The intersection point rule for homologues in gas chromatography was discovered many years ago,now more and more application and development are occurring in recent years~[2-6], but there are few systemic theoretical ...The intersection point rule for homologues in gas chromatography was discovered many years ago,now more and more application and development are occurring in recent years~[2-6], but there are few systemic theoretical studies.In this paper,based on the basic equation of reten- tion values in gas chromatography,we prove the intersection point rule of homologues from mathematics,study the factors affecting intersection point position,give the physical meaning of intersection point,and explain the experimental rules in references.展开更多
The fractal curve is proposed as a novel scanning path used in Layered Manufacturing. Aiming at a limitation that the fractal curve can only fill a square region, a method is developed to realize the trimming of frac...The fractal curve is proposed as a novel scanning path used in Layered Manufacturing. Aiming at a limitation that the fractal curve can only fill a square region, a method is developed to realize the trimming of fractal curve in arbitrary boundary layer by means of judging intersection points between parameterized arbitrary boundary and a FASS (space filling, self avoiding, simple and self similar) fractal curve. Accordingly, the related algorithm concerning with determining intersection points has been investigated according to the recursion feature of the fractal curve, and in the process of the fractal curve traversed, the rule of judging intersection points is ascertained as well, so that the laser scanning beam can “walk” along the fractal curve inside the desired boundary, and arbitrary contour components are fabricated.展开更多
Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscrib...Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.展开更多
Two wheels are the best way to get around BeijingPut your hand up if you hate sitting in a traffic jam-yes,me too!As I would imagine,right now,over 7billion hands would be reaching for the sky,fingers pointed toward t...Two wheels are the best way to get around BeijingPut your hand up if you hate sitting in a traffic jam-yes,me too!As I would imagine,right now,over 7billion hands would be reaching for the sky,fingers pointed toward the clouds,emphasizing just how much they hate car traffic.So what’s the solution？展开更多
文摘The intersection point rule for homologues in gas chromatography was discovered many years ago,now more and more application and development are occurring in recent years~[2-6], but there are few systemic theoretical studies.In this paper,based on the basic equation of reten- tion values in gas chromatography,we prove the intersection point rule of homologues from mathematics,study the factors affecting intersection point position,give the physical meaning of intersection point,and explain the experimental rules in references.
文摘The fractal curve is proposed as a novel scanning path used in Layered Manufacturing. Aiming at a limitation that the fractal curve can only fill a square region, a method is developed to realize the trimming of fractal curve in arbitrary boundary layer by means of judging intersection points between parameterized arbitrary boundary and a FASS (space filling, self avoiding, simple and self similar) fractal curve. Accordingly, the related algorithm concerning with determining intersection points has been investigated according to the recursion feature of the fractal curve, and in the process of the fractal curve traversed, the rule of judging intersection points is ascertained as well, so that the laser scanning beam can “walk” along the fractal curve inside the desired boundary, and arbitrary contour components are fabricated.
文摘Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.
文摘Two wheels are the best way to get around BeijingPut your hand up if you hate sitting in a traffic jam-yes,me too!As I would imagine,right now,over 7billion hands would be reaching for the sky,fingers pointed toward the clouds,emphasizing just how much they hate car traffic.So what’s the solution？
