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Page "Computational chemistry" ¶ 23

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For and geometries

For example, automorphism groups of certain models of finite geometries are not " symmetry groups " in the usual sense, although they preserve symmetry.

For the cutting of complex geometries, there are also flexible versions of the linear shaped charge, these with a lead or high-density foam sheathing and a ductile / flexible liner material, which also is often lead.

For spherical and hyperbolic spatial geometries, the curvature gives a scale ( either by using the radius of curvature or its inverse ), a fact noted by Carl Friedrich Gauss in an 1824 letter to Franz Taurinus.

For quasi-two-dimensional situations analytic functions may be used to map different geometries to each other.

For certain geometries and material combinations, it can be referred to as a casting.

For complex geometries, a numerical solution method such as the finite element method is necessary.

For many applications the sufficient accuracy may be obtained with CCSD, and the more accurate ( and more expensive ) CCSD ( T ) is often called " the gold standard of quantum chemistry " for its excellent compromise between the accuracy and the cost for the molecules near equilibrium geometries.

For deconvolution to be effective, all variables in the image scene and capturing device need to be modeled, including aperture, focal length, distance to subject, lens, and media refractive indices and geometries.

For that reason different models of space-time use warped geometries.

For geometries defined using complex number or quaternion coordinates, however, the situation is more complicated.

For physical disk geometries the maximal sector number is determined by the low level format of the disk.

For simple element geometries ( e. g. planar triangles ) analytical integration can be used.

For each base pair, considered relative to its predecessor, there are the following base pair geometries to consider:

For and bond

For bridged alkenes, the Bredt's rule states that a double bond cannot be placed at the bridgehead of a bridged ring system, unless the rings are large enough.

For example, of the isomers of butene, the two methyl groups of ( Z )- but-2-ene ( aka cis-2-butene ) face the same side of the double bond, and in ( E )- but2-ene ( aka trans-2-butene ) the methyl groups face the opposite side.

For example, the C-C-C bond angle in propylene is 123. 9 °.

For example, if one purchases many risky bonds, then hedges them with CDSes, profiting from the difference between the bond spread and the CDS premium, in a financial crisis the bonds may default and the CDS writer / seller may itself fail, due to the stress of the crisis, causing the arbitrageur to face steep losses.

For instance an arbitrageur would first buy a convertible bond, then sell fixed income securities or interest rate futures ( to hedge the interest rate exposure ) and buy some credit protection ( to hedge the risk of credit deterioration ).

For example, it would sell U. S. Treasury securities and buy Italian bond futures.

For example, in the electrophilic addition of hydrogen bromide, an electrophile ( proton ) attacks the double bond forming a carbocation, which then reacts with the nucleophile ( bromine ).

For instance, hybrid instruments such as convertible bonds and / or convertible preferred may be listed on stock or bond exchanges.

For example, a benzene ring or double bond in conjugation with the carbonyl will bring the wavenumber down about 30 cm − 1 .

For example, oleic acid, with one double bond, has a " kink " in it, whereas linoleic acid, with two double bonds, has a more pronounced bend.

For example, the covalent bond present within HCl molecules is much stronger than the forces present between the neighbouring molecules, which exist when the molecules are sufficiently close to each other.

For example, N 2 , with eight electrons in bonding orbitals and two electrons in antibonding orbitals, has a bond order of three, which constitutes a triple bond.

For example, the Chicago Board of Trade has retained overwhelming dominance of trading in US Treasury bond futures despite the startup of Eurex US trading of identical futures contracts.

For instance, determination of the structure of the ribosome — an enzyme that catalyzes peptide bond formation — revealed that its active site is composed entirely of RNA.

For example, porous tantalum coatings are used in the construction of orthopedic implants due to tantalum's ability to form a direct bond to hard tissue.

For single crystals of sufficient purity and regularity, X-ray diffraction data can determine the mean chemical bond lengths and angles to within a few thousandths of an angstrom and to within a few tenths of a degree, respectively.

Pope John Paul II felt that, “ de facto free unions, i. e., those unions without any publicly recognized institutional bond, are an increasing concern .” As for the Jewish perspective, “ For example, normative Judaism forcefully rejects the claim that never marrying is an equally valid lifestyle to marriage.

For example, the system of chloroform ( CHCl 3 ) and acetone ( CH 3 COCH 3 ) has a negative deviation from Raoult's law, indicating an attractive interaction between the two components which has been described as a hydrogen bond.

For example, researchers have identified several pairs of peptides that are unstructured in isolation, but adopt stable secondary and tertiary structure upon forming a disulfide bond between them.

For example, during the Argentine economic crisis of 2002, small denomination, interest-free provincial bond IOUs issued by local governments quickly took on some of the characteristics of local currencies successfully.

For the bond in the molecule to be stable, the covalent bonding electrons occupy the lower energy bonding orbital, which may be signified by such symbols as σ or π depending on the situation.

For example, heats of fusion and vaporization are usually of the order of 10 kJ · mol − 1 , bond energies are of the order of 100 kJ · mol − 1 , and ionization energies of the order of 1000 kJ · mol − 1 .

For and lengths

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

For example, a physics lab course might ask students to record lengths in centimetres, and masses in grams, but force ( a derived unit ) in newtons, a usage consistent with the SI system.

For example, a jump instruction can reference an absolute address or an offset from the current location, and the offset could be expressed with different lengths depending on the distance to the target.

For example, can be used to determine the length of a list (, given a list ) as well as to generate a list skeleton of a given length (), and also to generate both list skeletons and their lengths together ().

For centuries, viola makers have experimented with the size and shape of the viola, often adjusting the proportions or shape to make a lighter instrument with shorter string lengths, but which still has a large enough sound box to create an unmistakable ' viola sound '.

For example, the Symphony No. 29 in A major K. 201 has a contrapuntal main theme in its first movement, and experimentation with irregular phrase lengths.

For example, if your data contains long lengths of repeated bytes, the RLE ( run-length encoding ) strategy may give good results at higher speed.

For example, length changes in tandemly repeating regions in the Runx2 gene lead to differences in facial length in domesticated dogs ( Canis familiaris ), with an association between longer sequence lengths and longer faces ( Fondon 2004 ).

For prograde rotation, the formula relating the lengths of the sidereal and solar days is

For larger purchases, standardized lengths of cotton cloth called quachtli were used.

For a cyclic quadrilateral that is also orthodiagonal ( has perpendicular diagonals ), suppose the intersection of the diagonals divides one diagonal into segments of lengths p 1 and p 2 and divides the other diagonal into segments of lengths q 1 and q 2 .

For 35 mm cameras, lenses producing rectilinear images can be found at focal lengths as short as 8 mm, including zoom lenses with ranges of 2: 1 that begin at 12 mm.

For the Looney Tunes Golden Collection DVD releases, WB went to great lengths to track down whatever elements of the original title credits still existed, in an effort to re-create as best they could the original versions of the altered " Blue Ribbon " shorts.

For example, the Waldmeier effect is the phenomenon that cycles with larger maximum amplitudes tend to take less time to reach their maxima than cycles with smaller amplitudes ; there is also a negative correlation between maximum amplitudes and the lengths of earlier cycles, which allows a degree of prediction.

For instance, an equilateral triangle is a triangle of equal edge lengths.

For each division, thirteen boats line up at the downstream end of the stretch, each cox holding onto a rope attached to the bank, leaving around 1. 5 boat lengths between each boat.

For example, a stabilized helium-neon laser can produce light with coherence lengths in excess of 5 m. Not all lasers are monochromatic, however ( e. g. for a mode-locked Ti-sapphire laser, Δλ ≈ 2 nm-70 nm ).

For example, lengths, angles and areas are preserved with respect to the Euclidean group of symmetries, while only the incidence structure and the cross-ratio are preserved under the most general projective transformations.

For this reason, the Japanese tend to go to great lengths to avoid conflict, especially within the context of large groups.

For an example of lengths in this unit, the diameter of a gold nucleus is approximately 8. 45 femtometres.

For example, a typical mathematics question will not ask what the second leg of a right-angled triangle is when the lengths of the first leg and the hypotenuse are given.

0.851 seconds.