The following theorem is proved:Let AT be the maximum of the curvature of a regular curve C, A Ban arc of C and /thelength of AB. If - then the angles formed by the chord of A Band the tangents at Aand B respectively arc< rK/.

Let σ be a regular curve, P and Q two simple polygons. This paper discusses the problem of deciding whether P collides with Q when P takes rigid body displacement along curve σ, and gives an O(mn) time decision algorithm, where m and n are the numbers of venices of P and Q, respectively. The algorithm is optimal in the worst case.

Collision with a fixed simple polygon Q may occur while a simple polygon P takes a rigid body displacement along regular curve σ . An optimal algorithm in worst case for collision test is given on O(mn) time, where m and n are sizes of P and Q . When P is a convex polygon, another practical algorithm for this collision test is designed by boundary combination operation of polygons and winding number with its algebraic properties.

The results show that the max UV dose rate is 500.0 mW m-2 and the min UV dose rate is 9.7 mW m-2 at local noon of 1997. For clear sky, the variations of daily UV dose rate are regular curve and UV dose rate at noon is larger than that at morning and evening.

By using least square theory(LST), the authors established geometric collation models of regular curve features such as road alignmnts (straight, circle, transition curve and the combination of them) and promoted relevant precision evaluation criteria of digitized features. All the researches are of practical reference values to deal with the precision evaluation and data quality control problems in GIS spatial database.

With the special kinematics and kinetics law of major-minor connecting rod mechanism in gas engine,based on expression function integrated into regular curve and optimizing module provided by UG software,the optimized structural parameters of major-minor connecting rod mechanism were educed through minimizing the differences tribology characteristic between in piston of major cylinder and piston of minor cylinder,and kinematics and kinetics characteristics were reappeared with emulational curve mode.

A regular curve in a pseudo-Riemannian manifold is called a circle if it is an extrinsic sphere.

We give an extension of the Fenchel-Borsuk result by introducing the total absolute torsion-curvature KT(γ) for regular curves γ whose tangent indicatrix is a piecewise regular curve (τ-closed curves).

Every regular curve can be parametrized to have a constant speed but the parametrization is rarely known explicitly.

The interpretation of the generalized Jacobian as a rigidificator for the Jacobian of a regular curve is not surprising (cf.

Let D denote the interior of a piecewise regular curve of R2 having a point with Gauss curvature different from zero.

By theoratical analysis and experimental research,it's certain that in the process of th epitaxial growth of silicon by the reduction Sicl_4-H_2 the difference of the ethickness of the stagnant layer over the silicon wafers is the main reason to cause the difference of the thickness of the epitaxial layers.In the experimental research,we get a regular curve for the growth of epitaxial layers.According to this curve,we made some selections among the technological condictions of the growth of the epitaxial...

By theoratical analysis and experimental research,it's certain that in the process of th epitaxial growth of silicon by the reduction Sicl_4-H_2 the difference of the ethickness of the stagnant layer over the silicon wafers is the main reason to cause the difference of the thickness of the epitaxial layers.In the experimental research,we get a regular curve for the growth of epitaxial layers.According to this curve,we made some selections among the technological condictions of the growth of the epitaxial layers.We have made a good improvement in the thickness consistence of the epitaxial layer,in prevention of the crown of the edge of the epitaxial layer,and in the elevation of the technical level.

Let r= r(t) be a regular curve on (a, b) and its torsion is identicallyzero. Is this curve a plane curve? Fristly we consider an example asfollows: We can show that r (t) is a C~∞ regular curve and its torsion is identically zero. But the curve lies in the xy plane for t<0 and in the xz plane for t>0. So the curve is not a plane curve. Then we can show the result as follows: Let r (t) be a C~∞ regular curve on (a, b ) and there are only singular point of curvatur...

Let r= r(t) be a regular curve on (a, b) and its torsion is identicallyzero. Is this curve a plane curve? Fristly we consider an example asfollows: We can show that r (t) is a C~∞ regular curve and its torsion is identically zero. But the curve lies in the xy plane for t<0 and in the xz plane for t>0. So the curve is not a plane curve. Then we can show the result as follows: Let r (t) be a C~∞ regular curve on (a, b ) and there are only singular point of curvatur K (t) = 0. The curvee is a plane curve if and onlyif its torsion is identically zero.

This paper shows a newest result taken by the authors, observing and studying the radiation characteristics of arid-cold type snowcover of thewestern hilly area of Tianshan Mt of our country, in the Tianshan Stationof Snowcover Research Academia Sinica, during the winter 1986 and the sp-ring 1937. In this article, some physical parameters and optical characteri-stics are given over western Tianshan hilly area's snowcover radiation, andaccording to the data obtained, is drawn a ten-days varied curve of snowco-ver's...

This paper shows a newest result taken by the authors, observing and studying the radiation characteristics of arid-cold type snowcover of thewestern hilly area of Tianshan Mt of our country, in the Tianshan Stationof Snowcover Research Academia Sinica, during the winter 1986 and the sp-ring 1937. In this article, some physical parameters and optical characteri-stics are given over western Tianshan hilly area's snowcover radiation, andaccording to the data obtained, is drawn a ten-days varied curve of snowco-ver's albedo. It is drafted the corresponding conjoining-equation: A= 1 -1.66X10~(-2)D, and is found the curve of the variation law of attenuation of sn-owcover to short wave radiation, and is pointed out satisfying the regularequation:R=Roe-ax. On this base, the authors pointed out the varied byday characteristic of the participated quantities of snowcover radiation, co-rresponding regular curve and relative equation. The report elaborated andexplicated theoretically the regular curves and phoeomena, especially men tioned an important phoenomenon that the variation of the wave-radiationof snowcover is presented as a convex type curve in winter and as a concave type curve in spring. The authors nominated the convex type curve nor-mal type" and concave type curve "anormal type". The authors recognizedthat two explications of two phoenomena, although imperfect, are reliableand convincing, in respect to the characteristics of hilly area in this region.The report studied also the close relationship between the daily variationof snow heat flux and underground heat flux and the sun radiation, resear-hed as well into some value relationship of the snowcover cumulation andmelting with the frozen ground layer. About the question that the particid-ated quantities of snowcover radiation presented a quasi-normal distributionin function of the sun, the authors gave also the corresponding functionalequation: