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Temitope Gbolahan Jaiyeola - One of the best experts on this subject based on the ideXlab platform.
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ON HOLOMORPHY OF FENYVES BCI-ALGEBRAS
Journal of the Nigerian Mathematical Society, 2019Co-Authors: Emmanuel Ilojide, Temitope Gbolahan Jaiyeola, Memudu Olaposi OlatinwoAbstract:Fenyves BCI-algebras are BCI-algebras that satisfy the Bol-Moufang identities. In this paper, the holomorphy of BCI-algebras are studied. It is shown that whenever a loop and its holomorph are BCI-algebras, the former is $p$-semisimple if and only if the latter is $p$-semisimple. Whenever a loop and its holomorph are BCI-algebras, it is established that the former is a BCK-algebra if and only if the latter has a BCK-subalgebra. Moreover, the holomorphy of the associative and some non-associative Fenyves BCI-algebras are also studied.
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Holomorphic Structure of Middle Bol Loops
2017Co-Authors: Temitope Gbolahan Jaiyeola, Emmanuel Ilojide, Sunday Peter David, Yakubu Tunde OyeboAbstract:A loop $(Q,cdot,backslash,/)$ is called a middle Bol loop if it obeys the identity $x(yzbackslash x)=(x/z)(ybackslash x)$.To every right (left) Bol loop corresponds a middle Bol loop via an isostrophism. In this paper, the structure of the holomorph of a middle Bol loop is explored. For some special types of automorphisms, the holomorph of a commutative loop is shown to be a commutative middle Bol loop if and only if the loop is a middle Bol loop and its automorphism group is abelian and a subgroup of both the group of middle regular mappings and the right multiplication group. It was found that commutativity (flexibility) is a necessary and sufficient condition for holomorphic invariance under the existing isostrophy between middle Bol loops and the corresponding right (left) Bol loops. The right combined holomorph of a middle Bol loop and its corresponding right (left) Bol loop was shown to be equal to the holomorph of the middle Bol loop if and only if the automorphism group is abelian and a subgroup of the multiplication group of the middle Bol loop. The obedience of an identity dependent on automorphisms was found to be a necessary and sufficient condition for the left combined holomorph of a middle Bol loop and its corresponding left Bol loop to be equal to the holomorph of the middle Bol loop.
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Holomorph of Generalized Bol Loops II
viXra, 2015Co-Authors: Temitope Gbolahan JaiyeolaAbstract:The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular.
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Holomorph of generalized Bol loops II
Discussiones Mathematicae - General Algebra and Applications, 2015Co-Authors: Temitope Gbolahan Jaiyeola, Bolaji Ajibola PopoolaAbstract:The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient condition for the holomorph of a RIPL to be a Bol loop are deduced. Some algebraic properties and commutative diagrams are established for a RIPL whose holomorph is a GBL.
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An Holomorphic Study Of Smarandache Automorphic and Cross Inverse Property Loops
arXiv: General Mathematics, 2008Co-Authors: Temitope Gbolahan JaiyeolaAbstract:By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop.
Walter M. Jaklitsch - One of the best experts on this subject based on the ideXlab platform.
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European species of Hypocrea part II: species with hyaline ascospores
Fungal Diversity, 2011Co-Authors: Walter M. JaklitschAbstract:To date 75 species of Hypocrea / Trichoderma forming teleomorphs are recognised in Europe. The 56 hyaline-spored species are here described in detail and illustrated in colour plates, including cultures and anamorphs. This number includes 16 new Holomorphs, two new teleomorphs and nine anamorphs of species previously described as teleomorphs. Phylogenetic placement and relationships of the species are shown on the strict consensus tree, based on sequences of RNA polymerase II subunit b ( rpb2 ) and translation elongation factor 1 alpha ( tef1 ) exon, comprising 135 species of the genus Hypocrea / Trichoderma . All available holotypes of species described from Europe including some from North America have been examined. A dichotomous key to the species is provided primarily utilising ecological and morphological traits of the teleomorphs and, where necessary, morphology of the anamorphs and cultures, and growth rates. Species descriptions are subdivided among five chapters, arranged primarily according to the larger phylogenetic clades, viz. section Trichoderma with 13 species, the pachybasium core group with 13 species including four species with stipitate stromata (‘ Podostroma ’), species forming large effused stromata with 10 species including the section Hypocreanum , 9 species of the Brevicompactum , Lutea and Psychrophila clades, and 11 residual species of various smaller clades or of unknown phylogenetic placement. Finally, a list comprising dubious names and species excluded from Hypocrea that are relevant for Europe, or species claimed to occur in Europe by other authors is provided. Hypocrea minutispora is by far the most common species in Europe. For H. moravica , H. subalpina and H. tremelloides the anamorphs are newly described. The anamorphs of the latter two species and H. sambuci produce hyaline conidia on unusual structures new to Trichoderma . These three species form a new subclade of the morphologically strikingly different section Longibrachiatum , which is currently only represented by H. schweinitzii in Europe as a holomorph. The subclade is not named yet formally due to low statistical support. H. fungicola f. raduli is described as the new species H. austriaca , while H. hypomycella was found not to belong to Hypocrea . The typification of H. pilulifera , H. tremelloides and H. lutea has been clarified. Gliocladium deliquescens , the anamorph of H. lutea , is combined in Trichoderma . Species are epitypified where appropriate. Anamorph names are established prospectively to avoid numerous new combinations in future when they may be possibly used as holomorphic names if the ICBN is altered accordingly.
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European species of Hypocrea part II: species with hyaline ascospores
2010Co-Authors: Walter M. JaklitschAbstract:forming teleomorphs are recognised in Europe. The 56 hyaline-spored species are here described in detail and illustrated in colour plates, including cultures and ana-morphs. This number includes 16 new Holomorphs, two new teleomorphs and nine anamorphs of species previously described as teleomorphs. Phylogenetic placement and relationships of the species are shown on the strict consensus tree, based on sequences of RNA polymerase II subunit b (rpb2) and translation elongation factor 1 alpha (tef1) exon, comprising 135 species of the genus Hypocrea/Trichoderma. All available holotypes of species described from Europe including some from North America have been examined. A dichotomous key to the species is provided primarily utilising ecological and morphological traits of the teleo-morphs and, where necessary, morphology of the anamorph
I E Grinshpon - One of the best experts on this subject based on the ideXlab platform.
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Normal Determinability of Torsion-Free Abelian Groups by Their Holomorphs
Journal of Mathematical Sciences, 2018Co-Authors: S. Ya. Grinshpon, I E GrinshponAbstract:We investigate torsion-free Abelian groups that are decomposable into direct sums or direct products of homogeneous groups normally defined by their Holomorphs. Properties of normal Abelian subgroups of Holomorphs of torsion-free Abelian groups are also studied.
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determinateness of torsion free abelian groups by their Holomorphs and almost holomorphic isomorphism
Journal of Mathematical Sciences, 2014Co-Authors: Ya S Grinshpon, I E GrinshponAbstract:In this paper, we study holomorphically isomorphic Abelian groups, i.e., Abelian groups with isomorphic Holomorphs. We also study a generalization of the concept of holomorphic isomorphism, namely, almost holomorphic isomorphism, which is deeply connected with normal Abelian subgroups of Holomorphs of Abelian groups. Torsion-free Abelian groups that are determined by their Holomorphs are highlighted from different classes. In particular, it has been found that any homogeneous separable group can be determined by its holomorph in the class of all Abelian groups.
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Vector Groups with Isomorphic Holomorphs
Journal of Mathematical Sciences, 2014Co-Authors: I E GrinshponAbstract:In this paper, vector groups whose Holomorphs are isomorphic are studied. In connection with the studied problem, the concepts of a semi-characteristic and Γ(G)-decomposition of a group are introduced. The properties of such decompositions are described. Isomorphism conditions of holomorphically isomorphic vector groups are found.
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Normal subgroups of Holomorphs of Abelian groups and almost holomorphic isomorphism
Journal of Mathematical Sciences, 2008Co-Authors: I E GrinshponAbstract:Two groups are said to be almost holomorphically isomorphic if each of them is isomorphic to a normal subgroup of the holomorph of the other group. In this paper, we study normal subgroups of Holomorphs of Abelian groups and highlight some torsion-free groups for which almost holomorphic isomorphism implies isomorphism. In addition, we consider the problem of determinateness of a group by its holomorph.
Jinke Hai - One of the best experts on this subject based on the ideXlab platform.
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the normalizer property for integral group rings of Holomorphs of finite groups with trivial center
Acta Mathematica Sinica, 2020Co-Authors: Jinke Hai, Yi Xin ZhuAbstract:Let G = Hol(H) be the holomorph of a finite group H. If there is a prime q dividing ⋎H⋎ such that every q-central automorphism of H is inner and Z(H) = 1, then every Coleman automorphism of G is inner. In particular, the normalizer property holds for G.
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The normalizer property for integral group rings of Holomorphs of finite nilpotent groups and the symmetric groups
Journal of Algebra and Its Applications, 2017Co-Authors: Jinke HaiAbstract:Let H be a finite group and let G be the holomorph of H. If H is a finite nilpotent group or a symmetric group Sn of degree n, then the normalizer property holds for G.
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The normalizer property for integral group rings of Holomorphs of finite nilpotent groups and the symmetric groups
Journal of Algebra and Its Applications, 2017Co-Authors: Jinke HaiAbstract:Let [Formula: see text] be a finite group and let [Formula: see text] be the holomorph of [Formula: see text]. If [Formula: see text] is a finite nilpotent group or a symmetric group [Formula: see text] of degree [Formula: see text], then the normalizer property holds for [Formula: see text].
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coleman automorphisms of Holomorphs of finite abelian groups
Acta Mathematica Sinica, 2014Co-Authors: Jinke HaiAbstract:Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.
Dubussy Christophe - One of the best experts on this subject based on the ideXlab platform.
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Convolution cohomologique holomorphe, transformation de Laplace enrichie et applications
Université de Liège Liège Belgique, 2019Co-Authors: Dubussy ChristopheAbstract:The Hadamard product of power series has been studied for more than one hundred years and has become a classical tool in complex analysis. Nonetheless, this product only concerns functions which are holomorphic near the origin. In 2009, T. Pohlen studied an extension of this Hadamard product on functions defined on open subsets of the Riemann sphere, which do not necessarily contain the origin. Using ad-hoc and explicit constructions, he could define this product thanks to a contour integration formula. However, his construction is non-symmetric with respect to 0 and the infinity. The first part of this thesis consists in the study of a generalization of Pohlen's extended Hadamard product. Using singular homology theory, we introduce more symmetric cycles and define a generalized Hadamard product which is equivalent to Pohlen's product when the functions vanish at infinity. Then, we show that this generalized Hadamard product is a particular case of a more general phenomenon called "holomorphic cohomological convolution". We study this convolution in detail on the multiplicative complex Lie group C^* and provide a contour integration formula to compute it. The second part of the thesis is devoted to the study of holomorphic Paley-Wiener type theorems due to Polya (in the compact case) and to Méril (in the non-compact case). These theorems use a contour integration version of the Laplace transform. Thanks to the theory of enhanced subanalytic sheaves developed by A. D'Agnolo and M. Kashiwara as well as the enhanced Laplace transform introduced by M. Kashiwara and P. Schapira, we show that such theorems can be understood from a cohomological point of view. Under some convex subanalytic conditions, we are even able to provide stronger Laplace isomorphisms between spaces which are described by tempered growth conditions. It appears that these spaces can be linked to certain spaces of analytic functionals. In the non-compact case, we define a convolution product between analytic functionals and conjecture that it is compatible with the additive version of the previously studied holomorphic cohomological convolution. Thanks to our results on the enhanced Laplace transform, we prove the conjecture in the subanalytic case.Le produit d'Hadamard entre séries de puissances entières a été étudié depuis plus de cent ans et est devenu un outil classique de l'analyse complexe. Néanmoins, ce produit concerne uniquement les fonctions holomorphes au voisinage de l'origine. En 2009, T. Pohlen a étudié une extension de ce produit d'Hadamard pour des fonctions définies sur des ouverts de la sphère de Riemann, qui ne contiennent pas nécessairement l'origine. En utilisant des constructions ad-hoc et explicites, il a pu définir ce produit via une intégrale de contour. Cependant, cette construction n'est pas symétrique par rapport à 0 et à l'infini. La première partie de cette thèse consiste en l'étude d'une généralisation du produit d'Hadamard étendu par Pohlen. Au moyen de la théorie de l'homologie singulière, nous introduisons des cycles plus symétriques et définissons un produit d'Hadamard généralisé, équivalent à celui de Pohlen quand les fonctions s'annulent à l'infini. Nous montrons ensuite que ce produit d'Hadamard généralisé est un cas particulier d'un phénomène plus général appelé "convolution cohomologique holomorphe". Nous étudions en détail cette convolution dans le cas du groupe de Lie complexe multiplicatif C^* et fournissons une formule à base d'intégrales de contour pour la calculer. La deuxième partie de la thèse est consacrée à l'étude de théorèmes de type Paley-Wiener holomorphes dus à Polya (dans le cas compact) et à Méril (dans le cas non compact). Ces théorèmes utilisent une version de la transformation de Laplace à base d'intégrales de contour. Grâce à la théorie des faisceaux sous-analytiques enrichis développée par A. D'Agnolo et M. Kashiwara, ainsi qu'à la transformation de Laplace enrichie introduite par M. Kashiwara et P. Schapira, nous montrons que ces théorèmes peuvent être compris d'un point de vue cohomologique. Sous certaines hypothèses de convexité et de sous-analyticité, il est même possible de prouver de plus forts isomorphismes de Laplace entre des espaces décrits par des conditions de croissance tempérée. Ces espaces peuvent être liés à certains espaces de fonctionnelles analytiques. Dans le cas non compact, nous définissons un produit de convolution entre fonctionnelles analytiques et conjecturons que ce produit est compatible avec la version additive de la convolution cohomologique holomorphe précédemment étudiée. Grâce à nos résultats sur la transformation de Laplace enrichie, nous prouvons cette conjecture dans le cas sous-analytique
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Convolution cohomologique holomorphe, transformation de Laplace enrichie et applications
Université de Liège Liège Belgique, 2019Co-Authors: Dubussy ChristopheAbstract:audience: researcherThe Hadamard product of power series has been studied for more than one hundred years and has become a classical tool in complex analysis. Nonetheless, this product only concerns functions which are holomorphic near the origin. In 2009, T. Pohlen studied an extension of this Hadamard product on functions defined on open subsets of the Riemann sphere, which do not necessarily contain the origin. Using ad-hoc and explicit constructions, he could define this product thanks to a contour integration formula. However, his construction is non-symmetric with respect to 0 and the infinity. The first part of this thesis consists in the study of a generalization of Pohlen's extended Hadamard product. Using singular homology theory, we introduce more symmetric cycles and define a generalized Hadamard product which is equivalent to Pohlen's product when the functions vanish at infinity. Then, we show that this generalized Hadamard product is a particular case of a more general phenomenon called "holomorphic cohomological convolution". We study this convolution in detail on the multiplicative complex Lie group C^* and provide a contour integration formula to compute it. The second part of the thesis is devoted to the study of holomorphic Paley-Wiener type theorems due to Polya (in the compact case) and to Méril (in the non-compact case). These theorems use a contour integration version of the Laplace transform. Thanks to the theory of enhanced subanalytic sheaves developed by A. D'Agnolo and M. Kashiwara as well as the enhanced Laplace transform introduced by M. Kashiwara and P. Schapira, we show that such theorems can be understood from a cohomological point of view. Under some convex subanalytic conditions, we are even able to provide stronger Laplace isomorphisms between spaces which are described by tempered growth conditions. It appears that these spaces can be linked to certain spaces of analytic functionals. In the non-compact case, we define a convolution product between analytic functionals and conjecture that it is compatible with the additive version of the previously studied holomorphic cohomological convolution. Thanks to our results on the enhanced Laplace transform, we prove the conjecture in the subanalytic case.Le produit d'Hadamard entre séries de puissances entières a été étudié depuis plus de cent ans et est devenu un outil classique de l'analyse complexe. Néanmoins, ce produit concerne uniquement les fonctions holomorphes au voisinage de l'origine. En 2009, T. Pohlen a étudié une extension de ce produit d'Hadamard pour des fonctions définies sur des ouverts de la sphère de Riemann, qui ne contiennent pas nécessairement l'origine. En utilisant des constructions ad-hoc et explicites, il a pu définir ce produit via une intégrale de contour. Cependant, cette construction n'est pas symétrique par rapport à 0 et à l'infini. La première partie de cette thèse consiste en l'étude d'une généralisation du produit d'Hadamard étendu par Pohlen. Au moyen de la théorie de l'homologie singulière, nous introduisons des cycles plus symétriques et définissons un produit d'Hadamard généralisé, équivalent à celui de Pohlen quand les fonctions s'annulent à l'infini. Nous montrons ensuite que ce produit d'Hadamard généralisé est un cas particulier d'un phénomène plus général appelé "convolution cohomologique holomorphe". Nous étudions en détail cette convolution dans le cas du groupe de Lie complexe multiplicatif C^* et fournissons une formule à base d'intégrales de contour pour la calculer. La deuxième partie de la thèse est consacrée à l'étude de théorèmes de type Paley-Wiener holomorphes dus à Polya (dans le cas compact) et à Méril (dans le cas non compact). Ces théorèmes utilisent une version de la transformation de Laplace à base d'intégrales de contour. Grâce à la théorie des faisceaux sous-analytiques enrichis développée par A. D'Agnolo et M. Kashiwara, ainsi qu'à la transformation de Laplace enrichie introduite par M. Kashiwara et P. Schapira, nous montrons que ces théorèmes peuvent être compris d'un point de vue cohomologique. Sous certaines hypothèses de convexité et de sous-analyticité, il est même possible de prouver de plus forts isomorphismes de Laplace entre des espaces décrits par des conditions de croissance tempérée. Ces espaces peuvent être liés à certains espaces de fonctionnelles analytiques. Dans le cas non compact, nous définissons un produit de convolution entre fonctionnelles analytiques et conjecturons que ce produit est compatible avec la version additive de la convolution cohomologique holomorphe précédemment étudiée. Grâce à nos résultats sur la transformation de Laplace enrichie, nous prouvons cette conjecture dans le cas sous-analytique.Holomorphic Cohomological Convolution, Enhanced Laplace Transform and Application