In current practice, the design is still based on the sequential design methodology, which makes the process or manufacture information not considered at the preliminary design stage. In addition, the quality of design and the time to perform them are largely dependent on the experience of the engineers. Casebased design is an intelligent method which involves retrieving the most similar previo...

The acceptance-rejection algorithm is often used to sample from non-standard distributions. For this algorithm to be efficient, however, the user has to create a hat function that majorizes and closely matches the density of the distribution to be sampled from. There are many methods for automatically creating such hat functions, but these methods require that the user transforms the density so...

By applying the direct symmetry method, the symmetry reductions and some new group invariant solutions were obtained, We have derived some exact solutions by using the relationship between the new solutions and the old ones, which include Weierstrass periodic solutions, elliptic periodic solutions, triangular function solutions and so on. Also, in order to reflect the characteristics and proper...

in the literature hardly any attention is paid to solving a fuzzy fixed charge transportation problem. in this paper, we consider the fully fixed-charge transportation problem and try to find both the lower and upper bounds on the fuzzy optimal value of such a problem in which all of the parameters are triangular fuzzy numbers. to illustrate the proposed method, a numerical example is ‎presented.‎

In the actual analysis of grey clustering evaluation, the length of a grey clustering interval was partially longer, which is determined by the grey clustering evaluation method based on the center-point triangular whitenization weight function. In response to problems like this, this paper proposes a new grey evaluation method on the basis of the reformative triangular whitenization weight fun...

The zeta functions for the Schr\"odinger equation with a triangular potential are investigated. Values of computed using both Weierstrass factorization theorem and analytic continuation via contour integration. results were found to be consistent where domains two methods overlap. Analytic is used compute values at zero negative integers, explore pole structure (and residue values), as well val...

The commutator length “cl G ” of a group G is the least natural number c such that every element of the derived subgroup of G is a product of c commutators. We give an upper bound for cl G when G is a d-generator nilpotent-by-abelian-by-finite group. Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over C that depends only on d and the degree of lineari...

The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular co...

the paper studies optimization of shell-and-tube heat exchangers using the particle swarm optimization technique. a total cost function is formulated based on initial and annual operating costs of the heat exchangers. six variables – shell inside diameter, tube diameter, baffle spacing, baffle cut, number of tube passes and tube layouts (triangular or square) – are considered as the design para...