ON THREE-DIMENSIONAL HOMOGENEOUS FINSLER MANIFOLDS

In this paper, we study a long existing open problem on Landsberg metrics in Finsler geometry. For this aim, we study the Landsberg curvature of three-dimensional homogeneous Finsler manifolds. First, we express the second Matsumoto torsion of three-dimensional Finsler manifolds, explicitly. Then, we show that the mean Landsberg curvature of three-dimensional homogeneous Finsler manifolds satisfy an ODE. Finally, we prove that every homogeneous 3-dimensional L-reducible Finsler manifold has constant relatively isotropic mean Landsberg curvature if and only if it is a Landsberg metric or a Randers metric of Berwald-type

ON THE STRECH CURVATURE OF HOMOGENEOUS FINSLER METRICS

In this paper, we prove that every homogeneous Finsler metric has relatively isotropic stretch curvature if and only if it is a Landsberg metric. It follows that every weakly Berwald homogeneous metric has relatively isotropic stretch curvature if and only if it is a Berwald metric. We show that a homogeneous metric of non-zero scalar flag curvature has relatively isotropic stretch curvature if and only if it is a Riemannian metric of constant sectional curvature. It turns out that a homogeneous (a,b)-metric with relatively isotropic stretch curvature is a Berwald metric. Also, it follows that ahomogeneous spherically symmetric metric with relatively isotropic stretch curvature reduces to a Riemannian metric. Finally, we prove that every homogeneous stretch-recurrent metric is a Landsberg metric

ON CONFORMALLY BERWALD M-TH ROOT (α, β)-METRICS

In this paper, we study the class of $m$-th root (α, β)-metrics which is a significant class mixed of two classes of metrics: $m$-th root metrics and (α, β)-metrics. First, we find the necessary and sufficient condition under which the quartic (α, β)-metrics are conformally Berwald. Then, we find the necessary and sufficient condition under which the cubic (α, β)-metrics are conformally Berwald. Finally, we construct some conformal Finslerian invariants

TWO NOTABLE CLASSES OF PROJECTIVE VECTOR FIELDS

Here, we find some necessary conditions for a projective vector field on a Randers metric to preserve the non-Riemannian quantities $\Xi$ and $H$.They are known in the contexts as the $C$-projective and $H$-projective vector fields. We find all projective vector fields of the Funk type metrics on the Euclidean unit ball $\mathbb{B}^n(1)$.

Geographic distribution of need and access to health care in rural population: an ecological study in Iran

Introduction: Equity in access to and utilization of health services is a common goal of policy-makers in most countries. The current study aimed to evaluate the distribution of need and access to health care services among Iran’s rural population between 2006 and 2009. Methods: Census data on population’s characteristics in each province were obtained from the Statistical Centre of Iran and National Organization for civil registration. Data about the Rural Health Houses (RHHs) were obtained from the Ministry of Health. The Health Houses-to-rural population ratio (RHP), crude birth rate (CBR) and crude mortality rate (CMR) in rural population were calculated in order to compare their distribution among the provinces. Lorenz curves of RHHs, CMR and CBR were plotted and their decile ratio, Gini Index and Index of Dissimilarity were calculated. Moreover, Spearman rank-order correlation was used to examine the relation between RHHs and CMR and CBR. Results: There were substantial differences in RHHs, CMR and CBR across the provinces. CMR and CBR experienced changes toward more equal distributions between 2006 and 2009, while inverse trend was seen for RHHs. Excluding three provinces with markedly changes in data between 2006 and 2009 as outliers, did not change observed trends. Moreover; there was a significant positive relationship between CMR and RHP in 2009 and a significant negative association between CBR and RHP in 2006 and 2009. When three provinces with outliers were excluded, these significant associations were disappeared. Conclusion: Results showed that there were significant variations in the distribution of RHHs, CMR and CBR across the country. Moreover, the distribution of RHHs did not reflect the needs for health care in terms of CMR and CBR in the study period