11th International Algebraic Conference in Ukraine dedicated to the 75th anniversary of VV ...

159 Pages·2017·1.2 MB·English

Taras Shevchenko National University of Kyiv
Institute of Mathematics of NAS of Ukraine
National University of Kyiv-Mohyla Academy
11th International Algebraic Conference in Ukraine
dedicated to the 75th anniversary of V. V. Kirichenko
July 3(cid:21) 7, 2017
Kyiv, Ukraine
ABSTRACTS
Kyiv (cid:22) 2017
˚Ł¤(cid:226)æ(cid:252)ŒŁØ (cid:237)(cid:224)(cid:246)i(cid:238)(cid:237)(cid:224)º(cid:252)(cid:237)ŁØ (cid:243)(cid:237)i(cid:226)(cid:229)(cid:240)æŁ(cid:242)(cid:229)(cid:242) i(cid:236)(cid:229)(cid:237)i (cid:210)(cid:224)(cid:240)(cid:224)æ(cid:224) (cid:216)(cid:229)(cid:226)(cid:247)(cid:229)(cid:237)Œ(cid:224)
I(cid:237)æ(cid:242)Ł(cid:242)(cid:243)(cid:242) (cid:236)(cid:224)(cid:242)(cid:229)(cid:236)(cid:224)(cid:242)ŁŒŁ ˝(cid:192)˝ (cid:211)Œ(cid:240)(cid:224)¤(cid:237)Ł
˝(cid:224)(cid:246)i(cid:238)(cid:237)(cid:224)º(cid:252)(cid:237)ŁØ (cid:243)(cid:237)i(cid:226)(cid:229)(cid:240)æŁ(cid:242)(cid:229)(cid:242) (cid:16)˚Ł„(cid:226)(cid:238)-(cid:204)(cid:238)ªŁº(cid:255)(cid:237)æ(cid:252)Œ(cid:224) (cid:224)Œ(cid:224)(cid:228)(cid:229)(cid:236)i(cid:255)(cid:17)
11-(cid:224) (cid:204)i(cid:230)(cid:237)(cid:224)(cid:240)(cid:238)(cid:228)(cid:237)(cid:224) (cid:224)ºª(cid:229)Æ(cid:240)(cid:224)¤(cid:247)(cid:237)(cid:224) Œ(cid:238)(cid:237)(cid:244)(cid:229)(cid:240)(cid:229)(cid:237)(cid:246)i(cid:255) (cid:226)
(cid:211)Œ(cid:240)(cid:224)¤(cid:237)i, (cid:239)(cid:240)Łæ(cid:226)(cid:255)(cid:247)(cid:229)(cid:237)(cid:224) 75-(cid:240)i(cid:247)(cid:247)(cid:254) ´. ´. ˚Ł(cid:240)Ł(cid:247)(cid:229)(cid:237)Œ(cid:224)
3(cid:21) 7 ºŁ(cid:239)(cid:237)(cid:255) 2017 (cid:240).
˚Ł¤(cid:226), (cid:211)Œ(cid:240)(cid:224)¤(cid:237)(cid:224)
(cid:210)¯˙¨ ˜˛ˇ˛´I˜¯(cid:201)
˚Ł¤(cid:226) (cid:22) 2017
11th International Algebraic Conference in Ukraine dedicated to the 75th anni-
versary of V. V. Kirichenko. July 3(cid:21)7, 2017, Kyiv, Ukraine. Abstracts. (cid:22) Kyiv: Institute
of Mathematics of NAS of Ukraine, 2017. (cid:22) 159 p.
11-(cid:224) (cid:204)i(cid:230)(cid:237)(cid:224)(cid:240)(cid:238)(cid:228)(cid:237)(cid:224) (cid:224)ºª(cid:229)Æ(cid:240)(cid:224)¤(cid:247)(cid:237)(cid:224) Œ(cid:238)(cid:237)(cid:244)(cid:229)(cid:240)(cid:229)(cid:237)(cid:246)i(cid:255) (cid:226) (cid:211)Œ(cid:240)(cid:224)¤(cid:237)i, (cid:239)(cid:240)Łæ(cid:226)(cid:255)(cid:247)(cid:229)(cid:237)(cid:224) 75-(cid:240)i(cid:247)(cid:247)(cid:254)
´. ´. ˚Ł(cid:240)Ł(cid:247)(cid:229)(cid:237)Œ(cid:224). 3(cid:21)7 ºŁ(cid:239)(cid:237)(cid:255) 2017 (cid:240)., ˚Ł¤(cid:226), (cid:211)Œ(cid:240)(cid:224)¤(cid:237)(cid:224). (cid:210)(cid:229)(cid:231)Ł (cid:228)(cid:238)(cid:239)(cid:238)(cid:226)i(cid:228)(cid:229)Ø. (cid:22) ˚Ł¤(cid:226): I(cid:237)æ(cid:242)Ł-
(cid:242)(cid:243)(cid:242) (cid:236)(cid:224)(cid:242)(cid:229)(cid:236)(cid:224)(cid:242)ŁŒŁ ˝(cid:192)˝ (cid:211)Œ(cid:240)(cid:224)¤(cid:237)Ł, 2017. (cid:22) 159 c.
Program Committee
Yu. Drozd (chairman)
V. Bavula (United Kingdom)
N. Chernikov (Ukraine)
M. Dokuchaev (Brazil)
V. Futorny (Brazil)
R. Grigorchuk (USA)
A. Kashu (Moldova)
L. Kurdachenko (Ukraine)
Ya. Lavrenyuk (Ukraine)
F. Lyman (Ukraine)
V. Mazorchuk (Sweden)
V. Nekrashevich (USA)
M. Nikitchenko (Ukraine)
B. Oliynyk (Ukraine)
A. Olshanskii (Russia-USA)
I. Protasov (Ukraine)
N. Semko (Ukraine)
I. Shestakov (Brazil)
Ya. Sysak (Ukraine)
V. Ustimenko (Poland)
P. Varbanets (Ukraine)
B. Zabavskyi (Ukraine)
E. Zelmanov (USA)
A. Zhuchok (Ukraine)
(cid:13)c Institute of Mathematics of NAS of Ukraine, 2017
ˆŁ(cid:236)(cid:237) (cid:192)ºª(cid:229)Æ(cid:240)(cid:224)Łæ(cid:242)(cid:238)(cid:226)
(cid:209).˜. `(cid:229)(cid:240)(cid:236)(cid:224)(cid:237) Ł ¸.(cid:192). ˚(cid:224)º(cid:243)(cid:230)(cid:237)Ł(cid:237)
ˇ(cid:238)º(cid:255) Ł Œ(cid:238)º(cid:252)(cid:246)(cid:224), ª(cid:240)(cid:243)(cid:239)(cid:239)ß Ł æ(cid:242)(cid:240)(cid:243)Œ(cid:242)(cid:243)(cid:240)ß
´º(cid:224)(cid:228)(cid:229)(cid:242)(cid:252) (cid:226)æ(cid:229)Ø (cid:236)(cid:224)(cid:242)(cid:229)(cid:236)(cid:224)(cid:242)ŁŒ(cid:238)Ø (cid:228)(cid:238)º(cid:230)(cid:237)ß,
(cid:210)(cid:224)Œ (cid:237)(cid:229) (cid:237)(cid:243)(cid:230)(cid:237)ß (cid:239)(cid:240)(cid:229)(cid:228)(cid:229)ºß, Œ(cid:226)(cid:224)(cid:228)(cid:240)(cid:224)(cid:242)(cid:243)(cid:240)ß,
¨ Ł(cid:237)(cid:242)(cid:229)ª(cid:240)(cid:224)ºß (cid:242)(cid:238)(cid:230)(cid:229) (cid:237)(cid:229) (cid:237)(cid:243)(cid:230)(cid:237)ß!
ˇ(cid:240)Ł(cid:239)(cid:229)(cid:226): ˛(cid:242)Æ(cid:240)(cid:238)æŁ(cid:226) æ (cid:239)(cid:240)(cid:229)(cid:231)(cid:240)(cid:229)(cid:237)(cid:252)(cid:229)(cid:236) (cid:228)Ł(cid:244)(cid:243)(cid:240)ß
´(cid:239)(cid:229)(cid:240)(cid:229)(cid:228) (cid:243)æ(cid:242)(cid:240)(cid:229)(cid:236)º(cid:255)(cid:229)(cid:236) æ(cid:226)(cid:238)Ø (cid:239)(cid:243)(cid:242)(cid:252).
¨ (cid:238)ÆøŁ(cid:229) (cid:237)(cid:224)łŁ æ(cid:242)(cid:240)(cid:243)Œ(cid:242)(cid:243)(cid:240)ß
˜(cid:224)(cid:254)(cid:242) (cid:237)(cid:229)æ(cid:238)(cid:236)(cid:237)(cid:229)(cid:237)(cid:237)(cid:243)(cid:254) (cid:236)(cid:243)(cid:242)(cid:252).
˝(cid:229) (cid:231)(cid:237)(cid:224)(cid:229)(cid:236) (cid:236)ß (cid:239)(cid:240)(cid:238) Ł(cid:237)(cid:242)(cid:229)ª(cid:240)(cid:224)º (cid:228)(cid:226)(cid:243)Œ(cid:240)(cid:224)(cid:242)(cid:237)ßØ,
˝(cid:238) Œ(cid:224)(cid:242)(cid:229)ª(cid:238)(cid:240)(cid:252)(cid:229)Ø (cid:237)(cid:224)æ (cid:237)(cid:229) Łæ(cid:239)(cid:243)ª(cid:224)(cid:242)(cid:252).
¨ (cid:239)(cid:240)Ł(cid:236)(cid:229)(cid:237)(cid:255)(cid:255) (cid:224)(cid:239)(cid:239)(cid:224)(cid:240)(cid:224)(cid:242) (cid:224)Ææ(cid:242)(cid:240)(cid:224)Œ(cid:242)(cid:237)ßØ
¸(cid:254)Æ(cid:238)Ø (cid:224)Ææ(cid:243)(cid:240)(cid:228) Łß (cid:236)(cid:238)(cid:230)(cid:229)(cid:236) (cid:228)(cid:238)Œ(cid:224)(cid:231)(cid:224)(cid:242)(cid:252).
ˇ(cid:240)Ł(cid:239)(cid:229)(cid:226).
(cid:247)Łæ(cid:242)(cid:224) æ(cid:242)(cid:238)(cid:240)i(cid:237)Œ(cid:224)
C O N T E N T S
˙ (cid:204) I (cid:209) (cid:210)
Volodymyr Kirichenko ................................................................. 11
Admiralova A. N., Benyash-Krivets V. V. On representation varieties
of some HNN extensions of free groups.................................................. 13
Al-Ezeh H., Alomari O., Abudayah M. Cube complementary graphs..................... 14
Babych V., Golovashchuk N. Classi(cid:28)cation problem for bimodule problems
with quasi multiplicative basis .......................................................... 15
Balaba I. N. Homological classi(cid:28)cation of graded rings................................... 16
Balychev S. V., Vasil’ev A. F. On (cid:28)nite groups factorizable by permutable subgroups ... 17
Baryshovets P. P. On (cid:28)nite dispersive groups with complemented
nonmetacyclic subgroups................................................................ 18
Bavula V. Generalized Weyl algebras and diskew polynomial rings....................... 19
Bedratyuk L. The star and frequently sequences of simple graphs........................ 20
Bezushchak O. O., Oliynyk B. V. Diagonal limits of linear groups....................... 21
Bilavska S. I., Zabavsky B. V. On (cid:28)nite homomorphic images of
commutative Bezout domains........................................................... 22
Bilous A. M. E(cid:27)ective duo ring......................................................... 23
Bokhonko V. V. Matrix reduction over Bezout stable range one
domains with Dubrovin and Z conditions................................................ 24
Bonacci E. A germinal approach to power sums......................................... 25
Bondarenko I., Kivva B. Non-residually (cid:28)nite CAT(0) groups from
bireversible automata................................................................... 26
Bondarenko V. M., Bortos M. Yu. On isomorphic objects of the category
of monomial matrices over a commutative local ring..................................... 27
Bondarenko V. M., Tertychna O. M. New matrix models of (cid:28)nite networks.............. 28
Can(cid:3)adas A. M., Gaviria I. D. M. The school of Kiev in Colombia and the theory
of algorithms of di(cid:27)erentiation for posets and its applications............................ 29
Chapovskyi Y. Y. On divergence-free and jacobian derivations........................... 30
Chen Jianmin, Lin Yanan, Liu Ping, Ruan Shiquan. Tilting bundles on weighted
projective lines.......................................................................... 31
Chernikov N. Locally graded groups with the minimal condition
for non-abelian non-complemented subgroups ........................................... 32
Derech V. D. Classi(cid:28)cation of (cid:28)nite structurally uniform groups......................... 33
5
Desiateryk O. O. Variants of the Rees matrix semigroup over the trivial group
with zero ............................................................................... 34
Dokuchaev M., Paques A., Pinedo H. A seven terms exact sequence related to
a partial Galois extension of commutative rings ......................................... 35
Domsha O. V. Kazimirsky condition for rings of stable range 1.......................... 36
Drozd Yu. A. Nodal curves and quasi-hereditary algebras................................ 37
Drozd Yu. A., Tovpyha O. Matrix factorizations of Cohen(cid:21)Macaulay modules
over the plane curve singularity of type T .............................................. 38
44
Dudenko M. A. Unicyclic graphs with two main vertices and metric dimension 2 ........ 39
Dunets R. B., Popovych B. R., Popovych R. B. On Gao conjecture connected
with high order elements in arbitrary (cid:28)nite (cid:28)eld......................................... 40
Dyachenko S. M. Representation type of Rees semigroup over a cyclic group
of prime order in modular case.......................................................... 41
Fedorchuk V. M., Fedorchuk V. I. Classi(cid:28)cation of low-dimensional Lie algebras......... 42
Fedorova M. V. Finite automaton actions of free groups of rank n....................... 43
Fryz I. V. Relations between orthogonality and retract orthogonality.................... 44
Futorny V. Construction of Gelfand-Tsetlin modules for gl ............................. 45
n
Gatalevych A. I. Range conditions for abelian rings ..................................... 46
Gatalevych A. I., Dmytruk A. A. Rings and elements of almost stable range one......... 47
Giambruno A., Zaicev M. Central polynomials codimension growth...................... 48
Goy T. P. On new Catalan identities using Toeplitz(cid:21)Hessenberg matrices ............... 49
Guo Hongyan, Li Haisheng, Tan Shaobin, Wang Qing. q-Virasoro algebra and a(cid:30)ne
Lie algebra.............................................................................. 50
Gutik O. Topological property of Taimanov semigroups.................................. 51
Ilash N. B. Hilbert polynomials of the algebras of SL -invariants........................ 52
2
Ishchuk Yu. B. Zero-divisors graphs of (cid:28)nite semigroups................................. 53
(cid:7)
Ka(cid:1)lnai P., Zemli(cid:7)cka J. Compactness in abelian categories............................... 54
Kashuba I. Indecomposable modules over Kantor superalgebras.......................... 55
Kaydan N. V., Pashchenko Z. D. On identity in (cid:28)nite rings............................. 56
Kirilyuk D. I. Self-returning and centroids of polygons of n-ary groups .................. 57
Klimenko I. S., Lysenko S. V., Petravchuk A. P. On Lie algebras of derivations
with large abelian ideals ................................................................ 58
Kniahina V. N. On the class of (cid:28)nite groups whose maximal B-groups are all Hall....... 59
Korolenko N. O. E(cid:27)ective generation of free groups of permutations..................... 60
Kostyshyn E. M. On Auslander algebra of the symmetric semigroup of degree 2......... 61
Kovaleva V. A. A criterion for a (cid:28)nite group to be σ-soluble ............................ 62
6
Kozerenko S. O. Constructing (cid:28)nite trees for given maps................................ 63
Krainichuk H. V. About classi(cid:28)cation of small length generalized binary
functional equations on quasigroups..................................................... 64
Krainichuk H. V., Tarasevych A. V. On classi(cid:28)cation of non-trivial
binary-ternary quasigroup equations in two functional variables ......................... 65
Kriukova G. V., Shvai N. O. Unitary similarity criterion for in(cid:28)nite upper
triangular matrices...................................................................... 66
Kukharev A. V., Puninski G. E. Serial group rings of simple (cid:28)nite groups............... 67
Kulakovska I. V., Zhuravska I. M. Mathematical modeling container network
via a connected graph................................................................... 68
Kulazhenko Yu. I. Thomsen’s (cid:28)gure, centroids and self-returning elements
of n-ary groups......................................................................... 69
Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S. Leibniz algebras
whose subideals are ideals............................................................... 70
Kuz’min A. Lattice of subvarieties of the variety generated by the Grassmann algebra... 71
Kuznetsova A. R., Vorob’ev N. N. On minimal composition Hartley functions
of partially composition Fitting classes.................................................. 72
Kuznitska B. M. Matrix reduction via invertible Hankel matrices and
square stable range one................................................................. 73
Kyrchei I. I. Cramer’s Rule for two-sided restricted quaternionic matrix equation........ 74
Kyrychenko V. V., Khybyna M. A., Maschenko L. Z. Semiperfect principal ideal rings... 75
Leshchenko Yu. On the normal structure of a transitive Sylow p-subgroup
of the (cid:28)nitary symmetric group......................................................... 76
Levandovskyy V. Factorization of noncommutative polynomials.......................... 77
Lishchynskyj I. I. A relationship between determinant and paradeterminant............. 78
Lukashova T. D., Lyman F. M., Drushlyak M. G. In(cid:28)nite periodic groups with
the locally nilpotent non-Dedekind norm of decomposable subgroups.................... 79
Luno N. B. On derivations for Chebyshev polynomials of the (cid:28)rst kind
and related identities.................................................................... 80
Lytvynchuk I. V. On one property of modular representations of the dihedral group
of order 8............................................................................... 81
Makhrovskaya N. A. Investigation and analysis of algorithms
for solving NP-complete problems....................................................... 82
Maloid-Hlyebova M. O., Ronska N. R. 2-good Bezout duo rings and
stable range conditions.................................................................. 83
Martsinkevich A. V. π-Normal products of Fitting classes with given properties ......... 84
Martsinkovsky A., Russell J. (Co-)torsion via stable functors............................ 85
Melnyk I. O. On Keigher semimodules.................................................. 86
7
Melnyk O. M., Kolyada R. V. On square roots of integer matrices....................... 87
Monakhov V. S., Sokhor I. L. Groups with A2-subnormal subgroups..................... 88
Murashka V. I. On the quasinilpotent hypercenter of a (cid:28)nite group...................... 89
Nikitchenko M. S., Shkilniak S. S. Multi-relational algebras as semantics
of quasiary logics ....................................................................... 90
Oliynyk A. S. Self-similar closures of free products of group ............................. 91
Oliynyk D. A. Commuting graphs of metabelian groups................................. 92
Oliynyk M. A. Honey encryption applied to Rabin cryptosystem......................... 93
Olshevska V. A. Algorithms for computations in Sylow 2-subgroups
of symmetric and alternating groups.................................................... 94
Olshevskyi M. S. Distances in Cayley graphs of alternating group........................ 95
Par(cid:28)ankou K. L., Vasil’ev A. F., Vasil’eva T. I. On threefactorized (cid:28)nite groups........ 96
Petechuk V. M., Petechuk J. V. Homomorphisms of matrix groups above
the associative rings .................................................................... 97
Petravchuk A. P., Shevchyk O. M., Sysak K. Ya. On locally nilpotent Lie algebras
of derivations........................................................................... 98
Petrychkovych V. M., Dzhaliuk N. S. A bound on degrees of solutions of
the matrix linear bilateral polynomial equation.......................................... 99
Pham Ngoc Anh. Peirce decomposition, Peirce idempotents and rings .................. 100
Pihura O. V. Commutative Bezout rings in which zero is adequate..................... 101
Plakhotnyk M. On the max-indecomposable exponent matrices......................... 102
Plakosh A. I. On cohomologies of the Kleinian 4-group................................. 103
Popovich T. V., Shcherbacov V. A. Parastroph orthogonality of alinear quasigroups.... 104
Popovych R. B., Skuratovskii R. V. Normal bases and elements of high order
in (cid:28)nite (cid:28)eld extensions based on cyclotomic polynomials .............................. 105
Prokhorchuk V. A. Automata that generate metabelian groups......................... 106
Prokip V. M. On solvability of the matrix equation AX XB over integral domains... 107
(cid:16)
Prokopchuk O. M. Free products in groups of in(cid:28)nite unitriangular matrieces........... 108
Pypka A. A. On locally (cid:28)nite groups whose cyclic subgroups are GNA-subgroups ...... 109
Pypka A. A., Storozhenko D. Yu. On Wiegold’s function............................... 110
Pyrch N. M. Equivalence of bundles and topological isomorphisms of function spaces... 111
Radova A., Varbanets S. On exponential sums involving the divisor function over Z i .. 112
r s
Raievska I. Iu., Raievska M. Iu. Local nearrings of order p3 ............................ 113
Ram(cid:1)irez L. E., Zadunaisky P. Gelfand(cid:21)Tsetlin modules with arbitrary characters....... 114
Romaniv A. M. The Smith normal form of the lest common multiples
of one class of matrices ................................................................ 115
8
Romaniv O. M., Sagan A. V. When R X and R X are ω-Euclidean domain.......... 116
p q x y
Savastru O. V. Summatory formula for Fourier coe(cid:30)cients of cusp forms over square... 117
Savchin V. M., Budochkina S. A. On some algebraic structures associated
with in(cid:28)nite-dimensional dynamical systems ........................................... 118
Savchuk A., Gutik O. On the semigroup ID .......................................... 119
8
Schwarz J. F. Noncommutative versions of Noether’s Problem ......................... 120
Semenchuk V. N., Skiba A. N. Finite groups with systems
of K-F-subnormal subgroups........................................................... 121
Semko N. N., Velychko T. V. On groups whose subgroups of in(cid:28)nite special rank
are transitively normal................................................................. 122
Shavarovskii B. Z. Improved triangular form of the matrix and its invariants........... 123
Shchedryk V. P. Helmer lemma for Bezout domains of stable range 1.5................. 124
Skobelev V. G. On languages accepted by quantum (cid:28)nite 1-way 1-qubit automata...... 125
Skobelev V. V. On compositions of attributed transition systems....................... 126
Skochko V. M. On growth function of initial invertible automata....................... 127
Sokhatsky F. M., Tarkovska O. O. On linearity of isotopes of Abelian groups........... 128
Stakhiv L. On the Tate-Shafarevich groups of certain elliptic curves .................... 129
Stepkin A. V. Finite graph exploration by two agents.................................. 130
Styopochkina M. V. On coe(cid:30)cients of transitiveness of posets of special type........... 131
Syrbu P. On a generalization of the Albert’s theorem .................................. 132
Tan Shaobin. On integrable representations for toroidal EALAs........................ 133
Tro(cid:28)muk A. A. On solvable groups with restrictions on cofactors of subgroups
from Fitting subgroup................................................................. 134
Tsimbolynets R. F. On bm-prime numbers............................................. 135
Tushev A. V. On primitivity of group algebras of certain groups of (cid:28)nite rank.......... 136
Tylyshchak A. A. On the estimation of the number of indecomposable representations
of given degree of a cyclic group ....................................................... 137
Ustimenko V. A. Wild and tame maps on free modules over commutative rings and
graph based cryptography ............................................................. 138
Varbanets P. r-divisors on Z and Z i .................................................. 139
r s
Varbanets S. Congruent generators of pseudo-random numbers......................... 140
Vorob’ev N. T., Vasilevich T. B. On Hartley sets and injectors of a (cid:28)nite group........ 141
Zabavsky B. V. K-theoretical aspect of elementary divisor ring......................... 142
Zaciha Ya. V. On characteristic properties of semigroups of order 3.................... 143
Zelenskiy O. V., Darmosiuk V. M., Kasyaniuk M. V. Minimal exponent matrices ...... 144
9
Zelisko H. On acts with the insertion-of-factor-property and two-sided subacts ......... 145
Zelisko V. R., Kuchma M. I. About (cid:28)nding all factorizations of symmetric matrices
over polynomial and quasipolynomial rings with involution............................. 146
Zhang Yingbo. Matrix bimodule problems.............................................. 147
Zhuchok A. V. On free commutative trioids............................................ 148
Zhuchok Yu. V. Representations of ordered trioids by binary relations.................. 149
ˆ(cid:224)º(cid:252)(cid:236)(cid:224)Œ (cid:192). (cid:204)., —(cid:243)æ(cid:224)Œ(cid:238)(cid:226) (cid:192). ˜., (cid:209)(cid:229)º(cid:252)ŒŁ(cid:237) (cid:204). ´. ˛Æ (cid:224)ææ(cid:238)(cid:246)Ł(cid:224)(cid:242)Ł(cid:226)(cid:237)(cid:238)æ(cid:242)Ł
Ł (cid:239)(cid:238)º(cid:243)(cid:224)ææ(cid:238)(cid:246)Ł(cid:224)(cid:242)Ł(cid:226)(cid:237)(cid:238)æ(cid:242)Ł (cid:238)(cid:228)(cid:237)(cid:238)Ø (cid:239)(cid:238)ºŁ(cid:224)(cid:228)Ł(cid:247)(cid:229)æŒ(cid:238)Ø (cid:238)(cid:239)(cid:229)(cid:240)(cid:224)(cid:246)ŁŁ.............................. 150
—(cid:243)æ(cid:224)Œ(cid:238)(cid:226) (cid:192). ˜. ˛ (cid:242)(cid:238)(cid:230)(cid:228)(cid:229)æ(cid:242)(cid:226)(cid:224)ı (cid:224)ææ(cid:238)(cid:246)Ł(cid:224)(cid:242)Ł(cid:226)(cid:237)(cid:238)æ(cid:242)Ł (cid:226) (cid:239)(cid:238)ºŁ(cid:224)(cid:228)Ł(cid:247)(cid:229)æŒŁı ª(cid:240)(cid:243)(cid:239)(cid:239)(cid:238)Ł(cid:228)(cid:224)ı......... 151
(cid:211)(cid:240)æ(cid:243) ´. ¨. ˚(cid:226)(cid:224)(cid:231)Ł(cid:242)(cid:238)(cid:230)(cid:228)(cid:229)æ(cid:242)(cid:226)(cid:224) (cid:237)Łº(cid:252)(cid:239)(cid:238)(cid:242)(cid:229)(cid:237)(cid:242)(cid:237)ßı Ø(cid:238)(cid:240)(cid:228)(cid:224)(cid:237)(cid:238)(cid:226)ßı º(cid:243)(cid:239)........................ 152
(cid:192)(cid:226)(cid:228)„„(cid:226)(cid:224) (cid:210). ´. C(cid:239)(cid:229)Œ(cid:242)(cid:240)Ł (cid:236)(cid:224)(cid:242)(cid:240)Ł(cid:246)(cid:252) æ(cid:243)(cid:236)i(cid:230)(cid:237)(cid:238)æ(cid:242)(cid:229)Ø æ(cid:224)ª(cid:224)Ø(cid:228)(cid:224)Œ(cid:224) Q A (cid:242)(cid:224)
p q
(cid:228)(cid:226)(cid:238)(cid:228)(cid:238)º(cid:252)(cid:237)(cid:238)ª(cid:238) ª(cid:240)(cid:224)(cid:244)(cid:224) PQ A (cid:237)(cid:229)(cid:242)(cid:229)(cid:240)(cid:238)(cid:226)(cid:238)ª(cid:238) æº(cid:224)Æ(cid:238)(cid:239)(cid:229)(cid:240)(cid:226)Ł(cid:237)(cid:237)(cid:238)ª(cid:238)
p q
(cid:237)(cid:224)(cid:239)i(cid:226)(cid:228)(cid:238)æŒ(cid:238)(cid:237)(cid:224)º(cid:238)ª(cid:238) 2-Œiº(cid:252)(cid:246)(cid:255) A ......................................................... 153
(cid:209)Œ(cid:243)(cid:240)(cid:224)(cid:242)(cid:238)(cid:226)æ(cid:252)ŒŁØ —. ´. (cid:209)(cid:242)(cid:240)(cid:243)Œ(cid:242)(cid:243)(cid:240)(cid:224) i (cid:236)i(cid:237)i(cid:236)(cid:224)º(cid:252)(cid:237)(cid:224) æŁæ(cid:242)(cid:229)(cid:236)(cid:224) (cid:242)(cid:226)i(cid:240)(cid:237)Łı
æŁº(cid:238)(cid:226)æ(cid:252)ŒŁı 2-(cid:239)i(cid:228)ª(cid:240)(cid:243)(cid:239) (cid:231)(cid:237)(cid:224)Œ(cid:238)(cid:231)(cid:236)i(cid:237)(cid:237)(cid:238)¤ ª(cid:240)(cid:243)(cid:239)Ł (cid:242)(cid:224) ¤ı (cid:246)(cid:229)(cid:237)(cid:242)(cid:240)(cid:224)ºi(cid:231)(cid:224)(cid:242)(cid:238)(cid:240)Ł...................... 154
(cid:210)(cid:243)(cid:240)Œ(cid:224) (cid:210). ´. ˜(cid:229)(cid:255)Œi (cid:239)(cid:240)ŁŒº(cid:224)(cid:228)Ł (cid:237)(cid:224)(cid:239)i(cid:226)ª(cid:240)(cid:243)(cid:239) (cid:226)i(cid:228)(cid:239)(cid:238)(cid:226)i(cid:228)(cid:237)(cid:238)æ(cid:242)(cid:229)Ø............................... 155
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