Based on the formula of complex ray expansion of incident plane wave and a novel parameter transformation, a single variable formula on simulation accuracy for complex ray expansion of incident plane wave is given.

This paper puts forward a single variable error calculation method of fixture comprehensive error calculation and makes the analyses and calculation in the concrete problem according to the character of working error.

For consideration of the non linearity of the welding process, a single variable self learning PID controller based on a neuron was developed with the combination of the merits of PID controller and neural controller.

The urban population model with a single variable can simulate the whole process that the city develops from a small one to a large one, and from an independent one to a higher grade one.

This paper applies a method of linear continuous variable feedback to the control of a kind of voltage collapses induced by reactive power changes, which only uses a single variable to feed back.

Detailed 13C-NMR studies reveal that the multiple reactive species anticipated Kinetic model,is reasonable. The ratio of different kinds/of reactive species could be traced approximately by a single variable function of THF/nBuLi,when the temperatuer Keeps constant.

The simple friction law and slow driving rate allow the state of this fourth order system to be described between slip events by a single variable, the difference in the stretch of the driving springs.

In this paper the sine and cosine functional equations are considered and solved on arbitrary polynomial hypergroups in a single variable.

Recent results on functional equations in a single variable, perspectives and open problems

Solutions with big graph of homogeneous functional equations in a single variable

As special cases we obtain well known results for Cauchy and Jensen equations and for functional equations in a single variable.

The object of this paper is to represent the regularity in the gradation of properties of congeners of chemical elements and their compounds by the same formula as the rule of homologous linearity for organic compounds.As a measure for the gross structural effect of the atoms of a series of congeners, the homologous factor has been used as a single variable to correlate the gradation in properties p of the main groups of elements by a linearequation.By means of this equation, about twenty kinds of properties...

The object of this paper is to represent the regularity in the gradation of properties of congeners of chemical elements and their compounds by the same formula as the rule of homologous linearity for organic compounds.As a measure for the gross structural effect of the atoms of a series of congeners, the homologous factor has been used as a single variable to correlate the gradation in properties p of the main groups of elements by a linearequation.By means of this equation, about twenty kinds of properties of different groups of elements and their compounds have been studied. These include the ionization potentials, electron affinity, various kinds of electronegativities, different kinds of atomic and ionic radii of elements, and also the bond energy, bond polarity, electric conductance, and the various energy quantities involved in the Born-Haber cycle for compoundts.In this paper the reasons for the relatively inferiority in the lin arity of the gradation for the elemental congeners to that for the homologous compounds have been discussed.

In the present paper, a new plate-to-plate method is developed for performance prediction of ideal systems and those close to ideal ones. The sum ofmole fractions of heavy components in the top product, ∑HP, as well as mole fraction ratios of heavy components in the upper part of a column and those of light components in the lower part, vij 's and μij' s, are selected as iterative variables instead of individual concentrations. Two parallel iterations are suggested. The first one is for ∑HP. The mole fractions...

In the present paper, a new plate-to-plate method is developed for performance prediction of ideal systems and those close to ideal ones. The sum ofmole fractions of heavy components in the top product, ∑HP, as well as mole fraction ratios of heavy components in the upper part of a column and those of light components in the lower part, vij 's and μij' s, are selected as iterative variables instead of individual concentrations. Two parallel iterations are suggested. The first one is for ∑HP. The mole fractions of various light components are calculated top-down towards the match plate. The mole fraction of various heavy components are calculated bottom-up towards the match plate. ∑HP is then relaxed with the total match tolerance of heavy components. The second one is for vij's and μij's. The subsequent guess of vij's and μij's is calculated from the solution of tridiagnol matrices with the phase equilibrium constants Kij's obtained from the plate-to-plate calculation. Consequently, the related loops consist of a single strong loop accompanied by a number of comparatively insignificant loops. Thus, a multi-variable system can be converted into a single variable system and the convergence can be dramatically accelear-ated. A rapid and stable convergence is finally achieved. This procedure has been successfully used for complex columns with multifeed and multi-side-stream .

In the previous paper, a new plate-to-plate method was successfully used by the proper selection of iterative variables for performance prediction of ideal systems. In the present paper, similar method is used for calculating extractive distillation processes. The mole fraction of solvent in the bottom product XEB, as well as mole fraction ratios of components to be seperated on various plates vij's are selected as iteractive variables. An outer loop iteration and an inner loop iteration are involved in. The...

In the previous paper, a new plate-to-plate method was successfully used by the proper selection of iterative variables for performance prediction of ideal systems. In the present paper, similar method is used for calculating extractive distillation processes. The mole fraction of solvent in the bottom product XEB, as well as mole fraction ratios of components to be seperated on various plates vij's are selected as iteractive variables. An outer loop iteration and an inner loop iteration are involved in. The outer loop iteration is for the solvent. The mole fraction of solvent is calculated from the bottom upward and is matched at the top; XEB is then relaxed with the match tolerance. The inner loop iteration is for the components to be seperated. The subsequent set of vij's is calculated using the program proposed in the previous paper with ralative volatilities αij's obtained from the stagewise calculation. The inner loop iteration is carried out with fixed αij's and much less computer time is needed. The outer-loop consists of a single strong loop together with a number of comparatively insignificant ones. Therefore, this multivariable system is transferred into a single variable like system as mentioned in the previous paper.