Somnuek Worawiset - Academia.edu (original) (raw)
Papers by Somnuek Worawiset
Turkish Journal of Mathematics
In the present paper, we consider the semigroup On,p of all order-preserving full transformations... more In the present paper, we consider the semigroup On,p of all order-preserving full transformations α on an n-elements chain Xn , where p ∈ Xn is the only fixed point of α. The nilpotent semigroup On,p was first studied by Ayik et al. in 2011. Moreover, On,1 is the maximal nilpotent subsemigroup of the Catalan Monoid Cn. Its rank is the difference of the (n − 1) th and the (n − 2) th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup On,p. We will calculate the rank of On,p for p > 1 and provide a semigroup presentation for On,1 .
In this research, we study the structure and properties of the endomorphism monoid of a strong se... more In this research, we study the structure and properties of the endomorphism monoid of a strong semilattice of left simple semigroups. In such semigroup, we consider mainly that the defining homomorphisms are constant maps or isomorphisms. For arbitrary defining homomorphisms the situation is in general extremely complicated, we have discussed some of the problems at the end. We obtain results for strong semilattices of groups which are known under the name of Clifford semigroups and we also consider strong semilattices of left or right groups as well. Both are special cases of the strong semilattices of left simple semigroups.
Asian-European Journal of Mathematics, 2017
In this paper, we study properties of the endomorphism monoids of strong semilattices of groups. ... more In this paper, we study properties of the endomorphism monoids of strong semilattices of groups. In Sec. 2, several properties for endomorphism monoids of finite semilattices are investigated. In Sec. 3, we collect some results on endomorphism monoids of strong semilattices of groups, i.e. Clifford semigroups.
International Journal of Pure and Apllied Mathematics, 2015
Let s, t, n be non negative integers such that n ≡ 5 (mod 20). In this paper, we found that all n... more Let s, t, n be non negative integers such that n ≡ 5 (mod 20). In this paper, we found that all non-negative integer solutions (x, y, z) of the Diophantine equation 483 x + 483 2s n y = z 2t are in the following form: (x, y, z) = (1 + 2s, 0, 22(483) s) ; t = 1, no solution ; otherwise.
International Journal of Pure and Apllied Mathematics, 2015
Let s, t, n be non-negative integers and n ≡ 5 (mod 20). In this paper, we found that all non-neg... more Let s, t, n be non-negative integers and n ≡ 5 (mod 20). In this paper, we found that all non-negative integer solutions (x, y, z) of the Diophantine equation 143 x + 143 2s n y = z 2t are in the following form: (x, y, z) = (1 + 2s, 0, 12(143) s) ; t = 1, no solution ; otherwise.
International Journal of Pure and Apllied Mathematics, 2014
In this paper, let n, s, t be any non-negative integers where n ≡ 5 (mod 20). We show that all no... more In this paper, let n, s, t be any non-negative integers where n ≡ 5 (mod 20). We show that all non-negative integer solution (x, y, z) of the Diophantine equation 3 x + 3 2s n y = z 2t are the following: (x, y, z) = (1 + 2s, 0, 2(3 s)) ; t = 1 No solution ; otherwise.
Endomorphism monoids have long been of interest in universal algebra and also in the study of par... more Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of the endomorphism monoid of a strong semilattice of left simple semigroups. In such semigroup we consider mainly that the defining homomorphisms are constant or isomorphisms. For arbitrary defining homomorphisms the situation is in general extremely complicated, we have discussed some of the problems at the end of the thesis. First we consider conditions, under which the endomorphism monoids are regular, idempotent-closed, orthodox, left inverse, completely regular and idempotent. Later, as corollaries we obtain results for strong semilattices of groups which are known under the name of Clifford semigroups and we also consider strong semilattices of left or right groups as well. Both are special cases of the strong semilattices of left simple semigroups.
Algebra and Discrete Mathematics
In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective ... more In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.
KMITL-Science and Technology Journal, 2017
Mathematica Slovaca, 2019
This paper deals with semihypergroups of order two from the point of view of the model theory. We... more This paper deals with semihypergroups of order two from the point of view of the model theory. We use basic knowledge to show that there are exactly 17 non-isomorphic semihypergroups of order two. Each of them corresponds in a canonical way to a semigroup of order three. We classify all of them by generalized identities a concept introduced by Lyapin. In particular, we classify all non-group semigroups of order three by one generalized identity.
Molecular similarity searching from molecular SMILES format using score base on reduced graphs wi... more Molecular similarity searching from molecular SMILES format using score base on reduced graphs with meaning factor has been proposed. The effectiveness of the method at is compared with searching using Tanimoto score. The searches have been carried out to find the potential drugs or molecules that form interactions by docking with Cov-Proteinase receptor which is SARS virus protein. Since the new proposed method yield almost higher scores than those obtained from Tanimoto method, the structurally diverse sets of active molecules are more retrieved.
Journal of Algebra and Its Applications
The purpose of this paper is the study of congruences on semigroups of transformations on a count... more The purpose of this paper is the study of congruences on semigroups of transformations on a countably infinite fence. We consider the monoid [Formula: see text] of all full transformations on the set [Formula: see text] of all natural numbers preserving the zig-zag order on [Formula: see text], as well as the monoid [Formula: see text] of all idempotent transformations in [Formula: see text] additionally preserving the usual linear order on [Formula: see text] We show that there are uncountably many congruences on [Formula: see text] and determine seven maximal congruences on [Formula: see text] which are all the maximal congruences containing a particular congruence on [Formula: see text] Moreover, we characterize all congruences on the monoid of all transformations in [Formula: see text] with infinite rank. For the semigroup of all transformations in [Formula: see text] with finite rank, we determine the Rees congruences.
TURKISH JOURNAL OF MATHEMATICS
Asian-European Journal of Mathematics
Let [Formula: see text] be a connected graph. For a configuration of pebbles on the vertices of [... more Let [Formula: see text] be a connected graph. For a configuration of pebbles on the vertices of [Formula: see text], a pebbling move on [Formula: see text] is the process of taking two pebbles from a vertex and adding one of them on an adjacent vertex. The pebbling number of [Formula: see text], denoted by [Formula: see text], is the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. The graph [Formula: see text] is said to be of Class 0 if its pebbling number equals its order. For a Class [Formula: see text] connected graph [Formula: see text], we improve a recent upper bound for [Formula: see text] in terms of [Formula: see text].
Asian-European Journal of Mathematics, 2015
We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transforma... more We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transformation semigroup [Formula: see text] on an [Formula: see text]-element set with [Formula: see text] for all [Formula: see text]. This classification differs from the already known classifications of Clifford inverse semigroups, it provides an algorithm for its construction. For a given natural number [Formula: see text], we find also the largest size of an inverse subsemigroup [Formula: see text] of [Formula: see text] satisfying [Formula: see text] with least rank [Formula: see text] for any element in [Formula: see text].
Asian-European Journal of Mathematics, 2015
We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transforma... more We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transformation semigroup [Formula: see text] on an [Formula: see text]-element set with [Formula: see text] for all [Formula: see text]. This classification differs from the already known classifications of Clifford inverse semigroups, it provides an algorithm for its construction. For a given natural number [Formula: see text], we find also the largest size of an inverse subsemigroup [Formula: see text] of [Formula: see text] satisfying [Formula: see text] with least rank [Formula: see text] for any element in [Formula: see text].
Turkish Journal of Mathematics
In the present paper, we consider the semigroup On,p of all order-preserving full transformations... more In the present paper, we consider the semigroup On,p of all order-preserving full transformations α on an n-elements chain Xn , where p ∈ Xn is the only fixed point of α. The nilpotent semigroup On,p was first studied by Ayik et al. in 2011. Moreover, On,1 is the maximal nilpotent subsemigroup of the Catalan Monoid Cn. Its rank is the difference of the (n − 1) th and the (n − 2) th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup On,p. We will calculate the rank of On,p for p > 1 and provide a semigroup presentation for On,1 .
In this research, we study the structure and properties of the endomorphism monoid of a strong se... more In this research, we study the structure and properties of the endomorphism monoid of a strong semilattice of left simple semigroups. In such semigroup, we consider mainly that the defining homomorphisms are constant maps or isomorphisms. For arbitrary defining homomorphisms the situation is in general extremely complicated, we have discussed some of the problems at the end. We obtain results for strong semilattices of groups which are known under the name of Clifford semigroups and we also consider strong semilattices of left or right groups as well. Both are special cases of the strong semilattices of left simple semigroups.
Asian-European Journal of Mathematics, 2017
In this paper, we study properties of the endomorphism monoids of strong semilattices of groups. ... more In this paper, we study properties of the endomorphism monoids of strong semilattices of groups. In Sec. 2, several properties for endomorphism monoids of finite semilattices are investigated. In Sec. 3, we collect some results on endomorphism monoids of strong semilattices of groups, i.e. Clifford semigroups.
International Journal of Pure and Apllied Mathematics, 2015
Let s, t, n be non negative integers such that n ≡ 5 (mod 20). In this paper, we found that all n... more Let s, t, n be non negative integers such that n ≡ 5 (mod 20). In this paper, we found that all non-negative integer solutions (x, y, z) of the Diophantine equation 483 x + 483 2s n y = z 2t are in the following form: (x, y, z) = (1 + 2s, 0, 22(483) s) ; t = 1, no solution ; otherwise.
International Journal of Pure and Apllied Mathematics, 2015
Let s, t, n be non-negative integers and n ≡ 5 (mod 20). In this paper, we found that all non-neg... more Let s, t, n be non-negative integers and n ≡ 5 (mod 20). In this paper, we found that all non-negative integer solutions (x, y, z) of the Diophantine equation 143 x + 143 2s n y = z 2t are in the following form: (x, y, z) = (1 + 2s, 0, 12(143) s) ; t = 1, no solution ; otherwise.
International Journal of Pure and Apllied Mathematics, 2014
In this paper, let n, s, t be any non-negative integers where n ≡ 5 (mod 20). We show that all no... more In this paper, let n, s, t be any non-negative integers where n ≡ 5 (mod 20). We show that all non-negative integer solution (x, y, z) of the Diophantine equation 3 x + 3 2s n y = z 2t are the following: (x, y, z) = (1 + 2s, 0, 2(3 s)) ; t = 1 No solution ; otherwise.
Endomorphism monoids have long been of interest in universal algebra and also in the study of par... more Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of the endomorphism monoid of a strong semilattice of left simple semigroups. In such semigroup we consider mainly that the defining homomorphisms are constant or isomorphisms. For arbitrary defining homomorphisms the situation is in general extremely complicated, we have discussed some of the problems at the end of the thesis. First we consider conditions, under which the endomorphism monoids are regular, idempotent-closed, orthodox, left inverse, completely regular and idempotent. Later, as corollaries we obtain results for strong semilattices of groups which are known under the name of Clifford semigroups and we also consider strong semilattices of left or right groups as well. Both are special cases of the strong semilattices of left simple semigroups.
Algebra and Discrete Mathematics
In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective ... more In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.
KMITL-Science and Technology Journal, 2017
Mathematica Slovaca, 2019
This paper deals with semihypergroups of order two from the point of view of the model theory. We... more This paper deals with semihypergroups of order two from the point of view of the model theory. We use basic knowledge to show that there are exactly 17 non-isomorphic semihypergroups of order two. Each of them corresponds in a canonical way to a semigroup of order three. We classify all of them by generalized identities a concept introduced by Lyapin. In particular, we classify all non-group semigroups of order three by one generalized identity.
Molecular similarity searching from molecular SMILES format using score base on reduced graphs wi... more Molecular similarity searching from molecular SMILES format using score base on reduced graphs with meaning factor has been proposed. The effectiveness of the method at is compared with searching using Tanimoto score. The searches have been carried out to find the potential drugs or molecules that form interactions by docking with Cov-Proteinase receptor which is SARS virus protein. Since the new proposed method yield almost higher scores than those obtained from Tanimoto method, the structurally diverse sets of active molecules are more retrieved.
Journal of Algebra and Its Applications
The purpose of this paper is the study of congruences on semigroups of transformations on a count... more The purpose of this paper is the study of congruences on semigroups of transformations on a countably infinite fence. We consider the monoid [Formula: see text] of all full transformations on the set [Formula: see text] of all natural numbers preserving the zig-zag order on [Formula: see text], as well as the monoid [Formula: see text] of all idempotent transformations in [Formula: see text] additionally preserving the usual linear order on [Formula: see text] We show that there are uncountably many congruences on [Formula: see text] and determine seven maximal congruences on [Formula: see text] which are all the maximal congruences containing a particular congruence on [Formula: see text] Moreover, we characterize all congruences on the monoid of all transformations in [Formula: see text] with infinite rank. For the semigroup of all transformations in [Formula: see text] with finite rank, we determine the Rees congruences.
TURKISH JOURNAL OF MATHEMATICS
Asian-European Journal of Mathematics
Let [Formula: see text] be a connected graph. For a configuration of pebbles on the vertices of [... more Let [Formula: see text] be a connected graph. For a configuration of pebbles on the vertices of [Formula: see text], a pebbling move on [Formula: see text] is the process of taking two pebbles from a vertex and adding one of them on an adjacent vertex. The pebbling number of [Formula: see text], denoted by [Formula: see text], is the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. The graph [Formula: see text] is said to be of Class 0 if its pebbling number equals its order. For a Class [Formula: see text] connected graph [Formula: see text], we improve a recent upper bound for [Formula: see text] in terms of [Formula: see text].
Asian-European Journal of Mathematics, 2015
We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transforma... more We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transformation semigroup [Formula: see text] on an [Formula: see text]-element set with [Formula: see text] for all [Formula: see text]. This classification differs from the already known classifications of Clifford inverse semigroups, it provides an algorithm for its construction. For a given natural number [Formula: see text], we find also the largest size of an inverse subsemigroup [Formula: see text] of [Formula: see text] satisfying [Formula: see text] with least rank [Formula: see text] for any element in [Formula: see text].
Asian-European Journal of Mathematics, 2015
We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transforma... more We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transformation semigroup [Formula: see text] on an [Formula: see text]-element set with [Formula: see text] for all [Formula: see text]. This classification differs from the already known classifications of Clifford inverse semigroups, it provides an algorithm for its construction. For a given natural number [Formula: see text], we find also the largest size of an inverse subsemigroup [Formula: see text] of [Formula: see text] satisfying [Formula: see text] with least rank [Formula: see text] for any element in [Formula: see text].