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2nd year student of the Faculty of Mathematics and Computer Science of Fergana State University
Ferghana State University, Uzbekistan
Annotation. Discrete mathematics, which is increasingly gaining popularity, has also been able to find its own application thanks to the introduction of new information sciences using the binary number system, both in the face of classical and quantum computer science. In this paper, the question of finding not only the indirect, but also the direct direct application of implication and equivalence operations known since the 60s of the XX century, the search for which has continued to the present time, is considered.
Keywords: discrete mathematics, implication, equivalence, direct application, practical application, technical understanding, electrical circuit.
Аннотация. Дискретная математика всё больше получающая популярность также смогла найти и собственное применение благодаря введению новых информационных наук с использованием двоичной системы счисления, как в лице классической, так и квантовой информатики. В данной работе рассмотрен вопрос относительно нахождения не только известного ещё с 60-х годов XX века косвенного, но и непосредственного прямого применения операций импликации и эквиваленции, поиск коих продолжался до настоящего времени.
Ключевые слова: дискретная математика, импликация, эквиваленция, прямое применение, практическое применение, техническое осмысление, электрическая схема.
At the moment, a variety of operations are actively used in discrete mathematics and logic to describe the conduct of actions on judgments. So the main operations are conjunction, disjunction and negation, so known as logical multiplication, logical addition and logical negation, respectively. They allowed us to operate on various judgments that accept the result either “true” – 1 or “false” – 0.
Each of the operations at the same time had its own truth table. For conjunction it is (Table 1), for disjunction – (Table 2) and logical negation – (Table 3).
At the same time, for the conjunction (logical “And”), a serial connection scheme takes place in the practical description (Fig. 1), described in the following cases:
1. If there is no current through “A” and through “B”, as a result there is no current;
2. If there is a current in “A”, but in the absence through “B”, as a result there is no current;
3. If there is no current in “A”, but in the presence of “B”, as a result there is no current;
4. If there is a current in “A” and in the presence of “B”, as a result, there is a current.
Fig. 1. Serial connection
For a disjunction (logical “OR”), a similar representation can be seen in the face of a parallel connection (Fig. 2), described already in the following cases:
1. If there is no current through “A” and through “B”, as a result there is no current;
2. If there is a current in “A”, but in the absence of through “B”, as a result, there is a current;
3. If there is no current in “A”, but in the presence of “B”, as a result, there is a current;
4. If there is a current in “A” and in the presence of “B”, as a result, there is a current.
Fig. 2. Parallel connection
For logical negation (logical “NOT”), everything is even simpler, because it can be represented as an ordinary reverse button (Fig. 3), describing the actions as follows:
1. If there is a current in “A”, as a result there is no current;
2. If there is no current in “A”, as a result, there is a current.
Fig. 3. “Button” – logical negation in the circuit
But along with these operations, there were also implication and equivalence operations, where implication is a logical consequence or statement “Follows from here”, and equivalence is logical equivalence and or the statement “Then and only then” had the following truth table (Table 4), and equivalence – (Table 5).
At the same time, both operations have not yet been applied in practice in direct form, as it looked for conjunction and disjunction. To date, the transformation is used for implication (1) and for equivalence (2).
That is, the implication can be represented as a negation of the first and a disjunction with the second statement, and the equivalence as a conjunction of the negations of both judgments on the disjunction of the conjunction of both judgments. If we check the truth of (1) and (2) on the table, then the result will be valid (Table 6—7).
And the methods presented were considered the only possible ones to this day, until finally an electric element was created, a kind of connection in which implication and equivalence would be performed in the direct case.
The first device, the implicator, consists of a vacuum flask 7 with a cathode 3 and an anode 1, between which an anode grid 2 is placed. The distance between the cathode and the anode l is verified with the accuracy that it is less than or equal to the free path of electrons that have flown from the cathode to the anode. There is also an isolated electrode 6, connected from the outside (behind the bulb) to the cathode pin 3, but not connected to it (Fig. 4).
Fig. 4. Implicature scheme
Thus, let the anode grid 2 act as the second statement, the cathode 3 as the first, and the anode 1 as the result. At the same time, a condition is introduced that before the current 4 arrives at the cathode 3, a divider 5 is supplied, which reacts to the magnitude of the incoming current, if the current is greater than or equal to a certain value taken as the truth of the first judgment, then it is connected to the cathode 3, otherwise to the electrode 6 coming out of the anode. In this case, the exception is the case when there is a current on the anode grid 2, while it is assumed that the current does not go to the cathode and to the cathode circuit at all.
So, in this scheme, we can consider four situations:
1. If there is no current at the cathode and there is no current on the anode grid, then the current flows through the electrode to the anode, as a result there is a current;
2. If there is current at the cathode, but there is no current on the anode grid, then the electrons reach the anode, as a result there is current;
3. If there is no current at the cathode, but there is no current on the anode grid, there are also no electrons in the bulb, which is why there is no current as a result;
4. If there is current at the cathode and there is current on the anode grid, then the electrons receive additional acceleration, which means that there is also current as a result.
This device, as you can see, although with a couple of conventions, which can be completely replaced by reducing elements, a kind of sensors or switches, fully performs the function of implication. But it is also interesting to mention here that neither conjunction nor disjunction was used, nor even negation, unless of course the “switch” is considered an extremely distant relative of negation, which would be inappropriate. Moreover, this system acts as a single element that fully fulfills the task.
Speaking of this type of connection, it should be called a “close mixed” connection, or a “Promichtovoe” connection, from the Latin prore – “close” and mixta – “mixed”, since both parallel and serial connection are involved here, but more figuratively, because of which this connection acts new – the third kind.
The situation with equivalence is similar, but the difference is that the distance between the cathode 3 and the anode 1 – L (for the equivalentor) must be strictly greater than the electron path length so that they cannot reach it without the help of an anode grid, which, however, explains why the implicator is connected “close-mixed” connection. When using the same equivalentor (Fig. 5) – a device that performs the function of equivalence, there are also 4 cases:
1. If there is no current at the cathode and there is no current on the anode grid, then the current flows through the electrode to the anode, as a result there is a current;
2. If there is current at the cathode, but there is no current on the anode grid, then the electrons do not reach the anode, as a result there is no current;
3. If there is no current at the cathode, but there is no current on the anode grid, there are also no electrons in the bulb, which is why there is no current as a result;
4. If there is a current at the cathode and there is a current on the anode grid, then the electrons receive additional acceleration, which means that there is a current as a result.
Fig. 5. The scheme is equivalent to
The equivalentor is similarly connected by the type of connection in this case by a “far-mixed” or “Longmichth” connection, from the Latin longe – “far away” and mixta – “mixed”.
Thus, it is possible to demonstrate two elements – an implicator and an equivalentor that fully perform the functions of implication and equivalence in modern electronics, finding perfect application, allowing to reduce space at times, because these circuits can be made in an arbitrarily small size, along with replacing the “diode-lamp” part with the presence of vacuum with modern triodes with the usual additional switchable connection for the implicator and more upgraded triodes with the same switches and connection for the equivalentator.
Presenting this scheme, we can hope that it will bring its benefits, contributing to the development of modern science and technology, improving and bringing new things to science, as well as opening up new even more grandiose horizons to the entire human civilization!
Used literature
1. Mendelson E. “Introduction to mathematical logic”. – M. Nauka, 1971.
2. Edelman S. L. Mathematical logic. – M.: Higher School, 1975. – 176 p.
3. Igoshin V. I. Taskbook-practical course in mathematical logic. – M.: Enlightenment, 1986. – 158 p.
4. Gindikin S. G. Algebra of logic in problems. – M.: Nauka, 1972. – 288 p
.5. Barabanov O. O. Implication / Proceedings of the XI International Kolmogorov readings: collection of articles. – Yaroslavl: YAGPU Publishing House, 2013. pp.49—53.
INFORMATION TECHNOLOGY
A WAY TO PROTECT INFORMATION FROM UNAUTHORIZED ACCESS TO THE VOLS
UDC 004.056
Kuldashov Obozjon Khakimovich
Doctor of Technical Sciences, Professor of the Scientific Research Institute “Physics of Semiconductors and Microelectronics” at the National University of Uzbekistan
Komilov Abdullazhon Odiljon ugli
Assistant of the Fergana branch of the Tashkent University of Information Technologies named after Muhammad al-Khorezmi
Ferghana branch of Tashkent University of Information Technologies named after Muhammad al-Khorezmi
Annotation. The article proposes a method for protecting an information signal from unauthorized access in a fiber-optic communication line, provides a block diagram and the principle of operation of the device.
Keywords: fiber-optic line, communication, information signal, protection method, device, block diagram.
Аннотация. В статье предложен способ защиты информационного сигнала от несанкционированного доступа в волоконно-оптической линии связи, приведена блок схема и принцип работы устройства.
Ключевые слова: волоконно-оптическая линия, связь, информационный сигнал, способ защиты, устройство, блок схема.
In recent years, one of the most promising and developing areas of building a communication network in the world is the VOLS.
The priority direction of the development of the transport network of Uzbekistan is the transfer of the network to the widespread use of fiber optic networks with digital transmission systems.
This made it possible to organize reliable high-quality communication not only between the “telephone continents”, but also communication on the National Telecommunications Network of Uzbekistan. The realization of this task has become possible since 1997 after the completion of the construction and commissioning of the national segment of TAE – a large-scale international project “Trans-Asian-European VOLS”.
In 2011, the task was to ensure the development and modernization of the telecommunications network based on the introduction of modern broadband and optical technologies, the introduction of over 950 kilometers of fiber optic lines, the expansion of the data transmission transport network to regional centers.
Throughout the country, at the level of district centers, obsolete analog telephone exchanges have been replaced with modern digital ones. High-speed digital channels have been created on the basis of the VOLS, work is underway to expand the network and improve its reliability. The created infrastructure serves as the basis for the rapid development of wireless technologies, in particular, mobile communications. As a result, the level of coverage by the digital telecommunications network of regions, district centers and cities of the Republic amounted to 100 percent, the level of coverage by the telecommunications network of rural settlements – 95.7 percent.
In 1999—2000, at the expense of the funds of the Cooperation Fund for Economic Development of the Republic of Korea (EDCF), technical re-equipment and development of the telecommunications network in the Andijan and Ferghana regions were carried out, a 354 km long fiber-optic line was built, switching equipment with a capacity of 46 thousand numbers was installed.
The widespread use of fiber-optic telecommunication systems in communication networks is due to a number of their advantages in comparison with electrically cable communication systems.
Based on this, the following main advantages of a fiber-optic line can be distinguished in comparison with electric cable communication systems:
– huge bandwidth with transmission speeds of up to 40 Gbit/s, operating today, and over 100 Gbit/s, expected in the near future. The factors limiting the growth of transmission rates are currently the inertial properties of receivers and radiation sources. However, the use of the spectral compaction method (WDM, wave division multiplexing) increases the total transmission rate over a single fiber to several Departures/s;
– fiber optic cables are completely unaffected by electromagnetic interference, lightning and high voltage surges. They do not create any electromagnetic or radio frequency interference;
– ensuring complete galvanic isolation between the receiver and the information transmitter, as well as the absence of a short circuit in the transmission line;
– the distance of information transmission for low-cost fiber-optic cables between repeaters is up to 5 km. For high-quality commercial systems, the distance between repeaters is up to 300 km. Distances close to 1000 km have been achieved under laboratory conditions;
– the size and weight of fiber optic cables compared to all other data cables are very small in diameter and extremely light. A four-core fiber optic cable weighs approximately 240 kg/km, and a 36-core fiber optic cable weighs only 3 kg more.
From the above it follows that the VOLS meet all the requirements of modern telecommunication communication systems. In this regard, many experts in telecommunications technologies argue that the VOLS will become the main means of transmitting information in the future. However, with the growth of the use of fiber-optic information transmission lines in telecommunication systems and their development, technical information intelligence systems are also developing, with the help of which information is secretly taken from the VOLS.
All over the world, great attention is paid to ensuring information security – the state of security of the information environment of society, ensuring its formation, use and development in the interests of citizens, organizations, and the state.
Therefore, the development of effective methods and technical means for the protection of information in the VOLS is one of the urgent tasks.
Structural, mechanical and electrical technical means are usually used to protect information in the VOLS. Some of the types of protective equipment of this group are built in such a way as to complicate the mechanical cutting of the cable and prevent access to the S [1]. Similar means of protection are widely used in traditional wired networks of special communication. Also promising is the use of a pair of longitudinal power elements of the OK, which are two steel wires arranged symmetrically in a polyethylene shell, and used for remote power supply and monitoring of sensors installed in the couplings, and monitoring of ND. It is also advisable to use a kit to protect the welding site, which fills the welding site with an opaque solidifying gel. One of the proposed methods of protection is the use of multilayer optical fiber with a special structure of reflective and protective shells [2]. The construction of such a fiber is a multilayer structure with a single-mode core. The selected ratio of the refractive coefficients of the layers makes it possible to transmit a multimode control noise optical signal along the annular guide layer. There is no connection between the control and information optical signals in the normal state. Ring protection also makes it possible to reduce the level of radiation of an information optical signal through the side surface of the S (by means of leakage modes arising at the bends of the fiber of various sections of the communication line). Attempts to penetrate to the core are detected by changing the level of the control (noise) signal or by mixing it with the information signal. The location of the ND is determined with high accuracy using a reflectometer.
Many works are devoted to methods and means of information protection in the VOLS, including in [3] to protect information, the magnitude of the inhomogeneity of electromagnetic radiation propagation through a cable in the radio frequency range is controlled, which is introduced into a waveguide channel with a constant length of wave resistance, made in the form of an electrically conductive shell covering at least one electronic conductor, located along the fibers, and the presence of unauthorized access to the information transmitted through the fibers is judged by the change in the magnitude of the inhomogeneity of the propagation of electromagnetic radiation in the radio frequency range. The protection system contains a combined cable and a lock for changing the parameters of the propagation of electromagnetic radiation of the radio frequency range connected to an electronic conductor.
A method of protecting information from unauthorized access in fiber-optic communication lines is proposed and can be used in fiber-optic systems for transmitting confidential information.
Figure 1 shows a block diagram of a device implementing the proposed method of protecting an information signal from unauthorized access in a fiber-optic communication line. A device implementing the proposed method of protecting an information signal from unauthorized access in a fiber-optic communication line contains: on the transmitting side 1, an information signal generator 2, a mixer 3, a source 4 of transmitted optical radiation, a noise signal photodetector 5, a directional coupler 6 with inputs 6—2 and output 6—1, a fiber-optic communication line 7, on the receiving 8 side there is a directional 9 coupler with inputs 9—1 and output 9—2, a total signal photodetector 10, a mixer 11, delay lines 12, an inverse noise signal shaper 13, source 14 of noise optical radiation and generator 15 of noise signal.
When implementing the proposed method of protecting the information signal from unauthorized access in the fiber-optic communication line, the following operations are performed:
– on the receiving side 8 of the fiber-optic communication line 7:
1) generate a noise signal using the generator 15,
2) an inverse noise signal is generated using the inverter 13,
3) using the delay line 12, delays of the inverse noise signal are produced for a time,
4) modulate the transmitted optical noise radiation in the optical radiation source 14 with a noise signal,
5) the transmitted noise optical radiation is introduced through the input 9—1 of the directional coupler 9, into the fiber-optic communication line 7,
– on the transmitting side 1 of the fiber-optic communication line 7:
1) form the transmitted information signal using the shaper 2,
2) output through the output 6—1 of the directional coupler 6, from the fiber-optic communication line
7 of the received optical noise radiation,
3) a noise signal is generated from the received optical noise radiation using a photodetector 5,
4) form a total signal by mixing an information and noise signal using a mixer 3,
5) modulate the transmitted optical radiation in the source 4 of the transmitted optical radiation with a total signal,
6) the transmitted optical radiation is introduced through the input 6—2 of the directional coupler 6, into the fiber-optic communication line 7,
