Tubular surface around a Legendre curve in BCV spaces

Explicit points on the Legendre curve III

Explicit points on the Legendre curve

We study the elliptic curve E given by y = x(x+1)(x+ t) over the rational function field k(t) and its extensions Kd = k(μd, t). When k is finite of characteristic p and d = p + 1, we write down explicit points onE and show by elementary arguments that they generate a subgroup Vd of rank d − 2 and of finite index in E(Kd). Using more sophisticated methods, we then show that the Birch and Swinner...

Construction of a surface pencil with a common special surface curve

In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $vec{W}_{0} $ of a surface curve $vec{r}(s)$ and unit surface normal $vec{n} $ along the curve $vec{r}(s)$ satisfy the condition $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. We point out that a $D$-type curve is a geodesic curve or an...

A Cruise Around the Phillips Curve

For Britain, during the long period Phillips studied, an unemployment rate of about 2.5% was associated with a rise in wages of about 2% each year. Allowing for productivity growth, that was roughly consistent with stable prices. By and large, higher rates of unemployment were observed when prices were falling; lower rates were observed when prices were rising. The lower the rate of joblessness...

Element Content of Surface and Underground Water Sources around a Cement Factory Site in Calabar, Nigeria

Background: Cement production is associated with heavy metal emissions and environmental pollution by cement dust. The degree of contamination of drinking water sources by major and trace elements present in cement dust generated by united cement factory (UNICEM) is still uncertain. This study estimated the element content of ground and surface water samples (hand-dug wells, boreholes and strea...