‎A common approach to determine efficient solutions of a multiple objective optimization problem‎ ‎is reformulating it to a parameter dependent scalar optimization problem‎. ‎This reformulation is called scalarization approach‎. Here, a well-known scalarization approach named Pascoletti-Serafini scalarization is considered‎. First, some difficulties of this scalarization are discussed and then ...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

directional simulation, among techniques for reliability analysis of engineering structures, is well known. in this context, directional simulation in load space, because of the considerable advantages of lower dimension of working space, is of considerable interest. as is expected due to structural resistance variability, the location of the relevant limit state(s) is no longer constant and mu...

Scaled experimentation is an important experimental approach for the investigation of complex systems. Unfortunately, scaling suffers scale effects, where changes in behaviour with can be so significant to undermine any scaled investigation. The state-of-the-art remains dimensional analysis, which unfortunately offers no solution effects and consequently experiments although provide only limite...

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

The rising number of components on a micro-chip is the go-to example roaring innovation. Intel's first microprocessor, 4004, released in 1971, had 2,300 transistors; half century later highest count surpasses 50 billion, for Apple M1 Max—an increase seven orders magnitude. Most other technical advances have lagged behind: During entire 20th century, maximum travel speeds rose less than tenfold,...