In this paper, we introduce a new labeling called Totally Vertex-Magic Cordial(TVMC) labeling. A graph $G(p,q)$ is said to be TVMC with a constant $C$ if there is a mapping $f:V(G)\cup E(G)\to \{0,1\}$ such that

$$\left[f(a)+{\displaystyle \sum _{b\in N(a)}f(ab)}\right]\equiv C(\mathrm{mod}2)$$

for all vertices $a\in V(G)$ and $|n_f(0)-n_f(1)|\le 1$, where $N(a)$ is the set of vertices adjacent to the vertex $a$ and $n_f(i)(i=0,1)$ is the sum of the number of vertices and edges with label $i$.

A graph $G$ is said to have totally magic cordial(TMC) labeling with constant $C$ if there exists a mapping $f:V(G)\cup E(G)\to \{0,1\}$ such that $f(a)+f(b)+f(ab)\equiv C\hspace{0.17em}(\text{Mod\hspace{0.17em}}2)$ for all $ab\in E(G)$ and $|n_f(0)-n_f(1)|\le 1$, where $n_f(i)(i=0,1)$ is the sum of the number of vertices and edges with label $i$. In this paper, we investigate some new families of graphs that admit totally magic cordial labeling.

For multi-way contingency tables of same classifications with ordered categories, this paper proposes two generalized marginal cumulative logistic models. Those indicate that the difference between two marginal cumulative logits, or two conditional marginal cumulative logits on condition that all values of the variables are not identical, is a polynomial function of the category value. This paper also gives a theorem that the marginal homogeneity model holds if and only if both the proposed model and moment equality model hold. An example is given.

The object of the present paper is to study $LP$-Sasakian manifolds with quasi-conformal curvature tensor.

In this paper, we propose a modified scaling BFGS method for unconstrained minimization. A remarkable feature of the proposed method is that it can improve the performance of the BFGS method and possesses a global convergence property without convexity assumption on the objective function. Under certain assumptions, we also establish superlinear convergence of the method. Finally we show numerical results.