A Slight Improvement to the Colored Bárány's Theorem
نویسنده
چکیده
Suppose d+ 1 absolutely continuous probability measures m0, . . . ,md on Rd are given. In this paper, we prove that there exists a point of Rd that belongs to the convex hull of d+1 points v0, . . . , vd with probability at least 2d (d+1)!(d+1) , where each point vi is sampled independently according to probability measure mi.
منابع مشابه
A stronger version of Bárány's theorem in the plane
First, we may assume, without loss of generality, that the points of the sets > > are located on the unit circle, by projecting these points on the circumference of the circle. Second, by Carathéodory Theorem (see [3]), we may assume, without loss of generality, that the cardinality of each set + is at most ? , for 45X2= >8 @? . In fact, we can further assume that * + * 5? , for 45X2' 98( ...
متن کاملOn intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...
متن کاملThe effect of Inorganic Nanoparticles on Camouflage Properties of Cotton/Polyester Fabrics
Drawing upon reflectance behavior of woodland colors involving dark brown in the UV-Vis-IR bands, two colored pigments were used to print cotton/polyester Co/PET goods. Inorganic nanoparticles of TiO2, ZnO and AL2O3 were also loaded onto the printing formulation. The reflectance profile of treated samples was studied using Jasco V-670 reflectance spectrophotometer. SEM analysis of printed fabri...
متن کاملNobel Prize centenary: Robert Bárány and the vestibular system
The hundredth anniversary of Robert Bárány's Nobel Prize in Medicine offers the opportunity to highlight the importance of his discoveries on the physiology and pathophysiology of the vestibular organs. Bárány developed the method of caloric vestibular stimulation that revolutionized the investigation of the semicircular canals and that is still widely used today. Caloric vestibular stimulation...
متن کاملA Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 21 شماره
صفحات -
تاریخ انتشار 2014