*Correspondence: jhcha@ewha.ac.kr 3Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea Full list of author information is available at the end of the article Abstract In the present paper we consider ageing properties in a deterioration model in which the stochastic process measuring deterioration is a process with independent increments. Preservation of increasing and decre...

A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of closed circular discs of radius r. A convex disc-polygon of radius r is a set with nonempty interior that is the intersection of a finite number of closed circular discs of radius r. We prove that the maximum area and perimeter of convex disc-n-gons of radius r contained in a hyperconvex disc of ra...

In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...

This paper sheds a new light on submodular function minimization and maximization from the viewpoint of discrete convex analysis. L-convex functions and M-concave functions constitute subclasses of submodular functions on an integer interval. Whereas L-convex functions can be minimized efficiently on the basis of submodular (set) function minimization algorithms, M-concave functions are identif...

We derive a lower bound on the differential entropy of a log-concave random variable X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the rate-distortion function and the channel capacity. Specifically, we study the rate-distortion function for log-concave sources and distortion measure |x− x̂|,...

the effective factors of forward speed, cylinder rotation, and clearance between a combine’s cylinder and concave on wheat kernel breakage and seed germination were studied in karaj area using a 955 model john dear combine. this study was conducted on three levels of adjustment for each of the variables, 1.2, 1.8 and 2.5 km/hr for forward speed, 800, 900, 1000 rpm for cylinder rotation as well ...

The production-transportation problem (PTP) is a generalization of the transportation problem. In PTP, we decide not only the level of shipment from each source to each sink but also the level of supply at each source. A concave production cost function is associated with the assignment of supplies to sources. Thus the objective function of PTP is the sum of the linear transportation costs and ...

This short note presents an alternate approximation of concave cost functions used to reflect economies of scale in process design and supply chain optimization problems. To approximate the original concave function, we propose a logarithmic function that is exact and has bounded gradients at zero values in contrast to other approximation schemes. We illustrate the application and advantages of...