Immigration and economic mobility

We examine how immigration affects natives’ relative prime-age labor market outcomes by economic class background, with class background established on the basis of parents’ earnings rank. Exploiting alternative sources of variation in immigration patterns across time and space, we find that immigration from low-income countries reduces intergenerational mobility and thus steepens the social gradient in natives’ labor market outcomes, whereas immigration from high-income countries levels it. These findings are robust with respect to a wide range of identifying assumptions. The analysis is based on high-quality population-wide administrative data from Norway, which is one of the rich-world countries with the most rapid rise in the immigrant population share over the past two decades. Our findings suggest that immigration can explain a considerable part of the observed relative decline in economic performance among natives with a lower-class background.

The Metric Dimension and Local Metric Dimension of Relative Prime Graph

This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be shown the value of the metric dimension and the local metric dimension of graphs are and respectively, where is the number of vertices groups that formed multiple 2,3, … , and is the cardinality of set . This research can be developed by determining the value of the fractional metric dimension, local fractional metric dimension and studying the advanced properties of graphs related to their forming rings.Key Words : metric dimension; modulo ; relative prime graph; resolving set; rings.

Isomorphisms of Direct Products of Finite Cyclic Groups

Summary In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.

ORDER CONVERGENCE OF ORDER BOUNDED SEQUENCES IN RIESZ SPACES

We consider sequences in a Dedekind $\sigma$-complete Riese space, satisfying a recursive relation \[ x_{n+p}\ge \sum_{j=1}^p \alpha_{n,j} x_{n+p-j} \qquad \text{for } n=1, 2, \cdots\] where $p$ is a given natural number and $\alpha_{n,j}$ are nonnegative real numbers satisfying $\sum_{j=1}^p\alpha_{n,j}=1$. We obtain a sufficient condition on coefficients $\alpha_{n,j}$ for which order boundedness of such a sequence $(x_n)_{n=1}^\infty$ implies its order convergence. In a particular case when $\alpha_{n,j}=\alpha_{j}$ for all $n$ and $j$, it is shown that every order bounded sequence satisfying the above recursive relation order converges if and only if natural numbers $j \le p$ for which $\alpha_{j}>0$, are relative prime.

MULTICOMPONENT CHIRAL POTTS MODELS

It is shown that an (Nρ,Nσ) chiral Potts model, which is a generalization of the Ashkin-Teller model and consists of two chiral Potts models which are coupled together by four-spin interactions, can always be mapped to a single chiral Potts model of NρNσ states if Nρ and Nσ are relative prime. Moreover, if on every lattice site there are d spins with Nρ,…,Nσ states, respectively, similar mappings exist: If there are chiral two-spin interactions between nearest neighbor spins of the same kind and if the d sublattices are coupled together by chiral 2j-spin interactions for j≤d between the j pairs of spins, this defines a composite (Nρ,…,Nσ) state chiral Potts model. If (Ni,Nj)=1, for i≠j, i,j=1,…,d, then the composite model with (Nρ,…,Nσ) states can be mapped into a [Formula: see text]-state chiral Potts model. Finally, it is shown that if one or more of the spins of a unit cell sits on the dual lattice whereas the other spins sit on the original lattice, so that this is a generalization of the eight-vertex model in the spin language, such a mapping also exists. This mean that results obtained for the chiral Potts models can be used for many such composite models.