Abstract: A process for the production of liquid sugar by forming a sugar solution of water and natural sugar containing juice, adjusting the pH of a sugar solution to the range of from 1.0 to 2.0 to obtain an inverted juice, filtering the inverted juice, decolorizing the inverted juice to obtain sugar syrup, demineralizing the sugar syrup, evaporating the demineralized sugar syrup, and cooling the sugar syrup to form the liquid sugar.

Abstract: The present invention relates to a sugarcane juice spread and more particularly, the present invention relates to a sugarcane juice spread which incorporates ginger and cumin flavors and a process for preparing the same.

Abstract: A method for producing sugar or sugar-containing products from sugar-containing vegetable raw materials involves production the sugar or sugar-containing products in the presence of added natural food-compatible resins. An extraction liquid containing the natural food-compatible resins is used in the method. As a result of the method, sugar or sugar-containing product is manufactured that also includes the natural food-compatible resins.

Abstract: A method for producing a work product including the steps of receiving a first fluid composed of a liquid, a target substance and at least one residual substance; passing the first fluid through a first work station for separating the residual substance from the first fluid to produce a secondary fluid substantially composed of the liquid and the target substance; and treating the secondary fluid to reduce the proportion of the liquid relative to the target substance in the secondary fluid to form the work product.

Abstract: The present invention relates to an improved process for the preparation of ready-to-drink, shelf stable sugarcane juice beverage using a membrane-processing unit and subsequent pasterurization.

Abstract: A process for treating impure cane-derived sugar juice comprises subjecting, in a clarification stage, the juice to microfiltration/ultrafiltration to decrease the levels of suspended solids, organic non-sugar impurities and/or color therein. The resultant clarified sugar juice is sequentially passed through an ion exchange stage by bringing the juice into contact with a strong acid cation ion exchange resin in the hydrogen form, and thereafter into contact with an anion ion exchange resin in the hydroxide form. A purified sugar solution is withdrawn from the ion exchange stage, and concentrated to produce a syrup. The syrup is subjected to primary crystallization in a primary crystallization stage, to produce refined white sugar and primary mother liquor. The primary mother liquor is subjected to secondary crystallization in a secondary crystallization stage, to produce impure crystallized sugar and white strap molasses.

Abstract: The invention relates to a process for purifying a maltose-containing liquor from a undesired impurities, such as maltotriose. The process of the invention is characterized by nanofiltering said liquor and recovering a purified maltose solution as the permeate.

Abstract: The invention relates to a separation process of fractionating a solution comprising betaine and sucrose by subjecting said solution to chromatographic fractionation and nanofiltration and recovering a fraction enriched in betaine and optionally a fraction enriched in sucrose. The solution to be fractionated in accordance with the present invention is typically a sugar beet-derived solution, for instance a molasses solution.

Abstract: Method for producing refined sugar from sugared juice, such as raw juice from sugar cane or from sugar beet, containing sugar and impurities. The method includes the steps of tangential filtration of the sugared juice in order to obtain a retentate and a filtrate, softening of the filtrate in order to obtain a softened filtrate, concentration of the softened filtrate in order to obtain a softened syrup, chromatography of the softened syrup in order to obtain an extract enriched in sugars and a raffinate enriched in impurities, crystallisation of the extract in two or more crystallisation/separation steps in order to obtain refined sugar and a run-off, and combination of the run-off with the softened syrup in order that they are both subjected to the chromatography operation.

Abstract: Method for producing refined sugar from sugared juice, such as raw juice from sugar cane or from sugar beet, containing sugar and impurities. The method includes the steps of tangential filtration of the sugared juice in order to obtain a retentate and a filtrate, softening of the filtrate in order to obtain a softened filtrate, concentration of the softened filtrate in order to obtain a softened syrup, chromatography of the softened syrup in order to obtain an extract enriched in sugars and a raffinate enriched in impurities, crystallisation of the extract in two or more crystallisation/separation steps in order to obtain refined sugar and a run-off, and combination of the run-off with the softened syrup in order that they are both subjected to the chromatography operation.

Abstract: The invention relates to a chromatographic separation process of recovering mannose with high purity. The invention is based on the use of a chromatographic separation resin including a resin which is at least partly in a Ba2+ form resin and a resin which is in other than Ba2+ form.

Abstract: An improved corn wet milling process is disclosed in which a first stream comprising water, starch, and protein (e.g., gluten) is generated by separating fiber from wet milled de-germed corn particles (e.g. fiber separation step). Membrane filtration (e.g. starch-protein stream thickening) is performed on the first stream, producing a first retentate and a first aqueous permeate. The first retentate (e.g. thickened starch-protein stream) is separated into a second stream and a third stream (e.g. primary starch separation step). The second stream comprises water and a majority of the starch present in the first retentate, and the third stream comprises water and a majority of the protein (e.g., gluten) present in the first retentate. This process provides an economical means of recovering a higher percentage of the available cornstarch for inclusion in high value products.

Abstract: A method for separating sucrose and a second dissolved component from a sucrose-containing solution, preferably a beet-derived sucrose-containing solution, wherein the solution is subjected to a first fractionation by a continuous or sequential chromatographic simulated moving bed process to yield a sucrose-enriched fraction and a fraction enriched with the second dissolved component. The resulting fraction enriched with the second component is subjected to a second chromatographic fractionation that is a simulated moving bed or batch type process, to yield a second sucrose-enriched fraction and a second fraction enriched with the second dissolved component wherein both fractions have an improved yield or purity.

Abstract: The present deodorizing substance is obtained by treating a raw material selected from sugar cane juice and sugar cane-derived molasses by column chromatography, and characterized in that the substance is a fraction obtained by passing the aforesaid raw material through a column packed with a synthetic adsorbent as a fixed carrier and eluting ingredients adsorbed on said synthetic adsorbent with a solvent selected from water, methanol, ethanol and a mixture thereof. The present deodorizing substance is inexpensive and has high safety. It may be used widely in foods and environmental protection fields.

Abstract: A method for producing sugar or sugar-containing products from sugar-containing vegetable raw materials involves production the sugar or sugar-containing products in the presence of added natural food-compatible resins. An extraction liquid containing the natural food-compatible resins is used in the method. As a result of the method, sugar or sugar-containing product is manufactured that also includes the natural food-compatible resins.

Abstract: An embodiment of the present invention described and shown in the specification is a method for the preparation of a purified sugary juice from raw juices obtained from sacchariferous material of vegetable origin. The embodiment of the method that is disclosed includes the steps of coarse-filtering the raw juices, adding a suitable processing adjuvant to the juice, separating the juice from suspended phases and membrane-filtering the juice thus obtained. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. 37 CFR 1.72(b).

Abstract: A method of extracting and purifying recombinant protein(s) from transgenic sugarcane is disclosed. Fractioning of sugarcane juice that has been extracted from the cane stalks is obtained by using a multiple stage filtering process that uses multiple stages of decreasing porosity (preferably screening) followed by preferably membrane type filters, ion exchange, membrane adsorber, and chromatographic processes.

Abstract: A method for producing a work product including the steps of receiving a first fluid composed of a liquid, a target substance and at least one residual substance; passing the first fluid through a first work station for separating the residual substance from the first fluid to produce a secondary fluid substantially composed of the liquid and the target substance; and treating the secondary fluid to reduce the proportion of the liquid relative to the target substance in the secondary fluid to form the work product.

Abstract: A process for producing sugar from beets includes the step of filtering a sucrose-containing feed juice, which has been obtained from macerated sugar beets, through a first ultrafiltration membrane that has a first molecular weight cutoff. This ultrafiltration step produces a first ultrafiltration permeate and a first ultrafiltration retentate. The first ultrafiltration permeate is filtered through a second ultrafiltration membrane that has a second molecular weight cutoff that is lower than the first molecular weight cutoff. This second ultrafiltration step produces a second ultrafiltration permeate and a second ultrafiltration retentate. The second ultrafiltration permeate is nanofiltered through a nanofiltration membrane, thereby producing a nanofiltration permeate and a nanofiltration retentate.

Abstract: A nanofiltration process for obtaining sucrose uses a feed syrup, such as molasses, that comprises sucrose and no less than about 2% by weight invert sugars (on a dry solids basis). The nanofiltration produces a permeate and retentate. The nanofiltration permeate will comprise invert sugars that have passed from the feed through the nanofiltration membrane, and preferably will also comprise ash from the feed. The nanofiltration retentate has a higher concentration of sucrose and a lower concentration of invert sugars than the feed syrup. Sucrose can then be crystallized from the nanofiltration retentate. The reduction of the invert content in the syrup facilitates crystallization and thus enhances sucrose recovery.

Abstract: A process for producing sugar from cane includes the step of filtering a sucrose-containing feed juice, which has been obtained from macerated sugar cane, through a first ultrafiltration membrane that has a first molecular weight cutoff. This ultrafiltration step produces a first ultrafiltration permeate and a first ultrafiltration retentate. The first ultrafiltration permeate is filtered through a second ultrafiltration membrane that has a second molecular weight cutoff that is lower than the first molecular weight cutoff. This second ultrafiltration step produces a second ultrafiltration permeate and a second ultrafiltration retentate. The second ultrafiltration permeate is nanofiltered through a nanofiltration membrane, thereby producing a nanofiltration permeate and a nanofiltration retentate.

Abstract: A process for producing sugar from beets includes the step of filtering a sucrose-containing feed juice, which has been obtained by diffusion from sliced sugar beets, through a first ultrafiltration membrane that has a first molecular weight cutoff. This ultrafiltration step produces a first ultrafiltration permeate and a first ultrafiltration retentate. The first ultrafiltration permeate is filtered through a second ultrafiltration membrane that has a second molecular weight cutoff that is lower than the first molecular weight cutoff. This second ultrafiltration step produces a second ultrafiltration permeate and a second ultrafiltration retentate. The second ultrafiltration permeate is nanofiltered through a nanofiltration membrane, thereby producing a nanofiltration permeate and a nanofiltration retentate.

Abstract: The present invention relates to a process for producing sugar from beets, comprising the steps of: (a) macerating beets or pieces thereof; (b) mechanically separating juice from the macerated beets; and (c) membrane filtering the separated juice, producing a retentate and a permeate. The mechanical extraction of juice can be done on a moving porous vacuum filtration belt with countercurrent flow of macerated beets and water. The pH of the vacuum extracted juice can be adjusted to at least about 7 by addition of sodium hydroxide. This process does not use conventional beet diffusion. No lime and no carbon dioxide are required to be contacted with the juice or the permeate in this process.

Abstract: The present invention relates to a process for producing sugar from cane that includes the steps of: (a) grinding sugar cane or pieces thereof into pulp; (b) mechanically separating juice from the pulp; and (c) membrane filtering the separated juice, for example through a ultrafiltration membrane, producing a retentate and a permeate. Preferably in step (a), the cane is cut into pieces having an average fiber length of less than 10 millimeters, more preferably into pieces having an average fiber length of less than 5 mm with a fiber diameter of about 200 microns or less. The mechanical separation of juice from cane pieces can be done suitably by filtration or centrifugation. It is preferred to adjust the pH of the separated juice to at least about 7 prior to membrane filtration, more preferably to at least about 7.5, for example by adding lime or sodium hydroxide. The permeate can be evaporated and crystallized by conventional means to produce white sugar.

Abstract: Disclosed is a process for preparing an improved sugar product comprising (a) providing a raw sugar solution having color of 50 to 1,000 Icumsa units and a concentration of 10 to 70 Brix; (b)(1) injecting ozone into the raw sugar solution while imparting agitation to the solution effective to reduce the size of said color-imparting particles into smaller particles, and then (b)(2) discontinuing said injection, but continuing said agitation for a period of time in excess of the duration of step (b)(1), wherein said smaller particles react with ozone, and (c) optionally repeating steps (b)(1) and (b)(2) at least once, wherein the solution is at no point subjected to a precipitation or carbonation step.

Abstract: In the method raw starch is treated with the amylase with the enzyme classification EC 3.21.133 below the gelatinization temperature, whereafter the maltose and the limit dextrin are recovered. The method is simple and cheap and gives rise to a maltose of high purity and to a cheap limit dextrin useable as a fat replacer in foods.

Abstract: A nanofiltration process for obtaining sucrose uses a feed syrup, such as molasses, that comprises sucrose and no less than about 3% by weight invert sugars (on a dry solids basis). The nanofiltration produces a permeate and retentate. The nanofiltration permeate will comprise invert sugars that have passed from the feed through the nanofiltration membrane, and preferably will also comprise ash from the feed. The nanofiltration retentate has a higher concentration of sucrose and a lower concentration of invert sugars than the feed syrup. Sucrose can then be crystallized from the nanofiltration retentate. The reduction of the invert content in the syrup facilitates crystallization and thus enhances sucrose recovery.

Abstract: The present invention relates to a process for producing sugar from cane that includes the steps of: (a) grinding sugar cane or pieces thereof into pulp; (b) mechanically separating juice from the pulp; and (c) membrane filtering the separated juice, for example through a ultrafiltration membrane, producing a retentate and a permeate. Preferably in step (a), the cane is cut into pieces having an average fiber length of less than 10 millimeters, more preferably into pieces having an average fiber length of less than 5 mm with a fiber diameter of about 200 microns or less. The mechanical separation of juice from cane pieces can be done suitably by filtration or centrifugation. It is preferred to adjust the pH of the separated juice to at least about 7 prior to membrane filtration, more preferably to at least about 7.5, for example by adding lime or sodium hydroxide. The permeate can be evaporated and crystallized by conventional means to produce white sugar.

Abstract: The present invention relates to a process for producing sugar from beets, comprising the steps of: (a) macerating beets or pieces thereof; (b) mechanically separating juice from the macerated beets; and (c) membrane filtering the separated juice, producing a retentate and a permeate. The mechanical extraction of juice can be done on a moving porous vacuum filtration belt with countercurrent flow of macerated beets and water. The pH of the vacuum extracted juice can be adjusted to at least about 7 by addition of sodium hydroxide. This process does not use conventional beet diffusion. No lime and no carbon dioxide are required to be contacted with the juice or the permeate in this process.

Abstract: The present invention relates to a method of producing oligosaccharide syrups, in particular to the production of syrups having a high concentration of saccharides with a degree of polymerization of at least 2, comprising the steps of: enzymatic reaction of a substrate at a temperature in the range of 50° C. to 100° C. obtaining a saccharide solution comprising monosaccharides and disaccharides, trisaccharides and higher saccharides; nanofiltration of the saccharide solution at a temperature in the range of 60° C. to 100° C. obtaining a syrup essentially comprising disaccharides, trisaccharides and higher saccharides; recovering said syrup; optionally recycling the permeate resulting from the nanofiltration step to the enzymatic reaction.

Abstract: The present invention relates to a method for the production of saccharide preparations, i.e., syrups, by saccharifying a liquefied starch solution, which method comprises a saccharification step during which step one or more enzymatic saccharification stages takes place, and the subsequent steps of one or more high temperature membrane separation steps, and re-circulation of the saccharification enzyme, in which method the membrane separation steps are carried out as an integral part of the saccharification step. In another specific aspect, the invention provides a method of producing a saccharide preparation, which method comprises an enzymatic saccharification step, and the subsequent steps of one or more high temperature membrane separation steps and re-circulation of the saccharification enzyme.

Abstract: A method is provided for extracting and processing sugar cane juice from sugar cane sticks to produce a natural juice product. The method includes the steps of: providing sugar cane sticks having a high sucrose level; extracting sugar cane juice from the sugar cane sticks using a roller mill apparatus; filtering the extracted sugar cane juice through a screen filter; stabilizing the pH of the juice in a non-acidic solution of calcium hydroxide; flocculating the sugar cane juice with a mixture of water and at least one natural flocculate product; evaporating the sugar cane juice to form a sugar cane juice concentrate and extracting the sugar cane juice concentrate from the evaporator.

Abstract: The invention provides novel cationic flocculant dispersion polymers that can be utilized in the methods disclosed herein. This invention also provides methods for detecting cationic flocculants wherein said flocculants may be made via a dispersion process, a latex process or a dry polymer process. The flocculants are used to flocculate solids from liquid components of an industrial food process. The detection method involves the use of monoclonal antibodies to determine the presence or concentration of the cationic flocculants in the liquids.

Abstract: A process for purifying cane sugar from an aqueous composition thereof comprises the steps of (a) contacting an aqueous cane sugar feed composition with sufficient lime to increase the pH of the composition to at least about 9.5; (b) filtering the composition through a membrane having a pore size no greater than about 0.5 microns and having a molecular weight cutoff no less than about 5 kD, thereby producing a retentate and a permeate; and (c) contacting the permeate with sufficient carbon dioxide, or other materials designed to precipitate calcium and lower the pH, to adjust the pH to about 6.5-9.0. The feed composition preferably is cane juice, cane syrup, an aqueous composition of raw sugar, a cane sugar refinery stream, or a mixture of one or more such materials.

Abstract: Nanofiltration is used to decolorize sugar juice or syrup. The resulting permeate may be used directly to crystallize white sugar without an intermediate step of producing a raw sugar, even though the color of the permeate is substantially higher than the highest color that is acceptable in a conventionally decolorized syrup used to crystallize white sugar. Significant cost savings are thus achieved in producing white sugar.

Abstract: The invention relates to a process for preparing a crystalline &agr; anhydrous dextrose from a starch hydrolysate, characterized in that a starch hydrolysate is prepared, said starch hydrolysate is nanofiltered over membranes in a manner such as to obtain a nanofiltration permeate constituting a syrup with a high glucose content and a nanofiltration retentate, said syrup enriched in glucose is concentrated to a dry matter content of at least 70 wt. % of glucose and at a temperature in the range 50° C. to 110° C., said concentrated syrup is crystallized by evaporation and agitation in such a manner as to obtain a crystalline mass containing at least 30 wt. % of crystals and the crystals of &agr; anhydrous dextrose thus obtained are separated, recovered and dried.

Abstract: A process for purifying cane sugar from an aqueous composition thereof comprises the steps of (a) contacting an aqueous cane sugar feed composition with sufficient lime to increase the pH of the composition to at least about 9.5; (b) filtering the composition through a membrane having a pore size no greater than about 0.5 microns and having a molecular weight cutoff no less than about 5 kD, thereby producing a retentate and a permeate; and (c) contacting the permeate with sufficient carbon dioxide, or other materials designed to precipitate calcium and lower the pH, to adjust the pH to about 6.5-9.0. The feed composition preferably is cane juice, cane syrup, an aqueous composition of raw sugar, a cane sugar refinery stream, or a mixture of one or more such materials.

Abstract: The present invention relates to a method for the production of saccharide preparations, i.e., syrups, by saccharifying a liquefied starch solution, which method comprises a saccharification step during which step one or more enzymatic saccharification stages takes place, and the subsequent steps of one or more high temperature membrane separation steps, and re-circulation of the saccharification enzyme, in which method the membrane separation steps are carried out as an integral part of the saccharification step. In another specific aspect, the invention provides a method of producing a saccharide preparation, which method comprises an enzymatic saccharification step, and the subsequent steps of one or more high temperature membrane separation steps and re-circulation of the saccharification enzyme.

Abstract: The invention concerns a process for the manufacture of a starch hydrolysate with high dextrose content comprising the stages of:(a) liquefying starch milk with the aid of an .alpha.-amylase so as to obtain a liquefied starch milk;(b) saccharifying the liquefied starch milk, with the aid of a glucogenic enzyme, to obtain a raw saccharified hydrolysate;(c) separating the raw saccharified hydrolysate by nanofiltration over membranes so as to collect a nanofiltration permeate constituting said starch hydrolysate with high dextrose content and a nanofiltration retentate.

Abstract: Nanofiltration is used to decolorize sugar juice or syrup. The resulting permeate may be used directly to crystallize white sugar without an intermediate step of producing a raw sugar; even though the color of the permeate is substantially higher than the highest color that is acceptable in a conventionally decolorized syrup used to crystallize white sugar. Significant cost savings are thus achieved in producing white sugar.

Abstract: The invention relates to a method for the fractionation of molasses using a chromatographic simulated moving bed system in which the liquid flow is effected in a single direction in a system comprising at least two chromatographic partial packing material beds. In the method of the invention, the product or products are recovered during a multi-step sequence comprising the following phases: feeding phase of molasses, eluting phase and recycling phase. The liquid present in the partial packing material beds with their dry solids profile is recycled in the recycling phase in a loop comprising one, two or several partial packing material beds.

Abstract: A composition for use as a processing aid in the concentration of whole cheese whey and in the recovery of lactose from cheese whey by a separation process followed by a concentrating process via reverse osmosis filtration or evaporation, wherein, in one embodiment, the composition includes a sodium hexametaphosphate having phosphate chain lengths of 12 to 28 in combination with tetrasodium or tetrapotassium pyrophosphate. In another embodiment, a blend of sodium hexametaphosphate is employed having a phosphate chain lengths of 12 to 14 in one instance and 21 to 28 in another instance. The composition results in increased yields of lactose and an easily removable scale from processing equipment-mainly heat transfer equipment. A method of employing the processing aid composition is also presented.

Abstract: A method of providing a stabilized sugar cane juice product for use in soft drinks, that includes providing cleaned sugar cane sticks and extracting cane juice from the sticks. Thereafter, the extracted cane juice is acidified immediately upon extraction by feeding it into a solution comprising ascorbic acid for preventing discoloration of the cane juice and also by feeding it simultaneously into an acidic solution of one of citric acid, malic acid, tartaric acid, phosphoric acid and a mixture thereof, for lowering the pH of the cane juice below a pH of 5. Furthermore, one of a sodium citrate solution, a potassium citrate solution, a sodium phosphate di-basic solution or a mixture thereof, is added to the cane juice for stabilizing it. The cane juice is then coagulated and flocculated to remove unwanted foulants and aromas.

Abstract: Diffusion juice of a sugar plant is heated under stable sucrose conditions, notably alkaline pH, and held above 70.degree. C. for sufficient duration to effect significant agglomeration. The agglomerated particulates are removed by phase separation procedures, leaving a clarified juice containing a very low, typically 0.1-0.5 volume percent, solids load.

Abstract: A food starch seperator comprising a serially connected centrifuge and a membrane seperator further comprising a sintered pipe providing pore flow paths including a pumped source of food plant liquor, outputs for the centrifuge and membrane seperator and a control system to regulate the flow of the food plant liquor.

Abstract: The present invention provides a process for the preparation of a noncentrifugal sugar composition. The process comprises the following steps: cane juice is filtered; a pH of the juice is adjusted to 5.0-6.0; sucrose or liquid sucrose or both is added to adjust a purity of the mixture to a range of 87.0 to 95.1% by weight; the mixture is heated and evaporated; and then the mixture is cooled to solidify with a strong shearing force being applied to obtain granules.

Abstract: A process for decolorizing sugar solutions by contacting them with highly crosslinked, macroporous copolymers functionalized with weak-acid or weak-base ion exchange functional groups is disclosed. Treatment of sugar syrups using macroporous functionalized adsorbents allows for multiple regeneration cycles without loss of sugar decolorization properties.

Abstract: A process is described for clarifying a crude inulin extract by ultrafiltration and separating an aqueous inulin solution containing carbohydrates having a range of degrees of polymerization into fractions having different average degrees of polymerization which comprises subjecting an aqueous inulin solution to ultrafiltration through a membrane having a predetermined pore size whereby inulin fractions having average degrees of polymerization less than a predetermined value pass through said membrane as permeate and inulin fractions having average degrees of polymerization greater than said predetermined value are collected as retentate.

Abstract: A method and an apparatus for performing a continuous reaction with at least one liquid reaction phase incorporating at least one starting compound in the presence of at least one solid-phase catalyst, wherein the phases to be contacted are circulated through at least one pulsed reaction column (1). The liquid reaction phase is continuously fed into the middle or lower portion of the pulsed column (1), the liquid phase is circulated upwards through the pulsed column (1), and a counterflow made up of lumps (9) of a solid selective extraction compound is continuously circulated. Furthermore, each solid catalyst is continuously circulated through the pulsed column (1) in contact with the liquid phase.

Abstract: The present invention is related to a process for refining raw sugar comprising the steps of: (a) dissolving either washed raw sugar or raw sugar directly to produce a melter liquor; (b) clarifying the melter liquor; (c) crystallising the melter liquor to produce a mixture of a very low colour intermediate sugar and a syrup; (d) separating the very low colour intermediate sugar from the syrup; (e) redissolving the separated very low colour intermediate sugar to produce a fine liquor; (f) filtering the fine liquor to remove any foreign particles which may have contaminated the sugar produced in step (d); and (g) crystallising refined sugar from the fine liquor. The invention is also related to a process for producing very low colour (VLC) intermediate sugar by the steps of (a) to (d) defined above.