Aequationes Mathematicae最新文献

Let (T_n(mathbb {K})) be the ring of all (ntimes n) upper triangular matrices over a field (mathbb {K}). For fixed positive integers n, s satisfying (frac{n}{2}le s<n), it is proved that (f: T_n(mathbb {K})rightarrow T_n(mathbb {K})) is additive if and only if (f(A+B)=f(A)+f(B)) for all rank-s matrices (A,Bin T_n(mathbb {K})), which has been proved to be true for (M_n(mathbb {K})) the ring of all (ntimes n) full matrices over (mathbb {K}) [Xu X., Liu H., Additive maps on rank-s matrices, Linear Multilinear Algebra 2017; 65: 806-812].

Let S be a semigroup, Z(S) be the center of S and (sigma :Srightarrow S) is an involutive automorphism. In this paper, we describe the complex-valued solutions of one of d’Alembert’s functional equations

where (tau :Srightarrow {mathbb {C}}) is a multiplicative function such that (tau (xsigma (x))=1) for all (xin S). This allows us to solve Van Vleck’s functional equation

where (mu ) is a measure that is a linear combination of Dirac measures ((delta _{z_i})_{iin I}), such that (z_iin Z(S)) for all (iin I), and I is a finite set. Many consequences of these results are presented.

We study Wilson’s functional equation with an anti-endomorphism on semigroups and derive its optimal links to d’Alembert’s functional equation. As an application, we solve d’Alembert’s functional equation on semigroups with both an involutive endomorphism and an anti-endomorphism.

We construct a measure which determines a two variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also study the properties and behavior of such generalized means that are obtained by a measure, and we provide some applications as well.

In this paper we consider a semiclassical version of the fractional Klein-Gordon equation on the lattice (hbar mathbb {Z}^{n}.) Contrary to the Euclidean case that was considered in [2], the discrete fractional Klein-Gordon equation is well-posed in (ell ^{2}left( hbar mathbb {Z}^{n}right) .) However, we also recover the well-posedness results in the certain Sobolev spaces in the limit of the semiclassical parameter (hbar rightarrow 0).

In this study, the Ulam stability of quantum equations on time scales that alternate between two quanta is considered. We show that linear equations of first order with constant coefficient or of Euler type are Ulam stable across large regions of the complex plane, and give the best Ulam constants for those regions. We also show, however, that linear equations of first order of period-1 type are not Ulam stable for any parameter value in the complex plane. This is due to the importance of pre-positioning the non-autonomous term for Ulam stability.

The concept of an n-NTT (neighborly translational tessellation of the n-torus) is introduced as a tessellation where every pair of tiles are translates of each other, and share precisely one of their facets. An n-NTT with cubic tiles is studied for each (n in mathbb {N}), and particular attention is given to a 4-NTT whose tiles are isometric 24-cells. We also use this concept to describe a tessellation of (mathbb {E}^4) with isometric tiles with fractal boundary, as well as a NTT of an infinite-dimensional space.

We calculate the K-theory of a crossed product (C^*)-algebra of the noncommutative torus with real multiplication by elliptic curve (mathscr {E}(K)) over a number field K. This result is used to evaluate the rank and the Shafarevich-Tate group of (mathscr {E}(K)).

(Conditional) distributivity plays an important role in the field of integration construction and utility theory. In this work, we aim to characterize distributive and conditionally distributive bi-uninorms over uninorms in the most general setting.