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Topic: Mixed derivatives

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Hessian matrix

Mixed partial derivatives

	Partial derivative - Wikipedia, the free encyclopedia
		In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant.
		is a rounded 'd' known as the 'partial derivative symbol,' which coincides with the cursive Cyrillic letter "de" and is pronounced as its English counterpart "d" - that incidentally was the notation first introduced by Legendre).
		However, if all partial derivatives exist in a neighborhood of a and are continuous there, then f is totally differentiable in that neighborhood and the total derivative is continuous.
	en.wikipedia.org /wiki/Partial_derivative (449 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		styrene derivative to obtain phenol aralkylation polymer, with a portion of the phenolic component joined to the aryl diolefin with a portion of the phenolic linkages being para in orientation.
		The phenolic aralkylation polymers particularly useful in the practice of the invention are derived from a phenolic monomer, at least one styrene derivative, and a coupling agent.
		In accordance with this embodiment, a phenolic monomer and at least one styrene derivative are reacted in the presence of an acid catalyst.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=98/30596.980716&ELEMENT_SET=DECL (10277 words)

	Encyclopedia: Symmetry of second derivatives (Site not responding. Last check: 2007-10-29)
		The entries in it off the main diagonal are the mixed derivatives; that is, successive partial derivatives with respect to different variables.
		Firstly the derivative of any function can be defined (provided it is integrable), as a distribution.
		This leads to the construction of pathological examples in which the symmetry of second derivatives is not true.
	www.nationmaster.com /encyclopedia/Symmetry-of-second-derivatives (1244 words)

	Cosmetic compositions on the basis of alkyl-hydroxypropyl-substituted chitosan derivatives, new chitosan derivatives ... (Site not responding. Last check: 2007-10-29)
		The invention is directed, in addition, to a process for producing the chitosan derivatives of the formula I, as well as cosmetic compositions for the treatment of hair or skin, particularly compositions for strengthening hair, comprising a content of these chitosan derivatives.
		The alkyl-hydroxypropyl-substituted chitosan derivatives of formula I are obtained, according to the invention, in that chitosan is reacted either in a two-step reaction, first with propylene oxide and then with an alkyl halide, or the two alkylating agents can act simultaneously, but at two different reaction temperatures.
		The compositions containing chitosan derivatives of formula I, according to the invention, are suitable in general for the treatment of the skin and/or the hair.
	www.patentstorm.us /patents/4845204.html (3249 words)

	Derivative of a Bézier Curve
		The directional derivative of a surface at x(u) with respect to d is given by A geometric interpretation: in the domain, draw the straight line through u that is parallel to d.
		We may continue taking derivatives, arriving at The r-th directional derivative at b(u) is therefore found by performing r steps of the de Castlejau algorithm with respect to d, and then by performing n-r more steps with respect to u.
		Mixed directional derivatives In the same way, we may compute mixed directional derivatives: if d1 and d2 are two vectors in the domain, then their mixed directional derivatives are This blossom result may also be expressed in terms of Bernstein polynomials.
	www.math.hmc.edu /~gu/math142/mellon/Application_to_CAGD/Bezier_curves/derivative.html (389 words)

	Protein-S-S-glutathione mixed disulfides as models of unfolded proteins. (Site not responding. Last check: 2007-10-29)
		The intrinsic fluorescence of the derivatives and the binding of the hydrophobic fluorescent dye ANS were characteristic of fully unfolded proteins.
		Mixed disulfides between glutathione and the reduced forms of disulfide-bonded proteins were generated and characterized to explore their suitability as models of the unfolded state of newly-synthesized secretory proteins.
		The results indicate that these GS-S-protein mixed disulfide derivatives are ideal model unfolded proteins that can be used as substrates for detailed studies on secretory protein folding in vitro and on the interactions between unfolded proteins and facilitators of protein folding.
	www.pdg.cnb.uam.es /UniPub/iHOP/gp/8057096.html (232 words)

	Partial derivative - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-29)
		The partial derivative of a function f with respect to the variable x is represented as or or f
		As an example, consider the volume V of a cone; it depends on the cone's height h and its radius r according to the formula
		The vector consisting of all partial derivatives of f at a given point a is called the gradient of f at a:
	encyclopedia.learnthis.info /p/pa/partial_derivative.html (440 words)

	Infusion solution for parenteral feeding - United States Patent 4,005,190
		The hydroxy-substituted cholanic acid derivatives are present in the infusion solution in an amount sufficient to yield a weight ratio of normally water-insoluble phosphatides to hydroxy-substituted cholanic acid derivatives of from about 1:1 to 3:1.
		Of particular importance is the fact that the hydroxy-substituted cholanic acid derivatives as well as the alcohol components used in the infusion solution of the present invention function not only as auxiliary solvent intermediary materials but also bring additional useful physiological effects to the infusion solutions and are incorporated in the metabolism of the organism.
		While it is apparent that the quantitative ratios of hydroxy-substituted cholanic acid derivatives and lipids are not linearly proportional, the curves exemplify the approximate relationship of lipids and hydroxy-substituted cholanic acid derivatives.
	xrint.com /patents/us/4005190 (1724 words)

	Vitalethine Proofs and Molecular Weight Evidence
		The sulfenate-linked benzyl derivative in this analysis produces a relative molecular weight of about 562.7, a rearrangement consistent with a proposed dehydration that may also explain the observed differences in carbon and proton NMR spectra for this compound in protic (D2O) and aprotic (D6-DMSO) solvents.
		The dabsyl amide derivative of cystamine elutes in the vicinity of the reagent peak.
		Thus, it appears that heating causes a disproportionate decomposition of vitalethine, the authentic compound decomposing to the dabsyl amides of a mixed disulfide of vitaletheine with cysteamine and of the amino acid, beta-alanine.
	www.nmia.com /~galenvtp/vtlmolwt.htm (919 words)

	Process for the synthesis of mixed polyimino derivatives of aluminium and alkaline earth metals - Patent 4179459
		A single stage process is provided for the direct synthesis of mixed polyimino derivatives of aluminium and alkaline earth metals consisting of reacting aluminium, an amine, the alkaline earth metal or hydride or amide derivative thereof, in the presence of hydrogen, the reaction being promoted by an activator in either hydrocarbon or ether solvents.
		A process for the synthesis of mixed polyimino derivatives of aluminum and alkaline earth metals, said process consisting of reacting aluminum, a primary or secondary amine, and an alkaline earth metal or a hydride or amide derivative thereof, in the presence of hydrogen.
		Various activators promote the reaction, and are chosen from metals of the first three groups of the periodic table, their hydrides or alkyl derivatives, or mixed hydrides thereof.
	www.freepatentsonline.com /4179459.html (3336 words)

	Calculus III (Math 2415) - Partial Derivatives - Higher Order Partial Derivatives
		Just as we had higher order derivatives with functions of one variable we will also have higher order derivatives of functions of more than one variable. However, this time we will have more options since we do have more than one variable..
		The second and third second order partial derivatives are often called mixed partial derivatives since we are taking derivatives with respect to more than one variable. Note as well that the order that we take the derivatives in is given by the notation for each these. If we are using the subscripting notation, e.g.
		from the derivatives. This is fairly standard and we will be doing it most of the time from this point on. We will also be dropping it for the first order derivatives in most cases.
	tutorial.math.lamar.edu /AllBrowsers/2415/HighOrderPartialDerivs.asp (728 words)

	12 (Site not responding. Last check: 2007-10-29)
		So we know that a derivative of a function of one variable at a specified point is the instantaneous rate of change of the function, or the slope of its tangent line at the point.
		Then the partial derivatives of w with respect to x,y, and z are defined in a similar manner and are computed in a similar manner:
		Conclusion: if we have a parallelogram as described, the area is changing by 10 units per unit change of a where it is changing by 100 times square root of 3 units per unit change of q.
	www.ac.cc.md.us /~donr/CalcIII/unit3/lesson3/u3l3.html (586 words)

	5. Derivatives of Functions of Several Variables
		instead of d to indicate that this is the derivative of a function of several variables.
		This symbol is named partial and the result of equation 5.2 is called a partial derivative.
		To emphasize the fact that there are other variables being held constant during the process, they are often (but not always) written as subscripts after the closing parenthesis, as on the right-hand side of equation 5.2 However, when no confusion can result, both the parentheses and the subscript are sometimes dropped.
	scholar.chem.nyu.edu /0652/notes/math/node6.html (533 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Preferably the catalyst is contacted with the aromatic compound at a temperature higher than that of the condensation and/or re-arrangement reaction in which the optionally substituted MDI and derivatives thereof is produced.
		A process according to claim 7 in which the catalyst is contacted with the aromatic compound at a temperature higher than that of the condensation and/or re-arrangement reaction in which the optionally substituted MDI and derivatives thereof is produced.
		and derivatives thereof is produced wherein the aromatic compound comprises a substituent having activating characteristics with respect to electrophilic substitution as compared to the aromatic compound without the said substituent.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/97969.011227&ELEMENT_SET=DECL (3466 words)

	Study Guide 1 (Site not responding. Last check: 2007-10-29)
		Use the chain rule to calculate the derivatives of functions with respect to a single independent variable.
		Use the chain rule to calculate the partial derivatives of a function with respect to several independent variables.
		Give an example of a function for which the partial derivatives exist, but which is not differentiable.
	www-math.cudenver.edu /~billups/courses/ma2422/final_review.html (495 words)

	Main Trends and Basic Achievements
		Mixed cellulose derivatives were synthesized by cyanoethylation of methylcellulose, oxyethylcellulose and oxypropylcellulose.
		Temperature-concentration conditions of LC order formations of synthesized mixed cellulose derivatives were studied by polar microscopy, X-ray analysis, reological and sorption methods.
		Reaction ability of cellulose fibres and flax boon were studied in frames of conception of flax technology waste using as example of carboxymethylation and nitration reaction.
	www.macro.ru /05/page3.html (1319 words)

	Dihydroxypropyl mixed ether derivatives of cellulose - Patent 4523010
		However, such anionic mixed cellulose ethers are susceptible to degradation by acid catalyzed hydrolysis.
		The resulting slurry is mixed for one hour under nitrogen and 45.0 g glycidol dissolved in 25 ml isopropanol is added.
		In this regard, while specific embodiments of this invention have been described in considerable detail, variations and modifications of these embodiments can be effected without departing from the spirit and scope of the invention as disclosed and claimed.
	www.freepatentsonline.com /4523010.html (2611 words)

	Research Theme
		Mixed quantum/classical procedures development for determining non-linear optical properties of condensed phases.
		Elaboration of quantum chemical methods to determine the mixed derivatives with respect to Cartesian coordinates and oscillating electric fields; application to the Raman spectroscopy and to nonlinear optical properties.
		Mixed quantum/classical procedures development for determining linear and non-linear optical properties of condensed phases.
	www.fundp.ac.be /recherche/thematiques/en/95.html (149 words)

	on dealing with mixed derivatives in ADI
		after applying the coodinate transformation, i obtained one mixed derivative term in the difussion part of each equation.
		Re: on dealing with mixed derivatives in ADI - yf yap, Thu, 18 Jan 2001, 10:19 p.m.
		Re: on dealing with mixed derivatives in ADI - Abhijit Tilak, Thu, 18 Jan 2001, 11:48 p.m.
	www.cfd-online.com /Forum/main_archive_2001.cgi?read=14675 (123 words)

	NDSolve::mixed
		Generated when the specification of the solution of a partial differential equation includes mixed partial derivatives.
		A mixed partial derivative is a derivative that involves differentiation with respect to more than one variable.
		An error occurs in this example because one of the initial conditions includes a mixed partial derivative of the solution function.
	documents.wolfram.com /v4/OtherInformation/NDSolve_mixed.html (77 words)

	600-233 Calculus and Analytic Geometry III (Site not responding. Last check: 2007-10-29)
		An example of a function whose mixed partial derivatives are not equal.
		A worksheet illustrating that the gradient of a function is orthogonal to its level curves or level surfaces.
		The partial derivatives of a function give the rates of change of the function in directions parallel to the co-ordinate axes.
	www.uwm.edu /People/kevinm/teaching/233/ws.htm (179 words)

	Partial Derivatives (Site not responding. Last check: 2007-10-29)
		For such functions it is still possible to calculate the derivatives with respect to a specified variable.
		As the variable used in the differentiation is important, such derivatives are never denoted by primes or dots.
		The functions commonly met in most engineering applications have the following property: the mixed partial derivatives do not depend on the order in which the derivatives are taken.
	web.mit.edu /aa-math/www/glossary/node5.html (142 words)

	Savvysoft - A New Spin on Software
		Savvysoft makes and sells the market’s most comprehensive range of derivatives models, portfolio and risk management systems, daily corporate credit default probabilities, and now, TurboExcel, a groundbreaking Excel-based robotic programmer that lets you write programs in C++ using only an Excel spreadsheet.
		With over 3000 installations in 15 countries, the company's flagship product, TOPS is fast becoming the standard by which all other derivatives software is measured.
		Four of the "Big Four" auditors use TOPS for their derivatives valuations.
	www.savvysoft.com (135 words)

	Computer Algebra Group at SFU - Meetings, Colloquia (Site not responding. Last check: 2007-10-29)
		A consequence of this is that Maple cannot graph this derivative.
		The problem, which I do not know how to solve, is how to do this for mixed derivatives.
		This work was motivated by professor Yury Brychkov's work where he gave formulae for derivatives of special functions w.r.t.
	www.cecm.sfu.ca /CAG/abstracts/07062002b.html (157 words)

	Partial derivative Article, Partialderivative Information (Site not responding. Last check: 2007-10-29)
		As an example, consider the volume V of a cone ; it depends on the cone's heighth and its radius r according to the formula
		However, if all partialderivatives exist in a neighborhood of aand are continuous there, then f is totally differentiable in thatneighborhood and the total derivative is continuous.
		If all mixed partial derivatives exist and are continuous, we callf a C
	www.anoca.org /function/derivatives/partial_derivative.html (428 words)

	Aromatics
		Annual market estimates and projections are presented in millions of metric tons and growth rates for the years 1999 through 2005.
		Benzene and mixed xylenes are further segmented into their derivative products and analyzed.
		Benzene's derivatives include ethylbenzene, cumene, cyclohexane, nitrobenzene, and alkylbenzene and mixed xylenes' derivatives are para-xylene, ortho-xylene and other solvents.
	www.marketresearch.com /researchindex/454706.html (276 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Express properties as derivatives of the energy with respect to "applied perturbations".
		E.g., harmonic force constants are second derivatives with respect to displacing the nuclei.
		Can have mixed second derivatives: differentiating once with respect to an applied electric field and once with respect to nuclear displacements gives a dipole derivative, whose square is the IR intensity.
	www.sdsc.edu /~kimb/scf_results.html (564 words)

	Dáil Éireann - Volume 392 - 07 November, 1989 - Written Answers. - Halogenated Derivatives.
		Garland asked the Taoiseach the number of tonnes of halons which were imported into Ireland in (a) 1986, (b) 1987, (c) 1988 and (d) to date in 1989.
		The Taoiseach: For the years 1986 and 1987 the available data relates to halogenated derivatives (mixed) of acyclic hydrocarbons.
		In general it should be noted that commodity detail from external trade statistics does not include: (a) transactions (non-dutiable) of less than £100 for 1986 and £200 for 1987, 1988 and 1989; (b) trade by firms operating in Shannon Free Airport; (c) postal packages not covered by customs entries.
	www.oireachtas-debates.gov.ie /D/0392/D.0392.198911070032.html (178 words)

	Representation of second derivatives as matrix element of effective interactions
		are local densities and currents, which are derived from the general density matrices for protons and neutrons
		The second derivatives of the energy functional in Eq.
		Last of all are the mixed functional derivatives involving both
	www.fuw.edu.pl /~dobaczew/qrpa16w/node10.html (464 words)

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