Methodological analysis of period fertility in Saudi Arabia 2018

Exact measurement and evaluation of indicators of period fertility in a multiracial society could help explaining disparities. This paper represents a methodological and analytical attempt to systematically analyze period fertility and discuss differentials in its level and pattern between domestic and expatriate women in Saudi Arabia as far as available data allow. The data used are obtained from official Sources published by General Authority for Statistics in the Household Health Survey 2018. Estimated period fertility indicators, started from the simplest rates to the more elegant ones with adequate illustration of the advantages and disadvantages of each of them. The purpose was to establish fertility differentials and historical pattern. The paper has consistently shown that the fertility of expatriates in Saudi Arabia is lower than the fertility of the Saudi domestic women, but the reason for the disparity was not established as contraceptive practice has not confirmed sufficient influence. It was also revealed that the fertility transition that had been taking place since early eighties will continue but it will have precautions in the future.

Econometric Models in Resident Value of Investment

The aim of the study is to analyze what is the impact of: analyze period, resident value estimation method, discount rate and economic sector of the investor on the level of resident value to initial value of investment ratio. In the article, basing on 43 investments made by investors form MSP sector whose purpose was to purchase truck car of capacity to 3,5t, four econometric models were prepared: logit, probit, tobit, and logit-tobit to explain the dependence described in the aim of the study. All models are statistically important. In all models only one independent variable is always statistically important – analyze period. The longer analyze period is, the smaller resident value to initial value of investment ratio is. In order to compare models: MSE, RMSE, MAE, MAPE ratios were used. The best adaptation to data was observed when logit-tobit model is used

A local-global question in automorphic forms

In this paper, we consider the $\mathrm{SL} (2)$ analogue of two well-known theorems about period integrals of automorphic forms on $\mathrm{GL} (2)$: one due to Harder–Langlands–Rapoport about non-vanishing of period integrals on ${\mathrm{GL} }_{2} ({ \mathbb{A} }_{F} )$ of cuspidal automorphic representations on ${\mathrm{GL} }_{2} ({ \mathbb{A} }_{E} )$ where $E$ is a quadratic extension of a number field $F$, and the other due to Waldspurger involving toric periods of automorphic forms on ${\mathrm{GL} }_{2} ({ \mathbb{A} }_{F} )$. In both these cases, now involving $\mathrm{SL} (2)$, we analyze period integrals on global$L$-packets; we prove that under certain conditions, a global automorphic $L$-packet which at each place of a number field has a distinguished representation, contains globally distinguished representations, and further, an automorphic representation which is locally distinguished is globally distinguished.