Let $A^p$ be the Banach space of all continuous functions on the torus ${\mathbb T} = \{ z \in {\mathbb C} \vert \vert z \vert = 1 \}$ whose Fourier coefficients are in $\ell ^p$. We show that $A^p$ is not an algebra for all $1 \lt p \lt 2$.

In this paper we give a complete characterization of linear, quadratic, and geometric Legendre multiplier sequences. We also prove that all Legendre multiplier sequences must be Hermite multiplier sequences, and describe the relationship between the Legendre and generalized Laguerre multiplier sequences. We conclude with a list of open questions for further research.

The aim of this paper is to introduce a separation axiom using $(1,2)^*$-$\psi$-closed sets.

$\omega$-open sets are used to introduce two new classes of sets in bitopological spaces, namely, $u-\omega$-open sets and $q-\omega$-open sets. Several properties of these classes are given. The new classes of sets are used to introduce several types of continuity. Several results related to two known Lindelöfness bitopological concepts are introduced.

For a simple graph $G$, let $C(G) = \min \{ \vert N(u) \cup N(v) \vert : u,v \in V(g), \ uv \notin E(G) \}$. In this paper we prove that if $NC(G) + \delta (G) \ge \vert V(G) \vert$, then either $G$ is Hamiltonian-connected, or $G$ belongs to a well-characterized class of graphs. The former result by Dirac, Ore and Faudree et al. are extended.

This paper studies the existence of nonoscillatory solutions of a higher-order nonlinear neutral delay difference equation \begin{align*} \Delta \big(a_{kn} \cdots & \Delta (a_{2n} \triangle (a_{1n} \Delta (x_n + b_n x_{n-d}) ) ) \big) \\ &{} + f(n,x_{n-r_{1n}}, x_{n-r_{2n}}, \ldots , x_{n-r_{sn}} ) = 0, \ \ n \ge n_0, \end{align*} where $n_0 \ge 0$, $n \ge 0$, $d > 0$, $k > 0$, $s > 0$ are integers, $\{ a_{in} \} _{n \ge n_0}$ ($i = 1, 2, \ldots , k)$) and $\{ b_n \} _{n \ge n_0}$ are real sequences, $f \colon \{ n : n \ge n_0 \} \times {\mathbb R}^n \to {\mathbb R}$ is a mapping and $\bigcup _{j=1}^s \{ r_{jn} \} _{n \ge n_0} \subseteq {\mathbb Z}$. By applying Krasnoselskii's Fixed Point Theorem, some sufficient conditions for the existence of nonoscillatory solutions of this equation are established and indicated through five theorems according to the range of value of the sequence $b_n$.

The bibliography introduces literature on graph thickness, outerthickness, and arboricity. In addition to the pointers to the literature we also give some conjectures concerning known open problems on the field.

Unsteady natural convection flow of electrically conducting fluid in the presence of magnetic field past an accelerated vertical plate in a thermally stratified fluid is studied here. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity, skin friction, and Nusselt numbers are studied for different parameters like Prandtl numbers, thermal Grashof numbers, magnetic field parameters, stratification parameters, and time.