Related papers: A note on Khabibullin's conjecture for integral in…
Results in the preliminary version have been strengthed. In addition, Batyrev's conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\Pee^n$ is partially verified.
Some sharp inequalities between the triangular ratio metric and the Cassinian metric are proved in the unit ball.
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
New cases of the multiplicity conjecture are considered.
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
In this note, we confirm two conjectural supercongruences on double sums of binomial coefficients due to El Bachraoui.
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the…
We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of…
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…
We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.
As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…
In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.