Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper, we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests.     

Optimization of screen-printing parameters of SN9000 ink for pinholes using Taguchi method in chip on film packaging

The influence of pinholes on the chip on film (COF) in screen-printing was studied in this paper. Yield improvement is the most challenging part of COF manufacturing in view of its processing complexity, mainly in the screen-printing process. The process parameters such as ink capacity, origin control distance, angle of the squeezer, method of mixing, freshness of ink, speed of printing, and speed of scraper are considered to improve the pinholes. In Taguchi method, a two level orthogonal array is used to determine the signal-to-noise (S/N) ratio. Analysis of variance and the F-test values are used to determine the most significant process parameters affecting the pinholes. Confirmation analysis tests with the optimal levels of process parameters are carried out. The results of the experiment show that Taguchi method is a very suitable approach with regard to solving quality problems related to such pinholes.     

Some algebraic methods for solving multiobjective polynomial integer programs

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.     

The truncation method for identifying the heat source dependent on a spatial variable

This paper deals with the ill-posed problem of determining an unknown source depending only on the spatial variable in the heat equation. In this problem, the truncation method is employed to get the regularization solution. Moreover, the Hölder type error estimate is also obtained between this regularization solution and the exact solution. Various typical examples are given to verify the efficiency and accuracy of the proposed method.     

Valuation of European continuous-installment options

This paper is concerned with the valuation of European continuous-installment options where the aim is to determine the initial premium given a constant installment payment plan. The distinctive feature of this pricing problem is the determination, along with the initial premium, of an optimal stopping boundary since the option holder has the right to stop making installment payments at any time before maturity. Given that the initial premium function of this option is governed by an inhomogeneous Black-Scholes partial differential equation, we can obtain two alternative characterizations of the European continuous-installment option pricing problem, for which no closed-form solution is available. First, we formulate the pricing problem as a free boundary problem and using the integral representation method, we derive integral expressions for both the initial premium and the optimal stopping boundary. Next, we use the linear complementarity formulation of the pricing problem for determining the initial premium and the early stopping curve implicitly with a finite difference scheme. Finally, the pricing problem is posed as an optimal stopping problem and then implemented by a Monte Carlo approach.     

A new homotopy perturbation method for solving systems of partial differential equations

In this paper, a new homotopy perturbation method (NHPM) is introduced for obtaining solutions of systems of non-linear partial differential equations. Theoretical considerations are discussed. To illustrate the capability and reliability of the method three examples are provided. Comparison of the results of applying NHPM with those of applying HPM reveal the effectiveness and convenience of the new technique.     

On the determination of the steady film profile for a non-Newtonian thin droplet

A shooting method is used to determine a solution to a third-order ODE modeling the steady profile of a non-Newtonian thin droplet. We compare a direct approach to an iterative approach using a secant method. We obtain a nonlinear relationship between the contact angle ? and the position of the contact line r. From this nonlinear relationship we use curve fitting to obtain an empirical law of the form tan?∝r^f(k) where k is the power law coefficient and f is a nonlinear function of k.     

A piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire

In this paper, we introduce a piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire. For the nonlinear oscillator, the present method can produce a good approximation to the exact solution in a very large region, while the standard variational iteration method (VIM) gives a good approximation only in a small region. The numerical results obtained show that the present method does not share the drawback of the standard VIM and can provide very accurate analytical approximate solutions for both small and large values of the oscillation amplitude and parameter.