The present paper is primarily concerned with the study of L-guilds in an L-merotopic space. It is shown that every L-cluster is an L-guild; however the converse is not true. For contigual and regular L-merotopies, where on one side we gave an example of a space, which is neither contigual nor binary, on the other side we constructed L-merotopic spaces that are contigual and binary. It is shown...

In the present paper we analyze Fréchet frame of the form {φ(·−j) | j ∈ Z}. With a known condition on φ, we show that the given sequence constitutes a frame for a test space isomorphic to the space of periodic smooth functions so that its dual is the multiple of the space of periodic distributions by φ̂. AMS Mathematics Subject Classification (2000): 42C15,42C40,42C99,46A35,46B20

Some fixed and coincidence point theorems for R-weakly commuting mappings are obtained. Our results generalize some recent results of Daffer and Kaneko [2] and many of the others. AMS Mathematics Subject Classification (2000): 54H25

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new notions of ellipticity and hypoellipticity, study their interrelation, and give a number of new examples and counterexamples. Using the concept of G∞-regularity of...

The beginning of the study of non-symmetric affine connection spaces is especially in relation with the works of A. Einstein on United Field Theory (UFT). The paper is a short survey of the development of the theory of these spaces. AMS Mathematics Subject Classification (2000): 53C25, 53A45, 53B05

We introduce the concept of Mσ-approachability for a semicontinuous function (i.e. a nonadditive measure) on a σ-complete sublattice of a locally complete σ-continuous lattice L and using it we extend a nonadditive measure from a sublattice of L to a σ-complete sublattice of L. AMS Mathematics Subject Classification (2000): 28A12, 28C15, 28B10

We discuss some basic concepts of semi-Riemannian geometry in low-regularity situations. In particular, we compare the settings of (linear) distributional geometry in the sense of L. Schwartz and nonlinear distributional geometry in the sense of J.F. Colombeau. AMS Mathematics Subject Classification (2000): Primary: 83C75; secondary: 46T30, 53B30, 46F10, 46F30.

Let a graph Γ be locally disjoint union of three copies of complete graphs Kq−1 and let Γ be cospectral with the Hamming graph H(3, q). Bang and Koolen [Asian-Eur. J. Math. 1 (2008), 147–156] proved that if q > 3, then Γ is isomorphic to H(3, q). We present a short proof of this result. AMS Mathematics Subject Classification (2000): 05C50, 05E30.

We study ∨-semilattices with the greatest element 1 where on each interval [a,1] an antitone bijection is defined. We characterize these semilattices by means of two induced binary operations proving that the resulting algebras form a variety. The congruence properties of this variety and the properties of the underlying semilattices are investigated. We show that this variety contains a single...

The main purpose of this paper is to give fundamental properties of real lightlike hypersurfaces of paraquaternionic manifolds and to prove the non-existence of real lightlike hypersurfaces in paraquaternionic space form under some conditions. AMS MATHEMATICS SUBJECT CLASSIFICATION. Primary 53C15, Secondary 53C42, 53C50.