Abstract: Photoresist monomers, photoresist polymers prepared therefrom, and photoresist compositions using the polymers are disclosed. More specifically, photoresist polymers comprising a photoresist monomer containing fluorine-substituted benzylcarboxylate represented by Formula 1, and a composition comprising the polymer are disclosed. The photoresist composition has excellent etching resistance, heat resistance and adhesiveness, and can be developed in aqueous tetramethylammonium hydroxide (TMAH) solution. And, the present photoresist composition is suitable to form a fine pattern using deep ultraviolet light source such as VUV (157 nm), since the composition has low light absorbance at 193 nm and 157 nm wavelength. wherein, X1, X2, R1, l and m are defined in the specification.

Abstract: Fluoroolefin/acid group or protected acid group-containing copolymers for photoresist compositions and microlithography methods employing the photoresist compositions are described. These copolymer compositions comprise 1) at least one fluoroolefin, preferably hexafluoroisobutylene, and 2) an acid group or a protected acid group (e.g., a t-alkyl ester, preferably a t-butyl ester), which together impart high ultraviolet (UV) transparency and developability in basic media to these materials. The materials of this invention have high UV transparency, particularly at short wavelengths, e.g., 157 nm and 193 nm, which makes them useful for lithography at these short wavelengths.

Abstract: Covalently-bound, hydrophilic copolymer coatings for implants are disclosed. The copolymer coatings comprise a hydrophobic aryl acrylic monomer, a hydrophilic monomer selected from the group consisting of hydroxyalkyl (meth)acrylates, n-vinyl pyrrolidone and acrylamides, and a reactive plasticizer.

Abstract: The present invention provides a vinylpyrrolidone (co)polymer excellent in the color tone and the thermal yellowing resistance despite its low molecular weight. The vinylpyrrolidone (co)polymer, according to the present invention, is a vinylpyrrolidone (co)polymer which has a Hazen value of not more than 30 in the form of 5% aqueous solution and a K value of not more than 60 and is obtained by a process including the step of polymerizing a polymerizable monomer component with an azo compound initiator and/or an organic peroxide initiator, wherein the polymerizable monomer component includes N-vinylpyrrolidone, and wherein the azo compound initiator has a chemical structure as shown by —C(CH3)2—N═N—C(CH3)2—, and wherein the organic peroxide initiator is soluble in water or ethyl alcohol of 25° C. in an amount of not smaller than 3 weight %.

Abstract: The invention is related to non-linear olefin-carbon monoxide copolymer composition which is derived from an olefin feedstream and a synthesis gas feedstream. The invention is also related to a method for preparing olefin-carbon monoxide copolymers by heating an olefin feed and a synthesis gas feed in the presence of a free radical polymerization initiator. More particularly, the synthesis gas feed comprises predominantly carbon monoxide and hydrogen. The copolymers of the invention are useful as polyvinyl chloride plasticizers.

Abstract: A new, facile, general one-phase method of generating thio-functionalized transition metal nanoparticles and surfaces modified by (co)polymers synthesized by the RAFT method is described. The method includes the stops of forming a (co)polymer in aqueous solution using the RAFT methodology, forming a colloidal transition metal precursor solution from an appropriate transition metal; adding the metal precursor solution or surface to the (co)polymer solution, adding a reducing agent into the solution to reduce the metal colloid in situ to produce the stabilized nanoparticles or surface, and isolating the stabilized nanoparticles or surface in a manner such that aggregation is minimized. The functionalized surfaces generated using these methods can further undergo planar surface modifications, such as functionalization with a variety of different chemical groups, expanding their utility and application.

Abstract: A free radical polymerization process is provided which comprises polymerizing at least one radically polymerizable monomer in the presence of the multi-component liquid azo-peroxide initiator mixture under polymerization conditions to provide a radically polymerized homopolymer or copolymer, the multi-component liquid azo-peroxide initiator mixture comprising (a) at least 6 different azodinitriles; and (b) one or more liquid organic peroxides. Also provided is the stable multi-component liquid azo-peroxide initiator mixture.

Abstract: The present invention provides a vinylpyrrolidone (co)polymer excellent in the color tone and the thermal yellowing resistance despite its low molecular weight. The vinylpyrrolidone (co)polymer, according to the present invention, is a vinylpyrrolidone (co)polymer which has a Hazen value of not more than 30 in the form of 5% aqueous solution and a K value of not more than 60 and is obtained by a process including the step of polymerizing a polymerizable monomer component with an azo compound initiator and/or an organic peroxide initiator, wherein the polymerizable monomer component includes N-vinylpyrrolidone, and wherein the azo compound initiator has a chemical structure as shown by —C(CH3)2—N═N—C(CH3)2—, and wherein the organic peroxide initiator is soluble in water or ethyl alcohol of 25° C. in an amount of not smaller than 3 weight %.

Abstract: The present invention relates to partially branched polymers having a number-average molecular weight Mn in the range from 500 to 20 000 daltons and synthesized from ethylenically unsaturated monomers including:

Abstract: The invention concerns a method for preparing a first generation polymer comprising a step which consists in radical polymerization of a composition containing: at least an ethylenically unsaturated monomer a free radical source, and at least a disulfide compound.

Abstract: A chlorotrifluoroethylene homopolymer is prepared by polymering chlorotrifluoroethylene monomers in an ester solvent and in the presence of t-butyl peroxypivalate as a radical initiator. The polymerization application can be carried at about 60° C., and the resulting chlorotrifluoroethylene homopolymer has a number average molecular weight of about 1700.

Abstract: Photoresist monomers of following Formula 1, photoresist polymers thereof, and photoresist compositions using the same. The photoresist composition has excellent etching resistance, heat resistance and adhesiveness, and is developable in aqueous tetramethylammonium hydroxide (TMAH) solution. In addition, the photoresist composition has low light absorbance at the wavelength of 193 nm, 157 nm and 13 nm, and thus is suitable for a photolithography process using ultraviolet light sources such as VUV (157 nm) and EUV (13 nm) in fabricating a minute circuit for a high integration semiconductor device. wherein, R1, R2, R3, Y, W, m and n are as defined in the specification.

Abstract: The invention is accomplished with a curable composition, which contains a resin component A with a subsidiary component a, a resin, which can be polymerized by free radicals, and a curing agent component B with a subsidiary component b, a peroxide curing agent. Before use of the curable composition, the components A and B are kept spatially separated and curing takes place only after components A and B have been mixed. To improve such curable compositions, it is proposed that a subsidiary component c, the leuco form of a dye, especially of a triphenylmethane dye, be added to component A. By following such a procedure, it is achieved that the peroxide activity and the progress of the mixing are monitored simultaneously without delaying the curing of the composition.

Abstract: Biodegradable anionic polymers are disclosed which include recurring polymeric subunits preferably made up of dicarboxylic monomers such as maleic anhydride, itaconic anhydride or citraconic anhydride. Free radical polymerization is used in the synthesis of the polymers. The polymers may be complexed with ions and/or mixed with fertilizers or seeds to yield agriculturally useful compositions. The preferred products of the invention may be applied foliarly or to the earth adjacent growing plants in order to enhance nutrient uptake by the plants.

Abstract: Compounds corresponding to formula (I)

Abstract: A new polymerization process (atom transfer radical polymerization, or ATRP) based on a redox reaction between a transition metal (e.g., Cu(I)/Cu(II), provides “living” or controlled radical polymerization of styrene, (meth)acrylates, and other radically polymerizable monomers. Using various simple organic halides as model halogen atom transfer precursors (initiators) and transition metal complexes as a model halogen atom transfer promoters (catalysts), a “living” radical polymerization affords (co)polymers having the predetermined number average molecular weight by &Dgr;[M]/[I]0 (up to Mn>105) and a surprisingly narrow molecular weight distribution (Mw/Mn), as low as 1.15. The participation of free radical intermediates in ATRP is supported by end-group analysis and stereochemistry of the polymerization. In addition, polymers with various topologies (e.g.

Abstract: A method of making a copolymer composition containing a copolymer, which includes the steps of (a) providing a donor monomer composition that includes an isobutylene type monomer; (b) mixing the donor monomer composition with an ethylenically unsaturated monomer composition that includes one or more ethylenically unsaturated acceptor monomers, and is substantially free of maleate type monomers and fumarate type monomers, and (c) polymerizing the mixture resulting from step (b) in the presence of a free radical polymerization initiator. The polymerization is carried out in the substantial absence of Lewis acids and/or transition metals. The isobutylene type monomer is present at a molar excess of at least 10 mol % based on the molar concentration of monomers in the ethylenically unsaturated monomer composition. The ethylenically unsaturated acceptor monomers are present in an amount of at least 15 mol % of the total monomer composition.

Abstract: In a process for polymerizing ethylene and, if desired, further monomers in a high-pressure reactor at from 140 to 320° C. and pressures of from 1000 to 4000 bar, but in any case under pressure and temperature conditions under which water displays supercritical behavior, water is introduced continuously or intermittently into the reactor.

Abstract: In a process for preparing ethylene-vinyl acetate copolymers in which a mixture of ethylene and vinyl acetate is polymerized continuously in the presence of free-radical polymerization initiators and, if desired, molecular weight regulators in a cooled tube reactor at a pressure in the range from 1000 to 3500 bar, and the poly-merization initiator is added at the beginning and at two or more points along the tube reactor, and temperature changes in the reaction mixture along the tube reactor, between the first temperature maximum and the last addition of the polymerization initiator, are within a range of not more than 20° C.

Abstract: There is provided: a (meth)acrylic acid (salt) polymer which has high properties and is little colored; and a process which can produce this polymer with a high polymerization conversion without causing the corrosion of the reaction vessel.

Abstract: A radical (co)polymerization of ethylene is carried out under high pressure in the presence of at least one initiating free radical (Z&Circlesolid;) and of at least one controlling stable free radical (SFR&Circlesolid;) which comprises the indoline nitroxide backbone represented by the formula (I). Mention may be made, by way of examples, of the radicals (SFR&Circlesolid;) of formula (II).

Abstract: A compound of Formula 10, an organic anti-reflective polymer having the structure of Formula 1 synthesized from the compound of Formula 1 and a preparation method thereof. An anti-reflective coating composition including the above organic anti-reflective polymer, as well as a preparation method of an anti-reflective coating. The anti-reflective coating comprising the disclosed polymer eliminates standing waves caused by the optical properties of lower layers on the wafer and by the changes in the thickness of the photoresist, prevents back reflection and also solves the problem of CD alteration cause by the diffracted and reflected light from such lower layers. Such advantages enable the formation of stable ultrafine patterns suitable for 64M, 256M, 1G, 4G, and 16G DRAM semiconductor devices and an increase of the production yields.

Abstract: A process is provided for producing ethylene (co)polymer nanocomposites in a high pressure polymerization reactor. The process by which nanocomposites having organically modified clays incorporated and intimately dispersed therein involves polymerizing ethylene and one or more optional comonomers under high pressure polymerization conditions in the presence of an organic peroxide initiator and organically modified clay.

Abstract: This invention concerns a process for production of copolymers, especially functionalized, or, at least partially fluorinated copolymers by means of a polymerization process comprising: co-polymerizing, in aqueous emulsion, one or more monomers selected from the group consisting of tetrafluoroethylene, trifluoroethylene, vinylidene fluoride, vinyl fluoride, ethylene, chorotrifluoroethylene, hexafluoropropylene, perfluoromethyl vinyl ether, and perfluoroethyl vinyl ether with a fluorinated co-monomer having limited water solubility, said comonomer being dispersed in the form of droplets of certain sizes.

Abstract: The use of concurrent reverse and normal initiation processes in an ATRP enables the use of highly active catalysts under “reverse ATRP” conditions and leads to the synthesis of well-defined polymers with low molecular weight distributions while employing much lower levels of the transition metal in the system. This dual activation/initiating system allows use of active catalysts that are added to the reaction in an oxidatively stable form. The benefits of this dual initiating system can be attained in bulk, solution and multi-phase ATRP processes, including emulsions, miniemulsions and polymerization from surfaces.

Abstract: Anaerobic adhesive compositions, the reaction products of which demonstrate improved cure speed and bond strength are disclosed. A high percentage of ultimate bond strength is reached within the first hour of room temperature cure. Higher ultimate bond strengths as compared to conventional compositions are achieved. The anaerobic adhesive compositions incorporate an adhesion promoter which contributes to these properties.

Abstract: The invention relates to a method of forming carbon monoxide-containing polymers from multi-component syngas feeds and at least one vinyl comonomer. Feeds useful in the practice of the invention comprise ethylene in an amount ranging from about 5 to about 40 mole %, carbon monoxide is an amount ranging from about 1 to about 40 mole %, hydrogen in an amount ranging from about 4 to about 55 mole %, carbon dioxide in an amount ranging from about 3 to about 10 mole %, and methane in an amount ranging from about 4 to about 85 mole %. The feed may also include acetylene in an amount ranging up to about 10 mole %. The feed may contain at least one free radical-polymerizable vinyl comonomer, or a cofeed containing such a comonomer can be used.

Abstract: The present invention provides a polymer that can be used as an anti-refelctive coating (ARC) polymer, an ARC composition comprising the same, methods for producing the same, and methods for using the same. The polymer of the present invention is particularly useful in a submicrolithographic process, for example, using KrF (248 nm) or ArF (193 nm) lasers as a light source. The polymer of the present invention comprises a chromophore that is capable of absorbing light at the wavelengths used in a submicrolithographic process. Thus, the ARC of the present invention significantly reduces or prevents back reflection of light and the problem of the CD alteration caused by the diffracted and/or reflected light. The ARC of the present invention also significantly reduces or eliminates the standing wave effect and reflective notching.

Abstract: Process for the copolymerization of free radical polymerizable comonomers such as vinyl acetate with an unsaturated diester such as diakyl fumarate which is carried out in the presence of water to produce copolymers such as fumarate vinyl acetate copolymers useful as lubricating oil and fuel oil additives, for example, as wax crystal modifiers and flow improvers.

Abstract: Disclosed is a process which comprises (a) reacting allyl bromide with diethyl amine in a molar ratio of at least about 1 mole of allyl bromide per about 1.15 moles of diethyl amine and in a molar ratio of no more than about 1 mole of allyl bromide per about 2 moles of diethyl amine, thereby generating allyl diethyl amine in a monomer reaction mixture; (b) subsequently filtering the monomer reaction mixture to remove impurities; (c) subsequently reacting the allyl diethyl amine with allyl bromide, thereby generating solid diallyl diethyl ammonium bromide; (d) subsequently isolating the solid diallyl diethyl ammonium bromide; (e) subsequently dissolving the diallyl diethyl ammonium bromide in a solvent and adding thereto a polymerization initiator to form a polymerization reaction mixture; (f) subsequently heating the polymerization reaction mixture in a vessel equipped with a reflux condenser to a temperature of from about 90 to about 100° C.

Abstract: A process for production of a polyolefin-based composite material of high rigidity, containing a polyolefin and a layered clay, involves impregnating a layered, swellable clay which is interstratified with a tetraalkyl cation, with at least one polymerizable monomer and then mixing this impregnated clay with a polyolefin and a peroxide, at a temperature above the melting point of the polyolefin. A polyolefin-based composite material containing 98-50 wt. % of a polyolefin, 1-50 wt. % of another homo- or copolymer and 1-50 wt. % of a layered clay, wherein the ratio between the modulus of elasticity of the material and that of the initial polyolefin, at a temperature which is 30° C. below the melting temperature of the polyolefin, is higher than or equal to 1 has high rigidity.

Abstract: The invention pertains to a method for producing ethylene homopolymerizates and ethylene copolymerizates exhibiting a lower mass density of up to 0.930 g/cm3 and a melt index ranging from 0.15 to 25 g/10 min (2.16 kg; 463 K). Said polymerizates exhibit an improved processing stability and improved availability in the installation at pressures greater than 1000 bar and at temperatures of up to 603 K. The polymerizates are produced in tubular reactors in the presence of radical-forming initiators, oxygen thereunder and chain transfer agents, of which at least one comprises an aldehydic structure. According to the inventive method, chemokinetic characteristics of the reactive feed materials (thermal half-life periods, concentrations, dosing quantities) are coupled with fluidically relevant characteristics of the tubular reactor (flow rate) while taking the target product quality (melt index, flow figure) into consideration.

Abstract: A continuous process for oligomers which do not contain, as polymerized units, carboxylic acid-containing monomers and their salts, including the steps of: (1) forming a reaction mixture, substantially free of carboxylic acid-containing monomers and their salts, containing: (i) 0.5 to 99.95% by weight of the reaction mixture of at least one ethylenically unsaturated monomer; and (ii) 0.05 to 25% by weight, based on the weight of the ethylenically unsaturated monomer, of at least one free-radical initiator; and (2) continuously passing the reaction mixture through a heated zone wherein the reaction mixture is maintained at a temperature of at least 150° C. and a pressure of at least 30 bars for from 0.1 seconds to 4 minutes to form terminally-unsaturated oligomers. In addition, processes for forming oligomers of vinyl acetate and oligomers of vinyl alcohol are disclosed. Mixtures of fully saturated and terminally unsaturated oligomers are also disclosed.

Abstract: A method for polymerization of substituted ethylene monomers in an enzyme-mediated process is disclosed. The reaction proceeds under mild conditions with a wide variety of monomers, and is capable of producing stereoregular polymers. In certain embodiments, no organic solvent is necessary.

Abstract: The present invention provides (1) a thermopolymerizable composition containing a thermopolymerizable compound having (meth)acrylate having a moiety consisting of oxyalkylene, fluorocarbon, oxyfluorocarbon and/or carbonate group within the molecule, an electrolyte salt, an organic polymerization initiator having no benzene ring, and a polymerization retarder having vinyl group within the molecule, (2) a solid electrolyte obtained by heat-curing the composition, (3) a primary battery, a secondary battery and an electric double-layer capacitor each using the solid electrolyte, and processes for manufacturing the same.

Abstract: Preparing pigment preparations by mixing a dyestuff with a monomer and simultaneously polymerizing the monomers in an extruder at elevated temperatures, wherein the following steps are carried out:

Abstract: The invention provides a process for producing a saponified vinyl acetate polymer (a saponified ethylene-vinyl acetate copolymer in particular) which features a minimum of coloration of molding pellets, a well-inhibited emanation of an odor in melt-molding, a high transparency of the product film and a low incidence of fish-eyes in the film, and a process for producing a vinyl acetate polymer (particularly an ethylene-vinyl acetate copolymer) for use as the starting material for said saponified vinyl acetate polymer having said favorable properties. In accordance with the invention, either vinyl acetate alone or vinyl acetate and one or more other monomers are polymerized in the presence of a hydroxylactone compound and a polymerization catalyst. The resulting vinyl acetate polymer (particularly the ethylene-vinyl acetate copolymer) is then saponified.

Abstract: An aqueous composition suitable for use, when dry, as an improved coating is provided including an aqueous emulsion polymer, the polymer having a glass transition temperature (Tg) from greater than 20° C. to 80° C., formed by the free radical polymerization of at least one ethylenically unsaturated nonionic acrylic monomer and 0-7.5%, by weight based on the total weight of the polymer, ethylenically unsaturated acid monomer in the presence of 0.01-1.0%, by weight based on the total weight of the polymer, t-alkyl hydroperoxide, t-alkyl peroxide, or t-alkyl perester wherein the t-alkyl group includes at least 5 Carbon atoms and, optionally, at least one other oxidant. A method of preparing the emulsion polymer is also provided.

Abstract: The present invention is directed to precipitation polymerization processes for the manufacture of essentially non-crosslinked polymers prepared from N-vinyl acetamide monomer which exhibit reduced levels of residual non-polymerizable contaminants, particularly residual acetamide, the processes including the steps of contacting the N-vinyl acetamide monomer with a polymerization medium containing a diluent selected from ethyl acetate and acetone and a free-radical initiator, under conditions effective to polymerize the N-vinyl acetamide monomer, thereby forming a precipitate of the polymer in the polymerization medium; and isolating the precipitated polymer from the polymerization medium.

Abstract: Disclosed is a method for producing polymer/silicate nanocomposites via emulsion polymerization, which comprises the steps of:

Abstract: A radical (co)polymerization of ethylene is carried out under high pressure in the presence of at least one initiating free radical (Z•) and of at least one controlling stable free radical (SFR•) which comprises the indoline nitroxide backbone represented by the formula (I). A is a hydrocarbonaceous chain forming an aromatic ring with the two carbon atoms to which it is attached, this ring being able to carry substituents or being able to carry one or more rings placed side by side, which rings are aromatic or aliphatic and optionally substituted, the carbon atoms forming the nitrogenous ring and in the alpha- and beta-position with respect to the nitrogen atom being able to carry hydrogen atoms or substituents.

Abstract: It has been discovered that the polymerization of unsaturated compounds, such as butadiene, may be inhibited by the addition of a diene and/or alkanolamine inhibitor. The inhibitor is believed to catalytically destroy peroxides present, such as hydrogen peroxide, which may be present in trace amounts. Particularly useful inhibitors include, but are not limited to, ethylenediamine (EDA) and monoethanolamine (MEA).

Abstract: The present invention relates to a process for the preparation of grafted polymers wherein in a first step A) a stable nitroxyl radical is grafted onto a polymer, which step comprises heating a polymer and a stable nitroxyl radical (NO.); and in a second step B) the grafted polymer of step A) is heated in the presence of an ethylenically unsaturated monomer or oligomer to a temperature at which cleavage of the nitroxyl-polymer bond occurs and polymerization of the ethylenically unsaturated monomer or oligomer is initiated at the polymer radical; maintaining said temperature for further polymerization and afterwards cooling down the mixture to a temperature below 60° C. Further subjects are grafted polymers prepared by said process, the use of the polymeric radical initiator and the use of NO radicals for grafting polymers.

Abstract: An anaerobic adhesive composition having enhanced toughness and resistance to crack propagation, particularly subsequent to thermal exposure, comprising a combination of three monomers consisting of (a) at least one (meth)acrylate monomer, (b) at least one (meth)acrylate-terminated urethane modified acrylonitrile/butadiene prepolymer, and (c) at least one (meth)acrylate-terminated acrylic/polyisocyanate adduct.

Abstract: The invention relates to a low-density polyethylene resin for laminates, a composition thereof, and a laminate and production method therefor. The low-density polyethylene resin is one obtainable by a high pressure radical polymerization method and has a density of 0.910 to 0.935 g/cm3, a melt flow rate of 0.1 to 300 g/10 min., and a terminal vinyl group number of 0.4 or more per 1,000 carbon atoms. According to the invention, a laminate having high interlayer adhesion strength can be obtained also by low-temperature, high-speed molding so that the occurrence of smoking and odor can be prevented. Also, the resin is excellent in productivity and economics. Further, the resin is excellent in productivity and economics because it can be readily made thinner. The laminate is suitable for application to, for example, food wrapping materials, containers, etc.

Abstract: A method for continuously preparing a heat resistant &agr;-methylstyrene-acrylonitrile copolymer by bulk polymerization, comprising the steps of: a) Continuously charging a mixture of monomers including following materials into a continuous polymerization system with two or more stirred-vessel reactors connected in series: i) 60 to 75% (by weight of Yá-methylstyrene; ii) 25 to 40% by weight of acrylonitrile; iii) 5 to 15% by weight of a solvent, and iv) 0.05 to 0.3% by weight of a mixed initiator of an organic peroxide with a multifunctional group and an organic peroxide with a monofunctional group, b) Continuously polymerizing the monomer mixture charged at step a) starting from the first reactor to convert 50 to 70% by weight of total charged monomers into a polymer; and c) transferring reacted liquid containing the polymer from step b) to an evaporator, and then separating the polymer by evaporating unreacted monomers and solvents.

Abstract: Disclosed is a process which comprises (a) reacting allyl bromide with diethyl amine in a molar ratio of at least about 1 mole of allyl bromide per about 1.15 moles of diethyl amine and in a molar ratio of no more than about 1 mole of allyl bromide per about 2 moles of diethyl amine, thereby generating allyl diethyl amine in a monomer reaction mixture; (b) subsequently filtering the monomer reaction mixture to remove impurities; (c) subsequently reacting the allyl diethyl amine with allyl bromide, thereby generating solid diallyl diethyl ammonium bromide; (d) subsequently isolating the solid diallyl diethyl ammonium bromide; (e) subsequently dissolving the diallyl diethyl ammonium bromide in a solvent and adding thereto a polymerization initiator to form a polymerization reaction mixture; (f) subsequently heating the polymerization reaction mixture in a vessel equipped with a reflux condenser to a temperature of from about 90 to about 100° C.

Abstract: The present invention relates to anaerobic adhesive compositions which have been optimized using experimental design techniques to produce desired physical properties. A simplified cure system is disclosed which permits enhanced fixture and cure times.

Abstract: Disclosed are methods of preparing solution polymers and compositions derived therefrom.

Abstract: A new class of “living” free radical initiators that are based on alkylperoxydiarylborane and its derivatives and that may be represented by the general formula.