Abstract keywords: chemical formula, index, coefficient, qualitative and quantitative composition, formula unit.
- this is a conditional record of the composition of a substance by means of chemical signs and indices.
The number that is in the formula at the bottom right of the sign of the element is called index. The index indicates the number of atoms of an element that make up a given substance.
If you want to designate not one, but several molecules (or individual atoms), then before the chemical formula (or sign) put the corresponding number, which is called coefficient. For example, three water molecules are denoted 3H 2 O, five iron atoms - 5Fe. Index 1 in chemical formulas and coefficient 1 do not write in front of chemical symbols and formulas.
The formulas shown in the figure read as follows: tri-cuprum-chloro-two, five-aluminum-two-o-three, tri-ferrum-chloro-tri . Recording 5H 2 O(five-ash-two-o) should be understood as follows: five water molecules are formed by ten hydrogen atoms and five oxygen atoms.
The chemical formula shows the atoms of which elements a substance consists of (that is, qualitative composition of matter); and what is the ratio of the atoms of these elements (i.e. quantitative composition of the substance).
formula unit
Chemical formulas of substances having a non-molecular structure, for example FeS, do not describe the composition of the molecule; but only show the ratio of the elements that form a given substance.
So, the crystal lattice of table salt - sodium chloride consists not of molecules, but of. For every positively charged sodium ion, there is one negatively charged chloride ion. It turns out that the ratio of indices in the record NaCl matches the relation; in which the chemical elements combine with each other to form a substance. In relation to substances having a non-molecular structure, it is more correct to call such a record not a formula, but formula unit.
This guide has been compiled from various sources. But its creation was prompted by a small book "Mass Radio Library" published in 1964, as a translation of the book by O. Kroneger in the GDR in 1961. Despite its antiquity, it is my reference book (along with several other reference books). I think time has no power over such books, because the foundations of physics, electrical and radio engineering (electronics) are unshakable and eternal.
Units of measurement of mechanical and thermal quantities.
Units of measurement of electromagnetic quantities
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Relations between units of magnetic quantities
in CGSM and SI systems
| In electrical and reference literature published before the introduction of the SI system, the magnitude of the magnetic field strength H often expressed in oersteds (uh) magnetic induction value AT - in gauss (gs), magnetic flux Ф and flux linkage ψ - in maxwells (µs). |
| 1e \u003d 1/4 π × 10 3 a / m; 1a / m \u003d 4π × 10 -3 e; 1gf=10 -4 t; 1tl=104 gs; 1mks=10 -8 wb; 1vb=10 8 ms |
| It should be noted that the equalities are written for the case of a rationalized practical MKSA system, which was included in the SI system as an integral part. From a theoretical point of view, it would be better to about in all six relationships, replace the equal sign (=) with the match sign (^). for example |
|
1e \u003d 1 / 4π × 10 3 a / m |
| which means: a field strength of 1 Oe corresponds to a strength of 1/4π × 10 3 a/m = 79.6 a/m |
| The point is that the units gs and ms belong to the CGMS system. In this system, the unit of current strength is not the main one, as in the SI system, but a derivative. Therefore, the dimensions of the quantities characterizing the same concept in the CGSM and SI systems turn out to be different, which can lead to misunderstandings and paradoxes, if you forget about this circumstance. When performing engineering calculations, when there is no basis for misunderstandings of this kind |
Off-system units
Some mathematical and physical concepts
applied to radio engineering
| Like the concept - the speed of movement, in mechanics, in radio engineering there are similar concepts, such as the rate of change of current and voltage. They can be either averaged over the course of the process, or instantaneous. |
|
i \u003d (I 1 -I 0) / (t 2 -t 1) \u003d ΔI / Δt |
| With Δt -> 0, we get the instantaneous values of the current change rate. It most accurately characterizes the nature of the change in the quantity and can be written as: |
|
i=lim ΔI/Δt =dI/dt |
| And you should pay attention - the average values and instantaneous values \u200b\u200bcan differ by dozens of times. This is especially evident when a changing current flows through circuits with a sufficiently large inductance. |
decibell |
| To assess the ratio of two quantities of the same dimension in radio engineering, a special unit is used - the decibel. |
| K u \u003d U 2 / U 1 Voltage gain; K u [dB] = 20 log U 2 / U 1 Voltage gain in decibels. Ki [dB] = 20 log I 2 / I 1 Current gain in decibels. Kp[dB] = 10 log P 2 / P 1 Power gain in decibels. |
| The logarithmic scale also allows, on a graph of normal sizes, to depict functions that have a dynamic range of parameter changes in several orders of magnitude. |
| To determine the signal strength in the reception area, another logarithmic unit of DBM is used - dicibells per meter. |
| P [dbm] = 10 log U 2 / R +30 = 10 log P + 30. [dbm]; |
| The effective load voltage at a known P[dBm] can be determined by the formula: |
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Dimensional coefficients of basic physical quantities
| In accordance with state standards, the following multiple and submultiple units - prefixes are allowed: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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When typing text in the Word editor, it is recommended to write formulas using the built-in formula editor, keeping the default settings in it. It is allowed to type formulas in larger type than the text, if it is necessary for the convenience of reading small indices. It is recommended to define a separate line for formulas with your own style (naming it, for example, Equation), in which you should set the necessary indents, intervals, alignment and style of the next line.
Formulas in the work are numbered with Arabic numerals. The formula number consists of the section number and the ordinal number of the formula in the section, separated by a dot. The number is indicated on the right side of the sheet at the formula level in parentheses. For example, (2.1) is the first formula of the second section. The formulas themselves should be written in the center of the page. The letter designations of the quantities included in the formula must be deciphered (if this has not been done in the text of the work earlier). For example: full number M deaths from malignant tumors as a result of exposure in the population will be equal to
where n(e) is the distribution density of individuals in the population by age, R(e) is the lifetime risk of death from malignant neoplasms for an individual of age e at the time of a single exposure or the onset of chronic exposure.
The designations are deciphered in the sequence corresponding to the order in which they appear in the formula. It is allowed to decipher each of the designations to write in a separate line.
You should strictly follow the rules for punctuation after writing formulas.
Equations and formulas must be separated from the text by free lines. If the equation does not fit on one line, then it must be moved after the equal sign (=) or after the addition (+), subtraction (-), multiplication (x), and division (:) signs. Floating point numbers should be written in the form, for example: 2×10 -12 s, denoting the multiplication sign with the symbol (×) from the Symbol font. You should not denote the multiplication operation with the symbol (*).
Units of measurement of physical quantities must be given only in the International System of Units (SI) in the accepted abbreviations.
Construction work
The names of the structural parts of the work "Abstract", "Contents", "Denotations and abbreviations", "Normative references", "Introduction", "Main part", "Conclusion", "List of used sources" serve as headings of the structural elements of the work.
The main part of the work should be divided into chapters "Literature Review", "Research Material and Methods", "Research Results and Discussion", sections, subsections and paragraphs. Items, if necessary, can be divided into sub-items. When dividing the text of the work into paragraphs and subparagraphs, it is necessary that each paragraph contains complete information. Chapters, sections, subsections should have titles. Section headings are placed symmetrically to the text. Subsection headings begin 15-17 mm from the left margin. Word hyphenation in headings is not allowed. Do not put a dot at the end of the title. If the title consists of two sentences, then they are separated by a dot. The distance between the title, subtitle and text should be 15-17 mm (12 pt with the same font size). Headings should not be underlined. Each section (chapter) of the work must begin on a new sheet (page).
Chapters, sections, subsections, paragraphs and subparagraphs should be numbered in Arabic numerals. Sections should be numbered sequentially within the entire text of the chapter, with the exception of appendices.
Do not put a dot after the number of the section, subsection, paragraph and subparagraph in the text. If the heading consists of two or more sentences, they are separated by a dot(s).
Section headings are printed in lowercase letters (except for the first capital) with a paragraph indent in bold type with a size of 1-2 points more than in the main text.
Subheadings are printed with a paragraph indent in lowercase letters (except for the first capital) in bold type with the font size of the main text.
The distance between the title (except for the title of the paragraph) and the text should be 2-3 line spacing. If there is no text between two headings, then the distance between them is set to 1.5-2 line spacing.
Illustrations
Illustrations (diagrams, graphs, diagrams, photographs) are located, as a rule, on separate pages, which are included in the general numbering. When computer-based illustrations are allowed to place them in the general text.
Illustrations should be placed in the work directly after the text in which they are mentioned for the first time, or on the next page. All illustrations must be referenced in the work.
The number of illustrations is determined by the content of the work and should be sufficient to make the material presented clear and specific. Drawings must be printed using a computer or done in black ink or ink. It is forbidden to make drawings in a different color, as well as in pencil. Color printing of drawings and photographs is allowed.
Illustrations should be arranged so that they can be easily viewed without turning the work or turning it clockwise. Illustrations are placed in the text after the first reference to them.
Illustrations (diagrams and graphs) that cannot be placed on an A4 sheet are placed on an A3 sheet and then folded to A4 size.
All illustrations should be referenced in the text of the work. All illustrations are denoted by the word "drawing" and numbered sequentially with Arabic numerals through numbering, with the exception of the illustrations given in the appendix. The word "figure" in the captions to the figure and in references to it is not abbreviated.
It is allowed to number illustrations within the section. In this case, the illustration number must consist of the section number and the sequence number of the illustration in the section. For example, Figure 1.2 is the second figure in the first section.
Illustrations, as a rule, have explanatory data (figure text) located in the center of the page. Explanatory data is placed under the illustration, and from the next line - the word "Figure", the number and name of the illustration, separating the number from the name with a dash. Do not put a dot at the end of the numbering and titles of illustrations. Wrapping of words in the title of the figure is not allowed. The word "Figure", its number and the name of the illustration are printed in bold, and the word "Figure", its number, as well as explanatory data to it - reduced by 1-2 points in font size.
An example of illustration design is given in Appendix D.
tables
Digital material, as a rule, should be presented in the form of tables.
The digital material of the dissertation is presented in the form of tables. Each table must have a short title, which consists of the word "Table", its number and title, separated from the number by a dash. The heading should be placed above the table on the left, without paragraph indentation.
Headings of graphs and lines should be written with a capital letter in the singular, and subheadings of graphs should be written with a lowercase letter if they make up one sentence with the heading, and with capital letters if they have an independent meaning.
The table should be placed after its first mention in the text. Tables are numbered in the same way as illustrations. For example, table 1.2. is the second table of the first section. In the name of the table, the word "Table" is written in full. When referring to a table in the text, the word "table" is not abbreviated. If necessary, tables can be placed on separate sheets, which are included in the overall page numbering.
When designing tables, you must follow the following rules:
it is allowed to use in the table a font 1-2 points smaller than in the text of the dissertation;
the column "Sequence number" should not be included in the table. If it is necessary to number the indicators included in the table, the serial numbers are indicated in the sidebar of the table immediately before their name;
a table with a large number of rows can be transferred to the next sheet. When transferring part of the table to another sheet, its heading is indicated once above the first part, the word "Continuation" is written to the left above the other parts. If there are several tables in the dissertation, then after the word "Continuation" indicate the number of the table, for example: "Continuation of table 1.2";
a table with a large number of columns can be divided into parts and placed one part under the other within one page, repeating a sidebar in each part of the table. The heading of the table is placed only above the first part of the table, and above the rest they write "Continuation of the table" or "End of the table" indicating its number;
a table with a small number of columns can be divided into parts and placed one part next to the other on the same page, separating them from each other with a double line and repeating the head of the table in each part. With a large size of the head, it is allowed not to repeat it in the second and subsequent parts, replacing it with the corresponding column numbers. In this case, the columns are numbered with Arabic numerals;
if the text repeated in different lines of the column of the table consists of one word, then after the first writing it is allowed to replace it with quotation marks; if from two or more words, then it is replaced by the words "The same" at the first repetition, and then - quotes. It is not allowed to put quotation marks instead of repeated numbers, marks, signs, mathematical, physical and chemical symbols. If digital or other data is not given in any line of the table, then a dash is put in it;
headings of graphs and lines should be written with a capital letter in the singular, and subheadings of a graph should be written with a lowercase letter if they form one sentence with the heading, and with capital letters if they have an independent meaning. It is allowed to number the columns with Arabic numerals, if it is necessary to give links to them in the text of the dissertation;
column headings, as a rule, are written parallel to the rows of the table. If necessary, it is allowed to place the headings of the columns parallel to the columns of the table.
An example of the design of the table is given in Appendix D.
Similar information.
METHODOLOGICAL INSTRUCTIONS
On the design of control works, term papers, final qualifying works, master's theses
For students of the Financial and Economic Institute
Considered at a meeting of the Institute's Educational and Methodological Commission,
protocol dated 08.11.2013 No. 4
Chairman
Educational and Methodological Commission of the Institute E.S. Korchemkina
Tyumen 2013
These guidelines have been prepared on the basis of the following regulatory and technical documents:
GOST 7.32-2001. Research report. Structure and rules of registration;
GOST 7.1-2003. Bibliographic record. Bibliographic description. General requirements and rules for drafting;
GOST 7.0.12-2011. Bibliographic record. Abbreviation of words and phrases in Russian;
General rules
The student's educational research work (hereinafter referred to as the work) must be printed on one side of a sheet of A4 white paper.
The title page of the work is drawn up in accordance with Annexes 1, 2, 3, 4, 5, 6, 7.
The text of the work should be printed, observing the following margins: right - 10 mm, left - 25 mm, top and bottom - 20 mm.
The text of the work is printed at 1.5 intervals using the font - Regular, Times New Roman, font size - 14. The saturation of letters and characters should be even within the line, page and the entire work. Entering individual words, formulas, conventional signs into the text is allowed only in black ink and approximately the density of the main text. The paragraph indent is 5 characters (1.25 cm).
Each new chapter starts on a new page. The same rule applies to other main structural parts of the work: list of abbreviations, introduction, conclusion, list of sources used, applications.
The names of the structural elements of the work: "CONTENTS", "LIST OF ABBREVIATIONS", "INTRODUCTION", "CONCLUSION", "LIST OF SOURCES", "APPENDICES", as well as the titles of the chapters of the main part are the headings of the structural elements of the work. They should be centered on the line without a dot and printed in capital letters, in normal type, without underlining.
Numbering issues
2.1. Pages should be numbered with Arabic numerals. All pages are numbered consecutively from the title page to the last page. The number 1 is not put on the title page, the number 2 is put on the next page. The page number is printed in the center at the top of the page without any additional characters (dots, dashes).
2.2. Illustrations and tables located on separate sheets are included in the general page numbering.
2.3. The main part of the work should be divided into chapters, paragraphs, paragraphs and subparagraphs.
2.4. The chapters should have serial numbers within the work, indicated by Arabic numerals with a dot. The title of the chapter is printed in capital letters without a dot at the end, without underlining. It is not allowed to carry a word to the next line, use Roman numerals, mathematical signs and Greek letters.
Each chapter is printed from a new sheet. The distance between the title of the chapter (paragraph) and the following text should be equal to two one and a half intervals. If the chapter is divided into paragraphs, then there should be no text between the title of the chapter and the paragraph.
2.5. The paragraphs are numbered within the chapter. The number of the paragraph consists of the number of the chapter and the paragraph, separated by a dot, for example, 1.1., a dot is put at the end of the paragraph number.
Paragraph headings should begin with a paragraph indent from a capital letter, without underlining, without a dot at the end. The distance between the title of the paragraph and the following text should be equal to two one and a half intervals. If the paragraph is divided into paragraphs, then there should be no text between them.
2.6. Items should be numbered consecutively within each paragraph. The number of the paragraph includes the number of the chapter and the serial number of the paragraph and paragraph separated by a dot; at the end of the paragraph number, a dot is not put, for example, 1.1.1., 1.1.2., and is printed from a paragraph indent. The paragraph may have a heading that is written in capital letters, with a paragraph indent. A free line between the title of the item and the following text is not left. If the paragraph is divided into subparagraphs, then there should be no text between them.
2.7. The number of the subparagraph includes the number of the chapter, paragraph, paragraph and the serial number of the subparagraph, separated by a dot, a dot is put at the end of the subparagraph number, for example, 1.1.1.1., 1.1.1.2, etc. A subparagraph may have a heading that is written in capital letters, with a paragraph indent. A free line between the title of the subparagraph and the following text is not left.
2.8. If the heading includes several sentences, they are separated by dots. Word hyphenation in headings is not allowed. There is no dot at the end of the heading. The title of the paragraph, paragraph and subparagraph should not be the last line on the page.
2.9. If a chapter or paragraph has only one paragraph, or a paragraph has one subparagraph, then the paragraph (subparagraph) should not be numbered.
Presentation of the text
3.1. The text of the work should be short, clear and not allow for various interpretations. When presenting mandatory requirements, the words “should”, “should”, “necessary”, “required”, “not allowed”, “prohibited”, “should not” should be used. The presentation of the text is given in an impersonal form. For example: "... measured ...", "accepted ..." or "... .. refer to ...".
3.2. The text is not allowed:
- apply turns of colloquial speech, technicalism, professionalism;
- apply for the same concept different scientific and economic terms that are close in meaning (synonyms), as well as foreign words in the presence of equivalent words and terms in Russian;
- abbreviate the designations of units of physical quantities, if they are used without numbers, for example, m, s, you should write "1 m, 1 s or meter, second", with the exception of units of physical quantities in the heads and sides of the tables, in the decoding of the letter designations included in formulas and figures;
– use the mathematical minus sign (–) before negative values of quantities (the word “minus” should be written);
- use mathematical signs without numerical values, for example, > (greater than),< (меньше), = (равно), ≠ (не равно), а также знаки № (номер), % (процент);
- abbreviation of words and phrases.
3.3. Abbreviations in the text are allowed only generally accepted:
- in the middle of sentences - "see", "t. e.";
- at the end of sentences - “etc.”, “etc.”, “etc.”;
- with the surname or name of the institution - abbreviations of academic degrees and titles, for example, Dr. Econ. Sciences Ivanov K.M.; cand. legal Sciences Petrov Yu.S.
- in the presence of a digital designation - "s." (page), "g." (year), "yy." (years), for example, S. 5, 2006
Abbreviations of the following words and phrases are not allowed: “since”, “so-called”, “thus”, “so”, “for example”.
3.4. Names should be written in the following order: surname, first name, patronymic (or - surname, initials, it is not allowed to transfer initials separately from the surname to the next line).
Formulas and Units
4.1. Formulas are written in a separate line, aligned in the center. There must be one free line above and below each formula.
4.2. After the formula, a list of all the symbols accepted in the formula is placed with a decoding of their meanings and an indication of the dimension (if necessary). Letter designations are given in the same sequence in which they are given in the formula.
4.3. Formulas are numbered by continuous numbering within the entire work in Arabic numerals. In this case, the number of the formula is indicated in parentheses in the extreme right position on the line. One formula is denoted by - (1).
4.4. In formulas, as symbols of physical quantities, the designations established by the relevant state standards (GOST 8.417) should be used. Explanations of the symbols and numerical coefficients included in the formula, if they are not explained earlier in the text, should be given directly below the formula and should correspond to the font type and size adopted when writing the formula itself. Explanations of each character should be given on a new line in the order in which the characters are given in the formula.
4.6. The first line of the explanation must begin with a paragraph indent with the word "where" without a colon after it. Signs "-" (dash) are located on one vertical line.
For example,
R = ∑ pi (Yi + Z i + Wi) (5)
where R is the value of environmental risk;
∑ is the sign of the sum;
pi is the probability of occurrence of the i-th hazardous factor affecting the environment, the population;
Yi - damage from the impact of the i-th hazard;
Z i - loss or damage to the person's property;
W i - expenses that a person has made to restore the right.
4.7. Punctuation marks before the formula and after it are placed according to the meaning. Formulas that follow one after another and are not separated by text are separated by a comma.
4.8. If the formula does not fit on a line, then part of it is transferred to another line only on the mathematical sign of the main line, necessarily repeating the sign in the second line. When transferring the formula on the multiplication sign, the “×” sign is used. When writing formulas, break lines are not allowed. In a multiline formula, the formula number is placed against the last line.
4.9. Symbolic letters, images or signs must comply with those adopted in state standards (GOST 8.417).
4.10. If it is necessary to use symbols, images or signs that are not established by the current standards, they should be explained in the text or in the list of symbols.
4.11. The text should use standardized units of physical quantities, their names and designations in accordance with GOST 8.417.
4.12. The unit of a physical quantity from a number is indicated through a space, including percentages, for example, 5 m, 99.4%.
4.13. Intervals of values in the form "from and to" are written through a dash without spaces. For example, 8-11% or s. 5-7 etc.
4.14. When bringing digital material, only Arabic numerals should be used, with the exception of the generally accepted numbering of quarters, half-years, which are indicated by Roman numerals. Cardinal numbers in the text are given without case endings.
Any dimension associated with finding numerical values physical quantities, with the help of them, the patterns of the phenomena that are being studied are determined.
concept physical quantities, For example, forces, weights, etc., is a reflection of the objectively existing characteristics of inertia, extension, and so on, inherent in material objects. These characteristics exist outside and independently of our consciousness, regardless of the person, the quality of the means and methods that are used in the measurements.
Physical quantities that characterize a material object under given conditions are not created by measurements, but are only determined using them. measure any quantity, this means to determine its numerical ratio with some other homogeneous quantity, which is taken as a unit of measurement.
Based on this, measurement is the process of comparing a given value with some of its value, which is taken as unit of measure.
Relationship formula between the quantity for which the derived unit is established and the quantities A, B, C, ... units they are installed independently, general view:
where k- numerical coefficient (in the given case k=1).
The formula for relating a derived unit to base or other units is called formuladimensions, and the exponents dimensions For convenience in the practical use of units, such concepts as multiples and submultiples have been introduced.
Multiple unit- a unit that is an integer number of times greater than a system or non-system unit. A multiple unit is formed by multiplying the basic or derived unit by the number 10 to the appropriate positive power.
submultiple unit- a unit that is an integer number of times less than a system or non-system unit. The submultiple unit is formed by multiplying the basic or derived unit by the number 10 to the appropriate negative power.
Definition of the term “unit of measure“.
Unification of the unit of measurement engaged in a science called metrology. Literally translated, it is the science of measurement.
Looking into the International Dictionary of Metrology, we find out that unit- this is a real scalar quantity, which is defined and accepted by agreement, with which it is easy to compare any other quantity of the same kind and express their ratio using a number.
A unit of measurement can also be considered as a physical quantity. However, there is a very important difference between a physical quantity and a unit of measurement: the unit of measurement has a fixed numerical value accepted by convention. This means that the units of measurement for the same physical quantity may be different.
For example, weight can have the following units: kilogram, gram, pound, pood, centner. The difference between them is clear to everyone.
The numerical value of a physical quantity is represented by the ratio of the measured value to the standard value, which is unit of measure. A number that has a unit of measure named number.
There are basic and derived units.
Basic units set for such physical quantities that are selected as the main ones in a particular system of physical quantities.
Thus, the International System of Units (SI) is based on the International System of Units, in which the main quantities are seven quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. So, in SI, the base units are the units of quantities that are indicated above.
Size of base units set by agreement within a specific system of units and fixed either with the help of standards (prototypes), or by fixing the numerical values of fundamental physical constants.
Derived units are determined through the main method of using those relationships between physical quantities that are established in the system of physical quantities.
There are a huge number of different systems of units. They differ both in the systems of quantities on which they are based and in the choice of base units.
Usually, the state, through laws, establishes a certain system of units that is preferred or mandatory for use in the country. In the Russian Federation, the units of quantities of the SI system are the main ones.
Systems of units of measure.
Metric systems.
- ICSS,
Systems of natural units of measurement.
- atomic system of units,
- planck units,
- Geometric system of units,
- Lorentz-Heaviside units.
Traditional systems of measures.
- Russian system of measures,
- English system of measures,
- French system of measures,
- Chinese system of measures,
- Japanese system of measures,
- Already obsolete (ancient Greek, ancient Roman, ancient Egyptian, ancient Babylonian, ancient Hebrew).
Units of measurement grouped by physical quantities.
- Mass units (mass),
- Temperature units (temperature),
- Distance units (distance),
- Area units (area),
- Volume units (volume),
- Units of measurement of information (information),
- Time units (time),
- Pressure units (pressure),
- Heat flux units (heat flux).
