Papers

When two machines M₁ and M₂ are in series the output of M₁ which is the semi finished product is the input for M₂. If M₁ goes to the down state the supply or input to M₂ is stopped and M₂ goes to the down state. The idle time cost of M₂ is high and prohibitive. Hence a reserve of semi finished product in between M₁ and M₂ is suggested. In this paper the optimal reserve size is determined under the assumption the interarrival times between breakdowns of M₁ is a random variable which undergoes a parametric change after a truncation point which is also a random variable. Numerical illustration is also provided.
 

Neural networks have received a great deal of attention over the last few years. They are being used in the area of prediction and classification, areas where regression models and other related statistical techniques have traditionally been used. There has been much publicity about the ability of artificial neural networks to learn and generalize. In fact, the most commonly used artificial neural networks, called multilayer perceptrons, are nothing more than nonlinear regression and discriminant models that can be implemented with standard statistical software. This paper explains what neural networks are, translates neural network terminology into statistical terminology, and shows the relationships between neural networks and statistical models such as generalized linear models, maximum redundancy analysis, projection pursuit, and cluster analysis. Neural networks and statistics are not competing methodologies for data analysis. There is considerable overlap between the two fields. Neural networks include several models such as MLPs that are useful for statistical applications. Statistical methodology is directly applicable to neural networks in a variety of ways, including estimation criteria, optimization algorithms, confidence intervals, diagnostics, and graphical methods. Better communication between the fields of statistics and neural networks would benefit both.

The formal method for the transformation depends on the values of l. For instances, if the values of l is equal to 2, it shows that the square transformation is needed. In this study, we calculated the optimal values of l based on the Newton Raphson procedure using modified normal probability distribution.
 

We study in this paper an approximation method for the calculation of various performance measures of a GI/G/1 queue. We analyze the idle-period distribution as the starting point. The result is then taken as input to many known results to get other performance measure. We show that the distribution of the GI/G/1 idle period satisfies a nonlinear integral equation. This equation directly leads to an accurate approximation solution of the idle-period distribution of the GI/G/1 queue where the interarrival times have a generalized hyperexponential distribution (GH).

B. Singh and S. Jain⁹ prove the existence of unique common fixed point of two weakly compatible pair of maps satisfying an expansive condition. This note examines the same expansive condition for existence of unique common fixed point of five self-maps and relaxing the condition of completeness. and introduced new condition.
 

In this paper present inventory system for time dependent deteriorating items has been developed with exponential demand rate and exponential production. The finite production rate is proportional to the demand rate and deterioration rate. The model with shortage case in inventory solved here. Sensitivity of the decision variable to changes in the parameter values is examine and affect of this changes on the optimal policy are discussed and numerical examples presented to illustrate the model developed.

An alternative approach to the existence of a vertex n Î V(G) such that c(G - n) ³ c(G) - 1 is presented. If such a vertex exists for a planar graph, we show that there must also be one of minimum degree.
 

In the present paper an analysis of velocity, temperature, concentration, skin-friction, heat transfer and mass transfer of the fully developed flow of a viscous incompressible fluid of small electrical conductivity is studied analytically. The flow is considered in porous medium past an oscillating, infinite porous horizontal plate in slip flow regime under the influence of transverse magnetic field of uniform strength. Exact solutions for velocity, temperature and concentration field are obtained. The expressions for skin-friction, heat and mass transfer rate are also derived. The results obtained are numerically presented through graphs or tabular form followed by discussion.

Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates and significance tests for each predictor involved may be underestimated. However many case in the econometric models reported with few observations multicollinearity which could be misleading inferences based on regression models. Ridge estimators are often used to alleviate the problem of multicollinearity. Ridge regression, based on adding a smally quantity k, to the diagonal of a correlation matrix of highly collinear independent variables, can reduce the error variance of estimators, but at the expense of introducing bias. Because bias is a monotonic increasing function of k, the problem of the appropriate amount of k to introduce as the ridge analysis increment has yet to be resolved This paper proposes alternative method for estimate regression coefficients used Bayesian method via Gibss sampling.

Given a graph G consisting of vertices and edges, a vertex labeling of G is an assignment f of labels to the vertices of G that produces for each edge xy a label depending on the vertex labels f (x) and f (y). A vertex labeling f is called a graceful labeling of a graph G with q edges if f is an injection from the vertices of G to the set {0,1,2,...q} such that when each edge xy is assigned the label |f (x)-f (y)| the resulting edge labels are distinct. A graph G is called graceful if there exists a graceful labeling of G (see figure 1). In this Paper we give some results on Central graphs (The Central Graph C(G) of a graph G is obtained by subdividing each edge of G exactly once and joining all the non-adjacent vertices of G (see figure 2)) and gracefulness of Central graphs of Cycles being investigated.