In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we cha... more In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
Let S be a non trivial additive cancellation commutative semigroup having a zero 0 with the quoti... more Let S be a non trivial additive cancellation commutative semigroup having a zero 0 with the quotient group G= { s1 - s2 | s1 , s2 ∈ S }. A prime ideal P of S is called strongly prime if for a, b ∈ G, whenever a +b ∈ P, we get a ∈ P or b ∈ P. We show that a prime ideal of S is strongly prime ⇔ it is powerful. Finally, we prove that if O is an oversemigroup of S and S and O have the nonzero ideal I where I is powerful in O, then 3I is a powerful ideal of S.
We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize ... more We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize the (normal) Γ-semigroup and normal regular Γ-semigroup in terms of elementary properties of bi-Γ-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1, I2 are any two normal Γideals of a Γ-semigroup S, then their product I1ΓI2 and I2ΓI1 are also normal Γ-ideals of S and I1ΓI2 = I2ΓI1. Finally, we show that the minimal normal Γ-ideal of a Γ-semigroup S is a Γ-group.The first author is partially supported by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India provided through Post-Doctoral Fellowship under grant number 2/(40)(30)/2015/R&D-II.Publisher's Versio
International Journal of Statistics and Applied Mathematics
Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathema... more Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathematics. Vedic age gave rise to a new era of progress in the field of Science, Technology and Development. The Hindu Scripture Vedas is synonymous with all kinds of original source of knowledge and intellectual wisdom in the universe leading to modern knowlege in modern mathematics. Indian mathematicians made tremendous contributions to the entire world of Mathematics and Science. Decimal number system as well as the invention of zero (0) are among the greatest contributions of Indian mathematicians. The theory of trigonometry, Mathematical Modelling, Algebra, algorithm, modern arithmetic, sine and cosine functions leading to modern trigonometry, Diophantine equation, square root, cube root, negative numbers are also developed by Indian mathematicians. In this review article, the work of some of the renowned Indian mathematicians from Indus Valley civilization and the Vedas to modern times are covered in short with the hope that it may reveal hidden fundamental mathematical ideas as basic ideal tools which may usefully motivate for further research work in every domain of mathematical sciences, natural and applied sciences, engineering and social sciences. Moreover, there are many more remarkable Indian mathematicians who contributed to the origin of mathematical sciences. They have made several general contributions to mathematics that have significantly influenced scientists and mathematicians in the modern times.
We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize ... more We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize the (normal) Γ-semigroup and normal regular Γ-semigroup in terms of elementary properties of bi-Γ-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1, I2 are any two normal Γideals of a Γ-semigroup S, then their product I1ΓI2 and I2ΓI1 are also normal Γ-ideals of S and I1ΓI2 = I2ΓI1. Finally, we show that the minimal normal Γ-ideal of a Γ-semigroup S is a Γ-group.
This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative... more This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative and largely non-commutative ring(semiring) theory.
This paper deals with the connections and interdependencies among prime ideals, primary ideals, v... more This paper deals with the connections and interdependencies among prime ideals, primary ideals, valuation ideals, valuation semigroups and semigroups. R. Gilmer and J. Ohm [1] studied primary ideals and valuation ideals for integral domains. In this article, we generalize this concept for semigroups. It is proved that if $T$ is a prime ideal of a semigroup $S$, and $\{Q_{\alpha }\}$ is the set of primary ideals that belongs to $T$. Further, if $I=\bigcap Q_{\alpha}$ and every $Q_{\alpha}$ is a valuation ideal, then $I$ is prime.
Boletim da Sociedade Paranaense de Matemática, 2021
In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is ... more In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is also proved that if (S,Γ,·,≤) is an ordered Γ-semigroup and m,n are nonnegative integers and R(m,0) and L(0,n) is the set of all (m,0)-Γideals and (0,n)-Γ-ideals of S, respectively. Then, S is (m,n)-regular ordered Γ semigroup ⇐⇒∀R ∈R(m,0)∀L ∈L(0,n),R∩L = (RmΓL∩RΓLn].
This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative... more This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative and largely non-commutative ring(semiring) theory. Mathematics Subject Classification: 16Y99, 16Y60
In this paper, we study ordered hyperideals in ordered semihypergroups. Also, we study (m, n)-reg... more In this paper, we study ordered hyperideals in ordered semihypergroups. Also, we study (m, n)-regular ordered semihypergroups in terms of ordered (m, n)-hyperideals. Furthermore, we obtain some ideal theoretic results in ordered semihypergroups.
In this paper, we introduce the concept of filters and apply it to study congruence in ordered Γ-s... more In this paper, we introduce the concept of filters and apply it to study congruence in ordered Γ-semigroups with involution. Then, we characterize intra-regular ordered Γ-semigroups with involution. We also construct examples of ordered Γ-semigroups as well as of ordered Γ-semigroups with involution to support that our results are not superfluous.
A semigroup is an algebraic structure together with a nonempty set and an associative binary oper... more A semigroup is an algebraic structure together with a nonempty set and an associative binary operation. The systematic study of semigroups started in the early 20th century. Semigroups are important in different areas of Mathematics. The concept of hyperstructures was introduced in 1934 as a suitable generalization of classical algebraic structures by Marty [1]. He obtained various results on hypergroups and applied them in different areas, for instance, in algebraic rational fractions, functions, and noncommutative groups. Thereafter, many research papers have been published on this subject and has been studied recently by many algebraists such as: Prenowitz, Corsini, Jantosciak, Leoreanu, Heideri, Davvaz, Hila, Gutan, Griffiths and Halzen.
In this paper, we introduce ordered (generalized) (m,n)-Γ-ideals in poΓ-semigroups. Then we chara... more In this paper, we introduce ordered (generalized) (m,n)-Γ-ideals in poΓ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple. 2000 AMS Classification: 06F99, 06F05.
The main purpose of this paper is to investigate ordered -semihypergroups in the general terms o... more The main purpose of this paper is to investigate ordered -semihypergroups in the general terms of ordered -hyperideals. We intro-duce ordered (generalized) (m; n)--hyperideals in ordered -semihypergroups. Then, we characterize ordered -semihypergroup by ordered (generalized) (0; 2)- -hyperideals, ordered (generalized) (1; 2)-{hyperideals and ordered (general- ized) 0-minimal (0; 2)--hyperideals. Furthermore, we investigate the notion of ordered (generalized) (0; 2)-bi--hyperideals, ordered 0-(0; 2) bisimple ordered -semihypergroups and ordered 0-minimal (generalized) (0; 2)-bi--hyperideals in ordered -semihyperoups. It is proved that an ordered -semihypergroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
Hacettepe Journal of Mathematics and Statistics, 2015
In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we cha... more In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
International Journal of Pure and Apllied Mathematics, 2017
The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, w... more The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, we introduce covered Γ-ideal in po-Γ-semigroups. We study some results based on covered Γ-ideals in po-Γ-semigroup.
The speed of internet has increased dramatically with the introduction of 4G and 5G promises an e... more The speed of internet has increased dramatically with the introduction of 4G and 5G promises an even greater transmission rate with coverage outdoors and indoors in smart cities. This indicates that the introduction of 5G might result in replacing the Wi-Fi that is being currently used for applications such as geo-location using continuous radio coverage there by initiating the involvement of IoT in all devices that are used. The introduction of Wi-Fi 6 is already underway for applications that work with IoT, smart city applications will still require 5G to provide internet services using Big Data to reduce the requirement of mobile networks and additional private network infrastructure. However, as the network access begins to expand, it also introduces the risk of cyber security with the enhanced connectivity in the networking. Additional digital targets will be given to the cyber attackers and independent services will also be sharing access channel infrastructure between mobile ...
In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. T... more In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. Then we characterize the po-Gamma-semigroup through ordered (generalized) (0; 2)--ideals, ordered (generalized) (1; 2)--ideals and ordered (generalized) 0-minimal (0; 2)--ideals. Also, we investigate the notion of ordered (generalized) (0; 2)-bi-Gamma-ideals, ordered 0-(0; 2) bisimple po-Gamma-semigroups and ordered 0-minimal (generalized) (0; 2)-bi--ideals in po-Gamma-semigroups. It is proved that a po-Gamma-semigroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. T... more In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. Then we characterize the po-Gamma-semigroup through ordered (generalized) (0; 2)--ideals, ordered (generalized) (1; 2)--ideals and ordered (generalized) 0-minimal (0; 2)--ideals. Also, we investigate the notion of ordered (generalized) (0; 2)-bi-Gamma-ideals, ordered 0-(0; 2) bisimple po-Gamma-semigroups and ordered 0-minimal (generalized) (0; 2)-bi--ideals in po-Gamma-semigroups. It is proved that a po-Gamma-semigroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
Water is one of the basic resource need for every human in the world. The improper management of ... more Water is one of the basic resource need for every human in the world. The improper management of water storage system can lead a human life to any extent. As a result of technology development, the proposed model is developed to manage the water storage systems like dam and lake through remotely placed sensor signals. The sensors which are placed in the storage places gives the strength and storage capacity of the dam and lakes. Similarly the sensors which are placed at the sender dam or lake are used to predict the incoming water level to the receiver lake. This improves the prediction rate of flood in the river paths and this prediction allows the incoming dam to send off some waters outside to allocate some space for incoming waters. The data which are generated by the connected dams are stored in a cloud space for analyzing the water flow management. The sensors connected in a lake or dam is connected with IoT platform to avoid wire connections. Hence this model avoids sudden fl...
In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we cha... more In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
Let S be a non trivial additive cancellation commutative semigroup having a zero 0 with the quoti... more Let S be a non trivial additive cancellation commutative semigroup having a zero 0 with the quotient group G= { s1 - s2 | s1 , s2 ∈ S }. A prime ideal P of S is called strongly prime if for a, b ∈ G, whenever a +b ∈ P, we get a ∈ P or b ∈ P. We show that a prime ideal of S is strongly prime ⇔ it is powerful. Finally, we prove that if O is an oversemigroup of S and S and O have the nonzero ideal I where I is powerful in O, then 3I is a powerful ideal of S.
We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize ... more We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize the (normal) Γ-semigroup and normal regular Γ-semigroup in terms of elementary properties of bi-Γ-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1, I2 are any two normal Γideals of a Γ-semigroup S, then their product I1ΓI2 and I2ΓI1 are also normal Γ-ideals of S and I1ΓI2 = I2ΓI1. Finally, we show that the minimal normal Γ-ideal of a Γ-semigroup S is a Γ-group.The first author is partially supported by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India provided through Post-Doctoral Fellowship under grant number 2/(40)(30)/2015/R&D-II.Publisher's Versio
International Journal of Statistics and Applied Mathematics
Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathema... more Indian mathematics has its deep roots in the Vedas, different from what is known as Vedic Mathematics. Vedic age gave rise to a new era of progress in the field of Science, Technology and Development. The Hindu Scripture Vedas is synonymous with all kinds of original source of knowledge and intellectual wisdom in the universe leading to modern knowlege in modern mathematics. Indian mathematicians made tremendous contributions to the entire world of Mathematics and Science. Decimal number system as well as the invention of zero (0) are among the greatest contributions of Indian mathematicians. The theory of trigonometry, Mathematical Modelling, Algebra, algorithm, modern arithmetic, sine and cosine functions leading to modern trigonometry, Diophantine equation, square root, cube root, negative numbers are also developed by Indian mathematicians. In this review article, the work of some of the renowned Indian mathematicians from Indus Valley civilization and the Vedas to modern times are covered in short with the hope that it may reveal hidden fundamental mathematical ideas as basic ideal tools which may usefully motivate for further research work in every domain of mathematical sciences, natural and applied sciences, engineering and social sciences. Moreover, there are many more remarkable Indian mathematicians who contributed to the origin of mathematical sciences. They have made several general contributions to mathematics that have significantly influenced scientists and mathematicians in the modern times.
We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize ... more We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize the (normal) Γ-semigroup and normal regular Γ-semigroup in terms of elementary properties of bi-Γ-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1, I2 are any two normal Γideals of a Γ-semigroup S, then their product I1ΓI2 and I2ΓI1 are also normal Γ-ideals of S and I1ΓI2 = I2ΓI1. Finally, we show that the minimal normal Γ-ideal of a Γ-semigroup S is a Γ-group.
This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative... more This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative and largely non-commutative ring(semiring) theory.
This paper deals with the connections and interdependencies among prime ideals, primary ideals, v... more This paper deals with the connections and interdependencies among prime ideals, primary ideals, valuation ideals, valuation semigroups and semigroups. R. Gilmer and J. Ohm [1] studied primary ideals and valuation ideals for integral domains. In this article, we generalize this concept for semigroups. It is proved that if $T$ is a prime ideal of a semigroup $S$, and $\{Q_{\alpha }\}$ is the set of primary ideals that belongs to $T$. Further, if $I=\bigcap Q_{\alpha}$ and every $Q_{\alpha}$ is a valuation ideal, then $I$ is prime.
Boletim da Sociedade Paranaense de Matemática, 2021
In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is ... more In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is also proved that if (S,Γ,·,≤) is an ordered Γ-semigroup and m,n are nonnegative integers and R(m,0) and L(0,n) is the set of all (m,0)-Γideals and (0,n)-Γ-ideals of S, respectively. Then, S is (m,n)-regular ordered Γ semigroup ⇐⇒∀R ∈R(m,0)∀L ∈L(0,n),R∩L = (RmΓL∩RΓLn].
This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative... more This paper contains some results on one-sided prime ideals in bsemirings analogous to commutative and largely non-commutative ring(semiring) theory. Mathematics Subject Classification: 16Y99, 16Y60
In this paper, we study ordered hyperideals in ordered semihypergroups. Also, we study (m, n)-reg... more In this paper, we study ordered hyperideals in ordered semihypergroups. Also, we study (m, n)-regular ordered semihypergroups in terms of ordered (m, n)-hyperideals. Furthermore, we obtain some ideal theoretic results in ordered semihypergroups.
In this paper, we introduce the concept of filters and apply it to study congruence in ordered Γ-s... more In this paper, we introduce the concept of filters and apply it to study congruence in ordered Γ-semigroups with involution. Then, we characterize intra-regular ordered Γ-semigroups with involution. We also construct examples of ordered Γ-semigroups as well as of ordered Γ-semigroups with involution to support that our results are not superfluous.
A semigroup is an algebraic structure together with a nonempty set and an associative binary oper... more A semigroup is an algebraic structure together with a nonempty set and an associative binary operation. The systematic study of semigroups started in the early 20th century. Semigroups are important in different areas of Mathematics. The concept of hyperstructures was introduced in 1934 as a suitable generalization of classical algebraic structures by Marty [1]. He obtained various results on hypergroups and applied them in different areas, for instance, in algebraic rational fractions, functions, and noncommutative groups. Thereafter, many research papers have been published on this subject and has been studied recently by many algebraists such as: Prenowitz, Corsini, Jantosciak, Leoreanu, Heideri, Davvaz, Hila, Gutan, Griffiths and Halzen.
In this paper, we introduce ordered (generalized) (m,n)-Γ-ideals in poΓ-semigroups. Then we chara... more In this paper, we introduce ordered (generalized) (m,n)-Γ-ideals in poΓ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple. 2000 AMS Classification: 06F99, 06F05.
The main purpose of this paper is to investigate ordered -semihypergroups in the general terms o... more The main purpose of this paper is to investigate ordered -semihypergroups in the general terms of ordered -hyperideals. We intro-duce ordered (generalized) (m; n)--hyperideals in ordered -semihypergroups. Then, we characterize ordered -semihypergroup by ordered (generalized) (0; 2)- -hyperideals, ordered (generalized) (1; 2)-{hyperideals and ordered (general- ized) 0-minimal (0; 2)--hyperideals. Furthermore, we investigate the notion of ordered (generalized) (0; 2)-bi--hyperideals, ordered 0-(0; 2) bisimple ordered -semihypergroups and ordered 0-minimal (generalized) (0; 2)-bi--hyperideals in ordered -semihyperoups. It is proved that an ordered -semihypergroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
Hacettepe Journal of Mathematics and Statistics, 2015
In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we cha... more In this paper, we introduce ordered (generalized) (m, n)-Γ-ideals in po-Γ-semigroups. Then we characterize the po-Γ-semigroup through ordered (generalized) (0, 2)-Γ-ideals, ordered (generalized) (1, 2)-Γ-ideals and ordered (generalized) 0-minimal (0, 2)-Γ-ideals. Also, we investigate the notion of ordered (generalized) (0, 2)-bi-Γ-ideals, ordered 0-(0, 2) bisimple po-Γ-semigroups and ordered 0-minimal (generalized) (0, 2)-bi-Γ-ideals in po-Γ-semigroups. It is proved that a po-Γsemigroup S with a zero 0 is 0-(0, 2)-bisimple if and only if it is left 0-simple.
International Journal of Pure and Apllied Mathematics, 2017
The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, w... more The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, we introduce covered Γ-ideal in po-Γ-semigroups. We study some results based on covered Γ-ideals in po-Γ-semigroup.
The speed of internet has increased dramatically with the introduction of 4G and 5G promises an e... more The speed of internet has increased dramatically with the introduction of 4G and 5G promises an even greater transmission rate with coverage outdoors and indoors in smart cities. This indicates that the introduction of 5G might result in replacing the Wi-Fi that is being currently used for applications such as geo-location using continuous radio coverage there by initiating the involvement of IoT in all devices that are used. The introduction of Wi-Fi 6 is already underway for applications that work with IoT, smart city applications will still require 5G to provide internet services using Big Data to reduce the requirement of mobile networks and additional private network infrastructure. However, as the network access begins to expand, it also introduces the risk of cyber security with the enhanced connectivity in the networking. Additional digital targets will be given to the cyber attackers and independent services will also be sharing access channel infrastructure between mobile ...
In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. T... more In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. Then we characterize the po-Gamma-semigroup through ordered (generalized) (0; 2)--ideals, ordered (generalized) (1; 2)--ideals and ordered (generalized) 0-minimal (0; 2)--ideals. Also, we investigate the notion of ordered (generalized) (0; 2)-bi-Gamma-ideals, ordered 0-(0; 2) bisimple po-Gamma-semigroups and ordered 0-minimal (generalized) (0; 2)-bi--ideals in po-Gamma-semigroups. It is proved that a po-Gamma-semigroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. T... more In this paper, we introduce ordered (generalized) (m; n)-Gamma-ideals in po-Gamma-semigroups. Then we characterize the po-Gamma-semigroup through ordered (generalized) (0; 2)--ideals, ordered (generalized) (1; 2)--ideals and ordered (generalized) 0-minimal (0; 2)--ideals. Also, we investigate the notion of ordered (generalized) (0; 2)-bi-Gamma-ideals, ordered 0-(0; 2) bisimple po-Gamma-semigroups and ordered 0-minimal (generalized) (0; 2)-bi--ideals in po-Gamma-semigroups. It is proved that a po-Gamma-semigroup S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.
Water is one of the basic resource need for every human in the world. The improper management of ... more Water is one of the basic resource need for every human in the world. The improper management of water storage system can lead a human life to any extent. As a result of technology development, the proposed model is developed to manage the water storage systems like dam and lake through remotely placed sensor signals. The sensors which are placed in the storage places gives the strength and storage capacity of the dam and lakes. Similarly the sensors which are placed at the sender dam or lake are used to predict the incoming water level to the receiver lake. This improves the prediction rate of flood in the river paths and this prediction allows the incoming dam to send off some waters outside to allocate some space for incoming waters. The data which are generated by the connected dams are stored in a cloud space for analyzing the water flow management. The sensors connected in a lake or dam is connected with IoT platform to avoid wire connections. Hence this model avoids sudden fl...
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