Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій
This paper is devoted to the memory of Solomon Wolf Golomb (1932–2016) — a famous American mathematician, engineer, and professor of electrical engineering. He was interested in developing techniques for improving the quality indices of engineering devices and systems with respect to performance rel...
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2023
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System research and information technologies| _version_ | 1866391923897401344 |
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| author | Riznyk, Volodymyr |
| author_facet | Riznyk, Volodymyr |
| author_sort | Riznyk, Volodymyr |
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| description | This paper is devoted to the memory of Solomon Wolf Golomb (1932–2016) — a famous American mathematician, engineer, and professor of electrical engineering. He was interested in developing techniques for improving the quality indices of engineering devices and systems with respect to performance reliability, transmission speed, positioning precision, and resolving ability based on novel combinatorial configurations. In 1996 S. Golomb have supported the project “Researches and Applications of the Combinatorial Configurations for Innovative Devices and Process Engineering” as a scientific collaboration with the Former Soviet Union (FSU) research team from Lviv Polytechnic State University (Ukraine) under the Cooperative Grant Program by CRDF (U.S.). The underlying project to be edited by S. Golomb is presented, and short information on the development of the researches and applications of optimized systems with ring structure given. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2023.1.09 |
| first_indexed | 2025-07-17T10:27:56Z |
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V.V. Riznyk, 2023
Системні дослідження та інформаційні технології, 2023, № 1 113
UDC 621.396:519.15
DOI: 10.20535/SRIT.2308-8893.2023.1.09
RESEARCHES AND APPLICATIONS OF THE COMBINATORIAL
CONFIGURATIONS FOR INNOVATIVE DEVICES AND
PROCESS ENGINEERING1
V.V. RIZNYK
Abstract. This paper is devoted to the memory of Solomon Wolf Golomb (1932–
2016) — a famous American mathematician, engineer, and professor of electrical
engineering. He was interested in developing
techniques for improving the quality
indices of engineering devices and
systems with respect to performance
reliability, transmission speed, positioning
precision, and resolving ability based on
novel combinatorial configurations. In 1996
S. Golomb have supported the project “Re-
searches and Applications of the
Combinatorial Configurations for
Innovative Devices and Process
Engineering” as a scientific collaboration
with the Former Soviet Union (FSU)
research team from Lviv Polytechnic State
University (Ukraine) under the Cooperative
Grant Program by CRDF (U.S.). The underlying project to be edited by S. Golomb
is presented, and short information on the development of the researches and appli-
cations of optimized systems with ring structure given.
Keywords: project, combinatorial configuration, Ideal Ring Bundle, optimization,
model, scientific school.
INTRODUCTION
Solomon Wolf Golomb was a world-famous American scientist, specialist in the
field of telecommunications, digital electronics, cellular automata and informa-
tion theory. He was a world leader in the application of combinatorial mathe-
matics in coding theory and radiophysics. Golomb was the inventor of Golomb
coding, a form of entropy coding, the Golomb rulers used in astronomy and data
encryption, also named after him, as was one of the main methods for generating
Costas arrays, the Lempel–Golomb generation method.
S. Golomb developed the idea of using the advantages of multi-bit shift reg-
isters with a balanced number of 0 and 1, or 00, 01, 10, 11, revealing in them the
absence of autocorrelation, which made it possible to improve encoding systems –
1This material is based upon project of the Lviv State Polytechnic University (Ukraine) to
cooperate with the University of Southern California under of the U.S. Civilian Research
& Development Foundation (CRDF): Researches and Applications of the Combinatorial
Configurations for Innovative Devices and Process Engineering // CRDF Cooperative
Grants Program, Los Angeles, CA 90089-2565, US, March 5, 1996, 10 p.
V.V. Riznyk
ISSN 1681–6048 System Research & Information Technologies, 2023, № 1 114
decoding signals with correction of errors using sequences generated by shift
registers. S. Golomb used versions of these sequences (Reed-Solomon codes) to
encode video images of Mars, in CDMA cell phones (Codé Division Multiple
Access) with multiple access and code separation of communication channels. In
1956, he joined Glenn L. Martin Company, which later became a defense contrac-
tor [1]. This explains all his further scientific activities under conditions of strict
secrecy, developing military and space communications. Continuing to study se-
quences on shift registers to improve radio control systems for missiles,
S. Golomb with the help of the 85-foot Golstone radio antenna located in the Mo-
jave Desert, specified data on the distances Earth – Venus and the Earth – the
Sun. The sequences generated by the sequence shift registers made it possible to
clarify the distance to Venus using a radar system. In 1985, Golomb received the
Shannon Prize of the IEEE Society of Information Theory, and later the Medal of
the U.S. National Security Agency. He was also the winner of the Lomonosov
Medal of the Russian Academy of Sciences and the Kapitsa Medal of the Russian
Academy of Natural Sciences. In 2000, Golomb was awarded the Richard
W. Hemming IEEE Medal for his exceptional contributions to information sci-
ence and systems engineering. In 2016, he was awarded the Benjamin Franklin
Medal in Electrical Engineering for his pioneering work in space communications
and digital signal processing, secure data forwarding, improving methods for de-
ciphering cryptographic texts, rocket guidance systems, cellular communications,
radars, sonar, GPS [1].
In 1996, S. Golomb have supported the proposal of the Lviv State Polytech-
nic University (Ukraine) to cooperate with the University of Southern California
on the project “Researches and Applications of the Combinatorial Configurations
for Innovative Devices and Process Engineering”, which was sent to the U.S. Ci-
vilian Research & Development Foundation (CRDF). This non-profit organiza-
tion was founded in 1995 by the National Science Foundation of the United States
in accordance with the decision of the U.S. Congress in order to promote interna-
tional scientific and technical cooperation with the provision of grants, technical
resources, training for scientists and researchers. S. Golomb has edited the text of
the project, motivating the advantages of the proposed combinatorial configura-
tions with a ring topological structure over chain sequences.
NARRATIVE PROJECT
Research and Applications of Combinatorial Configurations for Innovative
Devices and Process Engineering
The objectives of the proposed project are as follows:
1. Research into the underlying mathematical principles relating to the opti-
mal placement of structural elements in spatially or temporally distributed sys-
tems, including the appropriate algebraic constructions based on cyclic groups in
extensions of Galois field; development of the scientific basis for technologically
optimum distributed systems theory; and the generalization of these methods and
results to the improvement and optimization of a larger class of technological sys-
tems.
2. Experimental verification of the effectiveness of this new methodology, as
it affects the whole range of new high-performance devices, systems, or technolo-
Researches and applications of the combinatorial configurations for innovative devices …
Системні дослідження та інформаційні технології, 2023, № 1 115
gies to which it can be applied, including applications to coded design of signals
for communications and radar, positioning of elements in an antenna array, and
other areas to which the mathematical apparatus of contemporary combinatorial
theory can be applied.
Expected results of the completed project:
1. Mathematical results – development of new algebraic results and tech-
niques, based on the idea of “perfect” combinatorial constructions, and expanding
the applicability of cyclic group relationships in Galois fields, and a variety of
results in number theory.
2. Physical results – a better understanding of the role of geometric structure
in the behavior of natural and man-made objects.
3. Technological results – the development of new directions in fundamental
and applied research in systems engineering, for improving such quality indices
as reliability, precision, speed, resolving ability, and functionality, using innova-
tive methodologies based on combinatorial techniques, with direct applications to
radio- and electronic engineering, radio astronomy, applied physics, and other
engineering areas.
“Ideal Ordered Chain” Combinatorial Constructions. The “ordered
chain” approach to the study of elements and events is known to be of widespread
applicability, and has been extremely effective when applied to the problem of
finding the optimum ordered arrangement of structural elements in a distributed
technological system.
Sums on ordered-chain numbers. Let us calculate all nS sums of the terms
in the numerical n-stage chain sequence of distinct positive integers
1 2{ , , , }n nC K K K , where we require all terms in each sum to be consecutive
elements of the sequence. Clearly the maximum such sum is the sum
1 2 nK K K T of all n elements; and the maximum number of distinct
sums is
1 2 ( 1) / 2nS n n n . (1)
If we regard the chain sequence nC as being cyclic, so that nK is followed
by 1K , we call this a ring sequence. A sum of consecutive terms in the ring se-
quence can have any of the n terms as its starting point, and can be of any length
(number of terms) from 1 to 1n . In addition, there is the sum T of all n
terms, which is the same independent of the starting point. Hence the maximum
number of distinct sums ( )S n of consecutive terms of the ring sequence is
given by
( ) ( 1) 1S n n n . (2)
Comparing the equations (1) and (2), we see that the number of sums ( )S n
for consecutive terms in the ring topology is nearly double the number of sums
nS in the daisy-chain topology, for the same sequence nC of n terms.
Ideal Numerical Rings. An n-stage ring sequence 1 2{ , , , }n nC K K K of
natural numbers for which the set of all ( )S n circular sums consists of the num-
bers from 1 to ( ) ( 1) 1S n n n (each number occurring exactly once) is called
V.V. Riznyk
ISSN 1681–6048 System Research & Information Technologies, 2023, № 1 116
an “Ideal Numerical Ring” (INR). Here is an example of an IRN with n=5 and
( ) 21S n , namely {1,3,10,2,5}. To see this, we observe:
1 1 6 5 1 11 2 5 1 3 16 1 3 10 2
2 2 7 2 5 12 10 2 17 10 2 5
3 3 8 2 5 1 13 3 10 18 10 2 5 1
4 1 3 9 5 1 3 14 1 3 10 19 5 1 3 10
5 5 10 10 15 3 10 2 20 3 10 2 5
21 1 3 10 2 5
Note that if we allow summing over more than one complete revolution
around the ring, we can obtain all positive integers as such sums. Thus:
22 1 3 10 2 5 1 , 23 2 5 1 3 10 2 , etc.
Next, we consider a more general type of INR, where the ( )S n ring-sums of
consecutive terms give us each integer value from 1 to M , for some integer M ,
exactly R times, as well as the value of 1M (the sum of all n numbers) exactly
once. Here we see that:
( 1) /M n n R .
An example with 4n and 2R , so that 6M , is the ring sequence (1, 1,
2, 3), for which the sums of consecutive terms are:
1, 1, 2, 3;
1 1 2, 1 2 3, 2 3 5, 3 1 4,
1 1 2 4, 1 2 3 6, 2 3 1 6, 3 1 1 5,
1 1 2 3 7.
We see that each “circular sum” from 1 to 6 occurs exactly twice ( 2)R .
We say that this INR has the parameters 4n , 2R .
The individual competence of the FSU research team:
1. Theoretical research on the ideal configurations named Ideal Numerical
Bundles (INB), in particular, Ideal Numerical Rings (INR), as modifications of
certain combinatorial block-designs (existence, enumeration, classification).
2. Cyclic difference sets and some properties of Galois Field cyclic groups.
3. Construction of BIB designs, using INRs and Golomb rulers, and the re-
verse.
4. Software for construction of BIB designs using INRs.
5. Compiling a general catalogue of INRs and Golomb rulers.
6. Circuit design for the high performance technology of information coding
and modulation.
7. Applied research and engineering design of concrete innovative devices
and technologies based on combinatorial theory.
8. INBs and some problems of harmony and optimization of systems.
The individual competence of the US research team:
1. Theoretical research on Golomb rulers and their relationships with differ-
ence (existence, enumeration, classification).
2. Construction of difference sets and Golomb rulers.
3. Compiling a general catalogue Golomb rulers.
Researches and applications of the combinatorial configurations for innovative devices …
Системні дослідження та інформаційні технології, 2023, № 1 117
4. Circuit design of high performance technology for coding of information
and the design of communication signals.
5. Applied research and engineering design of innovative devices and tech-
nologies based on combinatorial theory.
6. Using combinatorial designs to obtain sequences with favorable correla-
tion properties.
For carrying out the project, it is necessary to combine the achievements of
Golomb ruler theory (US) and possibilities of Ideal Bundles theory (FSU) for ex-
tending the sphere of practical applications, with the aim of obtaining commercial
products.
The FSU team developed the basis of the bundles theory as a new modifica-
tion of combinatorial configurations on graphs involving Golomb ruler theory and
proposed a new approach to the synthesis of technical devices and to engineering
technology.
The US team developed the basis of Golomb ruler theory and proposed areas
of their possible applications.
Equipment: 1) PC TSDX-4-120 540M, SVGA 0.28 LR NI 1M, 1, 2+1, 44;
2) Printer EPSON Stylus 800; 3) Telecommunications Services: Scanner
HEWLETT PACKARD Jet-555, Fax-modem US Robotics Sportster; 4) Writing
materials, floppy disk.
The FSU and U.S. co-investigators the project implementation and assess
progress ar regular intervals (monthly) by using Fax and E-mail.
PLANNED STEPS
Title of stages Stage duration Anticipated results
Theoretical research on Ideal
Numerical Rings (INR)
6 mos
Conditions of INR existence
will be determined
Research of properties of extended
Galois Field cyclic groups
6 mos
Patterns in the distribution
of cyclic group elements
will be established
Construction of INRs and Ideal
numbere ring configurations
6 mos Catalog of INRs
Applied research and engineering de-
sign of specific innovative
devices and technologies
6 mos
Creation of concrete
innovative devices and tech-
nologies
CONCLUSION
The Ideal Numerical Bundles (INB)s provide, essentially, a new conceptual model
of technical systems. Moreover, the optimization has been embedded in the un-
derlying combinatorial models. The remarkable properties and structural perfec-
tion of one- and multidimensional INBs provide an ability to reproduce the
maximum number of combinatorial varieties in the systems with a limited number
of elements and bonds. The favorable qualities of the combinatorial structures
provide many opportunities to apply them to numerous branches of science and
advanced technology. A perfection, beauty and harmony exist not only in the ab-
stract models but in the real world also.
V.V. Riznyk
ISSN 1681–6048 System Research & Information Technologies, 2023, № 1 118
Here is the print of the cover page of the project, worded by S. Golomb.
Note, S. Golomb personally signed the date of his birthday 31.05.1932 (not
30.05.1932, as indicated in the Wikipedia [1]).
AFTERWORD
In mathematics, a Golomb ruler is a set of marks at integer positions along a ruler
such that no two pairs of marks are the same distance apart. The Golomb ruler
was named for Solomon W. Golomb. There is no requirement that a Golomb rul-
er be able to measure all distances up to its length, but if it does, it is called
Researches and applications of the combinatorial configurations for innovative devices …
Системні дослідження та інформаційні технології, 2023, № 1 119
a perfect Golomb ruler. It has been proved that no perfect Golomb ruler exists for
five or more marks [2]. Unlike of them, an infinite quantity of one- and multidi-
mensional IRBs exist, and the more long is an n-stage of IRB, the more invariants
we can see by a majority. For example, the two variants of one-dimensional IRBs
{1,3,10,2,5} and {1,1,2,3,4} exist for 5n [3], while exactly the 1717 ones with
1R for 102n [4, p.163]. Of very interest are two-dimensional IRBs, which
properties hold for the same set of the rings in varieties permutations of terms in
the set, e.g. set of two-dimensional five-stages ( 5n ) ring sequences
{(1,1),(1,0),(1,4),(1,3),(1,2)} and {(1,1),(1,3),(1,0),(1,2), (1,4)}, called “Gloria to
Ukraine Stars” [5]. Examples of two paired pentagonal (n=5) such IRBs shown
below.
It is shown that the star{(1,1), (1,3), (3,3), (0,3),(2,3)} to be marked with
dash edges, and the {(1,1), (2,3), (1,3), (0,3), (3,3)} – solid ones is the paired star
(the outside star). The star {(1,1), (1,4), (1,2), (1,0), (1,3)} marked with dash
edges, аnd the star {(1,1), (1,0), (1,4), (1,3), (1,2)} – solid ones is paired star also
(the inner star). We have found numerous families of the two- and multidimen-
sional stars, originated from the remarkable geometric properties and creative
harmony of the real word [6].
S. Golomb’s aptitude allowed him to see in the proposed project not only the
“ideal ordered chain” combinatorial configurations but also the “ideal rings”,
which provide novel opportunities for the development of a new direction of fun-
damental and applied research in systems engineering with the direct use of one-
and multidimensional combinatorial configurations of ring topology in radio elec-
tronics, communication, and numerous fields of advanced technologies. He not
only approved our project, but also edited and substantiated the prospects for the
implementation and further development of fundamental and applied research of
combinatorial structures with ring topology, placing the right emphasis on the
advantages of the latter over systems with a chain structure. Our collaboration
was started in August 1996 from the report “Combinatorial Sequencing Theory
for Optimisation of Signal Data Vectors Converting and Signal Processing” [7].
However, shortly we have got refusal letters from the CRDF in financial support-
ing the project.
(1,4)
(1,1)
(1,3)
(1,2)
(1,1)
(1,3)
(3,3)(0,3)
(2,3)
Two paired pentagonal (n=5) “Gloria to Ukraine Stars”
V.V. Riznyk
ISSN 1681–6048 System Research & Information Technologies, 2023, № 1 120
Brief data on the scientific school of combinatorics at the Lviv Polytechnic
National University
The scientific school of сombinatorics at Lviv Polytechnic National University
became known due to the fundamental and applied research of the “intelligent”
two- and multidimensional combinatorial configurations prospected from the real
world law of “elegant” deviding rotational symmetry into two complementary
asymmetric parts. Each of them is an IRB with appropriate information parame-
ters which being interrelated by this symmetry [6]. Design of systems with the
“ideal” ring structures originated from solution of the engineering problem for
expanding the range of time delays in transient analyzer on capacitor storage for
researching dynamic processes in power electric stations on analog computers in
1968. One of the first publications for the perfect rings is connected with design-
ing optimized memory devices [8]. The mathematical problem was to fix four
switches on a moving rotor with different relative angular shifts of the ring
switch, with the possibility of obtaining the widest possible range of time delays
on a set of combination options for selecting the corresponding pair of swithes,
one of them should bring the flowing voltage value to the memorizing element,
and the second – to read the same value with a delay in time after turning the rotor
of the switch to the appropriate angle [9]. Currently, we have a lot of patents,
based on the idea of “perfect” one- and multidimensional IRBs.
The remarkable properties both optimal Golomb rulers and IRBs discover
many opportunities to apply them to numerous branches of science and advanced
technology, including vector information technologies and communications, vec-
tor data coding and multidimensional signal processing. These properties embed-
ded in the laws of real world penetrating rotational symmetry.
ACKNOWLEDGMENTS
Honoring the memory about the outstanding American scientist S. Golomb, the
research group “Vector Data Informatics” of Lviv Polytechnic National Univer-
sity expresses gratitude to all those who contributed to the development of scien-
tific cooperation between California and Lviv Universities in the field of research
and applications of combinatorial optimization methodology for information and
telecommunication technologies. I grateful also to my colleagues from Automated
Control Systems Department of Lviv Polytechnic National University for their
active participation in the R&S project “Designing Software for Vector Data Pro-
cessing and Information Protection Based on Combinatorial Optimization”, (No
state registration 0113U001360).
REFERENCES
1. Solomon W. Golomb. [Online]. Available: https://en.wikipedia.org/wiki/
2. Golomb_ruler. [Online]. Available: https://en.wikipedia.org/wiki/Golomb_ruler
3. Ideal ring bundl. [Online]. Available: https://uk.wikipedia.org/wiki/Iдеальна_
кільцева_в’язанка
4. V. Riznyk, Synthesis of Optimal Combinatorial Systems. Lviv: High School, 1989,
168 p.
5. V.V. Riznyk, “Information Technologies under the Manifold Coordinate Systems,”
Perspective trajectory of scientific research in technical sciences: Collective
Researches and applications of the combinatorial configurations for innovative devices …
Системні дослідження та інформаційні технології, 2023, № 1 121
monograph. Riga, Latvia: “Baltija Publishing”, pp. 521–538, 2021. Available:
https://doi.org/10.30525/978-9934-26-085-8-22
6. V. Riznyk, “Multi-modular Optimum Coding Systems Based on Remarkable Geo-
metric Properties of Space,” Advances in Intelligent Systems and Computing, no.
512, pp. 129–148, 2017. doi: 10.1007/978—319-45991-2_9.
7. S. Golomb, P. Osmera, and V. Riznyk, “Combinatorial Sequencing Theory for Op-
timisation of Signal Data Vectors Converting and Signal Processing,” Proc. All-
European Workshop on Design Methodologies for Signal Processing, Zakopane, Po-
land, 1996, pp. 43–44.
8. V.V. Riznyk, “Ideal Ring Relations and Possibilities of Their Practical Application,”
Avtomatika, no. 3, pp. 87–90, 1981.
9. Certificate of authorship USSR № 527725 (1976), G 08 C9/06.
Received 13.09.2022
INFORMATION ON THE ARTICLE
Volodymyr V. Riznyk, ORCID: 0000-0002-3880-4595, Institute of Computer Sciences
and Information Technologies, Lviv Polytechnic National University, Ukraine, e-mail:
ikv.riznyk@gmail.com
ДОСЛІДЖЕННЯ ТА ЗАСТОСУВАННЯ КОМБІНАТОРНИХ КОНФІГУРА-
ЦІЙ ДЛЯ ІННОВАЦІЙНИХ ПРИСТРОЇВ І ТЕХНОЛОГІЙ / В.В. Різник
Анотація. Присвячено пам’яті Соломона Вольфа Ґоломба (1932–2016) — ві-
домого американського математика, інженера, професора електротехніки, який
зробив значний внесок у розвиток теорії лінійних регістрів зсуву і комбінатор-
ної математики в теорії кодування та радіофізиці. Він цікавився розробленням
методів підвищення якісних показників інженерних пристроїв і систем з погляду
надійності, швидкості передавання, точності позиціонування і роздільної здат-
ності на основі нових комбінаторних конфігурацій. У 1996 р. С. Ґоломб під-
тримав проєкт “Дослідження та застосування комбінаторних конфігурацій для
інноваційних пристроїв та технологій” як наукову співпрацю дослідницької
групи Державного університету «Львівська політехніка» (Україна) і Південно-
каліфорнійського університету за спільною грантовою програмою Фонду ци-
вільних досліджень та розвитку (США). Подано основний проєкт під редакці-
єю С. Голомба, а також коротку інформацію про розвиток досліджень та
застосування оптимізованих систем з кільцевою структурою.
Ключові слова: проєкт, комбінаторна конфігурація, ідеальна кільцева
в’язанка, оптимізація, комбінаторна модель, наукова школа.
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| institution | System research and information technologies |
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| language | English |
| last_indexed | 2025-07-17T10:27:56Z |
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| spelling | journaliasakpiua-article-2639892023-05-24T21:28:17Z Researches and applications of the combinatorial configurations for innovative devices and process engineering ИССЛЕДОВАНИЯ И ПРИМЕНЕНИЕ КОМБИНАТОРНЫХ КОНФИГУРАЦИЙ ДЛЯ ИННОВАЦИОННЫХ УСТРОЙСТВ И ТЕХНОЛОГИЙ Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій Riznyk, Volodymyr проєкт комбінаторна конфігурація ідеальна кільцева в’язанка оптимізація комбінаторна модель наукова школа project combinatorial configuration Ideal Ring Bundle optimization model scientific school This paper is devoted to the memory of Solomon Wolf Golomb (1932–2016) — a famous American mathematician, engineer, and professor of electrical engineering. He was interested in developing techniques for improving the quality indices of engineering devices and systems with respect to performance reliability, transmission speed, positioning precision, and resolving ability based on novel combinatorial configurations. In 1996 S. Golomb have supported the project “Researches and Applications of the Combinatorial Configurations for Innovative Devices and Process Engineering” as a scientific collaboration with the Former Soviet Union (FSU) research team from Lviv Polytechnic State University (Ukraine) under the Cooperative Grant Program by CRDF (U.S.). The underlying project to be edited by S. Golomb is presented, and short information on the development of the researches and applications of optimized systems with ring structure given. Статья посвящена памяти Соломона Вольфа Голомба (1932-2016) - известного американского математика, инженера, профессора электротехники, который сделал весомый вклад в развитие теории линейных регистров сдвига и комбинаторной математики в теории кодирования и радиофизики. Он интересовался  розработкой методов повышения качественных показателей инженерных устройств и систем по надежности, скорости передачи, точности позиціонирования и разделительной способности на основе новых комбинаторных конфигураций. В 1996 г. С. Голомб поддержал проект «Исследования и применение комбинаторных конфигураций для инновационных устройств и технологий» как научное отрудничество Государственного университета «Львівська політехніка» (Украина) с Южнокалифорнийским университетом по совместной грантовой программе Фонда гражданських исследований и развития (США). Представлен основной проект под редакцией С.Голомба и подано краткую  информацию о розвитии исследований и применении оптимизированных систем с кольцевой структурой. Присвячено пам’яті Соломона Вольфа Ґоломба (1932–2016) — відомого американського математика, інженера, професора електротехніки, який зробив значний внесок у розвиток теорії лінійних регістрів зсуву і комбінаторної математики в теорії кодування та радіофізиці. Він цікавився розробленням методів підвищення якісних показників інженерних пристроїв і систем з погляду надійності, швидкості передавання, точності позиціонування і роздільної здатності на основі нових комбінаторних конфігурацій. У 1996 р. С. Ґоломб підтримав проєкт “Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв та технологій” як наукову співпрацю дослідницької групи Державного університету «Львівська політехніка» (Україна) і Південнокаліфорнійського університету за спільною грантовою програмою Фонду цивільних досліджень та розвитку (США). Подано основний проєкт під редакцією С. Голомба, а також коротку інформацію про розвиток досліджень та застосування оптимізованих систем з кільцевою структурою. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2023-03-30 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/263989 10.20535/SRIT.2308-8893.2023.1.09 System research and information technologies; No. 1 (2023); 113-121 Системные исследования и информационные технологии; № 1 (2023); 113-121 Системні дослідження та інформаційні технології; № 1 (2023); 113-121 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/263989/274366 |
| spellingShingle | проєкт комбінаторна конфігурація ідеальна кільцева в’язанка оптимізація комбінаторна модель наукова школа Riznyk, Volodymyr Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| title | Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| title_alt | Researches and applications of the combinatorial configurations for innovative devices and process engineering ИССЛЕДОВАНИЯ И ПРИМЕНЕНИЕ КОМБИНАТОРНЫХ КОНФИГУРАЦИЙ ДЛЯ ИННОВАЦИОННЫХ УСТРОЙСТВ И ТЕХНОЛОГИЙ |
| title_full | Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| title_fullStr | Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| title_full_unstemmed | Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| title_short | Дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| title_sort | дослідження та застосування комбінаторних конфігурацій для інноваційних пристроїв і технологій |
| topic | проєкт комбінаторна конфігурація ідеальна кільцева в’язанка оптимізація комбінаторна модель наукова школа |
| topic_facet | проєкт комбінаторна конфігурація ідеальна кільцева в’язанка оптимізація комбінаторна модель наукова школа project combinatorial configuration Ideal Ring Bundle optimization model scientific school |
| url | https://journal.iasa.kpi.ua/article/view/263989 |
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