021340   Majeed A A;Ali O S (Mathematics Dep, College of Science, Baghdad Univ, Baghdad, Iraq) : Bifurcation of the dynamics of prey-predator model with harvesting involving diseases in both populations. Int J Sci Nat 2017, 8(3), 565-82.

In this paper, an eco-epidemiological system which considers a prey-predator system and (SI) disease with harvesting, using Holling type II as a functional response for the susceptible predator, linear functional response for the infected predator and the harvesting effect on the infectious population. Bifurcation such as (saddle node, transcritical and pitchfork) of the proposed system is investigated by using Sotomayrs theory and Hopf bifurcation theory; it's observed that there is transcritical bifurcation near axial equilibrium point, the predator-free equilibrium point, the disease-free equilibrium point, the infected-predator-free equilibrium point and the infected-prey-free equilibrium point while there is a saddle-node bifurcation near coexistence equilibrium point, on the other hand there is no pitchfork bifurcation near all of these equilibrium points. Further investigations for the Hopf bifurcation near coexistence equilibrium point are carried out. Finally, numerical simulations are used to illustration the occurrence of local bifurcation of this system.

3 illus, 1 table, 11 ref

021339   Hanuma Reddy K;Janakamma K (Mathematics Dep, Hindu College, Guntur-522 602) : Generating function for partitions with parts in A.P. Int J latest Technol Engng Mgmt appl Sci 2017, 6(8), 134-9.

In this paper we derive the generating function for the number of ith over Ga partitions when the parts are in AP. we also obtain a formula for the number of the smallest parts of partitions of n.

3 ref

021338   Barai S D;Warbhe M S;Khobragade N W (Mathematics Dep, Gondwana Univ, Gadchiroli, Maharashtra) : Inverse transient thermoelastic problem of semi-infinite thick hollow cylinder. Int J latest Technol Engng Mgmt appl Sci 2017, 6(8), 1-6.

This paper is concerned with inverse transient thermoelastic problem in which we need to determine the temperature distribution, displacement function and thermal stresses of a semi-infinite hollow cylinder when the boundary conditions are known. Integral transform techniques are used to obtain the solution of the problem.

9 illus, 18 ref

020378   Vaidya S K;Mehta R N (Mathematics Dep, Saurashtra Univ, Rajkot-360 005, Email: samirkvaidya@yahoo.co.in) : Strong domination number of some cycle related graphs. Int J mathl Combinatorics 2017, 3(Sep), 72-80.

Let G = (V (G),E(G)) be a graph and u, v ∈ V (G). If uv ∈ E(G) and deg(u) ≥ deg(v), then we say that u strongly dominates v or v weakly dominates u. A subset D of V (G) is called a strong dominating set of G if every vertex v ∈ V (G). D is strongly dominated by some u ∈ D. The smallest cardinality of strong dominating set is called a strong domination number. In this paper we explore the concept of strong domination number and investigate strong domination number of some cycle related graphs.

2 illus, 11 ref

020377   Subramanian M;Subramanian T (NO, Anna Univ Regional Campus - Tirunelveli, Tirunelveli-627 007, Email: ms_akce@yahoo.com) : Equitable triple connected domination number of a graph. Int J mathl Combinatorics 2017, 3(Sep), 106-18.

A graph G is said to be triple connected if any three vertices lie on a path in G. A dominating set S of a connected graph G is said to be a triple connected dominating set of G if the induced subgraph hSi is triple connected. The minimum cardinality taken over all triple connected dominating sets is called the triple connected domination number and is denoted by γ_tc. A triple connected dominating set S of V in G is said to be an equitable triple connected dominating set if for every vertex u in V.S there exists a vertex v in S such that uv is an edge of G and |deg(v).deg(u)| ≤ 1. The minimum cardinality taken over all equitable triple connected dominating sets is called the equitable triple connected domination number and is denoted by γ_etc. In this paper we initiate a study on this parameter. In addition, we discuss the related problem of finding the stability of γ_etc upon edge addition on some classes of graphs.

8 illus, 6 ref

020376   Siddesha M S;Bagewadi C S (Mathematics Dep, New Horizon College of Engineering, Bangalore, Email: prof_bagewadi@yahoo.co.in) : Slant submanifolds of a conformal (k, μ)-contact manifold. Int J mathl Combinatorics 2017, 3(Sep), 39-50.

In this paper, authors study the geometry of slant submanifolds of conformal (k, μ)-contact manifold when the tensor field Q is parallel. Further, we give a necessary and sufficient condition for a 3-dimensional slant submanifold of a 5-dimensional conformal (k, μ)-contact manifold to be a proper slant submanifold.

22 ref

020375   Senyurt S;Caliskan A;Kilicoglu S (Mathematics Dep, Ordu Univ, Ordu, Turkey, Email: senyurtsuleyman@hotmail.com) : New approach on the striction curves belonging to bertrandian frenet ruled surfaces. Int J mathl Combinatorics 2017, 2(June), 1-10.

In this study, we think six special ruled surfaces associated to the Bertrand curves pair {α, α*}. We describe Bertrandian Frenet ruled surfaces and striction curves of these surfaces are expressed, as depending on the angle between the tangent vectors of the Bertrand curves pair {α, α*}. Also, we examined the situation of the tangent vectors belonging to Striction curves of Frenet and Bertrandian Frenet ruled surfaces.

4 illus, 11 ref

020374   Senyurt S;Altun Y;Cevahir C (Faculty of Arts and Sciences. Mathematics Dep, Ordu Univ, 52200, Ordu/Turkey, Email: senyurtsuleyman@hotmail.com) : Mannheim partner curve a different view. Int J mathl Combinatorics 2017, 2(June), 84-91.

In this study, we investigated special Smarandache curves belonging to Sabban frame drawn on the surface of the sphere by Darboux vector of Mannheim partner curve. Authors created Sabban frame belonging to this curve. It were explained Smarandache curves position vector is consisted by Sabban vectors belonging to this curve. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the Mannheim curve.

10 ref

020373   RejiKumar K;Varghese R P (Mathematics Dep, N. S. S. College, Cherthala, Kerala, Email: rkkmaths@yahoo.co.in) : Spectrum of (k, r) - regular hypergraphs. Int J mathl Combinatorics 2017, 2(June), 52-9.

Authors present a spectral theory of uniform, regular and linear hypergraph. The main result are the nature of the eigenvalues of (k, r) - regular linear hypergraph and the relation between its dual and line graph. We also discuss some properties of Laplacian spectrum of a (k, r) - regular hypergraphs.

1 illus, 12 ref

020372   Reddy P S K;Prakasha K N;Gavirangaiah K (Mathematics Dep, Siddaganga Institute of Technology, B.H. Road, Tumkur-572 103, Email: reddy_math@yahoo.com) : Minimum equitable dominating randic energy of a graph. Int J mathl Combinatorics 2017, 3(Sep), 81-9.

In this paper, we introduce the minimum equitable dominating Randic energy of a graph and computed the minimum dominating Randic energy of graph. Also, established the upper and lower bounds for the minimum equitable dominating Randic energy of a graph.

7 ref

020371   Reddy P S K;Prakasha K N;Gavirangaiah K (Mathematics Dep, Siddaganga Institute of Technology, B.H. Road, Tumkur-572 103, Email: reddy_math@yahoo.com) : Minimum dominating color energy of a graph. Int J mathl Combinatorics 2017, 3(Sep), 22-31.

In this paper, authors introduce the concept of minimum dominating color energy of a graph, E^D_c (G) and compute the minimum dominating color energy E^D_c (G) of few families of graphs. Further, we establish the bounds for minimum dominating color energy.

35 ref

020370   Rao K S;Murali R (Mathematics Dep, Shri Pillappa college of Engineering, Bangalore, Email: srinivas.dbpur@gmail.com) : Rainbow connection number in the brick product graphs C(2n, m, r). Int J mathl Combinatorics 2017, 2(June), 70-83.

Let G be a nontrivial connected graph on which is defined a coloring c : E(G) → {1, 2, ..., k}, k ∈ N of the edges of G, where adjacent edges may be colored the same. A path in G is called a rainbow path if no two edges of it are colored the same. G is rainbow connected if G contains a rainbow u - v path for every two vertices u and v in it. The minimum k for which there exists such a k-edge coloring is called the rainbow connection number of G, denoted by rc(G). In this paper we determine rc(G) for the brick product C(2n,m, r) associated with the even cycle C_2n for m = 1 and odd r ≥ 5 such that n = r + 1, r + 2 and n ≥ r + 3. Authors also discuss the critical property of the graphs with n = r + 1 and n = r + 2 with respect to rainbow coloring.

13 illus, 7 ref

020369   Rajput H;Som T;Kar S (Mathematical Sciences Dep, IIT (BHU), Varanasi) : Vehicular license plate localization using principal component analysis. IETE Tech Rev 2017, 34(2), 214-9.

The need of vehicular license plate recognition system (VLPR) has arisen based on the need to implement traffic control on transportation systems, since early 1970s. Since then, researchers are continuously proposing various approaches and solutions. One of the significant and challenging tasks is to localize the license plate of the moving car. Since the license plate standards are not strictly practiced in world, a large amount of variations are obtained like, size, location, type of font used, background and foreground colour, and so on. The principal component analysis (PCA) is one of the widely used and most successful techniques that have been used in image recognition and compression. In this paper, we propose a novel approach to identify the license plate using PCA.

6 illus, 1 table, 13 ref

020368   Prajapati U P;Gajjar R M (NO, St. Xavier's College, Ahmedabad-380 009, Email: udayan64@yahoo.com) : Cordiality in the context of duplication in web and armed helm. Int J mathl Combinatorics 2017, 3(Sep), 90-105.

Let G = (V (G),E(G)) be a graph - 21 - and let f : V (G) → {0, 1} be a mapping from the set of vertices to {0,1} and for each edge uv ∈ E assign the label |f(u). f(v)|. If the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labled with 0 and the number of edges labeled with 1 differ by at most 1, then f is called a cordial labeling. We discuss cordial labeling of graphs obtained from duplication of certain graph elements in web and armed helm.

6 ref

020367   Ponraj R;Singh R;Kala R (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: ponrajmaths@gmail.com) : Some more 4-prime cordial graphs. Int J mathl Combinatorics 2017, 2(June), 105-15.

Let G be a (p, q) graph, H ∝ G and f : V (G) → {1, 2, ..., k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). Then, f is called Smarandachely k-prime cordial labeling on G to H if |v_f^H (i) - v_f^H (j) ≤ 1, i,j ∈ {1, 2, ..., k} and | e_f^H (0) - e^H_f (1)| ≤ 1, but there exist integers 0 ≤ i ≠ j ≤ k such that |v^GH_f (i) - v^GH_f (j)| ≥ 2, or |e^GH_f (0) - e^GH_f (1) ≥ 2, where v^H_f (x), v^GH_f (x) respectively denotes the numbers of vertices of H, GH labeled with x, e^H_f (1), e^H_f (0) and e^GH_f (1), e^GH_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1 in H, GH. Particularly, a Smaran-dachely k-prime cordial labeling on G to G is called k-prime cordial labeling with v_f(x), e_f(1) and e_f(0) replacing notations v^H_f(x), e^H_f(1) and e^H_f(0) for abbreviation. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 4-prime cordial labeling behavior of lotus inside a circle, sunflower graph, S(K₂ + mK₁), S(P_n odot K₁), dodecahedron, and some more graphs.

4 illus, 3 tables, 10 ref

020366   Ponraj P;Singh R;Kala R (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: ponrajmaths@gmail.com) : Some new families of 4-prime cordial graphs. Int J mathl Combinatorics 2017, 3(Sep), 125-35.

Let G be a (p, q) graph. Let f : V (G) → {1, 2, ..., k} be a function. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |v_f(i) - v_f(j) ≤ 1, i,j ∈ {1, 2, ..., k} and |e_f(0) - e_f(1)| ≤ 1 where v_f(x) denotes the number of vertices labeled with x, e_f(1) and e_f(0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with admits a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 4-prime cordial labeling behavior of shadow graph of a path, cycle, star, degree splitting graph of a bistar, jelly fish, splitting graph of a path and star.

3 illus, 5 tables, 12 ref

020365   Pakade R N;Khobragade N W (Mathematics Dep, Gondwana Univ Gadchiroli, Maharashtra) : Transient thermoelastic problem of semi infinite rectangular beam with heat generation. Int J latest Technol Engng Mgmt appl Sci 2017, 6(6), 96-102.

This paper is concerned with transient thermoelastic problem in which we need to determine the temperature distribution, displacement function and thermal stresses of a semi-infinite square beam when the boundary conditions are known. Integral transform techniques are used to obtain the solution of the problem.

1 illus, - 20 - 

020364   Pakade R N;Khobragade N W (Mathematics Dep, Gondwana Univ Gadchiroli, Maharashtra) : Transient thermoelastic problem of semi-infinite circular beam with internal heat source. Int J latest Technol Engng Mgmt appl Sci 2017, 6(6), 47-53.

This paper is concerned with transient thermoelastic problem in which we need to determine the temperature distribution, displacement function and thermal stresses of a semi-infinite circular beam when the boundary conditions are known. Integral transform techniques are used to obtain the solution of the problem.

11 ref

020363   Murugan A N;Selvaraj P I (Mathematics Dep, V.O. Chidambaram College, Tamil Nadu, Email: anellai.vocc@gmail.com) : Path related n-cap cordial graphs. Int J mathl Combinatorics 2017, 3(Sep), 119-24.

4 illus, 12 ref

020362   MAO L (NO, Chinese Academy of Mathematics and System Science, Beijing 100190, P.R. China, Email: maolinfan@163.com) : Mathematical combinatorics with natural reality. Int J mathl Combinatorics 2017, 2(June), 11-33.

There are 2 contradictory views on our world, i.e., continuous or discrete, which results in that only partially reality of a thing T can be understood by one of continuous or discrete mathematics because of the universality of contradiction and the connection of things in the nature, just as the philosophical meaning in the story of the blind men with an elephant. Holding on the reality of natural things motivates the combination of continuous mathematics with that of discrete, i.e., an envelope theory called mathematical combinatorics which extends classical mathematics over topological graphs because a thing is nothing else but a multiverse over a spacial structure of graphs with conservation laws hold on its vertices. Such a mathematical object is said to be an action flow. The main purpose of this survey is to introduce the powerful role of action flows, or mathematics over graphs with applications to physics, biology and other sciences, such as those of G-solution of non-solvable algebraic or differential equations, Banach or Hilbert G(arrow)-flow spaces with multiverse, multiverse on equations, ... and with applications to complex systems, for examples, the understanding of particles, spacetime and biology. All of these make it clear that holding on the reality of things by classical mathematics is only on the coherent behaviors of things for its homogenous without contradictions, but the mathematics over graphs G is applicable for contradictory systems, i.e., complex systems because contradiction is universal only in eyes of human beings but not the nature of a thing itself.

25 illus, 28 ref

020361   Manshath A;Balaji V;Sekar P;Elakkiya M (Mathematics Dep, Sriram Engineering College, Thiruvallur-602 024, Email: pulibala70@gmail.com) : Non-existence of skolem mean labeling for five - 19 - star. Int J mathl Combinatorics 2017, 2(June), 129-34.

In this paper, authors prove if l ≤ m <60> n, the five star G = K_1,l ∪ K_1,l ∪ K_1,l ∪ K_1,m ∪ K_1,n is not a skolem mean graph if |m - n| <62> 4 + 3l for l = 2, 3, ... and m = 2, 3, ....

18 ref

020360   Makadia H M;Karavadiya H M;Kaneria V J (NO, Lukhdhirji Engineering College, Morbi-363 642, Email: makadia.hardik@yahoo.com) : Some results on α-graceful graphs. Int J mathl Combinatorics 2017, 2(June), 116-22.

In this paper we have proved that the graph obtained by merging t consecutive vertices of two cycles C_4r and C_4s is α-graceful graph. We also proved that G₁ be an α-graceful graph and G₂ be a graceful graph joining by path P_n is graceful in addition we proved G₁ and G₂ be α-graceful graphs joining by path P_n is an α-graceful graph too.

5 illus, 4 ref

020359   Maheswari N R S;Sekar C (Mathematics Dep, G. Venkataswamy Naidu College, Kovilpatti-628 502, Email: nrsmaths@yahoo.com) : On (r₁, r₂), m, (c₁, c₂))-regular intuitionistic fuzzy graphs. Int J mathl Combinatorics 2017, 3(Sep), 10-21.

In this paper, ((r₁, r₂),m, (c₁, c₂))-regular intuitionistic fuzzy graph and totally ((r₁, r₂),m, (c₁, c₂))-regular intuitionistic fuzzy graphs are introduced. A relation between ((r₁, r₂),m, (c₁, c₂))-regularity and totally ((r₁, r₂),m, (c₁, c₂))-regularity on Intuitionistic fuzzy graph is studied. A necessary and sufficient condition under which they are equivalent is provided. Also, ((r₁, r₂),m, (c₁, c₂))-regularity on some intuitionistic fuzzy graphs whose underlying crisp graphs is a cycle is studied with some specific membership functions.

5 illus, 18 ref

020358   Lokhande K;Khot P G;Khobragade N W (Mathematics Dep, RTM Nagpur Univ, Nagpur-440 033) : Alternative approach to the optimum solution of linear programming problem. Int J latest Technol Engng Mgmt appl Sci 2017, 6(6), 61-8.

In this paper, new alternative methods for simplex method, Big M method and dual simplex method are introduced. These methods are easy to solve linear programming problem. These are powerful methods. It reduces number of iterations and save valuable time.

8 ref

020357   Lokesha V;Deepika T (studies in Mathematics Dep, Vijayanagara Sri Krishnadevaraya Univ, Ballari, Email: v.lokesha@gmail.com) : Operations of n-wheel graph via topological indices. Int J mathl Combinatorics 2017, 3(Sep), 51-6.

In this paper, Authors discussed the Topological indices viz., Wiener, Harmonic, Geometric-Arithmetic(GA), first and second Zagreb indices of n-wheel graphs with bridges using operator techniques.

18 ref

020356   Liu Z;Chen Y;Li S (Mathematics Dep, Huizhou Univ, Huizhou, Guangdong, 516007, China, Email: zhongzhuliu@126.com) : First zagreb index, vertex-connectivity, minimum degree and independent number in graphs. Int J mathl Combinatorics 2017, 2(June), 34-42.

Let G be a simple, undirected and connected graph. Defined by M₁(G) and RMTI(G) the first Zagreb index and the reciprocal Schultz molecular topological index of G, respectively. In this paper, we determined the graphs with maximal M₁ among all graphs having prescribed vertex-connectivity and - 18 - minimum degree, vertex-connectivity and bipartition, vertex-connectivity and vertex-independent number, respectively. As applications, all maximal elements with respect to RMTI are also determined among the above mentioned graph families, respectively.

28 ref

020355   Liu F;Tian Z X;Li D (NO, Beijing Information Technology College, 100018, P.R. China, Email: liufengfirst@sina.com) : Supereulerian locally semicomplete multipartite digraphs. Int J mathl Combinatorics 2017, 2(June), 123-8.

A digraph D is eulerian if D is strongly connected and for every vertex v ∈ V (D), d⁺(v) = d^-(v). Bang-Jensen and Thomasse gave the conjecture for a digraph D that if λ(D) ≥ α(D), then D is supereulerian. Bang-Jensen and Maddaloni [Journal of Graph Theory, 79(2015)8-20] proved that this conjecture holds for every semicomplete multipartite digraph. In this paper, we generalized the above known results and show that this conjecture holds for every strong locally semicomplete multipartite digraph.

1 illus, 12 ref

020354   Laha B (Mathematics Dep, Shri Shikshayatan College, Kolkata, Email: barnali.laha87@gmail.com) : D-conformal curvature tensor in generalized (κ, μ)-space forms. Int J mathl Combinatorics 2017, 2(June), 43-51.

The object of the first two sections is to give brief history of generalized (κ, μ) space forms and some basic results related to such manifold. In the last section we have derived few results regarding D-conformal curvature tensor in generalized (κ, μ) space-forms.

12 ref

020353   Kahraman T;Ugurlu H H (NO, , Mathematics Dep, Manisa-Turkey, Email: tanju.kahraman@cbu.edu.tr) : Smarandache curves of curves lying in lightlike cone in R₁<. Int J mathl Combinatorics 2017, 3(Sep), 1-9.

In this paper, authors consider the notion of the Smarandache curves by considering the asymptotic orthonormal frames of curves lying fully on lightlike cone in Minkowski 3-space R³₁. Authors give the relationships between Smarandache curves and curves lying on lightlike cone in R³₁.

10 ref

020352   Cimdiker M;Ekici C (Mathematics Dep, Kirklareli Univ, 39100 Kirklareli, Turkey, Email: muradiye.1001@hotmail.com) : On the spacelike parallel ruled surfaces with darboux frame. Int J mathl Combinatorics 2017, 2(June), 60-9.

In this study, the spacelike parallel ruled surfaces with Darboux frame are introduced in Minkowski 3-space. Then some characteristic properties of the spacelike parallel ruled surfaces with Darboux frame such as developability, the striction point and the distribution parameter are obtained in Minkowski 3-space.

11 ref

020351   Arockiaraj S;Baskar A D;Kannan A R (Mathematics Dep, Kamarajar Government Arts College, Surandai-627 859, Email: psarockiaraj@gmail.com) : F-root square mean labeling of graphs obtained from paths. Int J mathl Combinatorics 2017, 2(June), 92-104.

A function f is called a F-root square mean labeling of a graph G(V,E) with p vertices and q edges if f : V (G) → {1, 2, 3, ..., q + 1} is injective and the induced function f* defined as f*(uv) = [√f(u)² + f(v)²/2] for all uv ∈ E(G), is bijective. A graph that admits a F-root square mean labeling is called a F-root square mean graph. In this paper, we study the F-root square meanness of the path P_n, the graph P_n masculine ordinal indicator S_m, the graph P_n masculine ordinal indicator K₂, the graph TW(P_n, the graph [P_n; S_m], the graph S(P_n masculine ordinal indicator K₁), the graph M(P_n), the graph T(P_n), the graph P₂ⁿ, the ladder graph L_n and the slanting ladder graph SL_n.

14 illus, 5 ref

020350   Alilou A (Mathematics Azarbaijan Shahid Dep, Madani Univ Tabriz, Iran, Email: abbasalilou@yahoo.com) : Cohen-macaulay of ideal I₂ (G). Int J mathl Combinatorics 2017, 3(Sep), 32-8.

In this paper, authors study the Cohen-Macaulay of ideal I₂ (G), where I₂ (G) = (xyz | x - y - z is 2 - path in G). Also, authors determined the 2-projective dimension R-module, R/I₂ (G) denoted by pd₂ (G) of some graphs.

1 illus, 9 ref

019414   Yadav M K;Bundel R;Chaudhary S;Tomer S K (Statistics Dep, Banaras Hindu Univ, Varanasi-221 005, Email: rashmi.bundel@gmail.com) : Reliability estimation for inverse Lindley distribution under progressive type-II censoring scheme. Int J agric statist Sci 2017, 13(2), 777-81.

In this paper, authors present the analysis of progressively type-II censored lifetime data. Assuming the lifetime of every unit to be inverse Lindley distribution, we obtain the maximum likelihood estimates and asymptotic confidence intervals for the parameter and reliability function of this distribution. We also evaluate Bayes estimates, Bayesian credible and highest posterior density intervals. For numerical illustrations, we present an extensive simulation study.

5 tables, 24 ref

019413   Victorbabu B R;Chiranjeevi P;Surekha C V V S (Statistics Dep, Acharya Nagarjuna Univ, Guntur-522 510, Email: victorsugnanam@yahoo.co.in) : On measure of rotatability for second order response surface designs using balanced incomplete block designs. Int J agric statist Sci 2017, 13(2), 439-43.

In this paper, measure of rotatability for second order response surface designs using balanced incomplete block designs when r<62>3λ for 5≤ v≤ 16 (v- number of factors) is suggested, which enables us to assess the degree of rotatability for second order response surface designs.

1 table, 10 ref

019412   Tripathy P K;Sukla S;Tripathy P (Statistics P.G Dep, Utkal Univ, Bhubaneswar-751 014, Email: msccompsc@gmail.com) : Game theory approach in management of mortality mutation. Int J agric statist Sci 2017, 13(2), 387-92.

Diminution in mortality mutation leads to enhancement in life expectancy. But the contribution of the mortality change of different age groups in expanding the life expectancy is not always informative. With the passage of time this contribution also undergoes a transition. The current study employs year wise ASDR to estimate life expectancy for different age groups in India and in BIMARUO states by constructing life tables and then game theory perspective is applied to discern the age group affecting life expectancy. The study is beneficial for demographers as well as researchers to have expertise germane to the age group playing important role in lifting up the life expectancy in a developing country like India and in demographically backward states of BIMARUO.

2 illus, 13 tables, 9 ref

019411   Talawar A S;Pujar H S (Statistics Dep, Karnatak Univ, Dharwad-580 003, Email: talwarappu@gmail.com) : Analysis of malaria epidemic model with constant immigration. Int J agric statist Sci 2017, 13(2), 409-15.

Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female Anopheles mosquitoes. We consider first a simple SIR model that describes the dynamics of malaria and human population compartments in terms of mathematical equations and these equations represent the relations between relevant properties of the compartments. The aim of this paper is to understand the important parameters in the transmission and spread of endemic malaria disease and try to find appropriate solutions and strategies for its prevention and controlled by applying mathematical modelling. In the second stage, we developed the malaria epidemic model considering the effect of constant immigration. We also derive the equilibrium points of the model and investigate their global stability. Our results show that, if the basic reproduction number (R₀) is less than 1, the disease-free equilibrium point is stable, so that the disease dies out. If it is greater than 1, then the endemic equilibrium point is globally asymptotically stable. For - 29 - illustration purpose, we have considered malaria data collected from the District Malaria Health Centre, Raichur, Karnataka State.

7 illus, 23 ref

019410   Talawar A S;Aundhakar U R;Mallappa D (Studies in Statistics Dep, Karnatak Univ, Dharwad-580 003, Email: talwarappu@gmail.com) : Stochastic modeling of vector borne disease. Int J agric statist Sci 2017, 13(2), 771-6.

Monte Carlo analysis was performed to determine the sensitivity of infection dynamics to the parameters. To initialize this process for evaluation of epidemic growth over time, initial values of transition rates are considered as a = 0.2, γ = 0.01, μ = 0.05, p = 0.8 and m = 0.05. For SIRD model, we have performed 25000 iterations for each run of the MCMC algorithm following 5000 burn-in. In order to avoid autocorrelation within successive samples, we have allowed every tenth observation to participate in making inference. The output was recorded to constitute samples from the posterior distribution and the convergence was visually assessed through trace plots. Trace plots provide a useful method for detecting problems with MCMC convergence and mixing. Here, all posterior means are characterised by its credible interval (Cr I). The results show that the posterior mean of the rate of infection from susceptible to infected is 0.0.1402 (0.1299, 0.1503) per day and the posterior mean rate of the rate of recovery in a community is 0.0125 (0.0118, 0.0132) per day. Also, the posterior mean of the rate of death due to disease is 0.0523 (0.0506, 0.0541), the posterior mean of death rate of recruitment of vectors or mosquito's is 0.8006 (0.7659, 0.9046) per day and the posterior mean of rate of removed or died mosquito's is 0.0425 (0.0414, 0.0437).

3 illus, 1 table, 20 ref

019409   Swain P K;Deo V;Gunjan Kumar (Statistics P.G. Dep, Utkal Univ, Vanivihar, Bhubaneswar-751 004, Email: prafulla86@gmail.com) : Quantile regression approach for child mortality analysis. Int J agric statist Sci 2017, 13(2), 457-63.

In this paper, we have explored a quantile regression approach to study the factors affecting the child mortality in India. The annual health survey data has been used for application and the results of quantile regression have been compared - 28 - with those of a linear regression (LR) model. Factors, such as safe delivery, private delivery, mothers' post natal check within 48 hours, breast feeding within 1 hour, full immunizations, fathers literacy rate., etc are found to be significantly associated with child mortality (P value <60> 0.05). The results have demonstrated that using quantile regression leads to better interpretation and more specific inference about the predictors of child mortality. Hence, we suggest that the quantile regression could be used as an alternative to LR in mortality analysis.

3 illus, 3 tables, 17 ref

019408   Sharma M K;Pandey A (NO, Addis Ababa Univ, Addis Ababa, Ethiopia, Email: ansuula.pandey@gmail.com) : Optimal block designs for diallel crosses in presence of specific combining abilities. Int J agric statist Sci 2017, 13(2), 633-8.

A simple method of construction of mutually orthogonal Latin square of order p = 2m + 1 is proposed. Incomplete block designs for a complete diallel cross experiment known as method (4) of Griffing (1956) are derived using proposed mutually orthogonal Latin square. Optimality of these designs is considered when, in addition to the block effects and general combining abilities, the model also includes specific combining abilities. It is found that these designs remain optimal even in the presence of specific combining abilities. The analysis includes the analysis of variance and the estimation of general combining ability and of specific combining ability. The analysis is illustrated numerically.

4 tables, 20 ref

019407   Saxena K K;Josephat P K;Ajay Kumar (Statistics Dep, College of Natural and Mathematical Sciences, Dodoma Univ, Dodoma, Tanzania, Email: saxkk@yahoo.com) : Symmetric functions, jackknife and u-statistics - a non-parametric approach. Int J agric statist Sci 2017, 13(2), 705-8.

In estimation problems, researchers generally use estimators, which are symmetric in observations. Given any function f (x₁, x₂, ... x_n) in n variables with values in an abelian group, a symmetric function can be constructed by summing values of f (x₁, x₂, ... x_n) over all permutations of the arguments. Similarly, an antisymmetric function can be constructed by summing over even permutations and subtracting the sum over odd permutations. These operations are of course not invertible, and could well result in a function that is identically zero for nontrivial functions f (x₁, x₂, ... x_n). The only general case where f (x₁, x₂, ... x_n) can be recovered if both its symmetrization and anti symmetrization are known, is when n = 2 and the abelian group admits a division by 2 (inverse of doubling); then f (x₁, x₂, ... x_n) is equal to half the sum of its symmetrization and its anti symmetrization [Joseph et al. (2009)]. To study properties of some of these estimators, a special class of symmetric functions, called U-statistics, has been found useful, particularly in non-parametric statistical theory. Fraser (1957) has given a comprehensive discussion of U-Statistics. In this paper, we have reviewed some of the properties of U-statistics and have proved necessary and sufficient condition that a jackknife estimator reduces to the ori ginal estim ator, if it is i n the form of a U-sta tistic. It has been il lustr ated by taking a n est i mator of P(X <60> Y) when data are censored and if U is any censoring point, then by taking the degree of kernel as one, the jackknife estimator of a U-statistic based on a sample of size n reduces to the same estimator. These results will be very useful in non-parametric statistical theory.

13 ref

019406   Sandeep Kumar;Sisodia B V S;Sunil Kumar;Singh D;Basak P (Agricultural Statistics Dep, N.D. Univ of Agriculture and Technology, Kumarganj, Faizabad-224 229, Email: bvssisodia@gmail.com) : On various approaches for estimating finite population total in survey sampling under ratio super population model. Int J agric statist Sci 2017, 13(2), 677-82.

Deville and Sarndal (1992) developed calibration estimator by using the auxiliary information to obtain a better estimate of the population total of study variatey. While calibration approach does not assume any explicit relationship between y and x but it assumes that only X, the population total of x is known. Prediction approach advocated by Royall and Herson (1973) leads to model based estimator of finite population under a assumption of specified super population model where x_i's are supposed to be known for all i = 1, 2, 3, ..., N. Wu and Sitter (2001) proposed a design oriented model based calibration estimator of population total, when they also assumed that X_i are known for all i = 1, 2, 3, ..., N. It has been shown that these three approaches i.e. calibration approach, model based approach and model based calibration approach provides the same estimator under some situation. However, their variances are different. In the present paper, an attempt has been made to conduct a limited simulation study to examine the relative performance of the estimators based on the aforesaid three approaches. From the results of the simulation study, it has been found that calibration estimates are best.

2 tables, 10 ref

019405   Rani S;Rajeev Kumar (Mathematics Dep, M. D. Univ, Rohtak-125 004, Email: kakoriasunita@gmail.com) : Two-unit water process system considering online repair of minor faults without automatic switching of components in redundant subsystem. Int J agric statist Sci 2017, 13(2), 553-61.

The aim of the present paper is to assess reliability and cost-benefit of a two identical units water process system wherein each unit comprises several redundant and non-redundant subsystems. The redundant subsystems are considered to be of two types, namely 1-out-of-2 (Type-I) and 2-out-of-3 (Type-II). On occurrence of a minor fault in the unit it goes to partial failure whereas in case of a major fault the unit goes to complete failure. Further, on partial failure of the unit, the repairman first inspects the unit to judge which subsystem has the minor fault and accordingly carries out the online repair of the subsystem without automatic switching of the components of redundant subsystem to avoid losses (including loss of power generation) etc. Various measures of system effectiveness for the model are obtained using Markov process and regenerative point technique. Using these measures, profit incurred to the system is computed. Using real data the reliability and cost analyses of the system are carried out as a particular case. Various conclusions are made by plotting graphs.

11 illus, 16 ref

019404   Rachokarn T;Lawson N (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology, North Bangkok, Bangkok, 10800, Thailand, Email: nuanpan.n@sci.kmutnb.ac.th ) : Class of ratio chain type exponential estimator for population mean in the presence of non-response. Int J agric statist Sci 2017, 13(2), 431-7.

This paper attempts to propose a new class of ratio chain type exponential estimator to estimate population mean in the presence of non-response is especially when the information regarding a study and auxiliary variables is incomplete. Motivation for the proposed class of estimator is based on Rachokarn and Lawson (2016) and Kumar (2013). To the first order of approximations, the bias and the mean squared error (MSE) of the - 26 - proposed class of estimators have been discussed. Other members were also derived from the proposed class by allocating the different suitable values of constants. In addition, theoretical and empirical studies were used in order to access the performance of the proposed class. The results of this study show that the proposed class of estimator is more efficient under percent of relative efficiencies (PREs) criterion compared to other relevant estimators.

3 tables, 18 ref

019403   Patel D T;Patel M N (NO, SLU Arts and H and P Thakor Commerce College, Ellisbridge, Ahmedabad-380 006, Email: divyapatel.1985@yahoo.com) : Bayesian approach to optimal warranty length for power function distributed product with general progressive type-II censoring scheme. Int J agric statist Sci 2017, 13(2), 623-31.

In this paper, we use a Bayesian approach to determine the optimal warranty length. The power function distribution is employed to describe the product life time under general progressive type-II censoring scheme. We have considered a combination of free replacement policy and pro-rata policy for warranty. The optimal warranty is obtained by maximizing the expected utility of the product. A numerical data is presented to examplify the theory. A sensitivity analysis is carried out to check the effect of hyper parameters on the optimal warranty length and the optimal value of expected utility.

4 tables, 23 ref

019402   Panda K B;Sen M (Statistics PG Dep, Utkal Univ, Bhubaneswar, Odisha-751 004, Email: kunja.st@utkaluniversity.ac.in) : Efficient ratio-type and product-type exponential estimators. Int J agric statist Sci 2017, 13(2), 639-44.

In this paper, two new estimators, one each on ratio-type and product-type methods of estimation are proposed. While the newly proposed ratio-type exponential estimator is found to perform better than the mean per unit estimator, customary ratio estimator and ratio-type exponential estimator due to Bahl and Tuteja (1991) under conditions that often hold good in practice, the newly proposed product-type exponential estimator fares better than the mean per unit estimator, usual product estimator and the product-type exponential estimator due to Bahl and Tuteja (1991) under practical conditions. The proposed estimators are also found to perform better than the competing estimators in two-phase sampling under the same conditions as in one-phase sampling. The percentage gains in precision due to the newly proposed estimators as compared to the competing estimators in respect of real-life examples have been evaluated.

3 tables, 10 ref

019401   Pal S K;Singh H P (School of Studies in Statistics, Vikram Univ, Ujjain-456 010, Email: suryakantpal6676@gmail.com) : Generalized efficient ratio-cum-product estimator in systematic sampling. Int J agric statist Sci 2017, 13(2), 713-20.

This paper considers a generalized ratio-cum-product estimator of population mean in systematic sampling using auxiliary information in sample surveys. A large number of estimators of different parameters of the study variables based on auxiliary information can be viewed as a member of - 25 - suggested class of estimators. The bias and mean squared error of the proposed class of estimator have been obtained under large sample Approximation. Optimum conditions are obtained for which the proposed class of estimators has minimum mean squared error. It has been proved theoretically that the suggested class of estimators at its optimum condition is more different than the regression estimator in systematic sampling. An empirical study is carried out in support of the present study.

3 tables, 13 ref

019400   Pal S;Dihidar K;Mandal G;Basak S;Ghosh A; Chakraborty A K;Pal S (Interdisciplinary Statistical Research Unit, Indian Statistical Institute, 203, Kolkata-700 108, Email: spbbr18@gmail.com) : Novel approach in robust estimation of optimum size of plots. Int J agric statist Sci 2017, 13(2), 423-9.

The problem of determination of Shape and Size of Plots remains at the foundation of planning and executing controlled field experiments. During sustained research investigations (more than a century) on experimental fields it has been established with confirmation that the premier action-point to be addressed before setting up of evaluation trials is to explore ways and means to minimize the inherent variability existing among the yield observations (role of determination of optimum shape and size of plots offers a milestone-discovery in the precinct of such controlled field experiments with the pioneering work of Smith (1938)). The concept of robust optimum plot size is introduced in the paper [Pal et al. (2015)] and subsequently, it is also considered in another paper in Pal and Basak (2016). An extensive review on the aspect of robust optimum plot size is available in Pal et al. (2016). In this paper, the theoretical model employed in Pal and Basak (2016) is considered under the set-up of a superimposed probability distribution (which mimics the real-life situations arising under the perspective of the class of field experiments) on it. The robust optimum plot sizes (determined basing on the overlaid exponential probability density for the intra-class correlation coefficient) in the form of three layers (in squared meters) are, Layer - I (14 (2x7), 18 (3x6), 21 (3x7), 28 (4x7) and 30 (5x6), robust very near to optimum plot sizes are, Layer - II (10 (2x5), 12 (2x6), and 24 (4x6)), and robust near to optimum plot sizes are, Layer -III (8 (2x4),12 (3x4) and 15 (3x5)), respectively.

4 tables, 15 ref

019399   Mohanty B S;Verma M R;Sharma V B;Roy P K (Livestock Economics Div, Statistics and Information Technology, ICAR-IVRI, Izatnagar, Bareilly-243 122, Email: medramverma@rediffmail.com) : Comparative study of lactation curve models in crossbred dairy cows. Int J agric statist Sci 2017, 13(2), 545-51.

The lactation curve is a graphical representation of the milk yield from an animal throughout a defined time period. The shape of the lactation curve provides relevance information about day to day farm management practices. It is a suitable tool in designing the breeding and management strategies for cattle. Lactation curve in dairy cattle reach to the peak yield after calving within 2 to 8 weeks then decline gradually up to the drying period. Cows with the flatter lactation curves are considered as more persistent which implies the lower incidence of metabolic and reproductive disorders. In our study, we had taken the data set of 6484 weekly test day milk yield (WTDMY) records over a period of five years (2010-2015) of 50 of crossbred dairy cows (Jerseyx Red Sindhi ) from the history cum pedigree records maintained at Central Cattle Breeding Farm, Chipilima, Odisha under Ministry of Agriculture, Govt. of India. The crossbred cows over a period of 150 days of lactation length were taken into consideration. The above data were analyzed by using five statistical models viz. Sikka (SIK), Wilmink (WK), Morant and Gnanasakthy (MG), Ali and Schaeffer (AS) and Mitscherlich x Exponential (ME) model. All the models were judged by different measures of goodness of fit tests. The models with the highest degree of adjusted coefficient of determination (R²_adj) with lowest value of root mean square error (RMSE), Akaike's information criterion (AIC), corrected Akaike's information criterion (AICc) and Schwartz Bayesian information criterion (SBC) were considered as best - 24 - fitted models. It was observed that among all the models, AS model showed best fit giving highest degree of accuracy (R²_adj = 97.8%), lowest value of RMSE (0.328), AIC (-91.208), AICc (-89.587) and SBC (-82.402) followed by MG models (R²_adj = 95.6%, RMSE = 0.468, AIC = -61.454, AICc = -60.401 and SBC = -82.402). Whereas, WK model was considered as least fitted model with lowest R²_adj (93.2%), however, all five models were estimated with more than 93% of degree of accuracy. Summary measures revealed that the observed lactation yield of crossbred cows attained peak yield of 81.42 kg on 5th weeks after calving. But estimated peak lactation yield by five models were varied from 77.48 kg to 84.39 kg with peak period ranged from 5 weeks to 10 weeks after calving. Higher lactation persistency was measured in SIK model followed by ME model. However, 305 days total milk yield estimated by above five models were very close to the observed total milk yield (2676.76 kg).

2 illus, 4 tables, 30 ref

019398   Maiti S S;Mukherjee I (Statistics Dep, Visva-Bharati Univ, Santiniketan-731 235, Email: dssm1@redimail.com) : Estimation of the PMF and CDF of some standard discrete distributions useful in reliability modelling. Int J agric statist Sci 2017, 13(2), 735-51.

This article addresses different methods of estimation of the probability mass function (PMF) and cumulative distribution function (CDF) of some standard discrete distributions, viz. Binomial, Poisson and Geometric. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), percentile estimator (PCE), least squares estimator (LSE), weighted least squares estimator (WLSE), Bayes estimate (BE). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation. Finally, real data sets have been analyzed for illustrative purposes.

9 illus, 4 tables, 21 ref

019397   Kshandakar S;Verma M R;Singh Y P;Sharma V B; Sanjay Kumar (Livestock Eco and Statistics and Information Tech. Div, ICAR-I.V.R.I., Izatnagar, Bareilly-243 122, Email: medramverma@rediffmail.com) : Effect of lameness on lactation curves of murrah buffaloes. Int J agric statist Sci 2017, 13(2), 693-703.

Indian economy is based on agriculture and allied sector where milk production plays a vital role. Milk production in India was 155.49 million tonnes in 2015-16. India ranks first in milk production in which the water buffalo (Bubalus bubalis) contributes 54% of total milk production. However, lameness remains one of the most expensive production diseases of buffalo. The aim of present study was to find best fitted lactation curve model explaining the lactation behaviour of Murrah buffalo in healthy and lameness conditions. The data consisted of daily test day milk yield (DTDMY) records of 272 Murrah buffaloes. Different standard lactation curve models such as Ali and Schaeffer (1987), Cobby and Le Du (1978), Dijkstra et al. (1997) Mitscherlich x Exponential [Rook et al. (1993)], Mixed log [Guo and Swalve (1995), - 23 - Wilmink (1987) and Wood (1967)] models were fitted. The goodness of fit of the models was judged by highest value of R_adj² and lowest values of RMSE, AIC and BIC. Durbin-Watson test was used to test the autocorrelation and Shapiro-Wilk's test was used to test the normality of the residuals. Based on the different measure of goodness of fit, Ali and Schaeffer model was the best fitted to DTDMY records of the healthy as well as lame Murrah buffaloes. The effect of Lameness on milk production of Murrah buffalo was estimated by Repeated measure ANOVA. The effect of disease was significant (p <60> 0.001) and healthy Murrah produces 20.66% more milk than lame Murrah buffalo.

6 illus, 14 tables, 34 ref