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By solving the inverse eigenvalue problem, necessary changes of design variables are determined and the desired natural frequencies are achieved so that resonance conditions are successfully avoided.
Through a linear perturbation analysis on the odd even decoupling problem, necessary conditions for designing a shock stable scheme are discussed.
Several useful properties, such as, the computational complexity of the sequencing problem, necessary and sufficient conditions that a conveyor stoppage occurs, lower and upper bounds of the objective function, and sufficient conditions for the optimality of a solution, are characterized.
This subsumes errors due to the modeling process as well as discretizations of the problem necessary for its numerical solution.
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Others are investing thousands of pounds in custom "mining rigs", computers specially built to solve the mathematical problems necessary to confirm a Bitcoin transaction.
This and other papers on the subject were recognised with a prize from the IEEE Information Theory Society; they possessed a superior understanding of multidimensional geometry, and they were solving crucial problems necessary for higher-dimensional coding.
By indexing problems with this framework (we call it "semantics of constraints: SOC"), it becomes possible to automatically extract the "differences between problems" necessary for the comparison and sequencing of problems.
Since the cost function in this case is multi-modal, non-smooth and non-convex, methods for solving the optimisation problems necessary to design multi-panel suction systems based on direct search techniques are developed.
In case of identified drug-related problems, necessary changes of the medication were made in collaboration with the responsible physician.
Generally, two sub-problems are necessary for solving the problem.
But organizations like the Child Welfare League of America say more information about the problem is necessary.
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