MATRIX NUMERIC ENCODING OF PHYSICAL REGULARITIES
MATRIX NUMERIC ENCODING OF PHYSICAL REGULARITIES
Е. Bessonov 4 Aug 2016
Abstract. The universal matrix is a numeric encoding of the physical laws and logical database codes, symbols and signs. Shows examples of the numerical coding of different formulas. The matrix allows for encoding and decoding physical and physical-chemical formula different structural complexity.
Аннотация. Предложены универсальная матрица числового кодирования физических закономерностей и логически выстроенная база кодов символов и знаков. Показаны примеры числового кодирования различных формул. Матрица позволяет производить кодирование и декодирование физических и физико-химических формул различной структурной сложности.
Keywords: database of symbols and signs; patterns; indices; coding; codes; matrix numeric coding; scientific catalog; physical formulas.
Ключевые слова: база символов и знаков; закономерности; индексы; кодирование; коды; матрица числового кодирования; научный каталог; физические формулы.
In this work a universal matrix for the numeric encoding of characters that make up the physical formula that allows you to automate the process of cataloging, search and identification of scientific information.
Statistical research – the collection, summary and analysis of the data conducted by the author on some of the fundamental sources on the subject [1, 2, 3] have established the principal characters and indices (tables 1, 2, 3), used in physics (including physical chemistry) when writing various types of formulas and determine the location (position), their structural location in these formulas.
The result of these studies was the development of the author of universal matrix numeric encoding and decoding formulas (Fig. 1), with the help of which it became possible to translate almost any physical formula into numeric form and Vice versa, from a numeric form to the traditional formula.
Fig. 1. Universal matrix numeric encoding and decoding physical formulas
{G} – physical group to which the formula; 1-20 positions, which are the symbols, indices or numbers (digits) constituting a separate block to be encoded (decoded) in the formula; r – index (team) repeating the encoding process (decoding) for the subsequent part of the formula at positions 1-20; z – index (team) transfer-encoding formula on a new line (for writing systems of equations or matrices); (D) the index of the footnote to address the dimension of patterns that can be identified on the table of the author [4], for a dimensionless physico-chemical formulas set index (d); [I] – index of information - General information on formula (name formula and source of information).
Some symbols and characters have a certain affiliation to the different positions of the formula. So, in position 1 have, primarily, a mathematical function and the first of the pair of characters (opening bracket of various types), the positions 8 and 10 alphabetic characters basic formulas, and 18, primarily, mathematical signs and the second of the pair of marks (closing parenthesis). Such a logic arrangement influenced the order of arrangement of symbols and signs in tables 1, 2 and 3 respectively on their assigned numeric codes. The logical order of the characters allowed us to optimize the encoding process by minimizing operations of the coding of formulas and cost reduction time encoding.
Examples of the numerical coding of formulas.
Example 1. The Avogadro Constant.
1.1. The traditional form of a record:
1.2. Coded entry values:
where, {II} is the group number of the physical quantity (physico-chemical, thermal and temperature values); upper values indicate the number of codes 95, 69 and 230, etc., which correspond to the symbols: N, A, =, etc. (tables 1, 2, 3), and the lower positions in which they are located (Fig. 1). Numeric value in parentheses (17-25) indicates coordinates of a table cell [4], in which the magnitude of NA and where are its dimension, where the numeral 17 indicates the line number and figure 25, a hyphen, the number of the table column.
Example 2. The formation of the polypeptide chain with a given sequence of amino acid residues.
2.1. The traditional form of the formula:
2.2. Coded entry of the formula:
where, {II} is the group number of the physical quantity (physico-chemical, thermal and temperature values); upper values indicate the number of codes 95, 83, 270, etc., which correspond to the symbols N, N+, etc. (tables 1, 2, 3), and the lower positions in which they are located (Fig. 1). The character enclosed in parentheses (d) indicates a lack of dimension formulas.
To simplify the encoding process some of the mathematical function and the values of formulas require entry in a modified form. So, the value under the radical sign mÖnk written as nk/m, and the exponential function e as exp.
Example 3. Structural scattering factor with indices h, k, l.
3.1. The traditional and the transformed form, of the formula:
3.1. Coded entry of the formula:
where, {III} is the group number of the physical quantity (light, acoustic, ionizing and nuclear size); upper values indicate the number of codes 79, 15, 84, etc., which correspond to the symbols: F, (, h, etc. (tables 1, 2, 3), and the lower positions in which they are located (Fig. 1). Numeric value in parentheses (32-25) indicates the coordinates of a table cell [4], in which the value of F and which indicates its dimension, where the number 32 is the number of rows and the number of 25 number of column of the table.
Examples 1-3 show that the coding of formulas perform consistently in position, observing the rule of ascending numeric values of the codes. That is, at one and the same position of the subsequent codes, in coding, must have a greater numerical value than the previous one. However, due to the large number of symbols and signs in the formula, this sequence can be observed only in coding some parts of it. Therefore, the matrix was introduced symbol – r command, which divides the formulas in the consecutive blocks, and returns the encoding process to the original position 1, that allows to observe the rule of ascending numeric values of the codes with further coding. To adhere to the rules of ascending numeric values is also required to automate the cataloging process, which will become possible after the translation of the numeric codes in the binary number system.
At the end of the coding formula are entered in the system directory coded physical laws (in this paper not shown).
The decoding formula contained in the directory, perform in reverse order, which also used a generic matrix (Fig. 1). There codes and item numbers contained in the database (tables 1, 2, 3) recognize symbols and signs and their structural arrangement and also step by step, by blocks, in cell positions 1 to 20, put all the necessary symbols and signs and get the traditional form of the formula.
The proposed method of numerical encoding of formulas with matrix in its properties is an analog of the well-known computer encoding OEM, ANSI and Unicode. However, it has to solve different scientific and technical task of systematization and cataloging of scientific knowledge. Therefore, unlike them, it is equipped with physico-mathematical symbols and signs with a special logical location in the database (tables 1, 2, 3), provided with the function of multi-level coding of formulas (systems of equations, matrices) and a systematic catalogue, which allows to encode and to store formulas of almost any complexity, and also to decode them and give them the old traditional form.
The matrix facilitates the process of encoding (decoding) of the physical laws that are described by complex formulas, and its principle of construction, features of the spatial design and the special logical formation of base codes symbols and characters that allow them to be used to create similar matrices for encoding mathematical and chemical formulas.
In tables 1-3 in a shortened version presented codes signs and symbols used in numerical coding of physical formulas.
Codes symbols characters and symbols
Table 1
|
Codes symbols characters and symbols |
|||||
|
Marking symbol |
The name of the symbol |
Сode |
Marking symbol |
The name of the symbol |
Сode |
|
1 |
arabic numerals
|
1 |
¶ |
partial derivative |
35 |
|
2 |
-«- |
2 |
det |
determinant |
36 |
|
… |
…. |
… |
… |
… |
…
|
|
log |
logarithm |
33 |
ℝ |
real numbers |
67 |
|
d |
derivative |
34 |
ℤ |
integers |
68 |
Codes symbols characters
Table 2
|
Codes symbols characters
|
|||||||
|
The name of the symbol |
Сode |
The name of the symbol |
Сode |
The name of the symbol |
Сode |
The name of the symbol |
Сode |
|
A |
69 |
u |
110 |
Y |
150 |
У |
190 |
|
a |
70 |
V |
111 |
y |
151 |
у |
191 |
|
… |
… |
… |
… |
… |
… |
… |
…
|
|
t |
108 |
Х |
148 |
Т |
188 |
ℤ |
228 |
|
U |
109 |
c |
149 |
т |
189 |
ħ |
229 |
Note. 154-228 codes are used to indicate letters of national alphabets and letters written in a special font (codes 212-228). In table 2 the Russian version codes 154-228.
Codes symbols mathematical signs and symbols
Table 3
|
Codes symbols mathematical signs and symbols:
|
|||||
|
Marking symbol |
The name of the symbol |
Сode |
Marking symbol |
The name of the symbol |
Сode |
|
= |
equal sign |
230 |
% |
interest |
294 |
|
· |
multiplier |
231 |
· |
a set of space-time variables |
295 |
|
… |
… |
… |
… |
… |
…
|
|
Ð |
angular |
292 |
®½ ½¬ |
the spacing of formulas |
356 |
|
| | |
absolute value, parallel |
293 |
``®½ ½¬ ®½ ½¬ |
the spacing between the columns formula |
357 |
List of references.
1. Физическая энциклопедия. Гл. редактор акад. А.М. Прохоров. Изд. «Российская энциклопедия». 1988-1999, том 1-5. Электронная версия «Физической энциклопедии». http://femto.com.ua/index1.html
2. I.Mills, T.Cvitas, K.Homann, N.Kallay, K.Kuchitsu. Quantities, Units and Symbols in Physical Chemistry.// Second edition. - (IUPAC).- Blackwell science. 1993.
3. В.Э. Фигурнов. IBM PC для пользователя. М.: ИНФРА-М, 1999.—480 с.
4. Е.А. Бессонов. Специализированная таблица многоуровневой системы СИ.cloud.mail.ru/public/ETNB/kvwdqnSxk