Related papers: Congruent numbers on the right trapezoid
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…
In this paper, we prove two conjectural supercongruences on the $(p-1)$th Ap\'ery number, which were recently proposed by Z.-H. Sun.
We survey recent developments on the Restriction conjecture.
The aim of this work is to establish congruences $\left( \operatorname{mod}p^{2}\right) $ involving the trinomial coefficients $\binom{np-1}{p-1}_{2}$ and $\binom{np-1}{\left( p-1\right)/2}_{2}$ arising from the expansion of the powers of…
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to…
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
We prove that a pair of continuous disjoint periodic curves in $\mathbb{C}$ inscribes an isosceles trapezoid with any similarity type. The case of smooth curves can be identified with a Lagrangian intersection problem for a pair of…
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
We establish some new theorems on pentagon and pentagram.
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.
Based on a $q$-congruence of the author and Petrov, we set up a $q$-analogue of Sun--Tauraso's congruence for sums of Catalan numbers, which extends a $q$-congruence due to Tauraso.
CSPTRQ is an interesting problem and its has attracted much attention. The CSPTRQ is a variant of the traditional PTRQ. As objects moving in a constrained-space are common, clearly, it can also find many applications. At the first sight,…
Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…