Band 68, Heft 1

There is a sizable literature on investigating the minimum and maximum numbers of cycles in a class of graphs. However, the answer is known only for special classes. This paper presents a result on the smallest number of cycles in Hamiltonian 3-connected cubic graphs. Further, it describes a proof technique that could improve an upper bound of the largest number of cycles in a Hamiltonian graph.

We study a basic problem: in what posets is the order-convergence topological? We introduce the notion of 𝓡 ∗ -doubly continuous posets, which extends the notion of doubly continuous posets, and then prove that the order-convergence in a poset is topological if and only if the poset is 𝓡 ∗ -doubly continuous. This is the main result which can be regarded as a complete characterization of posets for the order-convergence being topological.

Halaš and Jukl associated the zero-divisor graph G to a poset ( X ,≤) with zero by declaring two distinct elements x and y of X to be adjacent if and only if there is no non-zero lower bound for { x , y }. We characterize all the graphs that can be realized as the zero-divisor graph of a poset. Using this, we classify posets whose zero-divisor graphs are the same. In particular we show that if V is an n -element set, then there exist ∑ log2⁡ (n+1)≤ k≤ nnk2k− k− 1n− k$\begin{array}{} \sum\limits_{\log_2(n+1)\leq k\leq n}^{}\binom{n}{k}\binom{2^k-k-1}{n-k} \end{array} $ reduced zero-divisor graphs whose vertex sets are V .

Let H be a Hilbert space and B ( H ) the set of all bounded linear operators on H . In the paper we consider the generalized concept of order relations on B ( H ) which was proposed by Šemrl and which covers the star partial order, the left-star partial order, the right-star partial order, and the minus partial order. We also connect this concept with the sharp partial order.

In this paper, we introduce the notions of stabilizer of a subset and the stabilizer of a subset with respect to another one in triangle algebras and study them in details. It is shown that the stabilizer of a subset and stabilizer of an interval valued residuated lattice filter (IVRL-filter) with respect to another IVRL-filter are IVRL-filters. We state and prove some theorems which determine some properties of this stabilizers in triangle algebras. Also, we prove that in linearly ordered triangle algebras, stabilizer of a set is an IVRL-extended prime filter. Finally, we consider the influence of stabilizers on product and quotient triangle algebras.

This note is devoted to a solution of a problem posed by Ladislav Skula.

We present a detailed computation of two codensity monads associated to two canonical functors – the inclusion functor of FinSet into Top and the inclusion functor of the category of the powers of the Sierpiński space into Top . We show that the categories of algebras of the two monads are the categories of Stone spaces and of sober spaces, respectively. A new motivation for defining these classes of spaces is therefore obtained.

We give a criterion to prove that some groups are not acylindrically hyperbolic. As an application, we prove that the mapping class group of an infinite type surface is not acylindrically hyperbolic.

In this paper we are going to apply the Henstock-Kurzweil integrals defined on an unbounded intervals to differential and integral equations defined on such intervals. To deal with linear differential equations we examine convolution involving functions integrable in Henstock-Kurzweil sense. In the case of nonlinear Hammerstein integral equation as well as Volterra integral equation we look for solutions in the space of functions of bounded variation in the sense of Jordan.

Enough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains bounded by conic regions. Certain coefficient estimates are obtained for domains bounded by conical region. Finally interesting application of the results are also highlighted for the function Ω k , β defined by Noor.

The main aim of this article is to establish certain closed expressions for the Schlömilch series which members contain Anger function 𝐉 ν in order to generalize already known results. Closed expressions for the Schlömilch series with members containing some Lommel functions of the first kind s μ , ν and also a Weber function 𝐄 ν and Struve function 𝐇 ν are derived as a by–product of these results.

In the present paper we introduce generalized vector-valued Musielak-Orlicz sequence space l ( A ,𝓜, u , p ,Δ r ,∥·,… ,·∥) ( X ) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators of s -type and operator ideals by using the sequence of s -number (in the sense of Pietsch) under certain conditions on matrix A .

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the natural strict topology β . We study nuclear operators T : C b ( X , E ) → F in terms of their representing operator-valued Borel measures.

For two Banach algebras A and B , the T -Lau product A × T B , was recently introduced and studied for some bounded homomorphism T : B → A with ∥ T ∥ ≤ 1. Here, we give general nessesary and sufficent conditions for A × T B to be (approximately) cyclic amenable. In particular, we extend some recent results on (approximate) cyclic amenability of direct product A ⊕ B and T -Lau product A × T B and answer a question on cyclic amenability of A × T B .

We introduce the concept of matrix generalized ( θ , ϕ )-derivations on matrix normed algebras, and prove the Hyers-Ulam stability of matrix generalized ( θ , ϕ )-derivations on matrix Banach algebras.

Let B ( H ) be the algebra of all bounded linear operators on a complex Hilbert space H and 𝓐 ⊆ B ( H ) be a von Neumann algebra with no central summands of type I 1 . For A , B ∈ 𝓐, define by A ∙ B = AB + BA ∗ a new product of A and B . In this article, it is proved that a map Φ: 𝓐 → B ( H ) satisfies Φ( A ∙ B ∙ C ) = Φ( A ) ∙ B ∙ C + A ∙ Φ( B ) ∙ C + A ∙ B ∙Φ( C ) for all A , B , C ∈ 𝓐 if and only if Φ is an additive *-derivation.

A sequential implicit function theorem for the method of chords was proved in the paper cited in the title. In this paper we add to this theorem a statement regarding the Lipschitz continuity of the mapping involved together with a sketch of proof.

In this paper will be considered density-like points and density-like topology in the family of Lebesgue measurable subsets of real numbers connected with a sequence 𝓙= { J n } n ∈ℕ of closed intervals tending to zero. The main result concerns necessary and sufficient condition for inclusion between that defined topologies.

Let G n , k denote the complex Grassmann manifold of k -dimensional vector subspaces of ℂ n . Assume l , k ≤ ⌊ n /2⌋. We show that, for sufficiently large n , any continuous map h : G n , l → G n , k is rationally null homotopic if (i) 1 ≤ k < l , (ii) 2 < l < k < 2( l − 1), (iii) 1 < l < k , l divides n but l does not divide k .

We give some examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields defined on the plane. Namely, we study a tied-down Wiener bridge, tied-down scaled Wiener bridges, a Kiefer process and so called ( F , G )-Wiener bridges.

We consider structured population models with diffusion and dynamic boundary conditions. The respective approximation, called Rothe’s method, produces positive and exponentially bounded solutions. Its solutions converge to the exact solution of the original PDE.

In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [PATIL, A.—WAPHARE, B. N.—JOSHI, V.—POURALI, H. Y.: Zero-divisor graphs of lower dismantlable lattices I , Math. Slovaca 67 (2017), 285–296]. The present paper mainly deals with an Isomorphism Problem for the zero-divisor graphs of lattices. In fact, we prove that the zero-divisor graphs of lower dismantlable lattices with the greatest element 1 as join-reducible are isomorphic if and only if the lattices are isomorphic.

In this paper, we prove an identity of symmetry for the higher-order degenerate Frobenius-Euler polynomials and derive the recurrence relations and multiplication theorem type result for the degenerate Frobenius-Euler polynomials.