Reza Zomorrodian - Academia.edu (original) (raw)
Papers by Reza Zomorrodian
تخصصی زبان و ادبیات دانشکده ادبیات و علوم انسانی, Sep 12, 2004
JP Journal of Geometry and Topology, 2018
Macromolecules, 2021
Ethylene and 1-hexene were copolymerized by a hafnium salan-type catalyst activated by B(C6F5)3 p... more Ethylene and 1-hexene were copolymerized by a hafnium salan-type catalyst activated by B(C6F5)3 producing copolymers over a wide range of 1-hexene incorporation. GPC analysis of the resulting copol...
Illinois Journal of Mathematics, 2007
The derived series for all co-compact non-perfect Fuchsian groups are investigated. These groups ... more The derived series for all co-compact non-perfect Fuchsian groups are investigated. These groups are residually finite and residually soluble. The intersection of the derived series for these groups is the identity. We will show that if Γ is not perfect, then the number of terms in the derived series up to and including the first surface group cannot exceed 4. We then use this result to compute the derived series of some important general triangle groups.
Journal of Business & Economics Research (JBER), 2011
This paper empirically investigates, in the context of vector autoregression and error-correction... more This paper empirically investigates, in the context of vector autoregression and error-correction methodology, the link between three confidence measures of consumers, investors, businesses, and economic fluctuations. Using quarterly data for the United Sates from 1980 to 2005, we found that the hypothesis that these confidence measures do not Granger-cause GDP was rejected, even after controlling for other macroeconomic variables. Forecast Variance decompositions of GDP suggest that consumer confidence, stock return, and purchasing manger’s index, account for large variations in GDP. Overall, the results reconfirm the views that these measures play important roles in economic fluctuations.
DESCRIPTION In this paper, we investigate distinct types of groups of genus two in complete detai... more DESCRIPTION In this paper, we investigate distinct types of groups of genus two in complete detail. We prove that, there are exactly four types of groups of genus two and we give their presentations as finitely presented, transitive permutation representations of certain degrees. We give their character tables, matrix representations, and their primary invariants and their Cayley color graphs and/or their Shreier’s coset graphs. We also compute the equations of the hyperelliptic curves covered by these four types of groups, which happen to be the groups obtained from the maximal automorphism bound for the soluble (|G|=48(g-1)), supersoluble |G|=24, nilpotent (16(g-1)) and the quaternion (4, 4, 4)-group of order 8 for g = 2.
In this note we use a new technique involving invariant subspaces of certain vector space that ca... more In this note we use a new technique involving invariant subspaces of certain vector space that can be used to compute the soluble series and in particular to find all curves covered by the maximal soluble automorphism groups of Riemann surfaces of genus not exceeding some given integer N.
We extend the results of D. Garbe [Math. Ann. 235, 195-215 (1978; Zbl 0377.10014)], A. M. Macbeat... more We extend the results of D. Garbe [Math. Ann. 235, 195-215 (1978; Zbl 0377.10014)], A. M. Macbeath [Number Theory, Proc. Symp. Pure Math. 12, 14-32 (1969; Zbl 0192.35703)] and A. Sinkov [J. Algebra 12, 525-532 (1969; Zbl 0174.31201)] to classify all epimorphisms (l,m,n)→PSL(2,p f ) [PGL(2,p f )]. We obtain a complete set of conditions under which PSL(2,p f ) [PGL(2,p f )] is a factor group of any chosen finite or infinite triangle group.
Proceedings of the American Mathematical Society
The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earl... more The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earlier papers by this author. In this note the author wishes to correct the necessity of the condition given in Theorem (4.3) of Bounds for the order of supersoluble automorphism groups of Riemann surfaces (Proc. Amer. Math. Soc. 108 (1990), 587-600), which was left out at the time of writing the paper. The author also wishes to apologize to the readers for that.
Transactions of the American Mathematical Society, 1985
The action of nilpotent groups as automorphisms of compact Riemann surfaces is investigated. It i... more The action of nilpotent groups as automorphisms of compact Riemann surfaces is investigated. It is proved that the order of a nilpotent group of automorphisms of a surface of genus g ⩾ 2 g \geqslant 2 cannot exceed 16 ( g − 1 ) 16(g - 1) . Exact conditions of equality are obtained. This bound corresponds to a specific Fuchsian group given by the signature (0;2,4,8).
The Quarterly Journal of Mathematics, 2009
In this work, we generalize the theory of elliptic modular functions, to the case of genus 7. We ... more In this work, we generalize the theory of elliptic modular functions, to the case of genus 7. We investigate the equations of all algebraic curves of genus 7, their automorphism groups and their link to modern algebraic geometry and the theory of hyperelliptic curves. We discuss the cyclic covers of any curve of genus 7, the local structure of the moduli space at the corresponding Weierstrass points for each curve. We show that the largest finite group acting as the full automorphism group of a hyperelliptic curve of genus 7 has order 64 and we find its equation. We then obtain all the 3g − 3 = 18 hyperelliptic curves of genus 7 and their full automorphism groups. We discover that there are merely three other finite groups of the order >64 acting on some non-hyperelliptic curves of genus 7. We also obtain the equations of the non-hyperelliptic curves.
Proceedings of the American Mathematical Society, 1990
The maximal automorphism groups of compact Riemann surfaces for a class of groups positioned betw... more The maximal automorphism groups of compact Riemann surfaces for a class of groups positioned between nilpotent and soluble groups is investigated. It is proved that if G G is any finite supersoluble group acting as the automorphism group of some compact Riemann surface Ω \Omega of genus g ≥ 2 g \geq 2 , then: (i) If g = 2 g = 2 then | G | ≤ 24 |G| \leq 24 and equality occurs when G G is the supersoluble group D 4 ⊗ Z 3 {D_4} \otimes {{\mathbf {Z}}_3} that is the semidirect product of the dihedral group of order 8 and the cyclic group of order 3. This exceptional case occurs when the Fuchsian group Γ \Gamma has the signature (0;2,4,6), and can cover only this finite supersoluble group of order 24. (ii) If g ≥ 3 g \geq 3 then | G | ≤ 18 ( g − 1 ) |G| \leq 18\left ( {g - 1} \right ) , and if | G | = 18 ( g − 1 ) |G| = 18\left ( {g - 1} \right ) then ( g − 1 ) \left ( {g - 1} \right ) must be a power of 3. Conversely if ( g − 1 ) = 3 n , n ≥ 2 \left ( {g - 1} \right ) = {3^n},n \geq 2 ,...
Glasgow Mathematical Journal, 1987
In a previous paper [7], I have made a study of the ”nilpotent” analogue of Hurwitz theorem [4] b... more In a previous paper [7], I have made a study of the ”nilpotent” analogue of Hurwitz theorem [4] by considering a particular family of signatures called ”nilpotent admissible” [5]. We saw however, that if μN(g) represents the order of the largest nilpotent group of automorphisms of a surface of genus g < 2, then μN(g) < 16(g − 1) and this upper bound occurs when the covering group is a triangle group having the signature (0; 2,4,8) which is in its own 2-local formThe restriction to the nilpotent groups enabled me to obtain much more precise information than was available in the general case. Moreover, all nilpotent groups attaining this maximum order turned out to be ”2-groups”. Since every finite nilpotent group is the direct product of its Sylow subgroups and the groups of automorphisms are factor groups of the Fuchsian groups, it is natural for us to study the Fuchsian groups havin p-local signatures to obtain more precise information about the finite p-groups, and hence abo...
Glasgow Mathematical Journal, 2003
Using the definition of regular p-group given by M. Hall [1], a new class of finite groups called... more Using the definition of regular p-group given by M. Hall [1], a new class of finite groups called regular-nilpotent has been defined. The action of these groups as automorphisms of compact Riemann surfaces has been investigated. It is proved that a necessary and sufficient condition for a Fuchsian group to cover a regular-nilpotent group is that its orbit genus be zero and its periods satisfy the least common multiple condition, first defined by Harvey [2] and Maclachlan [4].
Transactions of the American Mathematical Society, 1985
Proceedings of American Mathematical Society, 2002
The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earl... more The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earlier papers by this author. In this note the author wishes to correct the necessity of the condition given in Theorem (4.3) of Bounds for the order of supersoluble automorphism groups of Riemann surfaces (Proc.
تخصصی زبان و ادبیات دانشکده ادبیات و علوم انسانی, Sep 12, 2004
JP Journal of Geometry and Topology, 2018
Macromolecules, 2021
Ethylene and 1-hexene were copolymerized by a hafnium salan-type catalyst activated by B(C6F5)3 p... more Ethylene and 1-hexene were copolymerized by a hafnium salan-type catalyst activated by B(C6F5)3 producing copolymers over a wide range of 1-hexene incorporation. GPC analysis of the resulting copol...
Illinois Journal of Mathematics, 2007
The derived series for all co-compact non-perfect Fuchsian groups are investigated. These groups ... more The derived series for all co-compact non-perfect Fuchsian groups are investigated. These groups are residually finite and residually soluble. The intersection of the derived series for these groups is the identity. We will show that if Γ is not perfect, then the number of terms in the derived series up to and including the first surface group cannot exceed 4. We then use this result to compute the derived series of some important general triangle groups.
Journal of Business & Economics Research (JBER), 2011
This paper empirically investigates, in the context of vector autoregression and error-correction... more This paper empirically investigates, in the context of vector autoregression and error-correction methodology, the link between three confidence measures of consumers, investors, businesses, and economic fluctuations. Using quarterly data for the United Sates from 1980 to 2005, we found that the hypothesis that these confidence measures do not Granger-cause GDP was rejected, even after controlling for other macroeconomic variables. Forecast Variance decompositions of GDP suggest that consumer confidence, stock return, and purchasing manger’s index, account for large variations in GDP. Overall, the results reconfirm the views that these measures play important roles in economic fluctuations.
DESCRIPTION In this paper, we investigate distinct types of groups of genus two in complete detai... more DESCRIPTION In this paper, we investigate distinct types of groups of genus two in complete detail. We prove that, there are exactly four types of groups of genus two and we give their presentations as finitely presented, transitive permutation representations of certain degrees. We give their character tables, matrix representations, and their primary invariants and their Cayley color graphs and/or their Shreier’s coset graphs. We also compute the equations of the hyperelliptic curves covered by these four types of groups, which happen to be the groups obtained from the maximal automorphism bound for the soluble (|G|=48(g-1)), supersoluble |G|=24, nilpotent (16(g-1)) and the quaternion (4, 4, 4)-group of order 8 for g = 2.
In this note we use a new technique involving invariant subspaces of certain vector space that ca... more In this note we use a new technique involving invariant subspaces of certain vector space that can be used to compute the soluble series and in particular to find all curves covered by the maximal soluble automorphism groups of Riemann surfaces of genus not exceeding some given integer N.
We extend the results of D. Garbe [Math. Ann. 235, 195-215 (1978; Zbl 0377.10014)], A. M. Macbeat... more We extend the results of D. Garbe [Math. Ann. 235, 195-215 (1978; Zbl 0377.10014)], A. M. Macbeath [Number Theory, Proc. Symp. Pure Math. 12, 14-32 (1969; Zbl 0192.35703)] and A. Sinkov [J. Algebra 12, 525-532 (1969; Zbl 0174.31201)] to classify all epimorphisms (l,m,n)→PSL(2,p f ) [PGL(2,p f )]. We obtain a complete set of conditions under which PSL(2,p f ) [PGL(2,p f )] is a factor group of any chosen finite or infinite triangle group.
Proceedings of the American Mathematical Society
The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earl... more The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earlier papers by this author. In this note the author wishes to correct the necessity of the condition given in Theorem (4.3) of Bounds for the order of supersoluble automorphism groups of Riemann surfaces (Proc. Amer. Math. Soc. 108 (1990), 587-600), which was left out at the time of writing the paper. The author also wishes to apologize to the readers for that.
Transactions of the American Mathematical Society, 1985
The action of nilpotent groups as automorphisms of compact Riemann surfaces is investigated. It i... more The action of nilpotent groups as automorphisms of compact Riemann surfaces is investigated. It is proved that the order of a nilpotent group of automorphisms of a surface of genus g ⩾ 2 g \geqslant 2 cannot exceed 16 ( g − 1 ) 16(g - 1) . Exact conditions of equality are obtained. This bound corresponds to a specific Fuchsian group given by the signature (0;2,4,8).
The Quarterly Journal of Mathematics, 2009
In this work, we generalize the theory of elliptic modular functions, to the case of genus 7. We ... more In this work, we generalize the theory of elliptic modular functions, to the case of genus 7. We investigate the equations of all algebraic curves of genus 7, their automorphism groups and their link to modern algebraic geometry and the theory of hyperelliptic curves. We discuss the cyclic covers of any curve of genus 7, the local structure of the moduli space at the corresponding Weierstrass points for each curve. We show that the largest finite group acting as the full automorphism group of a hyperelliptic curve of genus 7 has order 64 and we find its equation. We then obtain all the 3g − 3 = 18 hyperelliptic curves of genus 7 and their full automorphism groups. We discover that there are merely three other finite groups of the order >64 acting on some non-hyperelliptic curves of genus 7. We also obtain the equations of the non-hyperelliptic curves.
Proceedings of the American Mathematical Society, 1990
The maximal automorphism groups of compact Riemann surfaces for a class of groups positioned betw... more The maximal automorphism groups of compact Riemann surfaces for a class of groups positioned between nilpotent and soluble groups is investigated. It is proved that if G G is any finite supersoluble group acting as the automorphism group of some compact Riemann surface Ω \Omega of genus g ≥ 2 g \geq 2 , then: (i) If g = 2 g = 2 then | G | ≤ 24 |G| \leq 24 and equality occurs when G G is the supersoluble group D 4 ⊗ Z 3 {D_4} \otimes {{\mathbf {Z}}_3} that is the semidirect product of the dihedral group of order 8 and the cyclic group of order 3. This exceptional case occurs when the Fuchsian group Γ \Gamma has the signature (0;2,4,6), and can cover only this finite supersoluble group of order 24. (ii) If g ≥ 3 g \geq 3 then | G | ≤ 18 ( g − 1 ) |G| \leq 18\left ( {g - 1} \right ) , and if | G | = 18 ( g − 1 ) |G| = 18\left ( {g - 1} \right ) then ( g − 1 ) \left ( {g - 1} \right ) must be a power of 3. Conversely if ( g − 1 ) = 3 n , n ≥ 2 \left ( {g - 1} \right ) = {3^n},n \geq 2 ,...
Glasgow Mathematical Journal, 1987
In a previous paper [7], I have made a study of the ”nilpotent” analogue of Hurwitz theorem [4] b... more In a previous paper [7], I have made a study of the ”nilpotent” analogue of Hurwitz theorem [4] by considering a particular family of signatures called ”nilpotent admissible” [5]. We saw however, that if μN(g) represents the order of the largest nilpotent group of automorphisms of a surface of genus g < 2, then μN(g) < 16(g − 1) and this upper bound occurs when the covering group is a triangle group having the signature (0; 2,4,8) which is in its own 2-local formThe restriction to the nilpotent groups enabled me to obtain much more precise information than was available in the general case. Moreover, all nilpotent groups attaining this maximum order turned out to be ”2-groups”. Since every finite nilpotent group is the direct product of its Sylow subgroups and the groups of automorphisms are factor groups of the Fuchsian groups, it is natural for us to study the Fuchsian groups havin p-local signatures to obtain more precise information about the finite p-groups, and hence abo...
Glasgow Mathematical Journal, 2003
Using the definition of regular p-group given by M. Hall [1], a new class of finite groups called... more Using the definition of regular p-group given by M. Hall [1], a new class of finite groups called regular-nilpotent has been defined. The action of these groups as automorphisms of compact Riemann surfaces has been investigated. It is proved that a necessary and sufficient condition for a Fuchsian group to cover a regular-nilpotent group is that its orbit genus be zero and its periods satisfy the least common multiple condition, first defined by Harvey [2] and Maclachlan [4].
Transactions of the American Mathematical Society, 1985
Proceedings of American Mathematical Society, 2002
The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earl... more The maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earlier papers by this author. In this note the author wishes to correct the necessity of the condition given in Theorem (4.3) of Bounds for the order of supersoluble automorphism groups of Riemann surfaces (Proc.