Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multidimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression fun...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

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...

2 W. J. Crozier, J. Gen. Physiol., 10: 53, 1926. 3 C. S. Minot, "Age, Growth and Death," G. P. Putnam 's Sons, New York, 1908. 4 C. M. Child, " Senescence and Rejuvenescence," University of Chicago Press, 1915. 5 Sewall Wright, J. Amer. Statis. Assoc., 21: 493, 1926. was found by Davidson6 to give a good fit to growth in weight W of dairy cattle. Equation (3) was applied by Weymouth7 with excel...

In this paper we consider parametric integrals F with elliptic integrands depending on the surface normal. The main result is a stability criterion for F-extremal immersions, containing the result of Barbosa and do Carmo [1] as a special case. Using similar techniques we are also able to show a condition for instability. The last section contains a simple proof of the fact that the surface norm...