Moreover, reliable "observations" are added to the least-squares minimization function based on the modified equation to increase convergent effectiveness.

Trust region alogorithm is an important method in seeking solution to nonlinear programming. It is presented a trust region algorithm for the Minimax problem,in which continuous minimization function is used and got the global convergence result of the new algorithm in this paper.

All computations involve using the few sets of group parameters obtained for CH≡C/OH by a change of the number of HE experimental points and the minimization function.

Since the complexity of the network (connections, weights, and biases) is most important, the cooling state of the system will strongly relate to the entropy as a minimization function to reach the desired solution.

The higher dimensional surface evolution metric is defined by the prior model instead of by energy minimization function.

The primer set failure probability calculated by a model is used as a minimization function for both primer selection and primers clustering.

The wind force and direction are later part of the minimization function during pose tracking.

An approach to phase refinement for protein structures is proposed. Using a number of known atoms for which the restriction to "equal atoms" in the Sayre equation is relaxed, more exact fundamental equations and tangent formulas have been derived and discussed. This results in corrective terms in the equation and formulas, so that the calculated phases or their shifts can be corrected correspondingly. Moreover, reliable "observations" are added to the least-squares minimization function based on the modified...

An approach to phase refinement for protein structures is proposed. Using a number of known atoms for which the restriction to "equal atoms" in the Sayre equation is relaxed, more exact fundamental equations and tangent formulas have been derived and discussed. This results in corrective terms in the equation and formulas, so that the calculated phases or their shifts can be corrected correspondingly. Moreover, reliable "observations" are added to the least-squares minimization function based on the modified equation to increase convergent effectiveness. Chemical modification methods can therefore continuously play their role while direct methods are employed. Thus an alternating refinement procedure of atomic parameters and phases of obvious practical significance is hereby given for protein structure analysis.

At present, theq uestion of minimum rotors weight is usually discussed by using a optimal method of programming or criterion in consideration of the forbidden natural frequency bands only in optimal dynamic design of high speed rotors. In this paper, a better method of optimal dynamic design is presented for designing higher rotational speed rotor-system of centrifugal pumps. Therefore, the engineering requirements are more wholly met by using this method during design. In the paper, a perturbation converse...

At present, theq uestion of minimum rotors weight is usually discussed by using a optimal method of programming or criterion in consideration of the forbidden natural frequency bands only in optimal dynamic design of high speed rotors. In this paper, a better method of optimal dynamic design is presented for designing higher rotational speed rotor-system of centrifugal pumps. Therefore, the engineering requirements are more wholly met by using this method during design. In the paper, a perturbation converse solution, author presented previously, and a method combining both programming and criterion into one have been separately used, and dynamic flexibility has been taken as minimization-function in consideration of rotor's forced vibration and forbidden natural frequency bands as well as strength and stiffness. A practical example of rotor-system dynamic optimal design has also been given under the liquid-pump CY by once or twice re-analysis. This optimalm ethod can also be developed to the other fields of mechanical engineering optimal design as well as the engineering contruction optimal design.

The main objective of this paper is to study minimization methods for coupled problems in the following two directions:(1)to establish two minimum principles for the coupled thermo-elastodynamics:(2)to provide, for a wide class of coupled physical systems,an algorithm to construct the appropriate minimization functions.The main idea of the paper consists in the following steps:(1) to reduce the number of governing equations by elimination and the convolution theory;(2) to separate coupled variables...

The main objective of this paper is to study minimization methods for coupled problems in the following two directions:(1)to establish two minimum principles for the coupled thermo-elastodynamics:(2)to provide, for a wide class of coupled physical systems,an algorithm to construct the appropriate minimization functions.The main idea of the paper consists in the following steps:(1) to reduce the number of governing equations by elimination and the convolution theory;(2) to separate coupled variables using potential operator defined in a real Banach space ;(3) to derive a transformed minimum principle for Laplace transformation;(4) to establish the minimizing functional by the introduction of the set of admissible weight functions to the original space-time domain . The results of this paper are of great significance on constructing minimizing functionals for a wide class of coupled systems.