The center of a nearring $N$, in general, is not a subnearring of $N$. The center, however, is contained in a related structure, the generalized center, which is always a subnearring. We give three constructions of nearrings without multiplicative identity and characterize their centers and generalized centers. We find that the centers of these nearrings are always subnearrings.

We intend to solve Sudoku puzzles using various rules based on the structures and properties of the puzzle. In this paper, we shall present several structures related to either one potential solution or two potential solutions.

Let $E$ be an elliptic curve defined over the real numbers $R$ and let $P \in E(R)$. In this note we give an elementary proof of necessary and sufficient conditions for the preimages of $P$ under duplication to be real-valued.

We compute the spectrum and Smith normal form of the incidence matrix of disjoint transversals, a combinatorial object closely related to the $n$-dimensional case of Rota's basis conjecture.

Several separation axioms on topological spaces are described between Kolmogorov and Fréchet spaces as properties of the space at a particular point. After describing various equivalent descriptions, implications are established. Various examples are studied in order to show that the implications are strict.

In this paper we define strongly generalized neighborhood systems (in brief strongly $GNS$) and study their properties. It's proved that every generalized topology $\mu$ on $X$ gives a unique strongly $GNS$ $\psi_{\mu}:X\rightarrow \exp{(\exp{X})}$. We prove that if a generalized topology $\mu$ is given, then $\mu_{\psi_{\mu}}=\mu$; and if a strongly $GNS $ $\psi$ is given, then $\psi_{\mu_{\psi}}=\psi$. Strongly $(\psi_{1},\psi_{2})$-continuity is defined. We prove that $f:X\rightarrow Y$ is strongly $(\psi_{1},\psi_{2})$-continuous if and only if it is $(\mu_{\psi_{1}},\mu_{\psi_{2}})$-continuous.

In this paper we analyze the properties of a pure water oscillator by considering the pure water lake as a well mixed two layered system. While there is heating of and evaporation from the shallow top layer, the temperature of the deep bottom layer is assumed to be constant. By exploiting the nonlinear dependence of the density of pure water on temperature, we describe two complementary mathematical models to capture the vertical instability resulting from the variation of the density of the top layer with temperature.

This paper introduces nano resolvable spaces and nano irresolvable spaces. Also, a new form of nano subspace topology is established. Several new characterizations of nano strongly irresolvable spaces are found and precise relationships are noted between nano strongly irresolvability and nano irresolvable space. Some weaker forms related to nano irresolvable are discussed. Also, comparisons between them are given.

In this paper, by using the $t$-norm $T$ and $t$-conorm $S$, we introduce the intuitionistic fuzzy bi-normed $KU$-subalgebras of a $KU$-algebra. Some properties of intuitionistic fuzzy bi-normed $KU$-subalgebras of a $KU$-algebra under the homomorphism are discussed. The direct product and the $(T,S)$-product of intuitionistic fuzzy bi-normed $KU$-subalgebras are particularly investigated.