Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...

We develop the structure theory for transformations of weakly geometric rough paths bounded 1 < p $1 p$ -variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. derive an explicit combinatorial expression path lift a path, use to obtain fundamental identities such associativity integral, adjunction between pushforwards pu...

It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the asymmetric exclusion process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee–Yang theory of partition function zeros to ...

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.

Let f(k) denote the maximum such that every simple undirected graph containing two vertices s, t and k edge-disjoint s–t paths, also contains two vertices u, v and f(k) independent u–v paths. Here, a set of paths is independent if none of them contains an interior vertex of another. We prove that f(k) = ( k if k ≤ 2, and 3 otherwise. Since independent paths are edge-disjoint, it is clear that f...

the aim of the present study was to examine the casual relationship of parental bonding with bullying in schools, mediated bypersonality characteristics and student-teacher relationship quality. 200 second-grade male high-school students in ahvaz were selected using multi-stage random sampling method. the data were collected by the parental bonding instrument (pbi), neo-personality inventory-re...

the aim of this study was to test the model of the relationship between violence against women and aggressive behavior in children with mediation of maternal mental health. research design was correlation and path analysis. the study population included all of preschool children¢s mothers at the city of dezful. the sample was consisted of 250 pre-school children¢s mothers. that selected by mult...

The dependence of some thermodynamic properties of spin-polarized liquid 3He such as velocity of sound, adiabatic index, isentropic compressibility and temperature on the spin polarization has been investigated along different isentropic paths. The Lennard-Jones potential has been used in our calculations. It has been found that for higher values of entropy, the spin polarization has greate...