The present paper deals with a study of certain transformations on an (LCS)_n-manifold. It is shown that an (LCS)_n-manifold remains invariant under a D-homothetic deformation. We also study an infinitesimal CL-transformation on an (LCS)_n-manifold and obtain a necessary and sufficient condition for such an infinitesimal transformation to be a Killing or a conformal Killing vector field. Finally, we study CL-transformation on an (LCS)_n-manifold and obtained a new tensor field, called CL-curvature tensor field, which is invariant under such a transformation.

A module M is said to be quasi-continuous if it is extending with the condition (C₃) (cf. [7], [10]). In this paper, by using the notion of a G-extending module which is defined by E. Akalan, G. F. Birkenmeier and A. Tercan [1], we introduce a generalization of quasi-continuous “a GQC (generalized quasicontinuous)-module” and investigate some properties of GQC-modules. Initially we give some properties of a relative ejectivity which is useful in analyzing the structure of G-extending modules and GQC-modules (cf. [1]). And we apply them to the study of direct sums of GQC-modules. We also prove that any direct summand of a GQC-module with the finite internal exchange property is GQC. Moreover, we show that a module M is G-extending modules with (C₃) if and only if it is GQC-module with the finite internal exchange property.

We shall consider partially ordered rings as a generalization of ordered rings. We give properties or related matters of partially ordered rings, using convex ideals or non-negative semicones. Also, we consider order-preserving isomorphisms between residue class rings which are partially ordered rings.

In this paper we classify the finite groups of isometries which act on a prism manifolds M(b,d) and do not preserve any fibering. We construct nine distinct finite groups of isometries which act on M(1,2), and do not preserve any fibering. We then show that if a finite group of isometries G acts on M(b,d) and does not preserve any fibering, then M(b,d) = M(1,2) and G is conjugate to one of these nine groups which are: Z₃ × T, T, O, S₃ × O, Z₃ ∘ O, S₃ × T, Z₃ × O, Z₃ × I, and S₃ × I , where T, O, I and S₃ are the tetrahedral, octahedral, icosahedral, and symmetric groups respectively.

A continuum means a nonempty, compact and connected metric space. Given a continuum X, the symbols F_n(X) and C₁(X) denotes the hyperspace of all subsets of X with at most n points and the hyperspace of subcontinua of X, respectively. If n > 1, we consider the quotient spaces SF₁ⁿ(X) = F_n(X)/F₁(X) and C₁(X)/F₁(X) obtained by shrinking F₁(X) to a point in F_n(X) and C₁(X), respectively. In this paper, we study the continua X such that SF₁ⁿ(X) is homeomorphic to C₁(X)/F₁(X) and we analyze when the spaces F_n(X) and SF₁ⁿ(X) are homeomorphic to some sphere.

We give a method for finding a minimal point adjacent to 1 of the reduced lattice in cubic number fields using an isotropic vector of the quadratic form and two-dimensional lattice.

We consider the range of a one-parameter family of selfinteracting walks on the integers up to the time of exit from an interval. We derive the weak convergence of an appropriately scaled range. We show that the distribution functions of the limits of the scaled range satisfy a certain class of de Rham's functional equations. We examine the regularity of the limits.