Time-series–cross-section (TSCS) data consist of comparable time series data observed on a variety of units. The paradigmatic applications are to the study of comparative political economy, where the units are countries (often the advanced industrial democracies) and where for each country we observe annual data on a variety of political and economic variables. A standard question for such stud...

Linear programming has many important practical applications, and has also given rise to a wide body of theory. See Section 49.9 for recommended sources. Here we consider the linear programming problem in the form of maximizing a linear function of d variables subject to n linear inequalities. We focus on the relationship of the problem to computational geometry, i.e., we consider the problem i...

Linear programming has many important practical applications, and has also given rise to a wide body of theory. See Section 50.9 for recommended sources. Here we consider the linear programming problem in the form of maximizing a linear function of d variables subject to n linear inequalities. We focus on the relationship of the problem to computational geometry, i.e., we consider the problem i...

Numerical methods are not always convergent especially in higher velocities when shock waves are involved. A comparison analysis is performed to study the supersonic flow over conical bodies of three different cross sections circular, elliptic and squircle (square with rounded corners) shaped using  Perturbation techniques to find flow variables analytically. In order to find lift and drag forc...

This supplement document includes four sections. Section I gives an example of the environmental selection process in the grid based evolutionary algorithm (GrEA). Section II shows the convergence and diversity comparison results of the six algorithms (ε-MOEA, POGA, HypE, MSOPS, MOEA/D, and GrEA) on the DTLZ and DTLZ5(I,M ) test problem suites. Section III analyzes the time complexity of the pr...

Table of contents: Section 1. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Section 2. Sixteen embedded components . . . . . . . . . . . . . . . . . . . . 5 Section 3. 15(d+ 1) more embedded primes (plus d − d if n = 2) . . . . . . . . 7 Section 4. (n− 1)(d − d) more embedded primes, for n > 2 . . . . . . . . . . 11 Section 5. Reduction to another family . . . . . . ....