A partially ordered set P has the fixed point property if every orderpreserving mapping f of P to P has a fixed point, that is, f(a) = a for some aϵP; call P fixed point free if P does not have the fixed point property.

We construct several examples of higher-dimensional Calabi–Yau manifolds and prove their modularity.

A new look at Manià's classical example of the Lavrentiev Phenomenon leads to several pertinent observations.

The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan which characterized local group rings when both the ring and the group are commutative.

We assume throughout that all rings are associative with identity. If R is a ring we call R local if R/J(R) is a division ring where J(R) denotes the Jacobson radical of R. It is well known that R is local if and only if each element of R\J(R) is a unit. We need the following.

There are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. Using this Ricci curvature tensor, we shall have a better understanding of these non-Riemannian quantities.

The maximum density of packings of a given type into the whole of a Euclidean space is defined to be the limit of the maximum density of such packings into a cube as the edge of the cube goes to infinity.

For E2 in particular, a number of well known results such as those due to A. Thue [1], L. Fejes-Toth [2], and C. A. Rogers [3] yield precise information about packings into the whole space. They are however of limited applicability to problems of finite packing in so-far as each requires some restriction upon the boundary of the configuration.

Simply connected conformally flat Riemannian manifolds are characterized as hypersurfaces in the light cone of a standard flat Lorentzian space, transversal to its generators. Some applications of this fact are given.

We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.

Finite factor groups of are called Hurwitz groups. Here we prove that apart from 2G2(3), G2(2), G2(3) and G2(4), all the groups 2G2(32n+1) and G2(q), q = pn, p € P, are Hurwitz groups. For the proof, (2, 3, 7) structure constants are calculated from the character tables [2], [7], and then with the lists of maximal subgroups [8], [5], the existence of generating triples is deduced.

We consider a class of strongly $q$-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly $q$-log-convex. We also prove that the Bessel transformation preserves log-convexity.

Examining certain problems in physics M. Hosszu [l] obtained the functional equation

(1)

where x, y, f are real.

In another paper M. Hosszu [2] proved that the equation (1) is equivalent to the functional equation of Cauchy; i. e., to the equation

(1)

under the assumption that x is real and f is real and continuous.

The purpose of this expository note is to establish the fact mentioned in the title. While this is not difficult and requires no new ideas, it seems worth doing, as such a simple characterization does not appear explicitly in a recent treatise on the subject of flat modules [Bourbaki XXVII, Chapter 1].

There has been a great deal of work recently concerning the relationship between the commutativity of a ring JR and the existence of certain specified derivations of R. Bell, Herstein, Procesei, Schacher, Ligh, Martindale, Putcha, Wilson, and Yaqub [1, 2, 6, 8, 9, 10, 11, 12, 14] have studied conditions on commutators which imply the commutativity of rings.

Some structural results about quotients and tensor products of hereditary respectively quasi-hereditary algebras are presented. They are related to properties of stratifications of derived module categories. The concept of derived-simplicity for an algebra is introduced and studied.

In this paper, we consider the oscillatory behavior of the second order neutral delay differential equation

where t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

Recent work of Ding and Huang shows that if we perturb a bounded operator (between Hilbert spaces) which has closed range, then the perturbed operator again has closed range. We extend this result by introducing a weaker perturbation condition, and our result is then used to prove a theorem about the stability of frames for a subspace.

In Riemannian geometry the autoparallels associated with the affine connexion coincide with the geodesies which arise from the metric. This is not the case in a modification of Riemannian geometry suggested by Lyra. A sufficient condition that the two classes of curves coincide is obtained.

Consider the delay differential equation

where α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.

A Room design of order 2n, where n is a positive integer, is an arrangement of 2n objects in a square array of side 2n - 1, such that each of the (2n - 1)2 cells of the array is either empty or contains exactly two distinct objects; each of the 2n objects appears exactly once in each row and column; and each (unordered) pair of objects occurs in exactly one cell. A Room design of order 2n is said to be cyclic if the entries in the (i + l) th row are obtained by moving the entries in the i th row one column to the right (with entries in the (2n - l)th column being moved to the first column), and increasing the entries in each occupied cell by l(mod 2n - 1), except that the digit 0 remains unchanged.

We describe all degenerations of three-dimensional anticommutative algebras $\mathfrak{A}\mathfrak{c}\mathfrak{o}\mathfrak{m}_{3}$ and of three-dimensional Leibniz algebras $\mathfrak{L}\mathfrak{e}\mathfrak{i}\mathfrak{b}_{3}$ over $\mathbb{C}$. In particular, we describe all irreducible components and rigid algebras in the corresponding varieties.