ON THE FIXING NUMBER OF FUNCTIGRAPHS

Fazil, Muhammad,Javaid, Imran,Murtaza, Muhammad Korean Mathematical Society 2021 대한수학회보 Vol.58 No.1

The fixing number of a graph G is the smallest order of a subset S of its vertex set V (G) such that the stabilizer of S in G, ��S(G) is trivial. Let G1 and G2 be the disjoint copies of a graph G, and let g : V (G1) → V (G2) be a function. A functigraph FG consists of the vertex set V (G1) ∪ V (G2) and the edge set E(G1) ∪ E(G2) ∪ {uv : v = g(u)}. In this paper, we study the behavior of fixing number in passing from G to FG and find its sharp lower and upper bounds. We also study the fixing number of functigraphs of some well known families of graphs like complete graphs, trees and join graphs.

Buckling delamination of the PZT/Metal/PZT sandwich circular plate-disc with penny-shaped interface cracks

Fazile I. Cafarova,Surkay D. Akbarov,Nazmiye Yahnioglu 국제구조공학회 2017 Smart Structures and Systems, An International Jou Vol.19 No.2

The axisymmetric buckling delamination of the Piezoelectric/Metal/Piezoelectric (PZT/Metal/PZT) sandwich circular plate with interface penny-shaped cracks is investigated. The case is considered where open-circuit conditions with respect to the electrical displacement on the upper and lower surfaces, and short-circuit conditions with respect to the electrical potential on the lateral surface of the face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. The sought values are presented in the power series form with respect to the small parameter which characterizes the degree of the initial imperfection. The zeroth and first approximations are used for investigation of stability loss and buckling delamination problems. It is established that the equations and relations related to the first approximation coincide with the corresponding ones of the three-dimensional linearized theory of stability of electro-elasticity for piezoelectric materials. The quantities related to the zeroth approximation are determined analytically, however the quantities related to the first approximation are determined numerically by employing Finite Element Method (FEM). Numerical results on the critical radial stresses acting in the layers of the plate are presented and discussed. In particular, it is established that the piezoelectricity of the face layer material causes an increase (a decrease) in the values of the critical compressive stress acting in the face (core) layer.

Effect of Different Cole Crops on the Biological Parameters of Pieris brassicae (L.) (Lepidoptera: Pieridae) under Laboratory Conditions

Fazil Hasan,M. Shafiq Ansari 한국작물학회 2010 Journal of crop science and biotechnology Vol.13 No.3

The effect of different cole crops was studied on biological parameters of Pieris brassicae (L.) in the laboratory at 28 °C, 65% RH,and 12L:12D photoperiod. The results indicated that host plants significantly affected the life history , i.e. survival of developmental stages, oviposition period, and sex ratio of P. brassicae. Comparative study on different host plant revealed that P. brassicae required a maximum of 40 days to complete generation on cabbage, cauliflower, and broccoli. The survivorship and expectation of life declined gradually with the advancement of age; the life expectancy of newly deposited eggs was 23.96 days while it was 8.12 days at the time of adult emergence on cabbage. However, the fluctuations of mortality parameter were seen on all the cole crops. On cabbage,100% hatching of eggs with low larval mortality were noticed. The highest net reproductive rate (R0) occurred on cauliflower,i.e. 27.1 followed by cabbage 24.89, females per female per generation. Intrinsic rate of increase (rm), was found to be highest (0.09558954) on cauliflower followed by broccoli and cabbage, 0.078886 and 0.077551 females per female per day, respectively. The smallest rm (0.059469 females per female per day) occurred on radish which shows that P. brassicae did not perform well on radish. In addition, P. brassicae may double in 7.2 days on cauliflower, 8.7 days on broccoli, and 8.9 days on cabbage. The sex ratio was computed as 1.5:1, female:male, respectively on cabbage.

Analysis of Effects of Sizes of Orifice and Pockets on the Rigidity of Hydrostatic Bearing Using Neural Network Predictor System

Fazil Canbulut,cem Sinanoglu,sahin Yildirim 대한기계학회 2004 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.18 No.3

This paper presents a neural network predictor for analysing rigidity variations of hydrostatic bearing system. The designed neural network has feedforward structure with three layers . The layers are input layer, hidden layer and output layer. Two main parameter could be considered for hydrostatic bearing system. These parameters are the size of bearing pocket and the orifice dimension. Due to importancy of these parameters, it is necessary to analyse with a suitable optimisation method such as neural network. As depicted from the results, the proposed neural predictor exactly follows experimental desired results.<br/>

Effect of Different Cole Crops on the Biological Parameters of Pieris brassicae (L.) (Lepidoptera: Pieridae) under Laboratory Conditions

Hasan, Fazil,Ansari, M. Shafiq 한국작물학회 2010 Journal of crop science and biotechnology Vol.13 No.3

The effect of different cole crops was studied on biological parameters of Pieris brassicae (L.) in the laboratory at $28^{\circ}C$, 65% RH, and 12L:12D photoperiod. The results indicated that host plants significantly affected the life history, i.e. survival of developmental stages, oviposition period, and sex ratio of P. brassicae. Comparative study on different host plant revealed that P. brassicae required a maximum of 40 days to complete generation on cabbage, cauliflower, and broccoli. The survivorship and expectation of life declined gradually with the advancement of age; the life expectancy of newly deposited eggs was 23.96 days while it was 8.12 days at the time of adult emergence on cabbage. However, the fluctuations of mortality parameter were seen on all the cole crops. On cabbage, 100% hatching of eggs with low larval mortality were noticed. The highest net reproductive rate ($R_0$) occurred on cauliflower, i.e. 27.1 followed by cabbage 24.89, females per female per generation. Intrinsic rate of increase ($r_m$), was found to be highest (0.09558954) on cauliflower followed by broccoli and cabbage, 0.078886 and 0.077551 females per female per day, respectively. The smallest $r_m$ (0.059469 females per female per day) occurred on radish which shows that P. brassicae did not perform well on radish. In addition, P. brassicae may double in 7.2 days on cauliflower, 8.7 days on broccoli, and 8.9 days on cabbage. The sex ratio was computed as 1.5:1, female:male, respectively on cabbage.

Analysis of Effects of Sizes of Orifice and Pockets on the Rigidity of Hydrostatic Bearing Using Neural Network Predictor System

Canbulut, Fazil,Sinanoglu, Cem,Yildirim, Sahin The Korean Society of Mechanical Engineers 2004 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.18 No.3

This paper presents a neural network predictor for analysing rigidity variations of hydrostatic bearing system. The designed neural network has feedforward structure with three layers. The layers are input layer, hidden layer and output layer. Two main parameter could be considered for hydrostatic bearing system. These parameters are the size of bearing pocket and the orifice dimension. Due to importancy of these parameters, it is necessary to analyse with a suitable optimisation method such as neural network. As depicted from the results, the proposed neural predictor exactly follows experimental desired results.

A Highway Alignment Determination Model Incorporating GIS and Multi-Criteria Decision Making

Ferit Yakar,Fazil Celik 대한토목학회 2014 KSCE JOURNAL OF CIVIL ENGINEERING Vol.18 No.6

Construction, repair and maintenance costs of a highway as well as its operation performance and environmental-social effects are mostly depend on its alignment. Therefore, the most important step in the highway planning activity is the alignment determination step. In this study; a 3 stage model incorporating Multi-Criteria Decision Making (MCDM) and Geographical Information Systems (GIS) is developed for highway alignment determination process. In the model; many criteria are handled simultaneously at the beginning of the project according to a concrete procedure with the existence of spatial data, and thus, many drawbacks of existing alignment determination process are eliminated. Fuzzy functions were used in the standardization of criteria maps. Analytic Hierarchy Process (AHP) was used in the determination of criteria weights. Weighted Lineer Combination method was used for the combination of criteria maps. Developed model was tested in a highway project in Tokat, Turkey. IDRISI software was used in the case study for the application of the model. It is seen that use of three stages in the process makes it easy; to take constraints into evaluation, to create alignment alternatives with different viewpoints and to make selection between alternatives with different viewpoints.

Statistical Modelling and Forecasting of Cervix Cancer Cases in Radiation Oncology Treatment: A Hospital Based Study from Western Nepal

Sathian, Brijesh,Fazil, Abul,Sreedharan, Jayadevan,Pant, Sadip,Kakria, Anjali,Sharan, Krishna,Rajesh, E.,Vishrutha, K.V.,Shetty, Soumya B.,Shahnavaz, Shameema,Rao, Jyothi H.,Marakala, Vijaya Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.3

Background: To estimate the numbers and trends in cervix cancer cases visiting the Radiotherapy Department at Manipal Teaching Hospital, Pokhara, Nepal, statistical modelling from retrospective data was applied. Materials and Methods: A retrospective study was carried out on data for a total of 159 patients treated for cervix cancer at Manipal Teaching Hospital, Pokhara, Nepal, between $28^{th}$ September 2000 and $31^{st}$ December 2008. Theoretical statistics were used for statistical modelling and forecasting. Results: Using curve fitting method, Linear, Logarithmic, Inverse, Quadratic, Cubic, Compound, Power and Exponential growth models were validated. Including the constant term, none of the models fit the data well. Excluding the constant term, the cubic model demonstrated the best fit, with $R^2$=0.871 (p=0.004). In 2008, the observed and estimated numbers of cases were same (12). According to our model, 273 patients with cervical cancer are expected to visit the hospital in 2015. Conclusions: Our data predict a significant increase in cervical cancer cases in this region in the near future. This observation suggests the need for more focus and resource allocation on cervical cancer screening and treatment.

Threats to Fruit and Vegetable Crops: Fruit Flies (Tephritidae) - Ecology, Behaviour, and Management

M. Shafiq Ansari,Fazil Hasan,Nadeem Ahmad 한국작물학회 2012 Journal of crop science and biotechnology Vol.15 No.3

Approximately 4,000 known/described species of fruit flies (Tephritidae) are distributed in tropical, subtropical, and temperate regions of world, out of which 200 species are economically important and damaging/spoiling not only to fruits but also to a number of vegetable crops. Despite their tremendous importance, a limited amount of information is available on the ecology and behaviour of fruit flies especially when compared to fruit fly species complex. It is necessary to understand the ecology and behaviour before the formulation of management strategy. The present review may serves as a baseline data for scientists engaged in fruit fly management programs. Key themes include: (1) demography and population dynamics and, (2) behaviour (e.g. sexual, mating, oviposition,and feeding). The excess of literature on monitoring and management of fruit flies are available, which includes male sterilization and annihilation, mass trapping, chemical baits, mating disruption, and biological control. But few of them are easily adopted by users and give satisfactory control of fruit flies and rest are not easily adopted or if used does not give effective control, because of the lack of knowledge about the ecology and behaviour of fruit flies. If the information on population dynamics, behavior, and the related ecological factors are not jointly gathered, it is almost impossible to carry out an appropriate pest control at the right time and place. We hope that this synthesis will lay the groundwork for future ecological and behavioural studies of fruit fly species, populations,communities, and control.

The influence of initial stresses on energy release rate and total electro-mechanical potential energy for penny-shaped interface cracks in PZT/Elastic/PZT sandwich circular plate-disc

Akbarov, Surkay D.,Cafarova, Fazile I.,Yahnioglu, Nazmiye Techno-Press 2018 Smart Structures and Systems, An International Jou Vol.22 No.3

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.