A spherical fuzzy set is an advanced extension of classical fuzzy set in which it has an added advantage to deal with a wider sense of applicability in uncertain situations. In this paper, regular spherical fuzzy graphs and totally regular spherical fuzzy graphs are introduced. A necessary and sufficient condition for regular spherical fuzzy graphs is given. Some properties of regular and totally regular spherical fuzzy graphs are studied.

‎‎We introduce the notion of a minimal generator $G$ for the coded system $X$; that is a generator for coded system $X$ whenever $u \in G$‎, ‎then $u \not \in W(\overline{})$‎. ‎Such an $X$ is called \emph{minimally‎ ‎generated system}‎. ‎We ‎aim ‎to‎ introduce a class of minimally‎ ‎generated subshifts generated by some certain synchronizing blocks‎. ‎These systems are precisely the tool that will enable us to show that for such subshifts $X$‎, ‎each $x \in X$‎‎ can be written uniquely as‎ $x=\ldots v_{-1}v_{0}v_1v_2\ldots$, where $\{\ldots‎ ,‎v_{-1},v_{0},v_1,v_2,\ldots\}\in G$.‎‎‎‎‎‎ ‎Shows that the converse of that proposition isn't necessarily true‎.‎ {\color{red}‎ ‎‎‎‎‎‎We will show which of the components of the Kreiger graph of such a subshift could be a candidate to be suitable for a Fischer cover‎.‎‎‎‎‎ }

Let R be a commutative Noetherian ring. We prove that over a local ring R every  nitely generated R-module M of  nite Gorenstein projective dimension has a Gorenstein projective cover φ : C! M such that C is  nitely generated and the projective dimension of Ker φ is  nite and φ is surjective.

In this paper we study curvature properties of semi-symmetric type of totally umbilical radical transversal lightlike hypersurfaces (M, g) and (M, ~g) of a Kahler-Norden manifold (`M, `J, `g, ~`g) of constant totally real sectional curvatures `v and `~v (g and e g are the induced metrics on Mby the Norden metrics g and ~g, respectively). We obtain a condition for `v (resp.` v) which is equivalent to each of the following conditions: (M, g) (resp: (M, ~g)) is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein.

It is known that if G = AB is a product of its totally permutable subgroups A and B, then G 2 F if and only if A 2 F and B 2 F when F is a Fischer class containing the class U of supersoluble groups. We show that this holds when G = AB is a weakly totally permutable product for a particular Fischer class, F ⋄,N, where F is a Fitting class containing the class U and N a class of nilpotent groups. We also extend some results concerning the U-hypercentre of a totally permutable product to a weakly totally permutable product.

Hypergroups that have at least one identity element and where each element has at least one inverse are called regular hypergroup. In this regards, for a regular hypergroup $H$, it is shown that there exists a correspondence between the set of all strongly regular relations on $H$ and the set of all normal subhypergroups of $H$ containing $S_{\beta}$. More precisely, it has been proven that for every strongly regular relation $\rho$ on $H$, there exists a unique normal subhypergroup of $H$ containing $S_{\beta}$, such that its quotient is a group, isomorphic to $H/\rho$. Furthermore, this correspondence is extended to a lattice isomorphism between them.

The questions that the moral life forces on the philosophic thought are abundant. While men within wide limits always agreed as to the ways in which they ought to act as moral personalities, in our times as in former times they have disagreed with reference to the meaning and significance of morality. This paper will detach this one question: “Is there anything totally valuable in our moral life?” from this large background of ethical questions; we shall be able to answer the more directly, the more we focus our attention on this particular question and leave all others untouched. The present paper tends to conclude a positive answer through some considerations concerning moral action and self-valuation.