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Determinants of states' allocations of the master settlement agreement payments

Frank A Sloan1, Emily Streyer Carlisle, John R Rattliff

  • 1Center for Health Policy, Law and Management, Duke University, USA.

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Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
Average Value on a Rectangle01:27

Average Value on a Rectangle

A snowfall map can represent how snow depth varies across a region, such as Colorado, over a fixed time period. Since different locations may receive different amounts of snow, the snowfall depth is described by a function of two variables. If f(x,y) represents the snow depth at a point in a rectangular region, then the average snowfall over the entire region is found by comparing the total accumulated snowfall with the area being measured.Total Snowfall over a RegionThe total snowfall over a...
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
Design Example: Aggregate Gradation01:24

Design Example: Aggregate Gradation

The right type and quality of aggregates are crucial for concrete as they significantly influence its properties, mix proportions, and cost-effectiveness. If different sources are available for sand, the commonly used fine aggregate in concrete, the selection of sand is primarily based on its gradation.
The grading, or particle-size distribution, of sand is determined using sieve analysis, with standard sizes ranging from 150 μm to 10 mm (ASTM No. 100 sieve to 3⁄8 in. sieve). Sand is sampled...