Volume 69, Issue 2

We introduce two monads on the category of graphs and prove that their Eilenberg-Moore categories are isomorphic to the category of perfect matchings and the category of partial Steiner triple systems, respectively. As a simple application of these results, we describe the product in the categories of perfect matchings and partial Steiner triple systems.

We give examples showing that the Kolmogorov-Sinai entropy generator theorem is false for both upper and lower Riesz entropy of MV-algebraic dynamical systems, both two sided (i.e., analogous to two sided Bernoulli shifts) and one sided (i.e., analogous to one sided Bernoulli shifts).

In this paper, we extend properties Going Up and Lying Over from ring theory to the general setting of congruence-modular equational classes, using the notion of prime congruence defined through the commutator. We show how these two properties relate to each other, prove that they are preserved by finite direct products and quotients and provide algebraic and topological characterizations for them. We also point out many kinds of varieties in which these properties always hold, generalizing the results of Belluce on MV-algebras and Rasouli and Davvaz on BL-algebras.

Dmitriy Zhuk has proved that there exist relational structures which admit near unanimity polymorphisms, but the minimum arity of such a polymorphism is large and almost matches the known upper bounds. We present a simplified and explicit construction of such structures and a detailed, self–contained proof.

We derive approximate formulas for the logarithmic derivative of the Selberg and the Ruelle zeta functions over compact, even-dimensional, locally symmetric spaces of real rank one. The obtained formulas are given in terms of zeta singularities.

If a , b , c are non-zero integers, we considerer the following problem: for which values of n the line ax + by + cz = 0 may be tangent to the curve x n + y n = z n ? We give a partial solution: if n = 5 or if n – 1 is a prime a number, then the answer is the line cannot be tangent to the curve. This problem is strongly related to Fermat’ s Last Theorem.

Sums of products of two Gaussian q -binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the main theorems are proved and then some corollaries of them are derived. Then these q -binomial identities will be transformed into Fibonomial sums as consequences.

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and integrals of logarithmic functions. As applications of these relations, we show that multiple zeta values of the form ζ(1¯,1m−1,1¯,1k−1),(k,m∈N)$$\begin{array}{} \zeta ( {\bar 1,{{\left\{ 1 \right\}}_{m - 1}},\bar 1,{{\left\{ 1 \right\}}_{k - 1}}} ),\qquad (k,m\in \mathbb{N}) \end{array} $$ for m = 1 or k = 1, and ζ(1¯,1m−1,p,1k−1),(k,m∈N)$$\begin{array}{} \zeta ( {\bar 1,{{\left\{ 1 \right\}}_{m - 1}},p,{{\left\{ 1 \right\}}_{k - 1}}}),\qquad (k,m\in\mathbb{N}) \end{array} $$ for p = 1 and 2, satisfy certain recurrence relations which allow us to write them in terms of zeta values, polylogarithms and ln 2. Furthermore, we also obtain reductions for certain multiple polylogarithmic values at 12$\begin{array}{} \frac {1}{2} \end{array} $.

Given a field k of characteristic different from 2 and an integer d ≥ 3, let J be the Jacobian of the “generic” hyperelliptic curve given by y2=∏i=1d(x−αi)$\begin{array}{} \displaystyle y^2 = \prod_{i = 1}^d (x - \alpha_i) \end{array}$ , where the α i ’s are transcendental and independent over k ; it is defined over the transcendental extension K / k generated by the symmetric functions of the α i ’s. We investigate certain subfields of the field K ∞ obtained by adjoining all points of 2-power order of J ( K̄ ). In particular, we explicitly describe the maximal abelian subextension of K ∞ / K ( J [2]) and show that it is contained in K ( J [8]) (resp. K ( J [16])) if g ≥ 2 (resp. if g = 1). On the way we obtain an explicit description of the abelian subextension K ( J [4]), and we describe the action of a particular automorphism in Gal( K ∞ / K ) on these subfields.

This paper deals with semihypergroups of order two from the point of view of the model theory. We use basic knowledge to show that there are exactly 17 non-isomorphic semihypergroups of order two. Each of them corresponds in a canonical way to a semigroup of order three. We classify all of them by generalized identities a concept introduced by Lyapin. In particular, we classify all non-group semigroups of order three by one generalized identity.

In this paper, we shall establish a criterion for the weak potency of certain HNN extensions of weakly potent groups. Then, using this criterion, we shall prove certain HNN extensions of weakly potent group with finite subgroup, infinite cyclic subgroup, direct product of an infinite subgroup and a finite subgroup, or finite extensions of a central subgroup as the associated subgroups are again weakly potent.

By motivating the result of Ramachandran et al. [ Certain results on q-starlike and q-convex error functions , Math. Slovaca, 68 (2) (2018), 361–368], in this present investigation we derive the classical Fekete Szegö theorem for a close-to-convex error function of order β and the sharp estimates also obtained for real μ .

In this study we are concerned with spectrum of boundary value problems with retarded argument with discontinuous weight function, two supplementary transmission conditions at the point of discontinuity, spectral and physical parameters in the boundary condition and we obtain bounds for the distance between eigenvalues. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm-Liouville problems. In the special case that ω ( x ) ≡ 1, the transmission coefficients γ 1 = δ 1 , γ 2 = δ 2 and retarded argument Δ ≡ 0 in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

This paper considers a compact Finsler manifold ( M n , F ( t ), m ) evolving under the Finsler-Ricci flow and establishes global gradient estimates for positive solutions of the following nonlinear heat equation: ∂tu=Δmu,$$\begin{array}{} \partial_{t}u=\Delta_{m} u, \end{array} $$ where Δ m is the Finsler-Laplacian. As applications, several Harnack inequalities are obtained.

Let A and B be Banach 𝔄-bimodule and Banach 𝔅-bimodule algebras, respectively. Also let M be a Banach A , B -module and Banach 𝔄, 𝔅-module with compatible actions. In the case of 𝔄 = 𝔅, the author along with Pourabbas [5] have studied the weak 𝔄-module amenability of triangular Banach algebra T=AMB$\begin{array}{} \displaystyle \mathcal{T}=\left[\begin{array}{rr} A & M \\ & B \end{array} \right] \end{array}$ and showed that 𝓣 is weakly 𝔄-module amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable, where A , B and M are unital. In this paper we investigate a special structure of 𝔄 ⊕ 𝔅-bimodule derivation from 𝓣 into 𝓣 ∗ and show that 𝓣 is weakly 𝔄 ⊕ 𝔅-bimodule amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable and weakly 𝔅-module amenable, respectively, where A , B and M are essential and not necessary unital.

Conjecture 4 of Voiculescu implies that almost normal operators must satisfy a Fuglede-Putnam theorem, namely [ T ∗ , X ] is a Hilbert-Schmidt operator whenever [ T , X ] is in the same class for an arbitrary operator X . In this note, a partial answer to this question is given, namely when X ∈ 𝓒 4 , the Fuglede-Putnam theorem holds.

A simple polytope P is said to be B - rigid if its combinatorial structure is characterized by its Tor-algebra, and is said to be C - rigid if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over P . It is known that a B-rigid simple polytope is C-rigid. In this paper, we show that the B-rigidity is not equivalent to the C-rigidity.

We find non-regular Hausdorff rU -spaces (connected or not). We also prove that a countable Hausdorff connected space cannot be an rU -space.

Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

It is shown that in some non-discrete topological spaces, discrete subspaces with certain cardinality are C -embedded. In particular, this generalizes the well-known fact that every countable subset of P -spaces are C -embedded. In the presence of the measurable cardinals, we observe that if X is a discrete space then every subspace of υ X (i.e., the Hewitt realcompactification of X ) whose cardinal is nonmeasurable, is a C -embedded, discrete realcompact subspace of υ X . This generalizes the well-known fact that the discrete spaces with nonmeasurable cardinal are realcompact.