Standard Dutch and German have two reflexive forms: a weak form (zich in Dutch and sich in German) and a strong form (zichzelf in Dutch and sich selbst in German). The choice between the two reflexive forms in Dutch has been explained by the selectional restrictions of the verb, distinguishing between three verb classes: inherently reflexive verbs, accidentally reflexive verbs and transitive ve...

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

The present paper focuses on the Mandarin Intransitive keflexive Verbs. These verbs, such as zi-sha 'to commit suicide', and zi fen 'to burn oneself, are formed with a reflexive morpheme zi-'self' and a root verb. Take the verb zi-sha 'to commit suicide' for example, the reflexive morpheme contributes the reflexive meaning and the root verb sha 'to kill' contributes the meaning`to kill'; hence,...

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

The notion of super weak compactness for subsets Banach spaces is a strengthening the that can be described as local version super-reflexivity. A recent result K. Tu [32] which establishes closed convex hull weakly compact set has removed main obstacle to further development theory. In this paper we provide variety results around in order show great scope notion. We also give non linear charact...

In this paper we introduce certain classes of graphs that generalize φ-tolerance chain graphs. In a rank-tolerance representation of a graph, each vertex is assigned two parameters: a rank, which represents the size of that vertex, and a tolerance which represents an allowed extent of conflict with other vertices. Two vertices are adjacent if and only if their joint rank exceeds (or equals) the...

Most walking assist systems reported are not ready for using in real-world environment; where there are frequent perturbations .Our ultimate goal is to realize artificial reflexes to real-world walking support systems. This goal needs both qualitative and quantitative understanding of human reflexive mechanism. In this study we built a human walking simulator consisting of a Central Pattern Gen...