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There are two groups of vanadium steel alloys. Vanadium high-carbon steel alloys contain 0.15–0.25% vanadium, and high-speed tool steels (HSS) have a vanadium content of 1–5%. For high-speed tool steels, a hardness above HRC 60 can be achieved. HSS steel is used in surgical instruments and tools. [74]
The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
By comparison, m-CPBA, another epoxidizing agent, reacts with both alkenes, creating the products in a two to one ratio favoring reaction at the alkene away from the hydroxyl group. TBHP oxidizes VO(acac) 2 to a vanadium(V) species which coordinates the alcohol of the substrate and the hydroperoxide , directing the epoxidation to occur at the ...
These tables list values of molar ionization energies, measured in kJ⋅mol −1.This is the energy per mole necessary to remove electrons from gaseous atoms or atomic ions.
In three dimensions the cross product is invariant under the action of the rotation group, SO(3), so the cross product of x and y after they are rotated is the image of x × y under the rotation. But this invariance is not true in seven dimensions; that is, the cross product is not invariant under the group of rotations in seven dimensions, SO(7).
Vanadium compounds are compounds formed by the element vanadium (V). The chemistry of vanadium is noteworthy for the accessibility of the four adjacent oxidation states 2–5, whereas the chemistry of the other group 5 elements , niobium and tantalum , are somewhat more limited to the +5 oxidation state. [ 1 ]
As an example, summing bond orders in the ammonium cation yields −4 at the nitrogen of formal charge +1, with the two numbers adding to the oxidation state of −3: The sum of oxidation states in the ion equals its charge (as it equals zero for a neutral molecule). Also in anions, the formal (ionic) charges have to be considered when nonzero.