In refractive surgery, the cubic spline fit for the transition zone breaks down for myopia and myopic meridians in mixed astigmatism as in many cases the cubic spline function runs into negative values. In this paper,...In refractive surgery, the cubic spline fit for the transition zone breaks down for myopia and myopic meridians in mixed astigmatism as in many cases the cubic spline function runs into negative values. In this paper, the complementary error function is proposed instead of the cubic spline function as the transition zone function, due to the availability of analytical expression of its derivatives and the nonnegativity fact. It is shown that with the use of the complementary error function, transition zones for all refractive types work correctly.展开更多
The aim of this short note is to examine the properties of a special function defined by an integral which was appeared in a paper by Ersoy. It is revealed that the function for is expressed in terms of the gamma func...The aim of this short note is to examine the properties of a special function defined by an integral which was appeared in a paper by Ersoy. It is revealed that the function for is expressed in terms of the gamma function and it varies linearly with for . Its appropriate graphs are plotted and its pertinent values are tabulated.展开更多
When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has chang...When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.展开更多
文摘In refractive surgery, the cubic spline fit for the transition zone breaks down for myopia and myopic meridians in mixed astigmatism as in many cases the cubic spline function runs into negative values. In this paper, the complementary error function is proposed instead of the cubic spline function as the transition zone function, due to the availability of analytical expression of its derivatives and the nonnegativity fact. It is shown that with the use of the complementary error function, transition zones for all refractive types work correctly.
文摘The aim of this short note is to examine the properties of a special function defined by an integral which was appeared in a paper by Ersoy. It is revealed that the function for is expressed in terms of the gamma function and it varies linearly with for . Its appropriate graphs are plotted and its pertinent values are tabulated.
文摘When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.
