The Extension of a Cyclic Inequality to the Symmetric Form
نویسنده
چکیده
Let n be a natural number such that n ≥ 2, and let a1, . . . an be positive numbers. Considering the notations Si1... ik = ai1 + · · ·+ aik , S = a1 + · · ·+ an, we prove certain inequalities connected to conjugate sums of the form: ∑ 1≤i1<···<ik≤n Si1... ik S − Si1... ik Then provided that 1 ≤ k ≤ n − 1 we give certain lower estimates for expressions of the above form, that extend some cyclic inequalities of Mitrinovic and others. We also give certain inequalities that are more or less direct applications of the previous mentioned results.
منابع مشابه
Periodically correlated and multivariate symmetric stable processes related to periodic and cyclic flows
In this work we introduce and study discrete time periodically correlated stable processes and multivariate stationary stable processes related to periodic and cyclic flows. Our study involves producing a spectral representation and a spectral identification for such processes. We show that the third component of a periodically correlated stable process has a component related to a...
متن کاملExtension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials
متن کامل
Extension of Hardy Inequality on Weighted Sequence Spaces
Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...
متن کاملQUANTUM VERSION OF TEACHING-LEARNING-BASED OPTIMIZATION ALGORITHM FOR OPTIMAL DESIGN OF CYCLIC SYMMETRIC STRUCTURES SUBJECT TO FREQUENCY CONSTRAINTS
As a novel strategy, Quantum-behaved particles use uncertainty law and a distinct formulation obtained from solving the time-independent Schrodinger differential equation in the delta-potential-well function to update the solution candidates’ positions. In this case, the local attractors as potential solutions between the best solution and the others are introduced to explore the solution space...
متن کاملAn Ab Initio SCF-MO Study of Conformational Properties of Cyclodeca-1,2,3-triene
Ab initio calculation at HF/6-31G* level of theory for geometry optimization and MP2/6-31G*//HF/6-31G* for a single point total energy calculation are reported for the important energyminimumconformations and transition-state geometries of of cyclodeca-1,2,3-triene (1). The mostfavorable conformation of 1 is a unsymmetrical twist-chair (1-TC) structure. Degenerateinterconversion of 1-TC with it...
متن کامل