Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSome notes on a method for proving inequalities by computer
66
0
0.0
(
0
)
Added by
Branko Malesevic
Publication date
2006
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.
rate research
Read More
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural deduction system ``a la Prawitz. The rest of the material is more or less traditional but I emphasize partial functions more than usual (after all, programs may not terminate for all input) and I provide a fairly complete account of the basic concepts of graph theory.
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Morticis lemma.
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We derive the q-analogues of the q-integral transform and further apply to some general special functions such as : the exponential functions, the q-trigonometric functions, the q-hyperbolic functions and the Heaviside Function. Some further results involving convolutions and differentiations are also obtained.
We study the two-weighted estimate [ bigg|sum_{k=0}^na_k(x)int_0^xt^kf(t)dt|L_{q,v}(0,infty)bigg|leq c|f|L_{p,u}(0,infty)|,tag{$*$} ] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<pleq qleqinfty$, provided that the weight $u$ satisfies the certain conditions, the estimate $(*)$ holds if and only if the estimate [ sum_{k=0}^nbigg|a_k(x)int_0^xt^kf(t)dt|L_{q,v}(0,infty)bigg| leq c|f|L_{p,u}(0,infty)|.tag{$**$} ] is fulfilled. The necessary and sufficient conditions for $(**)$ to be valid are well-known. The obtained result can be applied to the estimates of differential operators with variable coefficients in some weighted Sobolev spaces.
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
