In this paper, we investigate four configurations \((12_{4}, 16_{3})) in cubic structures, introduced by Václav Metelka, and discover new unexpected extra collinearities in two Metelka’s configurations that arise from our realizations in cubic structures. Next, we establish the existence of various geometric concepts in four Metelka’s configuration including tangential points, inflection points, sextactic points, and quadrilaterals, and find and study significant relationships among these geometric concepts.
In this paper, we investigate four configurations (12(4), 16(3)) in cubic structures, introduced by V & aacute;clav Metelka, and discover new unexpected extra collinearities in two Metelka's configurations that arise from our realizations in cubic structures. Next, we establish the existence of various geometric concepts in four Metelka's configuration including tangential points, inflection points, sextactic points, and quadrilaterals, and find and study significant relationships among these geometric concepts.
In this article, we consider various classes of multi-dimensional rho-almost periodic type functions in general measure. We present several structural results about the introduced classes of generalized rho-almost periodic functions, providing also some applications to the abstract Volterra integro-differential inclusions.
In this paper, we prove that the density of a stochastic delay differential equation driven by a fBm with Hurst parameter H > 1/2 is strictly positive combining Nourdin-Viens' and Kohatsu-Higa's method.
This paper investigates nonparametric estimations of a density function in a mixture model. Firstly, a lower bound estimation under L-p(1 <= p < +infinity) error of an arbitrary density estimator is discussed. Secondly, a linear estimator and an adaptive nonlinear estimator of the unknown density function are constructed by the wavelet method. The rates of convergence of those two wavelet estimators are discussed with some mild conditions. Combining with the lower bound estimations, two wavelet estimators can attain the optimal convergence rate. Finally, numerical examples are given to verify the performance of the two wavelet estimators.
