1 citations · 4 across the 10 of their papers we have counts for
12 papers
Optimal bounds for the ratio of differences of quadratic, arithmetic, and harmonic means
Zamina E. Guliyeva, Narmin N. Aliyeva, Yagub N. Aliyev
We determine the optimal constants in inequalities comparing the differences of the quadratic, arithmetic, and harmonic means of nonnegative real numbers. Specifically, we prov…
The Maximum of the Volume of a Part of a Cevian Simplex
Zamina Guliyeva, Yagub Aliyev
The cevians passing through a point in a simplex create a cevian simplex, which is divided by these cevians into smaller simplices. We consider the problem about the maximum of the…
The Maximum of the Volume of a Cevian Simplex and its Parts
Yagub N. Aliyev
The cevian triangle corresponding to an interior point of a triangle is the triangle determined by the feet of the three cevians concurrent at . It is known that the area of…
Caustics of a Paraboloid and Apollonius Problem
Yagub N. Aliyev
We study caustics of an elliptical paraboloid and the history of their various representations from 3D models in XIX century to the recent computer graphics. In the paper two ways…
The dual of Philo's shortest line segment problem
Yagub N. Aliyev
We study the dual of Philo's shortest line segment problem and find the optimal line segments passing through two given points, with a common endpoint, and with the other endpoints…
The extremal values of the ratio of differences of power mean, arithmetic mean, and geometric mean
Yagub Aliyev
In the paper the maximum and the minimum of the ratio of the difference of the arithmetic mean and the geometric mean, and the difference of the power mean and the geometric mean o…
Inequalities about the area bounded by three cevian lines of a triangle
Yagub N. Aliyev
In the paper we prove generalization of Schlömilch's and Zetel's theorems about concurrent lines in a triangle. This generalization is obtained as a corollary of sharp geometric in…
The Best Constant For Inequality Involving Sum Of The Reciprocals And Product Of Positive Numbers With Unit Sum
Yagub N. Aliyev
In the paper we study a special parameter containing algebraic inequality involving sum of reciprocals and product of positive real numbers whose sum is 1. We determine the best va…
The number of inscribed and circumscribed graphs of a convex polyhedron
Yagub N. Aliyev
In the paper we prove that the number of graphs inscribed into graph of a convex polyhedron and circumscribed around another graph does not exceed 4. For this we first studied Ponc…
On integer linear combinations of terms of rational cycles for the generalized 3x+1 problem
Yagub N. Aliyev
In the paper, some special linear combinations of the terms of rational cycles of generalized Collatz sequences are studied. It is proved that if the coefficients of the linear com…
Geometric Properties of Planar and Spherical Interception Curves
Yagub N. Aliyev
In the paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used t…
Apollonius Problem and Caustics of an Ellipsoid
Yagub N. Aliyev
In the paper we discuss Apollonius Problem on the number of normals of an ellipse passing through a given point. It is known that the number is dependent on the position of the giv…