CN108062887A - A kind of apparatus for demonstrating for converting functional form - Google Patents

A kind of apparatus for demonstrating for converting functional form Download PDF

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Publication number
CN108062887A
CN108062887A CN201810163376.2A CN201810163376A CN108062887A CN 108062887 A CN108062887 A CN 108062887A CN 201810163376 A CN201810163376 A CN 201810163376A CN 108062887 A CN108062887 A CN 108062887A
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China
Prior art keywords
horizontal
water
suspension cylinder
water drum
coordinatometer
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CN201810163376.2A
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Chinese (zh)
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CN108062887B (en
Inventor
周莉
梁法库
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Qiqihar University
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Qiqihar University
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    • GPHYSICS
    • G09EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09BEDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B23/00Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
    • G09B23/02Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
    • GPHYSICS
    • G09EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09BEDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B23/00Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
    • G09B23/06Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Algebra (AREA)
  • Business, Economics & Management (AREA)
  • Educational Administration (AREA)
  • Educational Technology (AREA)
  • Theoretical Computer Science (AREA)
  • Instructional Devices (AREA)
  • Special Spraying Apparatus (AREA)

Abstract

A kind of apparatus for demonstrating for converting functional form is disclosed, belongs to teaching and experiment equipment.Mainly it is made of horizontal range position coordinates ruler, horizontal movable trolley, horizontal plane position coordinatometer, n shapes connecting rod, suspension cylinder, water drum, transparent drawing board, table and drawing pen, it is characterized in that:Together with the horizontal range position coordinates ruler is vertically fixed on horizontal movable trolley, and its upstream face of horizontal movable trolley and horizontal range position coordinates ruler edge line, on same vertical plane, the horizontal plane position coordinatometer, n shapes connecting rod and suspension cylinder are fixed together;Realize operator's function rule of liquid level position and range when depicting different tube diameters overflow pipe on transparent drawing board, the evolving trend of Study Function form, the person that is conducive to mathematical studying understands function rule under physical background, is eye-opening mathematics demonstration test instrument.This low manufacture cost, making are extremely simple, with obvious effects, can increase more educational functions in classroom teaching.

Description

A kind of apparatus for demonstrating for converting functional form
Technical field
This patent is related to the laboratory apparatus for demonstrating a kind of functional form conversion, belongs to College Maths and physics teaching experiment instrument Device field.
Background technology
Function is often used in higher mathematics and College Physics, is critically important concept, though there is Chinese patent application The demonstration of exponential function that publication No. is CN105059022A and image plotting device and Authorization Notice No. are CN203232609U's Exponential function demonstration device gives the design of some demonstration function rules, and prior art demo content is excessively dull, unfavorable student Development in an all-round way, also lacks functional form transformation demonstration laboratory apparatus, and another functional form is transformed into from a kind of functional form Research contents is demonstrated, it is low at one's side to how primary grades students of science and technology utilize for the initiative spirit and the ability of practice of training student Low cost materials provide a kind of demonstrating experiment device of functional form conversion, and this patent will solve the problems, such as this.This patent be National Nature fund project(Item number:11405092), the provincial institution of higher education's basic service in Heilongjiang Province take scientific research project(Project Number:135209251)And the educational reform of institution of higher education of Heilongjiang Province and application item(Item number:SJGY20170385)Support under it is complete Into.
Bibliography.
1. the exponential functions demonstration of king's book battalion and image plotting device [ZL] application publication number:CN105059022A, Shen It please date of publication:2015.11.18
2. autumn outstanding person etc. exponential functions demonstration device [ZL] Authorization Notice No.:CN203232609U, authorized announcement date: 2013.10.09。
The content of the invention
This patent is a kind of demonstration for solving the functional form conversion under classroom or class, is to utilize horizontal range position emphatically That puts the overflow pipe of coordinatometer, horizontal movable trolley, horizontal plane position coordinatometer, suspension cylinder and different inner diameters etc. is implemented in combination with letter A kind of technology of number form formula conversion.
The art of this patent scheme:A kind of apparatus for demonstrating for converting functional form, mainly by horizontal range position coordinates ruler, water Translate motor-car, horizontal plane position coordinatometer, n shapes connecting rod, suspension cylinder, water drum, transparent drawing board, table, suspension cylinder etc. High position-limiting tube and drawing pen are formed, it is characterized in that:The horizontal range position coordinates ruler is vertically fixed on one with horizontal movable trolley It rises, and its upstream face of horizontal movable trolley and horizontal range position coordinates ruler edge line are on same vertical plane(Horizontal movable trolley its Upstream face is with drawing pen center line on same vertical plane), the horizontal plane position coordinatometer, n shapes connecting rod and suspension cylinder are consolidated It is scheduled on together;There is trolley track of the row with through hole on the panel of the table, through hole is easy for water and flows to table in the following, the bottom of by Two transparent water drums of the portion with water nozzle are placed on horizontal positioned table panel, and make two with water drum communicating pipe connection water nozzle A transparent water drum(The transparent bucket of Cylindrical Homogeneous)Connection(Pay attention to the selection of material, it is ensured that after installation in communicating pipe spatial volume it is constant, Water drum not deformation), one of water drum band horizontal fitting hole can install overflow pipe, plane where the track of stream of overflow pipe with Trolley track is parallel;Drawing grid will be carried(Transparent grid mapping drawing)Transparent drawing board it is vertical close to transparent water drum(It hangs down Straight table panel)It is fixed on table panel, first blocks overflow pipe into water drum plus suitable quantity of water, the suitable quantity of water are suspension cylinder In whole immersion waters, water will not be overflowed from water drum;N shapes connecting rod passes through the contour position-limiting tube of suspension cylinder(Avoid two suspensions Cylinder horizontal swing is unstable, influences vertical direction movement), then horizontal plane position coordinatometer and n shape connecting rods be fixed together, The n shape connecting rod other ends are penetrated in suspension cylinder, are adjusted position of the suspension cylinder with respect to n shape connecting rods and are temporarily fixed, then will be outstanding Floating cylinder is put into transparent water drum, when suspension cylinder swims in and stablizes motionless in water drum, horizontal plane energy where the water surface in water drum Intersect with horizontal plane position coordinatometer, at this moment fix suspension cylinder and n shape connecting rods;It is, treat that suspension cylinder swims in water When stablizing motionless in cylinder, the position with water surface same level in water drum on horizontal plane position coordinatometer draws horizontal line(It paints Horizontal plane where figure nib), the horizontal line is for demarcating(Instruction)Water surface site in water drum;The contour limit of the suspension cylinder Position inside pipe wall it is smooth, the diameter of internal diameter and n shape connecting rods matches, n shapes rod surface be smooth cylinder, suspension cylinder it is contour Position-limiting tube is fixed on by straight-bar on transparent drawing board vertically;The overflow pipe is Cylindrical Homogeneous pipe, and outer diameter is horizontal with water drum band The aperture in insertion hole matches, and overflow pipe is sealed with horizontal fitting hole during installation, and overflow pipe keeps horizontal;The horizontal plane position Coordinatometer 2-1 is transparent ruler;
During demonstration, a certain amount of water is packed into water drum, water drum water surface calmness is treated, opens overflow pipe, water is projected in the form of a fluid stream Onto the panel of table, people's mobile and horizontal locomotive makes its upstream face that corresponding water be followed to fall on the position on the panel of table at any time It puts(Its upstream face of locomotive is with drawing pen in same vertical and vertical transparent drawing board plane), another people is in transparent drawing board On tracked at any time with drawing pen and draw the edge line of corresponding horizontal range position coordinates ruler and the water of horizontal plane position coordinatometer The point that horizontal line intersects;Drawing pen wants the transparent drawing board of horizontal vertical, makes the edge of drawing pen face horizontal range position coordinates ruler The point that line intersects with the horizontal line of horizontal plane position coordinatometer(Or horizontal range position coordinates ruler selects transparent ruler and at it On draw vertical curve by horizontal movable trolley upstream face, vertical curve and the horizontal plane position coordinate of horizontal range position coordinates ruler The point that the horizontal line of ruler intersects), drawing pen just depicts corresponding y-x curves on transparent drawing board(Video recorder can also be used auxiliary Mnemonic(al) is recorded, then read from computer map data or with directional light by the edge line of horizontal range position coordinates ruler with it is horizontal The point that the horizontal line of face position coordinates ruler intersects is projected on transparent drawing board, is more convenient for being marked with drawing pen);
The horizontal range position coordinates ruler and horizontal plane position coordinatometer surface are smooth(Horizontal range position coordinates ruler and level Both face position coordinates rulers do not contact), the overflow pipe is the Cylindrical Homogeneous pipe of inner wall smooth.
It selects that one group of pipe range is certain, different bores, can obtain with bore descending one group of liquid level y and range The track of x, that is, it is respectively d1 to select diameter<d2< d3 <d4 <D5 carries out experimental demonstration(Measurement), study and draw with pipe Interior diameter reduces the trend of liquid level y and range x functional forms.
It is noted that the water drum sectional area of dress water is appropriate with overflow pipe section area ratio, it should ensure that current form stream Line style, the faceplate for ensureing that timely mobile and horizontal locomotive tracking current is facilitated to fall on table again are put.
Theory analysis, it is x-axis forward direction to establish the horizontal direction using flowing water nozzle as coordinate origin, just projected along water, vertically Positive for y-axis upwards, the level height of panel of the overflow pipe spout away from table is h, if x and y is respectively horizontal range and the water surface Highly(The water drum water surface is to the vertical height of overflow pipe),
A) if water is perfect fluid(Overflow pipe is extra heavy pipe, and viscosity ignores situation)Have
It is drawn by the arrangement of upper three formula
B) or consider fluid viscosity(Overflow pipe is tubule, and viscosity cannot ignore situation), it is public by the poiseuille of pipe flow Formula(The respectively coefficient of viscosity of fluid, pipe range, bore, pipe both ends pressure difference)
Provide mean flow rate
Arrangement is drawn
Here it is the functional relation between water surface elevation y and flowing water range x generates query to this people:Water surface elevation y and stream First power or quadratic power functional relation are followed between water-jet journey x on earth, is seen by designing specific experiment and theoretical research Mathematical function rule is contained among physics, the conversion trend of Study Function form, to lower grade student's learning mathematics and object The classmate of reason has enlightenment well, and being conducive to mathematical studying, person understands function rule and physics under physical background Habit person understands the conversion of mathematical function, is eye-opening mathematics demonstration test instrument.This low manufacture cost makes extremely letter Easily, it is with obvious effects, it can increase more educational functions in classroom teaching.
The usefulness of this patent tracks liquid level position by two identical suspension cylinders, realizes that an operator only needs The position that is fallen with streamlined of tracking overflow pipe water, another operator track the edge line of corresponding horizontal range position coordinates ruler with The point that the horizontal line of horizontal plane position coordinatometer intersects with drawing pen on transparent drawing board, just depicts corresponding intrument Test function rule;Presentation record is carried out to different bores, can be obtained with the descending liquid level of bore(The water surface) The track of height y and range x, from a functional form to the trend of another functional form transition;The person that is learning mathematics is in physical back Understand function rule under scape, be eye-opening mathematics demonstration test instrument.
Description of the drawings
Attached drawing 1 is the schematic top plan view of patent
Attached drawing 2 is the structure diagram of patent
Wherein:1-1, horizontal range position coordinates ruler, 1-2, horizontal movable trolley, 2-1, horizontal plane position coordinatometer, 2-2, n shape connect Bar, 2-3, suspension cylinder, 3, water drum, 3-1, the water surface, 2-1-1, horizontal line, 3-2, water drum communicating pipe, 3-3, overflow pipe, 3-4, water Trajectory mark, 4, table, 4-1, the trolley track with through hole, 5, transparent drawing board, 6, drawing pen, 7, the contour /V of suspension cylinder Pipe.
Specific embodiment
Such as attached drawing 1, attached drawing 2:It is a kind of convert functional form apparatus for demonstrating, mainly by horizontal range position coordinates ruler 1-1, Horizontal movable trolley 1-2, horizontal plane position coordinatometer 2-1, n shape connecting rod 2-2, suspension cylinder 2-3, water drum 3, transparent drawing board 5, platform Table 4, the contour position-limiting tube 7 of suspension cylinder and drawing pen 6 are formed, it is characterized in that:The horizontal range position coordinates ruler 1-1 with Horizontal movable trolley 1-2 is vertically fixed on together, and its upstream face of horizontal movable trolley 1-2 and horizontal range position coordinates ruler 1-1 sides Edge line is on same vertical plane(Its upstream face of horizontal movable trolley 1-2 is with 6 center line of drawing pen on same vertical plane), the water Coordinatometer 2-1, n shape connecting rod 2-2 and suspension cylinder 2-3 are fixed together for plan-position;Have on the panel of the table 4 row with The trolley track 4-1 of through hole, through hole are easy for water and flow to table 4 in the following, two transparent water drums 3 of the bottom with water nozzle are placed Two transparent water drums 3 are connected on horizontal positioned 4 panel of table, and with water drum communicating pipe 3-2 connection water nozzle(Pay attention to selecting Material, it is ensured that spatial volume is constant in communicating pipe 3-2 after installation, 3 not deformation of water drum), one of water drum 3 is with horizontal fitting hole Overflow pipe 3-3 can be installed, plane where the track of stream 3-4 of overflow pipe 3-3 is parallel with trolley track 4-1;It will carry and draw Grid(Transparent grid mapping drawing)Transparent drawing board 5 it is vertical close to transparent water drum 3(4 panel of vertical table)It is fixed on table On 4 panels, overflow pipe 3-3 is first blocked into water drum 3 plus suitable quantity of water, the suitable quantity of water is in suspension cylinder 2-3 whole immersion waters, Water will not be overflowed from water drum 3;N shape connecting rods 2-2 passes through the contour position-limiting tube 7 of suspension cylinder, then by horizontal plane position coordinatometer 2-1 and n shape connecting rods 2-2 is fixed together, and the n shape connecting rod 2-2 other ends are penetrated in suspension cylinder 2-3, adjusts suspension cylinder 2-3 phases Position to n shape connecting rods 2-2 is simultaneously temporarily fixed, and then suspension cylinder 2-3 is put into transparent water drum 3, treats that suspension cylinder 2-3 floats It floating over when stablizing motionless in water drum 3, horizontal plane where water surface 3-1 can intersect with horizontal plane position coordinatometer 2-1 in water drum 3, this When suspension cylinder 2-3 and n shape connecting rods 2-2 is fixed;It is, when suspension cylinder 2-3 swims in and stablizes motionless in water drum 3, Position with water surface 3-1 same levels in water drum 3 on horizontal plane position coordinatometer 2-1 draws horizontal line 2-1-1(Drawing pen Horizontal plane where 6), the horizontal line 2-1-1 is for demarcating water surface 3-1 positions in water drum 3;The contour limit of the suspension cylinder Position 7 inner wall smooth of pipe, the diameter of internal diameter and n shape connecting rods 2-2 matches, and n shape connecting rod 2-2 surfaces are smooth cylinder, suspension column The contour position-limiting tube 7 of body is fixed on by straight-bar vertically on transparent drawing board 5;The overflow pipe 3-3 be Cylindrical Homogeneous pipe, outer diameter Match with aperture of the water drum 3 with horizontal fitting hole, overflow pipe 3-3 is sealed with horizontal fitting hole during installation, and overflow pipe 3-3 is kept It is horizontal;The horizontal plane position coordinatometer 2-1 is transparent ruler;During demonstration, a certain amount of water is packed into water drum, treats water drum water Face is tranquil, opens overflow pipe 3-3, and water is injected in the form of a fluid stream on the panel of table 4, a people mobile and horizontal locomotive 1-2 with When make the position that its upstream face follows corresponding water to fall on the panel of table 4(Its upstream face of locomotive is with drawing pen same perpendicular In straight and vertical transparent 5 plane of drawing board), another people on transparent drawing board 5 with drawing pen 6 tracks and draws corresponding water at any time The point that the edge line of point blank range position coordinates ruler 1-1 intersects with the horizontal line 2-1-1 of horizontal plane position coordinatometer 2-1;Drawing pen 6 The transparent drawing board 5 of horizontal vertical is wanted, makes 6 face horizontal range position coordinates ruler 1-1 of drawing pen(Light-proof material)Edge line The point intersected with the horizontal line 2-1-1 of horizontal plane position coordinatometer 2-1, drawing pen 6 just depict correspondence on transparent drawing board 5 Y-x curves(Video recorder auxiliary record can also be used, then reads from computer map data or with directional light by horizontal range The edge line of position coordinates ruler 1-1 projects transparent drawing with the horizontal line 2-1-1 of the horizontal plane position coordinatometer 2-1 points intersected On plate 5, it is more convenient for being marked with drawing pen 6);
One of preferred embodiment, overflow pipe 3-3 length of tube is constant, changes bore, that is, in total amount of liquid, liquid level with respect to flowing water Pipe 3-3 height, the sectional area of liquid level are constant, select one group of pipe range to be respectively for 3.0cm, bore=1.0mm、1.3mm、 2.0mm, 3.0mm, 5.0mm carry out presentation record, can obtain with the descending water surface elevation y of bore and horizontal range x Relation inquires into the trend of Study Function form conversion.

Claims (1)

1. a kind of apparatus for demonstrating for converting functional form, mainly by horizontal range position coordinates ruler 1-1, horizontal movable trolley 1-2, water Plan-position coordinatometer 2-1, n shape connecting rod 2-2, suspension cylinder 2-3, water drum 3, transparent drawing board 5, table 4, suspension cylinder etc. High position-limiting tube 7 and drawing pen 6 are formed, it is characterized in that:The horizontal range position coordinates ruler 1-1 is vertical with horizontal movable trolley 1-2 It is fixed together, and its upstream face of horizontal movable trolley 1-2 and horizontal range position coordinates ruler 1-1 edge lines are in same vertical plane On, horizontal plane position coordinatometer 2-1, n shape connecting rod 2-2 and suspension cylinder 2-3 are fixed together;The panel of the table 4 On have trolley track 4-1 of the row with through hole, through hole is easy for water and flows to table 4 in the following, by two of bottom with water nozzle thoroughly Bright water drum 3 is placed on horizontal positioned 4 panel of table, and connects two transparent water drums 3 with water drum communicating pipe 3-2 connection water nozzle Logical, one of water drum 3 can install overflow pipe 3-3, plane where the track of stream 3-4 of overflow pipe 3-3 with horizontal fitting hole It is parallel with trolley track 4-1;Transparent drawing board 5 with drawing grid is fixed on 4 panel of table vertically close to transparent water drum 3 On, overflow pipe 3-3 is first blocked into water drum 3 plus suitable quantity of water, the suitable quantity of water are in suspension cylinder 2-3 whole immersion waters, and water is not It can be overflowed from water drum 3;N shape connecting rods 2-2 passes through the contour position-limiting tube 7 of suspension cylinder, then by horizontal plane position coordinatometer 2-1 and N shape connecting rods 2-2 is fixed together, and the n shape connecting rod 2-2 other ends are penetrated in suspension cylinder 2-3, and suspension cylinder 2-3 is with respect to n shapes for adjustment The position of connecting rod 2-2 is simultaneously temporarily fixed, and then suspension cylinder 2-3 is put into transparent water drum 3, treats that suspension cylinder 2-3 is swum in When stablizing motionless in water drum 3, horizontal plane where water surface 3-1 can intersect with horizontal plane position coordinatometer 2-1 in water drum 3, at this moment will Suspension cylinder 2-3 and n shape connecting rods 2-2 is fixed;It is, when suspension cylinder 2-3 swims in and stablizes motionless in water drum 3, in water Position on the coordinatometer 2-1 of plan-position with water surface 3-1 same levels in water drum 3 draws horizontal line 2-1-1, the horizontal line 2-1-1 is used to demarcate water surface 3-1 positions in water drum 3;7 inner wall smooth of contour position-limiting tube of the suspension cylinder, internal diameter and n shapes The diameter of connecting rod 2-2 matches, and n shape connecting rod 2-2 surfaces are smooth cylinder, and the contour position-limiting tube 7 of suspension cylinder is vertical by straight-bar It is fixed on transparent drawing board 5;The overflow pipe 3-3 is Cylindrical Homogeneous pipe, outer diameter and aperture of the water drum 3 with horizontal fitting hole Match, overflow pipe 3-3 is sealed with horizontal fitting hole during installation, and overflow pipe 3-3 keeps horizontal;The horizontal plane position coordinatometer 2-1 is transparent ruler.
CN201810163376.2A 2018-02-27 2018-02-27 Demonstration device for converting function form Expired - Fee Related CN108062887B (en)

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Application Number Priority Date Filing Date Title
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Application Number Priority Date Filing Date Title
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CN108062887B CN108062887B (en) 2020-05-12

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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN203118298U (en) * 2012-12-28 2013-08-07 苏鹏宇 Object motion demonstration board
CN103921596A (en) * 2014-05-05 2014-07-16 黄河科技学院 Combined type drawing device of ruler drawing board
CN204990899U (en) * 2015-06-26 2016-01-20 西华师范大学 Multi -functional continuation projectile motion orbit demonstration appearance
CN205211261U (en) * 2015-11-02 2016-05-04 胡天元 Novel flat experiment demonstration that throws of physics device
CN208903503U (en) * 2018-02-27 2019-05-24 齐齐哈尔大学 A kind of apparatus for demonstrating converting functional form

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN203118298U (en) * 2012-12-28 2013-08-07 苏鹏宇 Object motion demonstration board
CN103921596A (en) * 2014-05-05 2014-07-16 黄河科技学院 Combined type drawing device of ruler drawing board
CN204990899U (en) * 2015-06-26 2016-01-20 西华师范大学 Multi -functional continuation projectile motion orbit demonstration appearance
CN205211261U (en) * 2015-11-02 2016-05-04 胡天元 Novel flat experiment demonstration that throws of physics device
CN208903503U (en) * 2018-02-27 2019-05-24 齐齐哈尔大学 A kind of apparatus for demonstrating converting functional form

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