‎a numerical technique based on the collocation method using legendre multiwavelets are‎‎presented for the solution of forced duffing equation‎. ‎the operational matrix of integration for‎‎legendre multiwavelets is presented and is utilized to reduce the solution of duffing equation‎‎to the solution of linear algebraic equations‎. ‎illustrative examples are included to demonstrate‎‎the validity...

Gauss-Kronrod product quadrature formulas for the numerical approximation of R 1 ?1 k(x)f (x)dx are shown to converge for every Riemann integrable f , and to possess optimal stability. Similar results are proved for the product formulas based on the Kronrod nodes only. An application to the uniform convergence of approximate solutions of integral equations is given.

In this study we present a novel integration between product portfolio management evaluation criteria and product design decisions involving the design of chemical-based configured consumer products.We consider the variance contributionmade by the product’s quality characteristics to the product’s economic performance that is measured via its net present value (NPV). The sensitivity-based time-...

alternative legendre polynomials (alps) are used to approximate the solution of a class of nonlinear volterra-hammerstein integral equations. for this purpose, the operational matrices of integration and the product for alps are derived. then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. the error analysis of the method is given an...

The current chemical engineering curriculum emphasizes product engineering, which was appropriate in an era when we had many large-volume and long-lived products, which needed a continuous process of cost reduction. Today, in the rapidly growing products of polymers, biomedical devices, and information material, the products tend to be smallvolume and short-lived, which needed continuous improv...

n*m to n + m (see Figure 1). However, to provide this service, they must deal with the problem of heterogeneity in their customers’product, catalog, and document descriptions. Effectively and efficiently managing different description styles becomes a key task for these marketplaces. In real-world marketplaces, developing a scalable approach for information integration has become the main prere...

Using a detailed data set of prices of consumer goods in European cities from 1990 to Spring 2003, we investigate the question of whether the introduction of the euro in January 1999 increased integration of consumer markets as reflected by consumer prices. In fact, we find no tendency for prices to converge after January 1999. This finding holds even when we control for a number of factors tha...

CAD data has grown in complexity while computer assisted tools must be improved in the following aspects: usability for non CAD experts, cooperation support, understanding of 3D geometries and integration between real and virtual models. We present a novel scenario for product development integration based on Augmented Reality. The main advantage of our approach is to add contextual information...

The integration phase represents a highly critical part of the product development process as components are combined and should work together. Errors and problems in product integration result in delays and rework as the results are needed for later phases. Standards and other reference models that include guidelines for product integration are available, but are not always used. Our proposal ...