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Journal articles on the topic 'Rational structure'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Barakat, Khaled H., Michael Houghton, D. Lorne Tyrrel, and Jack A. Tuszynski. "Rational Drug Design." International Journal of Computational Models and Algorithms in Medicine 4, no. 1 (January 2014): 59–85. http://dx.doi.org/10.4018/ijcmam.2014010104.

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For the past three decades rationale drug design (RDD) has been developing as an innovative, rapid and successful way to discover new drug candidates. Many strategies have been followed and several targets with diverse structures and different biological roles have been investigated. Despite the variety of computational tools available, one can broadly divide them into two major classes that can be adopted either separately or in combination. The first class involves structure-based drug design, when the target's 3-dimensional structure is available or it can be computationally generated using homology modeling. On the other hand, when only a set of active molecules is available, and the structure of the target is unknown, ligand-based drug design tools are usually used. This review describes some recent advances in rational drug design, summarizes a number of their practical applications, and discusses both the advantages and shortcomings of the various techniques used.

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2

Zhang, Louxin. "Rational strong codes and structure of rational group languages." Semigroup Forum 35, no. 1 (December 1986): 181–93. http://dx.doi.org/10.1007/bf02573102.

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3

Kanca, John. "Bonding to Tooth Structure: A Rational Rationale for a Clinical Protocol." Journal of Esthetic and Restorative Dentistry 1, no. 4 (July 1989): 135–38. http://dx.doi.org/10.1111/j.1708-8240.1989.tb00545.x.

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4

FILIPOVIĆ, DAMIR, MARTIN LARSSON, and ANDERS B. TROLLE. "Linear-Rational Term Structure Models." Journal of Finance 72, no. 2 (March 21, 2017): 655–704. http://dx.doi.org/10.1111/jofi.12488.

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5

Pál, Hegedus. "Structure of solvable rational groups." Proceedings of the London Mathematical Society 90, no. 02 (February 25, 2005): 439–71. http://dx.doi.org/10.1112/s0024611504015035.

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6

Medvedev, A. E., V. I. Samsonov, and V. M. Fomin. "Rational structure of blood vessels." Journal of Applied Mechanics and Technical Physics 47, no. 3 (May 2006): 324–29. http://dx.doi.org/10.1007/s10808-006-0059-3.

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7

Allen, Colin. "The evolution of rational demons." Behavioral and Brain Sciences 23, no. 5 (October 2000): 742. http://dx.doi.org/10.1017/s0140525x00223443.

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If fast and frugal heuristics are as good as they seem to be, who needs logic and probability theory? Fast and frugal heuristics depend for their success on reliable structure in the environment. In passive environments, there is relatively little change in structure as a consequence of individual choices. But in social interactions with competing agents, the environment may be structured by agents capable of exploiting logical and probabilistic weaknesses in competitors' heuristics. Aspirations toward the ideal of a demon reasoner may consequently be adaptive for direct competition with such agents.

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8

Dujella, Andrej, Matija Kazalicki, and Vinko Petričević. "Rational Diophantine sextuples containing two regular quadruples and one regular quintuple." Acta mathematica Spalatensia 1, no. 1 (January 4, 2021): 19–27. http://dx.doi.org/10.32817/ams.1.1.2.

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A set of m distinct nonzero rationals {a1,a2,…,am} such that aiaj+1 is a perfect square for all 1 ≤ i < j ≤ m, is called a rational Diophantine m-tuple. It is proved recently that there are infinitely many rational Diophantine sextuples. In this paper, we construct infinite families of rational Diophantine sextuples with special structure, namely the sextuples containing quadruples and quintuples of certain type.

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9

Collazos, Julio. "Rational structure of original research reports." Lancet 359, no. 9301 (January 2002): 174. http://dx.doi.org/10.1016/s0140-6736(02)07362-2.

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10

Hoenselaers, C. "Factor structure of rational electrovacuum metrics." Classical and Quantum Gravity 14, no. 9 (September 1, 1997): 2627–33. http://dx.doi.org/10.1088/0264-9381/14/9/017.

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11

Enders, Walter, and Xuejuan Su. "Rational Terrorists and Optimal Network Structure." Journal of Conflict Resolution 51, no. 1 (February 2007): 33–57. http://dx.doi.org/10.1177/0022002706296155.

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12

Hoenselaers, C., and Z. Perjes. "Factor structure of rational vacuum metrics." Classical and Quantum Gravity 7, no. 12 (December 1, 1990): 2215–24. http://dx.doi.org/10.1088/0264-9381/7/12/006.

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13

Miao, Jianjun, Jieran Wu, and Eric R. Young. "Multivariate Rational Inattention." Econometrica 90, no. 2 (2022): 907–45. http://dx.doi.org/10.3982/ecta18086.

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We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.

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14

Dubouloz, Adrien, and Alvaro Liendo. "Rationally integrable vector fields and rational additive group actions." International Journal of Mathematics 27, no. 08 (July 2016): 1650060. http://dx.doi.org/10.1142/s0129167x16500609.

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We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. Our results lead in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counterpart of the Makar–Limanov invariant for affine varieties and describe the structure of rational homogeneous additive group actions on toric varieties.

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15

Verdestar, L. "A Hopf Algebra Structure on Rational Functions." Advances in Mathematics 116, no. 2 (December 1995): 377–88. http://dx.doi.org/10.1006/aima.1995.1072.

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16

Vanin, G. A., and Nguyen Dinh Duc. "Determination of rational structure for spherofibrous plastics." Mechanics of Composite Materials 33, no. 2 (March 1997): 107–11. http://dx.doi.org/10.1007/bf02269595.

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17

Blaževica-Juhnevica, Olga, Dmitrijs Serdjuks, Raimonds Ozolins, Vadims Goremikins, and Leonids Pakrastins. "Choice of Rational Parameters of Combined Structure." Procedia Engineering 117 (2015): 85–93. http://dx.doi.org/10.1016/j.proeng.2015.08.128.

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18

Jackson, Colin J., Kahli Weir, Anthony Herlt, Jeevan Khurana, Tara D. Sutherland, Irene Horne, Christopher Easton, Robyn J. Russell, Colin Scott, and John G. Oakeshott. "Structure-Based Rational Design of a Phosphotriesterase." Applied and Environmental Microbiology 75, no. 15 (June 5, 2009): 5153–56. http://dx.doi.org/10.1128/aem.00629-09.

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ABSTRACT In silico substrate docking of both stereoisomers of the pesticide chlorfenvinphos (CVP) in the phosphotriesterase from Agrobacterium radiobacter identified two residues (F131 and W132) that prevent productive substrate binding and cause stereospecificity. A variant (W131H/F132A) was designed that exhibited ca. 480-fold and 8-fold increases in the rate of Z-CVP and E-CVP hydrolysis, respectively, eliminating stereospecificity.

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19

Botterill, George. "Rational Belief: Structure, Grounds and Intellectual Virtue." Analysis 76, no. 4 (July 10, 2016): 547–49. http://dx.doi.org/10.1093/analys/anw056.

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20

Lerer, Leonid, and Leiba Rodman. "Common Zero Structure of Rational Matrix Functions." Journal of Functional Analysis 136, no. 1 (February 1996): 1–38. http://dx.doi.org/10.1006/jfan.1996.0020.

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21

Fiorenza, Domenico, Hisham Sati, and Urs Schreiber. "The Rational Higher Structure of M‐theory." Fortschritte der Physik 67, no. 8-9 (May 6, 2019): 1910017. http://dx.doi.org/10.1002/prop.201910017.

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22

Himle, David P., Stephen Hnat, Bruce Thyer, and James Papsdorf. "Factor structure of the Rational Behavior Inventory." Journal of Clinical Psychology 41, no. 3 (May 1985): 368–71. http://dx.doi.org/10.1002/1097-4679(198505)41:3<368::aid-jclp2270410309>3.0.co;2-t.

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23

Di Francesco, P. "Structure constants for rational conformal field theories." Physics Letters B 215, no. 1 (December 1988): 124–28. http://dx.doi.org/10.1016/0370-2693(88)91082-9.

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24

Kuksova, Irina, and Irina Zinoveva. "RATIONAL STRUCTURE OF ENVIRONMENTAL MANAGEMENT ECONOMY MANAGEMENT." Actual directions of scientific researches of the XXI century: theory and practice 9, no. 2 (July 16, 2021): 18–27. http://dx.doi.org/10.34220/2308-8877-2021-9-2-18-27.

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The article is devoted to the development of the methodology of rational management of the economics of environmental management. The importance of this study stems from the need to establish principles and strategies for sound economic management to promote economic development, sustainable resource use, reduce environmental problems and support human livelihoods. This article highlights the latest developments in the field of economic development management strategies for environmental management. Regulatory forecasts are proposed to rationalize management in accordance with the strategic goals and the achievement of established measures for the development of the environmental economy, which allows to ensure the country's competitiveness. Theoretical approaches and practical recommendations for the formation of the structure of rational management of the economy of natural resource use have been developed. The article reflects the current research results in the field of development of the methodology of rational management of the economics of environmental management. The features of environmental management are revealed and their assessment is proposed, where the functional purpose of rationalization, the purpose and the direction of the results are highlighted as classification signs. The practical experience of the level of achievement of planned values of indicators of environmental state subprograms in the Russian Federation is analyzed. The advantages of rational management of nature management economics are shown. The key elements of this article can be used as theories and strategies for justifying, selecting and implementing economic and economic projects, integrating environmental protection measures, mitigating environmental impacts, mitigating the effects of climate change and managing climate change. The conclusions drawn are based on an assessment of good or bad governance and technical judgment.

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25

Schroeder, Mark. "RATIONAL STABILITY UNDER PRAGMATIC ENCROACHMENT." Episteme 15, no. 3 (July 19, 2018): 297–312. http://dx.doi.org/10.1017/epi.2018.24.

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ABSTRACTIn this paper I will be concerned with the relationship between pragmatic encroachment and the rational instability of belief. I will be concerned to make five points: first, that some defenders of pragmatic encroachment are indeed committed to predictable rational instability of belief; second, that rational instability is indeed troublesome – particularly when it is predictable; third, that the bare thesis of pragmatic encroachment is not committed to rational instability of belief at all; fourth, that the view that Jake Ross and I have called the ‘reasoning disposition’ account of belief has the right structure to predict limited and stable pragmatic encroachment on the rationality of belief; and fifth and finally, that the very best cases for pragmatic encroachment are rationally stable in the right ways.

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26

Wang, Shuya, Lei Qin, Gokay Yamankurt, Kacper Skakuj, Ziyin Huang, Peng-Cheng Chen, Donye Dominguez, Andrew Lee, Bin Zhang, and Chad A. Mirkin. "Rational vaccinology with spherical nucleic acids." Proceedings of the National Academy of Sciences 116, no. 21 (May 8, 2019): 10473–81. http://dx.doi.org/10.1073/pnas.1902805116.

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In the case of cancer immunotherapy, nanostructures are attractive because they can carry all of the necessary components of a vaccine, including both antigen and adjuvant. Herein, we explore how spherical nucleic acids (SNAs), an emerging class of nanotherapeutic materials, can be used to deliver peptide antigens and nucleic acid adjuvants to raise immune responses that kill cancer cells, reduce (or eliminate) tumor growth, and extend life in three established mouse tumor models. Three SNA structures that are compositionally nearly identical but structurally different markedly vary in their abilities to cross-prime antigen-specific CD8+ T cells and raise subsequent antitumor immune responses. Importantly, the most effective structure is the one that exhibits synchronization of maximum antigen presentation and costimulatory marker expression. In the human papillomavirus-associated TC-1 model, vaccination with this structure improved overall survival, induced the complete elimination of tumors from 30% of the mice, and conferred curative protection from tumor rechallenges, consistent with immunological memory not otherwise achievable. The antitumor effect of SNA vaccination is dependent on the method of antigen incorporation within the SNA structure, underscoring the modularity of this class of nanostructures and the potential for the deliberate design of new vaccines, thereby defining a type of rational cancer vaccinology.

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27

OSOFSKY, BARBARA L., JAE KEOL PARK, and S. TARIQ RIZVI. "PROPERTIES OF INJECTIVE HULLS OF A RING HAVING A COMPATIBLE RING STRUCTURE." Glasgow Mathematical Journal 52, A (June 24, 2010): 121–38. http://dx.doi.org/10.1017/s0017089510000248.

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AbstractIf the injective hull E = E(RR) of a ring R is a rational extension of RR, then E has a unique structure as a ring whose multiplication is compatible with R-module multiplication. We give some known examples where such a compatible ring structure exists when E is a not a rational extension of RR, and other examples where such a compatible ring structure on E cannot exist. With insights gleaned from these examples, we study compatible ring structures on E, especially in the case when ER, and hence RR ⊆ ER, has finite length. We show that for RR and ER of finite length, if ER has a ring structure compatible with R-module multiplication, then E is a quasi-Frobenius ring under that ring structure and any two compatible ring structures on E have left regular representations conjugate in Λ = EndR(ER), so the ring structure is unique up to isomorphism. We also show that if ER is of finite length, then ER has a ring structure compatible with its R-module structure and this ring structure is unique as a set of left multiplications if and only if ER is a rational extension of RR.

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28

Chen, Mingqing. "A study of low-carbon development, urban innovation and industrial structure upgrading in China." International Journal of Low-Carbon Technologies 17 (2022): 185–95. http://dx.doi.org/10.1093/ijlct/ctab097.

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Abstract This paper, based on the panel data of 281 prefecture-level cities in China, applies the difference-in-differences (DID) approach and the propensity score matching DID (PSM-DID) approach to an empirical study on the impacts of the low-carbon pilot program on industrial structure. It concludes that the program has contributed significantly to more rational industrial structures of pilot areas. The study shows that pilot areas have more rational industrial structures than non-pilot areas, recording an increase of 0.058 units in average rational level. This conclusion holds under various robustness tests. Further heterogeneity analysis suggests that the low-carbon pilot program has notably boosted the rational levels of industrial structures of cities in central China and small cities, while less so for other parts of China or other larger cities. Mechanism test shows that low-carbon cities have realized industrial structure upgrading by facilitating urban innovation. In light of this, the low-carbon pilot program should be further put in place steadily with a focus on tailoring pilot policies to local conditions and enhancing their economic adaptability. The role of the program in optimizing industrial structure should be fully leveraged to effectively add to efforts in actively exploring green, low-carbon sustainable development of economy and pulling off the transformation of both economic structure and energy mix.

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29

MIEMIETZ, VANESSA, and WILL TURNER. "RATIONAL REPRESENTATIONS OF GL2." Glasgow Mathematical Journal 53, no. 2 (December 8, 2010): 257–75. http://dx.doi.org/10.1017/s0017089510000686.

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AbstractLet F be an algebraically closed field of characteristic p. We fashion an infinite dimensional basic algebra ←p(F), with a transparent combinatorial structure, which controls the rational representation theory of GL2(F).

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30

Bronsard, Camille, and Lise Salvas-Bronsard. "Rational Expectations, Expectation Functions, and Slutsky Local Structure." Canadian Journal of Economics 21, no. 4 (November 1988): 846. http://dx.doi.org/10.2307/135269.

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31

Gane, Paul J., and Philip M. Dean. "Recent advances in structure-based rational drug design." Current Opinion in Structural Biology 10, no. 4 (August 2000): 401–4. http://dx.doi.org/10.1016/s0959-440x(00)00105-6.

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32

Gutiérrez-de-Terán, Hugo, Jessica Sallander, and Eddy Sotelo. "Structure-Based Rational Design of Adenosine Receptor Ligands." Current Topics in Medicinal Chemistry 17, no. 1 (November 14, 2016): 40–58. http://dx.doi.org/10.2174/1568026616666160719164207.

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33

Babelon, O., and M. Talon. "The symplectic structure of rational Lax pair systems." Physics Letters A 257, no. 3-4 (June 1999): 139–44. http://dx.doi.org/10.1016/s0375-9601(99)00298-4.

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34

Brody, Dorje C., Lane P. Hughston, and Ewan Mackie. "Rational term structure models with geometric Lévy martingales." Stochastics 84, no. 5-6 (June 25, 2012): 719–40. http://dx.doi.org/10.1080/17442508.2012.689835.

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35

Zsoldos, Zsolt, Irina Szabo, Zsolt Szabo, and A. Peter Johnson. "Software tools for structure based rational drug design." Journal of Molecular Structure: THEOCHEM 666-667 (December 2003): 659–65. http://dx.doi.org/10.1016/j.theochem.2003.08.105.

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36

Darling, S. B., A. T. Hanbicki, T. P. Pearl, and S. J. Sibener. "Rational Design of Interfacial Structure: Adsorbate-Mediated Templating." Journal of Physical Chemistry B 103, no. 45 (November 1999): 9805–8. http://dx.doi.org/10.1021/jp9928917.

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37

Jagels, Carl, and Lothar Reichel. "The structure of matrices in rational Gauss quadrature." Mathematics of Computation 82, no. 284 (April 9, 2013): 2035–60. http://dx.doi.org/10.1090/s0025-5718-2013-02695-6.

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38

Mucsi, Z., Z. Gaspari, G. Orosz, and A. Perczel. "Structure-oriented rational design of chymotrypsin inhibitor models." Protein Engineering Design and Selection 16, no. 9 (September 1, 2003): 673–81. http://dx.doi.org/10.1093/protein/gzg090.

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39

Wang, Xun, and Yadong Li. "Rational Synthetic Strategy. From Layered Structure to MnO2Nanotubes." Chemistry Letters 33, no. 1 (January 2004): 48–49. http://dx.doi.org/10.1246/cl.2004.48.

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40

Keun-Bok Kang. "The Structure and Application of Rational Policy Debate." Korean Public Management Review 27, no. 2 (June 2013): 27–52. http://dx.doi.org/10.24210/kapm.2013.27.2.002.

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41

Holmwood, Graham, and Michael Schindler. "Protein structure based rational design of ecdysone agonists." Bioorganic & Medicinal Chemistry 17, no. 12 (June 2009): 4064–70. http://dx.doi.org/10.1016/j.bmc.2009.01.008.

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42

Kurz, Mordecai. "On the structure and diversity of rational beliefs." Economic Theory 4, no. 6 (November 1994): 877–900. http://dx.doi.org/10.1007/bf01213817.

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43

Liu, Shu Ru, and Xing Kui Wang. "The Study on Building a Rational Evaluating Index System for the Industrial Structure." Applied Mechanics and Materials 58-60 (June 2011): 353–58. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.353.

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Rationality of the industrial structure is the essence of the economic development, as well as the key to promote the sustainable, steady, and harmonious development of the economy. Guided by the Scientific Development Concept and Sustainable Development Theory, this article has probed into the building of a rational evaluating index system of the industrial structure. It proposes a reasonable choice criterion of the industrial structure, which is based on the sustainable development with the coordination of “economy, society, resources, environment, and technology”. Accordingly, a set of rationale evaluating index system is designed, laying the foundation for the overall evaluation and measurement of the rationality level of the regional industrial structure.

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44

Karakurt, Çağrı, and Ferı̇t Öztürk. "Contact structures on AR-singularity links." International Journal of Mathematics 29, no. 03 (March 2018): 1850019. http://dx.doi.org/10.1142/s0129167x18500192.

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An isolated complex surface singularity induces a canonical contact structure on its link. In this paper, we initiate the study of the existence problem of Stein cobordisms between these contact structures depending on the properties of singularities. As a first step, we construct an explicit Stein cobordism from any contact 3-manifold to the canonical contact structure of a proper almost rational singularity introduced by Némethi. We also show that the construction cannot always work in the reverse direction: in fact, the U-filtration depth of contact Ozsváth–Szabó invariant obstructs the existence of a Stein cobordism from a proper almost rational singularity to a rational one. Along the way, we detect the contact Ozsváth–Szabó invariants of those contact structures fillable by an AR plumbing graph, generalizing an earlier work of the first author.

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45

Akan, A. Osman. "Modified rational method for sizing infiltration structures." Canadian Journal of Civil Engineering 29, no. 4 (August 1, 2002): 539–42. http://dx.doi.org/10.1139/l02-038.

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A simple method is presented to size infiltration structures like infiltration basins and trenches to control storm water runoff. The runoff hydrograph is assumed to be trapezoidal in shape with a peak runoff rate calculated using the rational formula. Given the watershed time of concentration and the allowable runoff rate, the method determines the required size of the infiltration structure. A practical application section is included to demonstrate the use of the method.Key words: rational method, infiltration basin, infiltration trench, capture volume, storage time.

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46

Nolan, Rita. "The new enlightenment hypothesis: All learners are rational." Behavioral and Brain Sciences 32, no. 2 (April 2009): 219–20. http://dx.doi.org/10.1017/s0140525x09001095.

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AbstractThe proposal to recruit available formal structures to build an algorithmic model of all learning falters on close examination of its essential assumption: that the input and output of the model are propositional in structure. After giving three framework considerations, I describe three possibly fatal problems with this assumption, concluding each with a question that needs answering to avoid fatality.

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47

Mayatskaya, Irina, and Victor Eremin. "Bionics and the choice of rational structural form." E3S Web of Conferences 110 (2019): 01042. http://dx.doi.org/10.1051/e3sconf/201911001042.

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The work is devoted to the development of such an interesting topic as bionics. The relevance of the study of this topic is due to the processes taking place both in our country and in the world. The aim of the work is to study the laws of formation of living organisms, their structure, design features, principles of operation and the use of this knowledge in the design of structures and constructions. The paper considers different areas of bionics and analyzes bionic principles. Particular attention is paid to architectural bionics in terms of the choice of optimal design. The study of natural objects allows creating structures and constructions that take into account properties, shape, structure, organization of life of living organisms and plants. The issues of creation of an optimum design are considered. To do this, it must have the following properties: reliability, durability, efficiency, maintainability, and of course, environmental friendliness. The paper provides the analysis of trends in bionics. It is worth noting that these trends are penetrating each other, creating a new one. The examples of constructions based on bionic principles are given. To solve this problem, it is necessary to apply methods of mathematical modeling. They allow choosing the best option using a numerical experiment. The results of the analysis of the problem can be used in the design of structures and constructions of unique structures, and should serve the further development of bionic science. The combination of bionic principles and optimization methods creates the basis for such developments.

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48

Lee, Dae-Woong. "Algebraic Structures Based on a Classifying Space of a Compact Lie Group." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/508450.

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We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. By using the Milnor-Moore theorem, we also investigate the concrete primitive elements in the Pontrjagin algebra.

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49

Wang, Chuanjian, Zhengde Dai, and Changfu Liu. "The Breather-Like and Rational Solutions for the Integrable Kadomtsev-Petviashvili-Based System." Advances in Mathematical Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/861069.

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The integrable Kadomtsev-Petviashvili-based system is studied. The breather-like (a pulsating mode) and rational solutions are presented applying Hirota bilinear method and Taylor series. The intricate structures of the rational solitary wave solution are discussed mathematically and graphically. The existence conditions of three different solitary wave solution structure for the short-wave field are given by the theory of extreme value analysis. By controlling the wave number of the background plane wave we may control the the behavior of rational solitary wave. However, the shape of the rational solitary wave solution for the real long-wave field is not affected as the wave number is varied.

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50

PAKOVICH, FEDOR. "Commuting rational functions revisited." Ergodic Theory and Dynamical Systems 41, no. 1 (August 15, 2019): 295–320. http://dx.doi.org/10.1017/etds.2019.51.

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Let $B$ be a rational function of degree at least two that is neither a Lattès map nor conjugate to $z^{\pm n}$ or $\pm T_{n}$. We provide a method for describing the set $C_{B}$ consisting of all rational functions commuting with $B$. Specifically, we define an equivalence relation $\underset{B}{{\sim}}$ on $C_{B}$ such that the quotient $C_{B}/\underset{B}{{\sim}}$ possesses the structure of a finite group $G_{B}$, and describe generators of $G_{B}$ in terms of the fundamental group of a special graph associated with $B$.

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