ab initio calculation at hf/6-31g* level of theory for geometry optimization and mp2/6-31g*//hf/6-31g* for a single point total energy calculation are reported for the important energyminimumconformations and transition-state geometries of of cyclodeca-1,2,3-triene (1). the mostfavorable conformation of 1 is a unsymmetrical twist-chair (1-tc) structure. degenerateinterconversion of 1-tc with it...

Algebraic geometry emerged from the study of subsets of C defined by polynomial equations, namely algebraic sets. Parallel to this, real algebraic geometry emerged from studying subsets of R defined by polynomial equations and inequalities, namely semi-algebraic sets. Like algebraic geometry, classical methods in real algebraic geometry provided useful but limited intuition on the relationship ...

A method of presenting optimization to rst semester calculus students is demonstrated. The method is based on the Lagrange Multiplier approach and the geometry of a given problem becomes the central focus of the eeorts to nd a solution. The method proposed here deviates from the traditional approach in that the student is asked to examine a constrained optimization problem and the geometry of t...

The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual NewtonRaphson-type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage s...

Real Algebraic Geometry in Convex Optimization

Vibration energy harvesting with piezoelectric materials currently generate up to 300 microwatts per cm2, using it to be mooted as an appropriate method of energy harvesting for powering low-power electronics. One of the important problems in bimorph piezoelectric energy harvesting is the generation of the highest power with the lowest weight. In this paper the effect of the shape and geometry ...

equilibrium geometry, electronic structures, and vibrational modes of cob8- were investigated in the pbepbe/6-311+g(d,p) level of theory. the nucleus independent chemical shift (nics) analysis and magnetizability values were used for studying of aromaticity in cob8-. the effects of different solvents on the structure and frontier orbital energies were calculated using the polarizable continuum ...

Topology optimization searches for an optimal distribution of material and void without any restrictions on the structure of the design geometry. Shape optimization tunes the shape of the geometry, while the topology is fixed. In this paper we proceed sequentially with the optimal topology and shape design so that a coarsely optimized topology is the initial guess for the following shape optimi...

This paper presents an optimization design method for centrifugal compressors based on one-dimensional calculations and analyses. It consists of two parts: (1) centrifugal compressor geometry optimization based on one-dimensional calculations and (2) matching optimization of the vaned diffuser with an impeller based on the required throat area. A low pressure stage centrifugal compressor in a M...