Related papers: Finding almost squares VI

Here is a square problem: in a unit square, is there a point with four rational distances to the vertices? A probability argument suggests a negative answer. This paper proves several special cases of the square problem: if the point sits…

We consider the problem of finding 4 rational squares, such that the product of any two plus the sum of the same two always gives a square. We give some historical background and exhibit one such quadruple.

We study the question whether properties like local/weak almost squareness and local octahedrality pass down from an absolute sum $X\oplus_F Y$ to the summands $X$ and $Y$.

We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We…

We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that…

We can give a slight improvement for a result related to the distribution of squares in Piatetski-Shapiro sequences of Liu-Shparlinski-Zhang \cite{lsz} by involving three different ideas.

We show that if A_1, A_2, ... , A_n are square matrices, each of them is either unitary or self-adjoint, and they almost commute with respect to the rank metric, then one can find commuting matrices B_1, B_2, ... , B_n that are close to the…

As an extension of positive or almost positive diagrams and links, we introduce a notion of successively almost positive diagrams and links, and good successively almost positive diagrams and links. We review various properties of positive…

We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the…

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…

The fundamental aim of this paper is to introduce and investigate a new property of quasi 2-normed space based on a question given by C. Park (2006) [2] for the completion quasi 2-normed space. Finally, we also find an answer for a question…

In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…

We study almost squareness and the strong diameter two property in the setting of projective (symmetric) tensor product. We prove that almost squareness is preserved by taking projective tensor product, providing non-trivial examples of ASQ…

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

The paper deals with continuous solutions of a Schilling's problem.

Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, we generalize the result of Vaughan for ternary admissible exponent. Moreover, we use the refined admissible…

We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…