Periodica Mathematica Hungarica最新文献

A set A of positive integers is called 3-free if it contains no 3-term arithmetic progression. Furthermore, such A is called maximal if it is not properly contained in any other 3-free set. In 2006, by confirming a question posed by Erdős et al., Savchev and Chen proved that there exists a maximal 3-free set ({a_1<a_2<cdots<a_n<cdots }) of positive integers with the property that (lim _{nrightarrow infty }(a_{n+1}-a_n)=infty ). In this paper, we generalize their result. On the other hand, a set A of nonnegative integers is called an asymptotic basis of order h if every sufficiently large integer can be represented as a sum of h elements of A. Such A is defined as minimal if no proper subset of A has this property. We also extend a result of Jańczak and Schoen about the minimal asymptotic basis.

In this paper, we give the structure of the Iwasawa module (X=X(k_{infty })) of the (mathbb {Z}_{2})-extension of infinitely many real biquadratic fields k. Denote by (lambda , mu ) and (nu ) the Iwasawa invariants of the cyclotomic (mathbb {Z}_{2})-extension of k. Then (lambda =mu =0 ) and (nu =2).

Differential uniformity is one of the most crucial concepts in cryptography. Recently Ellingsen et al. (IEEE Trans Inf Theory 66:5781–5789, 2020) introduced a new concept, the c-Difference Distribution Table and the c-differential uniformity, by extending the usual differential notion. The motivation behind this new concept is based on having the ability to resist some known differential attacks which is shown by Borisov et. al. (Multiplicative Differentials, 2002). In 2022, Hasan et al. (IEEE Trans Inf Theory 68:679–691, 2022) gave an upper bound of the c-differential uniformity of the perturbed inverse function H via a trace function ( {{,textrm{Tr},}}big (frac{x^2}{x+1}big )). In their work, they also presented an open question on the exact c-differential uniformity of H. By using a new method based on algebraic curves over finite fields, we solve the open question in the case ( {{,textrm{Tr},}}(c)=1= {{,textrm{Tr},}}(frac{1}{c})) for ( c in {mathbb {F}}_{2^n}setminus {0,1} ) completely and we show that the exact c-differential uniformity of H is 8. In the remaining case, we almost completely solve the problem and we show that the c-differential uniformity of H is either 8 or 9.

In this short note, we answer two questions of Chen and Ruzsa negatively and answer a question of Ma and Chen affirmatively.

This paper deals with a class of nonlocal variable s(.)-order fractional p(.)-Kirchhoff type equations:

Under some suitable conditions on the functions (p,s, {mathcal {K}}) and f, the existence and multiplicity of nontrivial solutions for the above problem are obtained. Our results cover the degenerate case in the (p(cdot )) fractional setting.

In this paper, we define the s-dimensional regular generalized Euler function and give a variant of Tóth’s identity in residually finite Dedekind domains, which can be viewed as a multidimensional version of the results by Wang, Zhang, Ji (2019) and Ji, Wang (2020).

The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence acceleration method known as Richardson extrapolation, as well as its variants (classical Richardson extrapolation and multiple Richardson extrapolation). The original (classical) version of Richardson extrapolation consists in taking a linear combination of numerical solutions obtained by two different time-steps with time-step sizes h and h/2 by the same numerical method. Multiple Richardson extrapolation is a generalization of this procedure, where the extrapolation is applied to the combination of some underlying numerical method and the classical Richardson extrapolation. This procedure increases the accuracy order of the underlying method from p to (p+2), and with each repetition, the order is further increased by one. In this paper we investigate the convergence of multiple Richardson extrapolation in the case where the underlying numerical method is an explicit Runge–Kutta method, and the computational efficiency is also checked.

Let p be a prime, A and B be subsets of ({mathbb {Z}/pmathbb {Z}}) and S be a subset of (Atimes B). We write (A{{mathop {+}limits ^{S}}}B:={a+b:;(a,b)in S}). In the first inverse result of this paper, we show that if (left| A{{mathop {+}limits ^{S}}}Bright| ) and (|(Atimes B)setminus S|) are small, then A has a big subset with small difference set. In the second theorem of this paper, we use the previous result to show that if (left| A{{mathop {+}limits ^{S}}}Bright| ), |A| and |B| are small, then big parts of A and B are contained in short arithmetic progressions with the same difference. As an application of this result, we get an inverse of Pollard’s theorem.