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In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure.
Matrix Toolkit Java is a linear algebra library based on BLAS and LAPACK. ojAlgo is an open source Java library for mathematics, linear algebra and optimisation. exp4j is a small Java library for evaluation of mathematical expressions. SuanShu is an open-source Java math library. It supports numerical analysis, statistics and optimization.
In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. [1] Actively used in the architecture of the 19th century, the methods of graphic statics were largely abandoned in the second half of the 20th century, primarily due to widespread use of frame structures of steel and reinforced concrete that ...
Solving this master problem will constitute a "first guess" at an optimal solution to the overall problem, with the value of unbounded below and taking on any feasible value. The set of cuts will be filled in a sequence of iterations by solving the inner maximization problem of the minimax formulation.
Special awards exist for solving special combinations of problems. For instance, there is an award for solving fifty prime numbered problems. A special "Eulerians" level exists to track achievement based on the fastest fifty solvers of recent problems so that newer members can compete without solving older problems.
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
The divide-and-conquer paradigm is often used to find an optimal solution of a problem. Its basic idea is to decompose a given problem into two or more similar, but simpler, subproblems, to solve them in turn, and to compose their solutions to solve the given problem. Problems of sufficient simplicity are solved directly.
In each iteration of the method, we increase the penalty coefficient (e.g. by a factor of 10), solve the unconstrained problem and use the solution as the initial guess for the next iteration. Solutions of the successive unconstrained problems will asymptotically converge to the solution of the original constrained problem.