Project portfolio management consists of repetitive cycles of Project evaluation، selection and execution. Project portfolio selection is the main part of Project portfolio management. Organization identifies and prioritizes Projects that are mostly aligned with stated strategic goals while considering real-world restrictions and considerations that are related to scheduling and resource allocation. In this paper، a new comprehensive model for the Project portfolio selection problem over a planning horizon with multiple periods by maximizing profit is developed in which simultaneous selection، scheduling and resource allocation of Projects are considered. The model incorporates Project interdependency and strategies of Project divisibility، reinvestment، external investment and resourcing in different ways at the same time in choosing the best execution schedule for the Projects in real-life applications. In addition، resource and budget constraints، cardinality restriction، precedence relationship and scheduling، setup and resource costs are included in the model. Numerical examples under eight scenarios are presented to highlight the characteristics of the proposed model.

Let G be a  nite group. The graph D(G) is a divisibility graph of G. Its vertex set is the non-central conjugacy class sizes of G and there is an edge between vertices a and b if and only if ajb or bja. In this paper, we investigate the structure of the divisibility graph D(G) for a non-solvable group with  ∗ (G) = 2, a  nite simple group G that satis es the one-prime power hypothesis, a group of type(A), (B) or (C) and certain metacyclic p􀀀 groups and a minimal non-metacyclic p􀀀 group where p is a prime number. We will show that the divisibility graph D(G) for all of them has no triangles.

The divisibility graph D (G) for a finite group G is a graph with vertex set cs (G) \ {1} where cs (G) is the set of conjugacy class sizes of G. Two vertices a and b are adjacent whenever a divides b or b divides a. In this paper we will find the number of connected components of D (G) where G is a simple Zassenhaus group or an sporadic simple group.

The divisibility of general foreign language ability and language skills has been a long-running question in applied linguistics. Formerly researchers believed that language skills are global but more recent views consider them as divisible. However, there is no consensus among researchers on the number and nature of the underlying components of language skills. The purpose of the present study is to investigate the divisibility of foreign language comprehension construct. To this end, an English comprehension test comprising two skills of listening and reading was analyzed with a multidimensional IRT model. Three competing models with one, two and four dimensions were fitted to the data. Findings showed that the four dimensional model fits the data best. The implications of the study for foreign language testing and teaching are discussed.