This paper is different from the existing
macroeconomic theory. It derives the relationship between the various
macroeconomic variables from the Cobb-Douglas function, and uses statistical data in United States to verify these
equations. We find that the Cobb-Douglas function is obtained in the case that the
marginal output is not 0, therefore it is a function with dynamic properties. On this basis, we use the difference
between the compound output and simple output to determine the incremental
output of a period, and its relationship with capital, interest rate, investment and other variables. These relations
not only deny the premise of Keynesian theory, but also because the proof of
the investment is not equal to the incremental capital, leaving the investment,
output growth, business cycle and other neoclassical theory crisis.

The Cobb-Douglas function not only leads to a
long-term relationship between the rate of output change and the interest rate, but also analyzes why they fluctuate in the short-term. This paper first divides the fluctuation cycle of the interest rate in
the statistical data of the past 45 years by using the mathematical phase
diagram method, and draws the phase diagram of the rate of output change on the
interest rate according to the cycle equation of output. From this phase
diagram, we explain the reason that the phase difference between the interest rate
and the rate of output change in the fluctuation. Then, according to the
optimal relation between L and K in the Cobb-Douglas function, we
further derive the employment equation and its relation to the real interest
rate and the rate of real output change, and verify the theoretical speculation
with statistical data. Finally, it is concluded that the business cycle is a
kind of endogenous production phenomenon.

The difficulty of inflation theory is to explain the fluctuations of the price
level in short-term. First, we use the relationship
between price and money in the traditional quantity equation to derive the
inflation equation that can explain changes of the price level in the long-term
and short-term. Then,
by analyzing the phase diagram of the single variable and the complex variable in the inflation
equation, we find that the fundamental reason of the periodic change of the
short-term price is the periodic change of the real interest rate. Because
fluctuations of the inflation rate and interest rate are the same in
phase, so there is no difference
in the business cycle. Finally, this paper analyzes
the rise and fall of core price under the influence of money and real interest
rate respectively. It lays the foundation for further discussion of the
relationship between inflation and unemployment in Phillips curve.

Traditional macroeconomic theory is difficult to
analyze the long-term growth and short-term decisions of output in a unified
model. In this paper, the concept of “unit resource output” is proposed by using
the difference of production factors combination on different rays in Cobb-Douglas
function, and its maximization condition is derived according to algebraic
principle. And then we use this condition to
explain the reason why the distribution parameter α in the Cobb-Douglas function is growing continuously in the US
statistical data and predict the evolution path of the factor combination in
the growth of the output. Finally, this paper compares the important
differences between our model and the Solow model.

In traditional
macroeconomics argues that the
decision and fluctuation of output level is short-term theory, and the growth of output is a
long-term theory. The former is determined by the demand; the latter is
determined by the production. No one
has questioned why the former is determined by production and the latter is
determined by demand. This
paper argues that the factors that affect the output are the same in the short
and long term, but there is no need to analyze the problem of fluctuation in
the long term. Based on the analysis of
the growth path in our previous paper, this paper first examines whether our
model is applicable to the Pontryagin maximum principle, and then analyzes the
difference of the Cobb-Douglas function in the exogenous growth model and the
endogenous growth model. Reveal the special role of parameter A in Cobb-Douglas function: as long as A is considered as output-related
variables, there is no substantial difference between the so-called exogenous
model and endogenous mode. Finally, according to the trend of the growth path and the nature
of A, the paper derives the final
state of Cobb-Douglas function.

There are two reasons for the financial crisis. One is the spontaneous specula-tion in the capital market. The P/E ratio of the speculative object is much high-er than the ratio of capital to output in the factual economic system. The other is the crisis triggered by the bubble environment. In addition, inflation has a strong inhibitory effect on asset bubbles, and high inflation and asset bubbles will not occur at the same time. These can be verified by statistical data and theoretical explanation from the marginal state equation of Cobb-Douglas function.

Abstract:
We calculate the reflection probability for ultracold alkali atoms incident on a solid surface. By considering the interatomic interaction and using the WKB method, it is shown that the repulsive interaction between atoms has the effect of increasing the reflection probability. The increasing amplitude is related with the interatomic interaction and the depth of atom-surface potential. In addition, we also perform a numerical calculation to testify the effect of the interatomic interaction, and the analytic result is proven by the numerical result.

Abstract:
An index system can be constructed according to Shaw's criterion to measure the degree of one country 's financial depth. The level of China's financial development can be assessed with this system while analyzing through the co integration test the equilibrium relationship among the representative variables of various index types. The results indicate that there are both identical and different aspects between the hypothesis and the features presented by China's financial depth. Moreover, its financial depth agenda is possibly less coordinated.

Abstract:
There are special requirements on image processing in speed and robustness for vision based mobile robot navigation. But mobile robot captured scene color image’s processing has a high computational complexity and low robustness. To reduce data volume and improve robustness, a novel preprocessing method on color image for mobile robot navigation based on principle of threshold segmentation in HSV color space is proposed. Firstly, color image changed from GRB to HSV. Thinking of H component is instable when saturation level is too low, so the principle for single threshold gray image segmentation be used to choose a threshold T on S and divide S into high saturation and low saturation region, we can use H as segmentation basis in high saturation region and V in low saturation region. Then project H component to high saturation region and V component to low saturation region, H and V is stretched to different scope after projection. So, the S component contains not only color information but also gray information and reduces color image from three-dimentions to two-dimentions. Experimental results show that this method has more significant effects in improving the processing speed and robustness of illumination variation and shadows.