Establishing complete and reliable coverage for a long time-span is a crucial issue in densely surveillance wireless sensor networks (WSNs). Many scheduling algorithms have been proposed to model the problem as a maximum disjoint set covers (DSC) problem. The goal of DSC based algorithms is to schedule sensors into several disjoint subsets. One subset is assigned to be active, whereas, all remaining subsets are set to sleep. An extension to the maximum disjoint set covers problem has also been addressed in literature to allow for more advance sensors to adjust their sensing range. The problem, then, is extended to finding maximum number of overlapped set covers. Unlike all related works which concern with the disc sensing model, the contribution of this paper is to reformulate the maximum overlapped set covers problem to handle the probabilistic sensing model. The problem is addressed as a multi-objective optimization (MOO) problem and the well-known decomposition based multi-objective evolutionary algorithm (MOEA/D) is adopted to solve the stated problem. A Multi-layer MOEA/D is suggested, wherein each layer yields a distinct set cover. Performance evaluations in terms of total number of set covers, total residual energy, and coverage reliability are reported through extensive simulations. The main aspect of the results reveals that the network's lifetime (i.e. total number of set covers) can be extended by increasing number of sensors. On the other hand, the coverage reliability can be increased by increasing sensing ranges but at the expense of decreasing the network's lifetime.
Multi-layer Multi-objective Evolutionary Algorithm for Adjustable Range Set Covers Problem in Wireless Sensor Networks
adjustable sensing range
multi-objective optimization
set covers
heterogeneous wireless sensor networks
Publication Date
Wed Jan 20 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
αg_Ị-open sets and αg_Ị-functions
αg_Ị-closed set
αg_Ị O-functions
αg_Ị C-functions
αg_Ị-continuous function
Strongly αg_Ị-continuous function
αg_Ị-irresolute function
ideal.
The objective of this paper is to show modern class of open sets which is an -open. Some functions via this concept were studied and the relationships such as continuous function strongly -continuous function -irresolute function -continuous function.
Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Fuzzy Semimaximal Submodules
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if Mâ„(Nis a semisimple R-module ).The main objective of this work is to fuzzify this concept
study the basic properties and we investigate the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple
semisimple) F- submodules and quotient F- modules are introduced and given some properties .
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
(1)
Publication Date
Sat Sep 01 2018
Journal Name
Polyhedron
Novel dichloro (bis {2-[1-(4-methylphenyl)-1H-1, 2, 3-triazol-4-yl-κN3] pyridine-κN}) metal (II) coordination compounds of seven transition metals (Mn, Fe, Co, Ni, Cu, Zn and Cd)
The 1
3-dipolar cycloaddition “click” reaction between an azide and an alkyne to give a 1
2
3-triazole was reported by Huisgen in 1961 [1]. In 2002 the Copper(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAC) to prepare a 1
2
3-triazole was reported [2]
[3]. The existence of relatively basic nitrogen atoms in the 1
2
3-triazole rings
and the possibility of introducing additional donor groups in the substituents (Fig. 1)
made the CuAAC “click” reaction an attractive method to prepare differently substituted 1
2
3-triazoles. These compounds have been used as ligands to coordinate to various metal ions that display a range of applications such as in electrochemical and photochemical studies
in supramolecular chemistry
magnetism
metal-ion sensing and catalysis [4]. The reasons for the success of the “click” reaction
is that it is easy to carry out and is widely applicable. It is not affected by a variety of functional groups
and can be carried out with a variety of Cu(I) catalysts and solvents
including aqueous conditions. The Cu(I) catalysts overcome the high activation energy barrier of the non-catalyzed Huisgen reaction by changing the mechanism of the reaction. A large variety of copper catalysts can be used for the CuAAC reaction
on condition that the maximum concentration of Cu(I) species is generated during the reaction. The pre-catalyst can be a Cu(II) salt (usually CuSO4) together with a reducing agent (often sodium ascorbate) or a Cu(I) compound in the presence of a base or amine ligand and a reducing agent to prevent oxidation to Cu(II). Some strong oxidising cupric salts or complexes such as Cu(OAc)2 also work. The solvent is very flexible from organic to aqueous
with the most commonly used combination water + an alcohol (t-BuOH
MeOH or EtOH). The key role of the solvent or solvent mixture is to solubilize the substrates and Cu(I) catalyst in order to ensure rapid reactions. Such aqueous conditions are very useful for biochemical conjugations
as well as for organic syntheses.
We recently reported on the synthesis of a series of differently substituted 1
2
3-triazole chromophores
the substituted 2-(1-phenyl-1H-1
2
3-triazol-4-yl)pyridine ligands [5]
see Fig. 2 middle
with substituents R = H (L1)
CH3 (L2)
OCH3 (L3)
COOH
F
Cl
CN
CF3
O(CH2)3CH3 and N(CH3)2. These versatile ligands were found to coordinate to various first row transition metals
such as manganese
cobalt and nickel [6]. Here we extend the series to include more first row transition metal(II) coordination compounds
iron
copper and zinc
as well as a second row transition metal(II) coordination compound
cadmium
containing the 2-(1-(4-methyl-phenyl)-1H-1
2
3-triazol-1-yl)pyridine chromophore (Fig. 2 right with R = CH3). This series of seven novel coordination compounds is the first series of pyridyl-triazole based transition metal coordination compounds where seven different transition metals are coordinated to the same 1
2
3-triazole chromophore
namely 2-(1-(4-methyl-phenyl)-1H-1
2
3-triazol-1-yl)pyridine.