Fractional derivative

Mutation. For industrial appHcations, mutations are induced by x-rays, uv irradiation or chemicals (iiitrosoguanidine, EMS, MMS, etc). Mutant selections based on amino acid or nucleotide base analogue resistance or treatment with Nystatin or 2-deoxyglucose to select auxotrophs or temperature-sensitive mutations are easily carried out. Examples of useful mutants are strains of Candida membranefaciens, which produce L-threonine Hansenu/a anomala, which produces tryptophan or strains of Candida lipolytica that produce citric acid. An auxotrophic mutant of S. cerevisiae that requires leucine for growth has been produced for use in wine fermentations (see also Wine). This yeast produces only minimal quantities of isoamyl alcohol, a fusel oil fraction derived from leucine by the Ehrlich reaction (10,11). A mutant strain of bakers yeast with cold-sensitive metaboHsm shows increased stabiUty and has been marketed in Japan for use in doughs stored in the refrigerator (12). 

During the past decade, MALDI-TOF MS has proven to be an effective tool for the analysis of oligo- and polymeric mannoglucans (for extensive reviews see [222,223]). SEC/MALDI mass spectrometry was employed in the analysis of hemicelluloses isolated by microwave heat-fractionation from spruce and aspen wood [94]. These methods allowed the separation and characterization of the oligo- and polysaccharide fractions derived from the xylan and mannan components of both woods [224]. 

Figure 1 Immunomodulating activity of fractions derived from GR-2IIc by endo-a-(l->4)-polygalacturonase digestion...

Figure 4 Effect of neutral oligosaccharide-alditol fractions derived from PG-lc by lithium degradation on mitogenic activity of PG-lc...

In modern terms, asphaltene is conceptually defined as the normal-pentane-insoluble and benzene-soluble fraction whether it is derived from coal or from petroleum. The generalized concept has been extended to fractions derived from other carbonaceous sources, such as coal and oil shale (8,9). With this extension there has been much effort to define asphaltenes in terms of chemical structure and elemental analysis as well as by the carbonaceous source. It was demonstrated that the elemental compositions of asphaltene fractions precipitated by different solvents from various sources of petroleum vary considerably (see Table I). Figure 1 presents hypothetical structures for asphaltenes derived from oils produced in different regions of the world. Other investigators (10,11) based on a number of analytical methods, such as NMR, GPC, etc., have suggested the hypothetical structure shown in Figure 2. 

In the work now reported coal fractions derived from a solubilised coal were reacted individually with Tetralin, without any additions of catalyst or gaseous hydrogen, and the reaction products studied to determine the effect that chemical type had on the reaction. The untreated whole coal was also reacted to test whether phenol, present in the coal fractions as a result of the fractionation procedure, was having any significant effect on the reaction with the fractions. 

The Effect of Phenol. Three types of phenol compounds have been identified in the fractions derived from the product of the phenol ati on reaction (.1,2) alkyl phenols and alkyl-aryl ethers, both formed by combining phenol with alkyl side chains cleaved from the coal molecule, and compounds made up of aromatic fragments attached to phenol by a methylene bridge, formed by... 

Benzoraffln A hydrofining process for treating naphtha fractions derived from coal. It is a fixed-bed, gas-phase process using a cobalt/molybdenum oxide catalyst. Developed jointly by BASF, Veba-Chemie, and Lurgi, Ground 1960. 

Farrow, J. T., and Van Vunakis, H. (1973) Characteristics of D-lysergic acid diethylamide binding to subcellular fractions derived from rat brain. Biochem. Pharmacol., 22 1103-1113. 

Takayama and coworkers (60) introduced the h.p.l.c. separation technique for such amphiphilic molecules as lipid A, and in earlier experiments they applied paired-ion reverse-phase h.p.l.c. for the preparation of homogeneous fractions deriving from 4,-monophosphated lipid A of S. typhimur-ium. The purified preparations obtained were suitable for f.a.b. - m.s. analysis. However, monophosphated lipid A isolated in this way expressed a considerable heterogeneity with respect to the number and location of 0-acyl residues (60). In order to further improve the purification procedure, as well as to obtain lipid A derivatives suitable for n.m.r. spectroscopy, Qureshi et al. (174) prepared the dimethyl phosphate derivative of S. minnesota (R595) lipid A, which, after purification by reverse-phase h.p.l.c. (C18), could be analyzed by1 H-n.m.r. The n.m.r. spectrum of, for example, the heptaacyl lipid A dimethyl monophosphate fraction, unequivocally revealed 0-acyl substitution [14 0(3-OH)J at position 3 and a free hydroxyl group at position 4 of GlcN(I). 

With the help of fractional calculus, Dassas and Duby123 have worked on the problem of diffusion towards the fractal interfaces. They have proposed the following generalized diffusion equation involving a fractional derivative operator ... 

Here, D< )s is the fractional diffusivity defined as (4-2d,) (2d,-4) )(3-dP) j js a constant related to the fractal dimension and R0 is the side length of a square electrode), and dv dtv means the Riemann-Liouville mathematical operator of fractional derivative ... 

Regarding the electrochemical method, the generalized forms of the Cottrell relation and the Randles-Sevcik relation were theoretically derived from the analytical solutions to the generalized diffusion equation involving a fractional derivative operator under diffusion-controlled constraints and these are useful in to determining the surface fractal dimension. It is noted that ionic diffusion towards self-affine fractal electrode should be described in terms of the apparent self-similar fractal dimension rather than the self-affine fractal dimension. This means the fractal dimension determined by using the diffusion-limited electrochemical method is the self-similar fractal dimension irrespective of the surface scaling property. 

Advantages of the carbonate-exchange technique are (1) experiments up to 1,400°C, (2) no problems associated with mineral solubility and (3) ease of mineral separation (reaction of carbonate with acid). Mineral fractionations derived from hydrothermal and carbonate exchange techniques are generally in good agreement except for fractionations involving quartz and calcite. A possible explanation is a salt effect in the quartz-water system, but no salt effect has been observed in the calcite-water system (Hu and Clayton 2003). 

Antiserum can be raised againsf lymphocyfes or fhymo-cyfes by fhe repealed injection of human cells into an appropriate recipient, usually a horse. The use of such antiserum or the immune globulin fraction derived from it has been used to produce immunosuppression. Although antilymphocytic serum can suppress cellular and often humoral immunity against a variety of tissue graft systems, the responses are variable, particularly from one batch of serum to another. 

Given that the number of a and d protons are the same, an identical set of equations with Ad in place of Aa can also be used. Here we have used an average of Aa and Ad with the areas assessed after Lorentzian deconvolution in order to provide better separation of the 2.99 and 3.02 ppm lines. Mole fractions derived using this NMR method for reaction over the unpromoted copper catalyst are shown as a function of time in Figure 5. Clearly IDA is formed largely via HEG as intermediate since the concentration of the latter passes through a well-defined maximum. 

Comparison of the main peak fractions derived from controls (Glc3Man9GlcNAc2) and internal standards (Man5GlcNAc2, Man7GlcNAc2) give a hint to the underlying defect in patients with a suspected CDG-I (Fig. 4.5.6), which allows subsequent analysis of the putative affected gene. 

The propylene-butylene fraction constitutes a large part of the useful hydrocarbons produced by synthesis. It differs from similar fractions derived from petroleum refining in its high olefin (over 80%) and low isobutylene content, but this is no handicap in converting it to high octane gasoline by polymerization or by alkylation, if isobutane is available from another source. Polymerization is effected readily over a phosphoric acid on quartz catalyst with high conversion of propylene as well as butylene. The polymer... 

Spectral Studies. UV ABSORPTION. The acetone fractions derived from drinking water exhibited intense UV absorption between 208 and 214 nm this behavior may be attributed to unsaturated acids or esters. The CFH samples presented maximum absorption at 254-256 nm, whereas an aquatic humus sample derived from the Satilla River showed a maximum absorption at 234 nm. Therefore, apparent differences in UV spectra among all sample groups were found. 

Expanding the derivative term permits the incorporation of the overall mass continuity equation and the isolation of the mass-fraction derivative,... 

After substituting the species-continuity equation for the mass-fraction derivative and algebraically simplifying we have an energy equation with temperature as the dependent... 

Gas Oil—A fraction derived in refining petroleum with a boiling range between kerosene and lubricating oil. 

Once the carotenoids have been isolated as described in Basic Protocol 1, they can generally be crystallized as an initial step to purification. Actually, what is most likely to happen is a co-crystallization. When working with a nonpolar fraction, a- and (3-carotene may co-crystallize. In the same way, a polar fraction may yield lutein-zeaxanthin crystals. A pure carotenoid product may be obtained by crystallization of a fraction derived from a preparatory chromatographic procedure, which can be done using TLC, HPLC unit F2.3), or in some cases column chromatography. 

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