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In planar dynamics a pole is a center of rotation, the polar is the force line of action and the conic is the mass–inertia matrix. [4] The pole–polar relationship is used to define the center of percussion of a planar rigid body. If the pole is the hinge point, then the polar is the percussion line of action as described in planar screw theory.
In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end. Polar molecules must contain one or more polar bonds due to a difference in electronegativity between the bonded atoms.
Such a relation between points and lines generated by a conic is called pole-polar relation or polarity. The pole is the point; the polar the line. By calculation one can confirm the following properties of the pole-polar relation of the ellipse: For a point (pole) on the ellipse, the polar is the tangent at this point (see diagram: ,).
If the polar line of C with respect to a point Q is a line L, then Q is said to be a pole of L. A given line has (n−1) 2 poles (counting multiplicities etc.) where n is the degree of C. To see this, pick two points P and Q on L. The locus of points whose polar lines pass through P is the first polar of P and this is a curve of degree n−1.
The matrix above can be used with the molar refractivity equation and other data to produce density data for crystallography. Each polarizability measurement along with the refractive index associated with its direction will yield a direction specific density that can be used to develop an accurate three dimensional assessment of molecular ...
Note the decrease in ΔG ‡ activation for the polar-solvent reaction conditions. This arises from the fact that polar solvents stabilize the formation of the carbocation intermediate to a greater extent than the non-polar-solvent conditions. This is apparent in the ΔE a, ΔΔG ‡ activation. On the right is an S N 2 reaction coordinate diagram.
The equations for x and y can be combined to give + = (+) [2] [3] or + = (). This equation shows that σ and τ are the real and imaginary parts of an analytic function of x+iy (with logarithmic branch points at the foci), which in turn proves (by appeal to the general theory of conformal mapping) (the Cauchy-Riemann equations) that these particular curves of σ and τ intersect at ...
The polar surface area (PSA) or topological polar surface area (TPSA) of a molecule is defined as the surface sum over all polar atoms or molecules, primarily oxygen and nitrogen, also including their attached hydrogen atoms. PSA is a commonly used medicinal chemistry metric for the