In this paper,we prove the inequality of the weight coefficient ω(k) as:ω(k)=k∑∞n=k1n~2∑nj=11j≤4(1-θk)(k∈N),where θ=1-14∑∞n=11n~2∑nk=11k=0.13788928~+ is the best value.
In this paper, by estimating the following inequality of the weight coefficient, W(k)=1k kn=1 ∞j=n1j 3/2 ≤4(1-nk)(k∈ N ,η=0.3469 +), we build a strengthened Hardy′s inequality( p =2).
This paper using multi objective decision and system theory advance the problem of defense weighting coefficient. Based on this foundation,the tactics of air defense attack task assignment is studied. Two kinds of assignment tactics for attack task are put forward.
By introducing parameters A,B andλ,and the weighting coefficient,multi-parameter generalization is made for Hardy-Hilbert’s inequality and its equivalent forms with optimized possible constant factors,in which the corresponding integral inequalities are also taken into consideration.
Optimization of connecting weighting coefficient will be more accurate,and the sharply discontinuous change of adaptability due to Vittorio granularity change can be avoided.
In this paper, the objective programming, a new method in determining weighted coefficients in combination forecasting is presented and the processes for problem-solving are discussed.
Comparing the results for different weighted coefficients of the earth pressure with the traditional solutions from Mohr-Coulomb's strength theory,the conclusion shows that the Mohr-Coulomb's solution in the current literatures is only a special case of the unified solutions,the active earth pressure is lower and the passive earth pressure higher than that of the latter.
The paper studys on the calculating fortilulas of the integral weighted coefficients when the duol weigheed function method is used to paranteter estimation witn discrete series.
In multi-goal decision,it is often transformed into one-goal decision by weighted co- efficient method,and the weighted coefficients are determined by Delphi and AHP meth- ods.
Four improved expressions of the emergence angle with weight coefficient were investigated through experimental data of 68 points observed from 12 aerators of 6 hydropower projects, of both model and prototype, on the basis of error theory.
With calculating the weight coefficient, we put forward several comparative coefficients and finish off the order of superior and inferior of all the decisions for several conflict objectives.
To convert the multi-objective optimization into a single-objective one, the method of changing weight coefficient is used, and then the individual fitness function is built up.
In addition, a closed-form expression of the approximately near-optimal weighting coefficient set is derived, and two simple weighting coefficient sets are proposed as well.
The analysis result also shows that the inference and the weighting coefficient are important in the high and low water data analysis, and it is suggested that w≥l should be taken in monthly high and low water data analysis.
In addition an economic weighting coefficient for the analysis of job contribution in the creation of added value, it is possible to control product pricing.
The work involves development of solution strategies for multipass multicriterion problems using geometric programming, dynamic programming and the weighting coefficient method.
We strengthen the well-known Oxtoby theorem for strictly ergodic transformations by replacing the standard Cesaro convergence by the weaker Riesz or Voronoi convergence with monotonically increasing or decreasing weight coefficients.
The AV filter with orthogonal AVs and optimal weight coefficients has the best performance, but requires considerable computational complexity and suffers from the numerical unstable operation.
In order to reduce its computational load while keeping the superior performance, several low complexity algorithms are proposed to efficiently calculate the AVs and their weight coefficients.
Finally, based on the above mentioned sufficient conditions, the conditions for the realization of optimal control are obtained, which provides a foundation for choosing the weighted coefficients for optimal control in engineering.
The weighted coefficients method is inherently suitable for parallel, coarse-grained implementation that enables exploration of the design space in the elapsed time of a single structural optimization.