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The total graph of a commutative ring with respect to proper ideals
Ahmad Abbasi,Shokoofe Habibi 대한수학회 2012 대한수학회지 Vol.49 No.1
Let R be a commutative ring and I its proper ideal, let S(I)be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(ΓI (R)). It is the (undirected) graph with all ele-ments of R as vertices, and for distinct x; y 2 R, the vertices x and y are adjacent if and only if x + y 2 S(I). The total graph of a commutative ring, that denoted by T((R)), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y 2 Z(R) which is due to Anderson and Badawi [2]. In the case I = f0g, T(ΓI (R)) = T(Γ(R)); this is an important result on the denition.
ON EIGENSHARPNESS AND ALMOST EIGENSHARPNESS OF LEXICOGRAPHIC PRODUCTS OF SOME GRAPHS
Abbasi, Ahmad,Taleshani, Mona Gholamnia Korean Mathematical Society 2022 대한수학회보 Vol.59 No.3
The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.
THE TOTAL GRAPH OF A COMMUTATIVE RING WITH RESPECT TO PROPER IDEALS
Abbasi, Ahmad,Habibi, Shokoofe Korean Mathematical Society 2012 대한수학회지 Vol.49 No.1
Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.
GENERALIZED LOCAL COHOMOLOGY AND MATLIS DUALITY
Abbasi, Ahmad The Honam Mathematical Society 2008 호남수학학술지 Vol.30 No.3
Let (R, m) be a Noetherian local ring with maximal ideal m, E := $E_R$(R/m) and let I be an ideal of R. Let M and N be finitely generated R-modules. It is shown that $H^n_I(M,(H^n_I(N)^{\vee})){\cong}(M{\otimes}_RN)^{\vee}$ where grade(I, N) = n = $cd_i$(I, N). We also show that for n = grade(I, R), one has $End_R(H^n_I(P,R)^{\vee}){\cong}Ext^n_R(H^n_I(P,R),P^*)^{\vee}$.
ARTINIANNESS OF LOCAL COHOMOLOGY MODULES
Abbasi, Ahmad,Shekalgourabi, Hajar Roshan,Hassanzadeh-lelekaami, Dawood The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.2
In this paper we investigate the Artinianness of certain local cohomology modules $H^i_I(N)$ where N is a minimax module over a commutative Noetherian ring R and I is an ideal of R. Also, we characterize the set of attached prime ideals of $H^n_I(N)$, where n is the dimension of N.
ARTINIANNESS OF LOCAL COHOMOLOGY MODULES
( Ahmad Abbasi ),( Hajar Roshan Shekalgourabi ),( Dawood Hassanzadeh-lelekaami ) 호남수학회 2016 호남수학학술지 Vol.38 No.2
In this paper we investigate the Artinianness of certain local cohomology modules Hi I (N) where N is a minimax module over a commutative Noetherian ring R and I is an ideal of R. Also, we characterize the set of attached prime ideals of Hn I (N), where n is the dimension of N.
A. Ahmad,S. Ahmed,F. M. Abbasi 한국자기학회 2017 Journal of Magnetics Vol.22 No.2
Flow of electrically conducting nanofluids is of pivotal importance in countless industrial and medical appliances. Fluctuations in thermophysical properties of such fluids due to variations in temperature have not received due attention in the available literature. Present investigation aims to fill this void by analyzing the flow of copper-water nanofluid with temperature dependent viscosity past a Riga plate. Strong wall suction and viscous dissipation have also been taken into account. Numerical solutions for the resulting nonlinear system have been obtained. Results are presented in the graphical and tabular format in order to facilitate the physical analysis. An estimated expression for skin friction coefficient and Nusselt number are obtained by performing linear regression on numerical data for embedded parameters. Results indicate that the temperature dependent viscosity alters the velocity as well as the temperature of the nanofluid and is of considerable importance in the processes where high accuracy is desired. Addition of copper nanoparticles makes the momentum boundary layer thinner whereas viscosity parameter does not affect the boundary layer thickness. Moreover, the regression expressions indicate that magnitude of rate of change in effective skin friction coefficient and Nusselt number with respect to nanoparticles volume fraction is prominent when compared with the rate of change with variable viscosity parameter and modified Hartmann number.
Leili Rabiei,Ahmad Ali Eslami,Mohammad Abbasi,Seyed Mohammad Afzali,Seyed Masih Hosseini,Reza Masoudi 대한가정의학회 2020 Korean Journal of Family Medicine Vol.41 No.2
Background: Caregivers of hemodialysis patients spend a large amount of time providing care to these patients while tolerating fatigue and stress. This study evaluated a family-centered empowerment program on the care burden and self-efficacy of hemodialysis patient caregivers based on social cognitive theory. Methods: In this randomized clinical trial, 70 family caregivers of hemodialysis patients in Isfahan, Iran, were selected and randomly allocated to intervention and control groups, in 2015–2016. Two questionnaires were used to collect the family caregivers’ characteristics, care burden, and self-efficacy, and patients’ negative and positive outcomes expectancies. Data were analyzed using SPSS before, immediately after, and 2 months after the intervention. Results: There was no significant difference in the mean scores of care burden, positive outcomes expectancies, negative outcomes expectancies, and self-efficacy between the two groups before the intervention. However, there were significant differences in the post-test and follow-up data analyses (P<0.05). Conclusion: Given the degenerative nature of chronic kidney disease, it can be considered as a source of long-term and chronic stress for caregivers. Therefore, by implementing an empowerment program, caregiving behaviors can be improved, positive outcomes expectancies can be increased, and negative outcomes expectancies can be reduced.
Behnam Firouzi,Ahmad Abbasi,Polat Sendur 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.28 No.1
In this paper we study the static deflection, natural frequency, primary resonance of an electrostatically actuated cracked gas sensor. Besides, a novel hybrid metaheuristic algorithm is proposed to detect the location and depth of possible crack on the microcantilever systems. The gas sensor configuration consists of a microcantilever with a rigid plate attached to its end. The nonlinear effects of the electrostatic force and fringing field are taken into account in the mathematical model. The crack is represented by a rotational spring. In the first part, the effect of crack on the static and dynamic pull-in instability are studied. The equations of motion are solved by the application of the perturbation methods. Next, an inverse problem is formulated to predict the location and depth of the crack in the gas sensor. For that purpose, the weighted squared difference of the analytical and predicted frequency response is considered as the objective function. The location and depth of the crack in the microsystem are determined using the hybrid Harris Hawk and Nelder Mead optimization algorithms. The accuracy and efficiency of the proposed algorithm are compared with the HHO, DA, GOA, and WOA algorithms. Taguchi design of experiments method is used in order to tune the parameters of optimization algorithms systematically. It is shown that the proposed algorithm can predict the exact location and depth of the open-edge crack on an electrostatically actuated microbeam with proof mass.