material preferably has significantly greater strength than the electrically conductive plastic material. It preferably provides the seat shell with mechanical stability. Inserts of the electrically conductive plastic material are preferably formed within the plastic material of the seat shell, which are heatable or which form the heating elements of the heating system.

[0014] It is further preferred that at least one heating element is applied to or incorporated into one side of the seat shell.

[0015] Here, "side" refers to a surface of the seat shell. The seat shell can be understood as a shaped, flat structure with a top surface that forms the seat, on which the user sits, and a back surface against which the user leans. Furthermore, the seat shell has a back surface that forms the underside beneath the seat and the back of the backrest.

[0016] In principle, the at least one heating element can be applied to any side of the seat shell – to the upper surface of the seat shell facing the user, to the back of a seat backrest, and / or to the underside. Preferably, the at least one heating element is positioned to ensure good heat transfer from the at least one heating element to the user while simultaneously providing good protection for the heating element – ​​for example, against vandalism. Positioning the at least one heating element on the upper surface generally improves heat transfer. Positioning the at least one heating element on the underside or back improves the protection of the heating element.

[0017] The heating element is preferably designed as a heating film. This heating film can be applied to the upper surface or the underside / back of the seat shell facing the user (e.g., laminated or welded on). Such a heating film is described in patent application DE 10 2020 127 121 A1. The applied or integrated heating film is preferably two-dimensionally curved on the seat shell and thus adapted to the shape of the seat shell. The seat shape preferably provides a seat depression for the user. The heating film's ability to be two-dimensionally deformed allows it to be adapted to the shape of the seat, its surface, or a seat depression. Preferably, a cover layer is applied to the heating element or heating film, which electrically insulates or protects the heating film.

[0018] An insulating structure is particularly preferred on the underside and / or on the back of the seat shell.

[0019] An insulating material on the underside can reduce unwanted heat loss downwards or backwards from the heat produced by the heater. Such an insulating structure can consist of an insulating material – for example, a foam material. It can also include a shield that, for instance, prevents airflow from passing directly over the underside or back of the seat and carrying away heat.

[0020] It is also preferred if the top of the seat shell is not padded.

[0021] Preferably, the seat has a solid surface. It is particularly advantageous for the heating element(s) to be located close to this surface. This facilitates heat transfer from the heating element(s) to the user of the seat.

[0022] It is further preferred if at least one heating element is designed for operation with voltages below 50 volts.

[0023] Particularly preferred are the seat or heating element and the at least one heating element designed for operation with voltages below 24 volts, e.g., approximately 16 volts. It is also preferred if the heating element is designed with current-generating structures that have a higher electrical conductivity than the electrically conductive plastic and with which the electrically conductive plastic can be supplied with current to generate heat.

[0024] The electrical current-generating structures are preferably metallic, and in particular metallic sheet metal elements, for example made of copper, silver, or aluminum, and / or coated with copper, silver, or aluminum. A voltage can be applied to the electrically conductive plastic via two separate electrical conductor structures. This generates an electric current (heating current) through the electrically conductive plastic, thereby generating heat within it.

[0025] In principle, the distance between the at least two separate electrical conductor structures in the plastic material is a parameter by which the necessary electrical voltage to generate a desired heating current can be set. Preferably, the distance is in a range between 1 mm and 10 mm.

[0026] Furthermore, it is advantageous if the at least two separate electrical current-supplying structures form comb-like structures that interlock at least in certain areas.

[0027] In comb-like structures, there is a small distance between at least two separate electrical conductors. Such comb-like structures are particularly suitable when a very uniform distribution of electric current across the plastic material is desired. Furthermore, these comb-like structures ensure that the electric current only travels relatively short paths through the plastic, thus allowing the operating voltage of the heating element to be kept at a low level.

[0028] It is particularly preferred that the shielding wall is made of an electrically insulating plastic material. Furthermore, it is preferred if the electrically conductive plastic exhibits PTC properties.

[0029] The electrically conductive plastic with PTC effect is preferably designed to have a switching temperature between 20°C and 40°C.

[0030] Furthermore, it is preferred if the electric heater has a heating area between 200 cm². 2 and 2,000 cm 2 covers one of the seat surfaces.

[0031] Preferably, approximately 15% to 65% of the total surface area of ​​the seat is temperature-controlled and, in particular, heated. It has been found that for a comfortable user experience, such a proportion of the seat's surface is sufficient to provide temperature control. This is especially true if the temperature control system includes a heating element.

[0032] The temperature control device is particularly preferred as a heater, and the total heating power of all electric heating elements of a seat is between 20 watts and 50 watts, especially approximately 40 watts.

[0033] Such heating output is sufficient for a user of the seat to maintain a very comfortable seating experience even in winter.

[0034] It is particularly preferred if a heating element is arranged at at least one of the following positions of the seat: in or on a seat surface; in or on a backrest surface.

[0035] It is also preferred that a first heating element is arranged in or on a seat surface of the system's seat, and that a further heating element is arranged in or on a backrest surface of the system's seats. Preferably, the heating element in the seat surface covers an area of ​​approximately 30 by 30 centimeters. More preferably, the heating element in the backrest surface covers an area of ​​approximately 20 by 30 centimeters. The heating element in the backrest surface is particularly located in a lower region of the backrest surface. In this region, the contact of a user of the seat with the backrest surface is normally more intensive than in an upper region.

[0036] Also described here is a system comprising a plurality of described seats, which are connected to at least one common power supply line, wherein the system further comprises a control device which is connected to the power supply line and is configured to communicate with control units of the seats via the power supply line using a DALI bus system.

[0037] Particularly preferably, the system comprises a server that is connected to the control device via a network connection, wherein the server provides a booking system with which the booking of heating for a seat can be made, wherein the server is configured to transmit control signals to control units of the seats depending on bookings via the control device.

[0038] The invention and its technical context are explained in more detail below with reference to the figures. The figures show preferred embodiments, to which the invention is not limited. It should be noted in particular that the figures, and especially the size relationships shown in the figures, are only schematic. It should also be noted that features shown in the figures can be omitted and / or supplemented or substituted with features from other figures. The figures show:

[0039] Fig. 1: an example of a described seat in a three-dimensional view; Fig. 2: a schematic representation of the seat from Fig. 1 in a sectional view;

[0040] Fig. 3: schematically a detail of the seat from Fig. 1;

[0041] Fig. 4: schematically a detail of the seat from Fig. 1 in a further embodiment;

[0042] Fig. 5: schematically shows the seat from Fig. 1 in a further embodiment in a sectional view;

[0043] Fig. 6: schematically shows the seat from Fig. 1 in yet another embodiment in a sectional view;

[0044] Fig. 7: schematic representation of the described system; and

[0045] Fig. 8: a flowchart of a procedure according to which the system shown in Fig. 7 can be operated.

[0046] Figure 1 shows an example of a described seat 1 in a three-dimensional view. The seat 1 preferably has a seat surface 12, which is particularly preferably concave in shape to offer the user of the seat 1 good seating comfort. The seat 1 also preferably has a backrest surface 13 against which the user of the seat 1 can lean. The seat 1 is typically formed by a seat shell 2. The seat shell is preferably made entirely of plastic. The seat 1 is preferably highly optimized for its application – for example, for use in a sports stadium. Mounting points 27 are shown here, for example, at which the seat shell 2 can be mounted on a support alongside a plurality of other seat shells 2 to form a row of seats.In preferred embodiments, the seat 1 can be quickly dismantled, for example, because a stadium can be reconfigured to offer more or fewer seats and / or to convert a standing area into a seating area and vice versa. A drainage structure 26, designed as a notch or indentation in the seat surface 12, is shown further. In particular, if the seat surface 12 is concave and forms a seat depression 32, water could collect on the seat surface 12 when it rains. The drainage structure 26 allows such water to drain away. The drainage structure 26 is particularly advantageous when the seat 1 is used outdoors, as is often the case with seats 1 in sports stadiums. An identifier 15 is preferably arranged on the seat 1, which can be used to identify the seat 1.The identifier 15 is preferably designed to be read by a mobile device. The identifier 15 can, for example, be a visible, readable QR code in which a unique identifier for seat 1 is integrated, with which seat 1 and, in particular, a heating element 3 of the seat can be activated.

[0047] Figure 2 schematically shows the seat 1 from Figure 1 in a sectional view with some optional additional features. The seat 1, or rather the seat shell 2, is shown in section 2, such that the seat surface 12 and the backrest surface 13 are cut away. A heater 3 is integrated into the seat 1. Here, the heater 3 is designed with heating elements 3 that are embedded in receiving areas 5 of the main material of the seat shell 2. Various ways in which the heater 3 is integrated into the seat are possible and feasible. In some embodiments, the receiving areas 5 in the seat shell 2 can, for example, be provided as recesses. The heating elements 4 can then be subsequently integrated into the receiving areas 5. If the heating elements 4 are made of an electrically conductive plastic, for example, then this electrically conductive plastic can be injected into the receiving areas 5 to form the heating elements 4.Current-carrying structures for energizing the electrically conductive plastic, not shown here, may have been previously inserted into the receiving areas 5 and then overmolded with the electrically conductive plastic. In other embodiments, it is also possible for the heating elements 4 of the heater 3 to be inserted into an injection mold for producing the seat shell 2 before the seat shell 2 material is introduced into the injection mold. The heater 3 or the heating elements 4 are preferably integrated into the seat 1 such that both a seat surface 12 and a backrest surface 13 of the seat can be heated by the heater 3. Particularly preferably, the heater 3 or the heating elements 4 are positioned close to a surface of the seat surface 12 or the backrest surface 13, respectively, so that the best possible contact and heat transfer from the heater 3 to the user is achieved when the user is seated.

[0048] The seat 1 or seat shell 2 typically also has an underside 7 facing away from the seat surface 12 and a rear side 8 facing away from the backrest surface 13. In the embodiment shown in Fig. 2, an insulating structure 9 is arranged on the underside 7 and on the rear side 8. This insulating structure 9 can, for example, be made of a foam-like material and / or a windshield, which prevents heat dissipation from the heat produced by the heater 3 via the underside 7 or the rear side 8.

[0049] As also shown in Fig. 2, a cover layer 31 can be arranged on the heater 3. The cover layer 31 impairs the heat transfer from the heater to a user sitting on the seat 1 as little as possible. The cover layer 31 preferably serves to protect the heater 3 and / or to provide electrical insulation for the heater 3. Such a cover layer 31 is shown by way of example only in Fig.

[0050] 2 shown. It can be provided in all embodiments of a seat 1 according to Figs. 3 to 6.

[0051] Figure 2 also shows, by way of example, that the seat 1 has a control unit 16 which is configured to either supply the heating 3 of the seat with power (to activate) or to supply the heating 3 of the seat with power.

[0052] 3 to interrupt. The control unit 16 is preferably connected to a power supply line 17, which can supply power to the seat 1 or the heater 3. The control unit 16 is further preferably able to receive and process activation and deactivation commands for the heater 3 via the power supply line 17 in order to activate and / or deactivate the heater 3. The control unit 16 thus preferably acts like a controllable switch. In particularly preferred embodiments, the control unit 16 can also operate the heater 3 at different intensities. In particular, the control unit 16 can be configured to regularly activate and deactivate the heater 3 in the manner of PWM operation (PWM = pulse width modulation) in order to provide a reduced heating output from the heater 3. The arrangement of the control unit 16 in Fig. 2 is only exemplary.The control unit 16 can also be arranged differently (in particular, outside the seat 1). The design of the control unit 16 can also be applied to the embodiments shown in the other figures (in particular Figs. 3 to 6).

[0053] The power supply line 17 is preferably connected to the seat 1 via a plug connection 33. The plug connection 33 can preferably be disconnected when the seat 1 is removed. This allows for faster assembly and disassembly of the seat 1, even though an electrical connection to the power supply line 17 must be established for each individual seat 1.

[0054] Figure 3 shows an example of how the heating element 3 of the seat 1 can be constructed. The embodiment shown in Figure 3 can also be designed according to the sectional view shown in Figure 2. Section AA, which corresponds to Figure 3, is shown in Figure 2. The seat surface 12 of the seat is shown in Figure 2. The features shown in Figure 3 can be transferred to the backrest surface of the seat, which can be designed accordingly.

[0055] The heating element 4, or heating component 3, is made of an electrically conductive plastic and is located in a receiving area 5 of the seat shell 2. The heating element 4 spans a heating element surface 11. Current-sensing structures 10 are integrated into the electrically conductive plastic of the heating element 4, through which the electrically conductive plastic of the heating element 4 can be supplied with an electric current. The current-sensing structures 10 are preferably made of metal. Preferably, there are two current-sensing structures 10, which are designed as interlocking combs. An electrical voltage is preferably applied between the current-sensing structures 10 to supply the electrically conductive plastic of the heating element 4 with an electric current. The electric current is converted into heat in the electrically conductive plastic of the heating element 4.

[0056] Figure 4 shows an alternative embodiment of the heating element 4. Also shown is the seat surface 2 of the seat 1, on which the heating element 4 spans a heating area 11. Here, the heating element 4 is designed as a resistive conductor 28 through which an electric current can flow. The electric current is converted into heat by or within the resistive conductor.

[0057] Figures 5 and 6 each show further embodiments of the seat in a sectional view. The sectional view in Figures 5 and 6 corresponds to the sectional view in Figure 2.

[0058] As shown in Fig. 5, the seat surface 12 is concave. The concave shape of the seat surface 12 can be present in the section through the seat 1 shown in Fig. 5, and also in another section through the seat 1 oriented perpendicular to it. The concave shape can thus form a kind of seat depression 32. This increases the seating comfort for a user of the seat. The heating element 4 is designed as a heating film 30, which is attached to the seat surface 12 and to the backrest surface 13. The heating film 30 can also be made of an electrically conductive plastic and be designed with current-enhancing structures (not shown here), the structure of which essentially corresponds to the structure of the current-enhancing structures according to Fig. 2 (interlocking combs). The heating film can be curved two-dimensionally and adapted to the shape of a concave seat surface 12 (to the seat depression 32). Not shown here is a top layer on the heating element 3, as shown in Fig.Figure 2 shows that such a covering layer on the heater 3 can also be provided. According to the embodiment shown in Figure 6, the heating elements 4 of the heater 3 are designed with resistance conductor tracks 28. The embodiment shown in Figure 6 essentially corresponds to the embodiment shown in Figure 3. A covering layer on the heater 3, as shown in Figure 2, is not shown here. However, such a covering layer on the heater 3 can also be provided. An insulating structure 9 on the underside 7 and on the back 8 of the seat shell 2 is shown here by way of example.

[0059] Figure 7 schematically shows the described system 18 comprising described seats 1. The system typically has a plurality of seats, arranged, for example, in the form of rows of seats for spectators in a sports venue. Each seat has at least one electric temperature control device 3, which may in particular be a heater 3. A control unit 16 is integrated into each seat 1. In other embodiments, one control unit 16 is provided for a group of seats 1, or the control unit 16 is assigned to the group of seats 1. The seats 1 or the temperature control devices 3 / heaters 3 of the seats 1 are connected to a power supply line 17. Control signals can also be sent to the seats 1 or to the control units 16 of the seats 1 via the power supply line 17. The control units 16 preferably comprise controllable switches.These controllable switches are controlled by control signals transmitted via the supply line 17. The control signals can be modulated onto the current transmitted via the supply line. A voltage is preferably permanently supplied to the seats 1 via the supply line 17. Activation and deactivation signals for the temperature control unit 3 / heating 3 of specific seats 1 can preferably be transmitted via the supply line 17. These activation and deactivation signals are then preferably received by the control units 16 of all seats, but only evaluated by the seats for which the respective activation and deactivation signals apply. The activation and deactivation signals preferably contain an address for the respective seat 1 to be addressed and the actual control command (e.g.,Activation signal and / or deactivation signal). In response to such control signals, activation and / or deactivation of the electric temperature control unit 3 / heating 3 of the seats can be carried out.

[0060] System 18 preferably includes a power supply 21 with which the current supplied to the seats via the supply line 17 can be fed in. System 18 preferably further includes a control device 19 which is suitable for converting commands provided via a data connection for activating and / or deactivating the temperature control devices 3 / heaters 3 of the seats in such a way that these can be transmitted (as described) via the supply line 17 to the seats 1 or the temperature control devices 3 / heaters 4 of the seats 1 and their control units 16. The control device 19 can in particular have a gateway 25 via which System 18 can communicate with Server 20. A corresponding gateway 25 for this communication is preferably provided on Server 20. The gateways 25 enable communication between the components of System 18 and Server 20 via a network 22 – preferably via the Internet.A business logic 23 and a device management system 24 for operating the system 18 are preferably provided on server 20. Seat temperature control / heating functions can be booked via mobile devices 14. Specific seats 1 can be identified by mobile devices 14 using identifiers 15 on the seats 1. Booking requests can then be transmitted from the mobile device 14 to server 20 or to the business logic 23 provided on server 20. Bookings are then managed there and, if necessary, translated into control commands for the seats 1 or their temperature control units 3 / heaters 3, which are transmitted by gateways 25, networks 22, control devices 19, etc., to the seats 1 or their control units 16.

[0061] Figure 8 shows a flowchart of a process according to which the system shown in Figure 7 can be operated. According to step a), the seat for which a temperature control function is to be activated is first identified by means of an attached identifier. This is preferably done with a mobile device. Subsequently, according to step b), the temperature control is booked. This is preferably done via the described system. This regularly requires payment for the activation of the temperature control device. The booking, payment, and activation are preferably carried out via a server of the system or via business logic running on a server. According to step c), the system transmits an activation command to the seat or to a control unit of the seat. Subsequently, according to

[0062] Step d) the temperature control of the seat (1) according to the booking made in step b).

[0063] Reference symbol list

[0064] 1 seat

[0065] 2 seat shells

[0066] 3 Heating

[0067] 4 heating elements

[0068] 5 Recording area

[0069] 6 Top

[0070] 7 Underside

[0071] 8 Back

[0072] 9 Insulation structure

[0073] 10 Power supply structure

[0074] 11 heating surface

[0075] 12 Seating area

[0076] 13 Backrest surface

[0077] 14 Mobile device

[0078] 15 Identifier

[0079] 16 Control unit

[0080] 17 Supply power line

[0081] 18 System

[0082] 19 Control unit

[0083] 20 servers

[0084] 21 Power supply

[0085] 22 Network

[0086] 23 Business Logic

[0087] 24 Device Management

[0088] 25 Gateway

[0089] 26 Drainage structure

[0090] 27 mounting points

[0091] 28 conductor track

[0092] 29 Concave surface

[0093] 30 heating film

[0094] 31 Top layer 32 Seating hollow

[0095] 33 Plug connection

Claims

Patent claims 1. Seat (1), in particular for a sports or event venue, comprising a seat shell (2) made of plastic, in which at least one electric heater (3) is integrated, wherein the electric heater (3) has at least one heating element (4) which is made of an electrically conductive plastic for generating heat.

2. Seat (1) according to claim 1, wherein the electrically conductive plastic is injected into at least one receiving area (5) in the seat shell (2).

3. Seat (1) according to claim 1, wherein at least one heating element (3) is overmolded with a plastic material of the seat shell (2).

4. Seat (1) according to claim 1, wherein at least one heating element (3) is applied or incorporated on one side (6, 7, 8) of the seat shell (2).

5. Seat (1) according to one of the preceding claims, wherein an insulating structure (9) is arranged on an underside (7) and / or on a rear side (8) of the seat shell (2).

6. Seat (1) according to one of the preceding claims, wherein the upper surface (6) of the seat shell (2) is not padded.

7. Seat (1) according to one of the preceding claims, wherein the at least one heating element (4) is designed for operation with voltages below 50 volts.

8. Seat (1) according to one of the preceding claims, wherein the heating element (4) is provided with current-energizing structures (10) which have a higher electrical conductivity than the electrically conductive plastic and with which the electrical plastic can be supplied with current to generate heat.

9. Seat (1) according to one of the preceding claims, wherein the electrically conductive plastic has PTC properties.

10. Seat (1) according to one of the preceding claims, wherein the electric heating (3) has a heating surface (11) between 200 cm 2 and 2,000 cm 2 covers a seating surface (12) of the seat (1).

11. Seat (1) according to one of the preceding claims, wherein the total heating power of all electrical heating elements (3) of the seat (1) is between 20 watts and 50 watts.

12. Seat (1) according to one of the preceding claims, wherein a heating element (4) is arranged at at least one of the following positions of the seat (1): in a seat surface (12); in a backrest surface (13).

13. System (18) comprising a plurality of seats (1) according to one of the preceding claims, which are connected to at least one common power supply line (17), wherein the system (18) further comprises a control device (19) which is connected to the power supply line (17) and is configured to communicate via the power supply line (17) with a DALI bus system with control units (16) of the seats (12).

14. System (18) according to claim 13 comprising a server (20) which is connected to the control device (19) via a network connection (21), wherein the server (20) provides a booking system with which the booking of heating for a seat (1) can be made, wherein the server (20) is configured to transmit control signals to control units (16) of the seats (1) depending on bookings via the control device (19).

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