What is the general principle of constructing graphs of physical quantities. What is the general principle of constructing a system of units of physical quantities? Graphing Rules

Using the principle of constructing a graph to find the critical sales volume, one can find - by a similar method, or with complications due to the introduction of relative indicators - both the critical price level and the critical

At first, conducting technical analysis of the market, especially with the help of such a specific method, seems difficult. But if you thoroughly understand this, at first glance, not very presentable and dynamic way of graphic construction, it turns out that it is the most practical and effective. One of the reasons is that when using "tic-tac-toe" there is no particular need to use various technical market indicators, without which many simply do not think the possibility of conducting an analysis. You will say that this is contrary to common sense, asking the question "Where is technical analysis then?" to write a whole book about him.

Charting principles

Principles of constructing statistical graphs

Graphic image. Many of the models or principles presented in this book will be expressed graphically. The most important of these patterns are labeled as key charts. You should read the appendix to this chapter on plotting graphs and analyzing quantitative relative relationships.

Sections A through C describe the use of retracements as trading tools. Corrections will first be associated with the PHI Fibonacci ratio in principle, and then applied as charting tools on daily and weekly datasets for various products.

For these cases, effective planning methods are based on the use of methods associated with the construction of network graphs (networks). The simplest and most common network building principle is the critical path method. In this case, the network is used to identify the impact of one job on another and on the program as a whole. The execution time of each work can be indicated for each element of the network diagram.

activities of subcontractors. Whenever possible, the project manager uses software and the principles of the partitioning structure (WBS) to plan the activities of the main subcontractors. Data from subcontractors should be Graphing Capability Level 1 or 2 depending on the level of detail required by the contract.

Analysis is related to statistics and accounting. For a comprehensive study of all aspects of production and financial activities, data from both statistical and accounting, as well as sample observations, are used. In addition, it is necessary to have basic knowledge of the theory of groupings, methods for calculating average and relative indicators, indices, principles for constructing tables and graphs.

Of course, one of the possible options for the work of the brigade is graphically depicted here. In practice, there will be a variety of options. Basically, there are a lot of them. And the construction of a graph makes it possible to clearly illustrate each of these options.

Let's consider the principles of building universal "verification charts" that allow graphically interpreting the results of verification with a certain (specified) reliability.

On electrified lines, when plotting schedules, it is necessary to take into account the conditions for the most complete and rational use of power supply devices. To obtain the highest train speeds on these lines, it is especially important to place trains on the graph evenly, according to the principle of a paired schedule, occupying the hauls by alternately passing even and odd trains, while preventing trains from crowding on the graph at certain hours of the day.

Example 4. Graphs on coordinates with a logarithmic scale. The logarithmic scale on the coordinate axes is based on the principle of constructing a slide rule.

The way of representation is material (physical, i.e. coinciding subject-mathematical) and symbolic (linguistic). Material physical models correspond to the original, but may differ from it in size, range of parameters, etc. Symbolic models are abstract and are based on describing them with various symbols, including in the form of fixing an object in drawings, drawings, graphs, diagrams, texts, mathematical formulas, etc. At the same time, they can be based on the principle of construction - probabilistic (stochastic) and deterministic according to adaptability - adaptive and non-adaptive in terms of changing output variables over time - static and dynamic in terms of the dependence of model parameters on variables - dependent and independent.

The construction of any model is based on certain theoretical principles and certain means of its implementation. A model built on the principles of mathematical theory and implemented using mathematical tools is called a mathematical model. It is on mathematical models that modeling in the field of planning and management is based. The scope of these models - economics - determined their commonly used name - economic and mathematical models. In economics, a model is understood as an analogue of any economic process, phenomenon or material object. A model of certain processes, phenomena or objects can be represented in the form of equations, inequalities, graphs, symbolic images, etc.

The principle of periodicity, which reflects the production and commercial cycles of an enterprise, is also important for building a management accounting system. Information for managers is needed when it is appropriate, neither earlier nor later. Shortening the time plan can significantly reduce the accuracy of the information produced by management accounting. As a rule, the management apparatus establishes a schedule for the collection of primary data, their processing and grouping in the final information.

The graph in fig. 11 corresponds to a coverage level of DM 200 per day. It was built as a result of an analysis carried out by an economist, who reasoned as follows: how many cups of coffee at a price of 0.60 DM are enough to sell to obtain a coverage of 200 DM, what additional quantity will need to be sold if, at a price of 0.45 DM, they want to keep the same DM200 coverage amount To calculate the target number of sales, you need to divide the target coverage amount per day of DM200 by the corresponding coverage amount per unit of product. The if principle applies. .., then... .

The outlined principles for constructing scale-free network diagrams were presented mainly in relation to site structures. The construction of network models for organizing the construction of the linear part of pipelines has a number of features.

In Section 2, the principles for constructing scale-free soybean graphs and graphs built on a time scale, izla-1>x "LS1> B, are set out mainly in relation to site structures. Variegated network models for organizing the construction of the front part of pipelines have a number of features.

Another fundamental advantage of the intraday single-cell reversal pip-figure chart is the ability to identify price targets using a horizontal reference. If you mentally return to the basic principles of building a bar chart and price patterns discussed above, then remember that we have already touched on the topic of price targets. However, almost every method of setting price targets using a bar chart is based, as we said, on the so-called vertical measurement. It consists in measuring the height of some graphical model (oscillation range) and projecting the resulting distance up or down. For example, on the "head and shoulders" model, the distance from the "head" to the "neck" line is measured, and the reference point is plotted from the breakout point, that is, the intersection of the "neck" line.

Must know the device of the equipment being serviced, the recipe, types, purpose and features of the materials to be tested, raw materials, semi-finished products and finished products, the rules for conducting physical and mechanical tests of varying complexity with the performance of work on their processing and generalization, the principle of operation of ballistic installations for determining magnetic permeability, the main components of vacuum systems foreline and diffusion pumps, thermocouple vacuum gauge basic methods for determining the physical properties of samples basic properties of magnetic bodies thermal expansion of alloys method for determining the coefficients of linear expansion and critical points on dilatometers method for determining temperature using high- and low-temperature thermometers elastic properties of metals and alloys rules for making corrections for geometric sample dimensions; methods for plotting; a system for recording tests; and a methodology for summarizing test results.

The same principle of constructing a calendar plan-schedule underlies schedules for planning production processes, which are distinguished by a complex structure. An example of the most characteristic schedule of this type is the cycle schedule for the manufacture of machines used in single and small-scale mechanical engineering (Fig. 2). It shows in what sequence and with what calendar advance in relation to the planned release date of finished machines the parts and assemblies of this machine must be manufactured and submitted for subsequent processing and assembly so that the designated deadline for the release of the series is met. Such a schedule is based on the technological. scheme for the manufacture of parts and the sequence of their knotting during the assembly process, as well as on standard calculations of the duration of the production cycle for the manufacture of parts for the main stages - the manufacture of blanks, mechanical. processing, heat treatment, etc. and the assembly cycle of units and machines as a whole. Hence the schedule is called a cycle. The calculated unit of time in its construction is usually a working day, and the days are counted on the chart from right to left from the end date of the planned release in reverse order of the machine manufacturing process. In practice, cycle schedules are drawn up for a large range of assemblies and parts with the division of the production time of large parts by stages of the production process (blank, machining, heat treatment), sometimes with the allocation of basic mechanical operations. processing. Such graphs are much more cumbersome and complex than the diagram in Fig. 2. But they are indispensable in planning and controlling the production of products in serial, especially in small-scale production.

The second example of a calendar task for optimization is to build a schedule that best coordinates the timing of production at several successive stages of production (processing) with different processing times for the product at each of them. For example, in a printing house, it is necessary to coordinate the work of typesetting, printing, and bookbinding shops, subject to different labor-intensity for individual shops of different types of products (form products, book products with simple or complex typesetting, with or without binding, etc.). The problem can be solved under various optimization criteria and various constraints. So, it is possible to solve the problem for the minimum duration of production, the cycle and, consequently, the minimum value of the average balance of products in the work in progress (backlog), while the restrictions should be determined by the available throughput of various shops (repartitions). Another formulation of the same problem is also possible, in which the optimization criterion is the maximum use of available production, capacity, with restrictions imposed on the timing of the release of individual types of products. An algorithm for the exact solution of this problem (the so-called Johnson problem a) was developed for cases where the product goes through only 2 operations, and for an approximate solution with three operations. With a larger number of operations, these algorithms are unsuitable, which practically devalues ​​them, since the need for solving the problem of optimizing the calendar schedule arises Ch. arr. in the planning of multi-operational processes (for example, in mechanical engineering). E. Bowman (USA) in 1959 and A. Lurie (USSR) in 1960 proposed mathematically rigorous algorithms based on the general ideas of linear programming and making it possible in principle to solve the problem for any number of operations. However, at present (1965) it is impossible to apply these algorithms in practice; they are too cumbersome in terms of calculation even for the most powerful of the existing electronic computers. Therefore, these algorithms are only of prospective value, either they can be simplified, or the progress of computer technology will make it possible to implement them on new machines.

For example, if you are going to visit a car dealership in order to get acquainted with new cars, their appearance, interior decoration, etc., then you are unlikely to be interested in graphs explaining the sequence of fuel injection into engine cylinders, or reasoning on the principles of construction engine management systems. Most likely, you will be interested in engine power, acceleration time to a speed of 100 km / h, fuel consumption per 100 km, comfort and vehicle equipment. In other words, you will want to imagine what kind of car you will drive, how good you would look in it, going on a trip with a girlfriend or boyfriend. As you imagine this trip, you will begin to think about all the features and benefits of the car that would be useful to you on the trip. This is a simple example of a use case.

In building codes and regulations, in technological instructions and in textbooks for decades, the principle of flow in construction production has been proclaimed. However, the theory of threading has not yet received a unified basis. Some employees of VNIIST and MINH and GP express the idea that the theoretical constructions and models created by the flow are not always adequate to construction processes, and therefore the schedules and calculations performed when designing a construction organization, as a rule, cannot be implemented.

Robert Reah studied Dow's writings and spent a lot of time compiling market statistics and supplementing Dow's observations. He noticed that indices are more prone than individual stocks to form horizontal lines or extended chart formations. He was also one of the first

1. Decoration of axes, scale, dimension. It is convenient to represent the results of measurements and calculations in graphical form. Graphs are built on graph paper; the dimensions of the graph should not be less than 150 * 150 mm (half a page of a laboratory journal). First of all, coordinate axes are applied to the sheet. For the results of direct measurements, as a rule, they are plotted on the x-axis. At the ends of the axes, the designations of physical quantities and their units of measurement are applied. Then scale divisions are applied to the axis so that the distance between divisions is 1, 2, 5 units or 1; 2; 5 * 10 ± n, where n is an integer. The point of intersection of the axes does not have to be zero on one or more axes. The origin along the axes and the scale should be chosen so that: 1) the curve (straight line) occupies the entire field of the graph; 2) the angles between the tangents to the curve and the axes should be close to 45º (or 135º) for as much of the graph as possible.

2. Graphical representation of physical quantities. After selection and drawing on the scale axis, the values ​​of physical quantities are applied to the sheet. They are denoted by small circles, triangles, squares, and numerical values ​​corresponding to plotted points are not carried off on the axis. Then, from each point up and down, to the right and to the left, the corresponding errors are plotted in the form of segments on the scale of the graph.

After plotting the points, a graph is drawn, i.e. a smooth curve or a straight line predicted by the theory is drawn so that it intersects all error regions or, if this is not possible, the sums of the deviations of the experimental points from below and above the curve should be close. In the right or in the upper left corner (sometimes in the middle) the name of the dependence that is depicted by the graph is written.

An exception is the calibration graphs, on which the points plotted without errors are connected by successive straight line segments, and the calibration accuracy is indicated in the upper right corner, under the name of the graph. However, if the absolute measurement error changed during the calibration of the instrument, then the errors of each measured point are plotted on the calibration graph. (This situation is realized when calibrating the “amplitude” and “frequency” scales of the GSK generator using an oscilloscope). Calibration graphs are used to find intermediate values ​​of linear interpolations.

Graphs are drawn in pencil and pasted into the laboratory journal.

3. Linear approximations. In experiments, it is often required to plot the dependence of the physical quantity obtained in the work Y from the obtained physical quantity X, approximating Y(x) linear function , where k,b- permanent. The graph of such a dependence is a straight line, and the slope k, often itself is the main goal of the experiment. It is natural that k in this case is also a physical parameter, which must be determined with the inherent accuracy of this experiment. One of the methods for solving this problem is the paired points method, described in detail in. However, it should be borne in mind that the method of paired points is applicable in the presence of a large number of points n ~ 10, in addition, it is quite laborious. More simple and with its accurate execution, not inferior in accuracy to the paired points method, is the following graphical method for determining:

1) According to the experimental points plotted with errors, a

straight line using the method of least squares (LSM).

The fundamental idea of ​​LSM approximation is to minimize

total standard deviation of experimental points from

desired line

In this case, the coefficients are determined from the minimization conditions:

Here are the experimentally measured values, n is the number

experimental points.

As a result of solving this system, we have expressions for calculating

coefficients according to experimentally measured values:

2) After calculating the coefficients, the desired straight line is drawn. Then the experimental point is selected, which has the largest, taking into account its error, deviation from the graph in the vertical direction DY max as shown in Fig. 2. Then the relative error Dk/k, due to the inaccuracy of the Y values, , where the measuring range of Y values ​​is from max to min. At the same time, dimensionless quantities are in both parts of the equation, therefore DY max and can be simultaneously calculated in mm according to the graph or taken simultaneously taking into account the dimension Y.

3) Similarly, the relative error is calculated due to the error in determining X.

.

4) If one of the errors, for example, , or the value X has very small errors D X, imperceptible on the graph, then we can assume d k=d k y.

5) Absolute error D k=d k*k. As a result .

Rice. 2.

Literature:

1. Svetozarov V.V. Elementary processing of measurement results, M., MEPhI, 1983.

2. Svetozarov V.V. Statistical processing of measurement results. M.: MEPhI.1983.

3. Hudson. Statistics for physicists. M.: Mir, 1967.

4. Taylor J.Z. Introduction to the theory of errors. M.: Mir. 1985.

5. Burdun G.D., Markov B.N. Basics of metrology. M.: Publishing house of standards, 1967.

6. Laboratory workshop "Measuring instruments" / ed. Nersesova E.A., M., MEPhI, 1998.

7. Laboratory workshop “Electrical measuring instruments. Electromagnetic Oscillations and Alternating Current”/ Ed. Aksenova E.N. and Fedorova V.F., M., MEPhI, 1999.

Appendix 1

Student Odds Table

n/p	0,8	0,9	0,95	0,98	0,99
	3.08 1.89 1.64 1.53 1.48 1.44 1.42 1.40 1.38 1.37 l.363 1.36 1.35 1.35 1.34 1.34 1.33 1 .33	6,31 2,92 2,35 2,13 2,02 1,94 1,90 1.86 1,83 1,81 1,80 1,78 1,77 1,76 1,75 1,75 1,74 1,73	12,71 4,30 3.18 2,77 2,57 2,45 2,36 2,31 2,26 2.23 2,20 2,18 2,16 2,14 2,13 2,12 2,11 2,10	31,8 6,96 4,54 3,75 3,36 3.14 3,00 2,90 2,82 2,76 2,72 2,68 2,65 2,62 2,60 2,58 2,57 2,55	63,7 9,92 5,84 4,60 4,03 4,71 3,50 3,36 3,25 3,17 3,11 3,06 3,01 2,98 2,95, 2,92 2,90 2,88

2. Ott V.D., Fesenko M.E. Diagnosis and treatment of obstructive bronchitis in children of early age. Kyiv-1991.

3. Rachinsky S.V., Tatochenko V.K. Respiratory diseases in children. M.: Medicine, 1987.

4. Rachinsky S.V., Tatochenko V.K. bronchitis in children. Leningrad: Medicine, 1978.

5. Smyan I.S. Pediatrics (course of lectures). Ternopil: Ukrmedkniga, 1999.

What is the general principle of constructing a system of units of physical quantities?

A physical quantity is a property that is qualitatively common to many physical objects, but quantitatively individual for each object. Physical quantities are objectively interconnected. With the help of equations of physical quantities it is possible to express relationships between physical quantities. A group of basic quantities is distinguished (the units corresponding to these quantities are called basic units) (their number in each field of science is defined as the difference between the number of independent equations and the number of physical quantities included in them) and derived quantities (the units corresponding to these quantities are called derived units), which are formed using basic quantities and units using equations of physical quantities. The values ​​and units that can be reproduced with the greatest accuracy are chosen as the main ones. The set of selected basic physical quantities is called the system of quantities, and the set of units of basic quantities is called the system of units of physical quantities. This principle of constructing systems of physical quantities and their units was proposed by Gauss in 1832.

Mechanical movement is represented graphically. The dependence of physical quantities is expressed using functions. designate

Graphs of uniform motion

Time dependence of acceleration. Since the acceleration is equal to zero during uniform motion, the dependence a(t) is a straight line that lies on the time axis.

Dependence of speed on time. The speed does not change with time, the graph v(t) is a straight line parallel to the time axis.

The numerical value of the displacement (path) is the area of ​​the rectangle under the speed graph.

Path versus time. Graph s(t) - sloping line.

The rule for determining the speed according to the schedule s(t): The tangent of the slope of the graph to the time axis is equal to the speed of movement.

Graphs of uniformly accelerated motion

Dependence of acceleration on time. Acceleration does not change with time, has a constant value, graph a(t) is a straight line parallel to the time axis.

Speed ​​versus time. With uniform motion, the path changes, according to a linear relationship. in coordinates. The graph is a sloping line.

The rule for determining the path according to the schedule v(t): The path of the body is the area of ​​the triangle (or trapezoid) under the velocity graph.

The rule for determining the acceleration according to the schedule v(t): The acceleration of the body is the tangent of the slope of the graph to the time axis. If the body slows down, the acceleration is negative, the angle of the graph is obtuse, so we find the tangent of the adjacent angle.

Path versus time. With uniformly accelerated movement, the path changes, according to