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Based on the methods of the theory of bifurcations, the problem of perturbation of linear equations by small analytic terms is considered. In contrast to the work of Trenogin [7], the case of an incomplete generalized Jordan set of a linear Fredholm operator acting from one Banach space to another Banach space is studied. A technique is proposed that uses the regularization of the Fredholm operator by a specially constructed finite-dimensional operator.

In this a paper perturbations of multiple eigenvalues of E. Schmidt spectral problems is considered. At the usage of the reductional method suggested in the articles [10, 11] the investigation of the multiple E. Schmidt perturbation eigenvalues is reduced to the investigation of perturbation of simple ones. At the end, as application of the obtained results the problem about the boundary perturbation for the system of two Sturm-Liouville problems with E. Schmidt spectral parameter is considered.

We use the reduction method, which allows one to reduce the study of perturbations of multiple eigenvalues to perturbations of simple eigenvalues, to analyze the general perturbation problem for Fredholm points of the discrete spectrum of linear operator functions analytically depending on the spectral parameter. The same method is used to study a perturbation of multiple Fredholm points of the discrete Schmidt spectrum (s-numbers) of a linear operator. We present an example of a problem on a perturbation of the domain of the Sturm–Liouville problem for a second-order differential operator.

We consider the computation of simple and multiple eigenvalues and the corresponding eigenelements of a multiparameter eigenvalue problem in the sense of Atkinson by the reduction pseudoperturbation method. Namely, we regularize the original operator functions by finite-dimensional linear operators, thus reducing the case of multiple eigenvalues to that of simple ones.

Carbohydrates from leaves, stems, and tubers of cultivated Helianthus tuberosus were studied. The quantitative contents of mono- and oligosaccharides, water-soluble polysaccharides, pectinic substances, and hemicellulose were determined. The qualitative monosaccharide composition and physical chemical properties were found. The amino-acid composition was determined. It was shown that syrup from the tubers exhibited hypoglycemic activity.

Dry extracts from roots and stems of Alcea rosea were prepared. Their chemical composition was studied by characterizing the carbohydrate, protein, and elemental compositions.

Structures of glucofructans isolated from Cousinii radians roots were studied by methylation, periodate oxidation, and IR and 13C NMR spectroscopies. It was found that fructofuranose units were bonded to each other by inulin-type β-(2→1)-gylcoside bonds.

By MNDO quantum-chemical semiempirical method it is simulated processes of formation of radiation defects in irradiated alcali metal sulphates. They are defined energies of anionic complex dissociation and formation of O3– of centre, as effect of stabilization of initial hole O0-centres. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Native acetylated glucomannan of molecular weight (MW) 32000 with a glucose:mannose ratio 1:30 was isolated from bulbs of Narcissus poeticus. Glucomannan was depolymerized to a fragment of MW 15000 with an unchanged primary structure and was studied using PMR and 13C NMR spectroscopy. It was found that the linear chain of the biopolymer consists of β→1-4-bound D-gluco- and D-mannopyranose units and the O-Ac groups are localized on C-2, C-3, and C-6 hydroxyls in certain anhydromannose units.

Roots of Arctium tomentosum (Compositae) were found to contain water-soluble polysaccharides (glucofructans), pectinic substances, and hemicellulose. The structure of the glucofructan was established by chemical methods and IR and 13C NMR spectroscopies.

The structure of the branched polysaccharide glucoarabinogalactan was investigated by periodate oxidation, methylation, and 13C NMR spectroscopy. The main chain consists of α-1→6-bonded galactopyranoses. 1→2-Bonded D-glucopyranoses and 1→3-bonded D-galactopyranoses are located on the unreducing ends. There is a short side chain with β-1→3-bonded L-arabinopyranoses.

The structure of the polysaccharide glucoarabinogalactan, which is a branched polysaccharide, was established by chemical and spectral methods. Its main chain consists of α-1→6-bound galactopyranose units. Galactopyranose atoms C-2 and C-3 act as branching points. The side chains contain galactopyranose, glucopyranose, and chains of β-(1→3)-bound arabinopyranose units. The linear structures of three galactooligosaccharides were identified and proved by partial acid hydrolysis.

Cultivation ofBacillus subtilis-7A on waste from alcohol production yielded an active extracellular enzyme α-amylase with MW 75 kDa. The enzyme was isolated from the culture medium by 60% saturated ammonium sulfate and purified until homogeneous by gel filtration on Sephadex G-100 and ion-exchange chromatography on DEAE-cellulose. The optimum temperatures for the complex and purified enzyme are 30 and 50°C, respectively. The optimum activity for both preparations occurred at pH 6.5. The substrate specificity of the isolated preparations was studied.

The acidic polysaccharide rhamnoglucouronan, the structure of which was studied by chromic and periodate oxidation, methylation, partial acid hydrolysis, and13C NMR spectroscopy, was isolated fromAlcea roseastems. The main polysaccharide chain consists ofα-1→2 andα-1→4 bound rhamnopyranoses and uronic acids and is branched

Galactomannans isolated from the seeds ofGleditsia macracantha (GMM) andGleditsia texana (GMT) have molecular masses (MM) of 750.000 and 795.000 and galactose to mannose ratios of 1.0∶4.9 and 1.0∶3.8, respectively. GMT and GMM are depolymerized to fragments of MM 25 and 19 kDa with retention of the primary structure and are studied by13C NMR spectroscopy. The principal chains of GMM and GMT are β-1-4-mannopyranose residues in which the hydroxyl groups of C-6 are substituted by single α-D-galactopyranose units.

It was established by studying carbohydrates of Iris pseudacorus during vegetative periods that the content of water-soluble polysaccharides in the rhizomes and roots is greatest during seed ripening; of pectinic substances, during budding. Glycomannan was isolated from seeds.

The fractional composition of the polysaccharides formed by some local strains of basidial fungi (Panus tigrinus, Pleurotus ostreatus, Fomes formentarius, andPhanarechaeta chrysosporium) in a submerged medium on various plant wastes (spent cottonseed pulp and cottonplant stems) has been investigated. Water-soluble polysaccharides, pectin substances, and hemicelluloses have been isolated from the products synthesized by the fungi, and their qualitative and quantitative monosaccharide compositions have been determined.

Galactomannan, a nontoxic compound that exhibits in experiments with intact rats a slight hypocholesterinemic and hypoglycemic activity, was isolated from the coating of Gleditsia macracantha seeds. It prevents significantly the development of experimental hyperglycemia and diabetes when administered simultaneously with alloxan.

A homogeneous native acetylated glucomannan of molecular weight 32000 was isolated from bulbs of N. poeticus. A linear chain polymer consisting of β-1→4-bound D-manno- and D-glucopyranoses was found using periodate and chromic oxidation and methylation. The glucomannan has low toxicity and exhibits distinct hypolipidemic activity.

The lipid composition of ripe and green fruit of Hibiscus esculenthus cultivated in Uzbekistan was studied. The fatty-acid composition of pod and seed lipids was determined. Carbohydrate components including water-soluble polysaccharides, pectinic substances, and hemicellulose were characterized.

The partial acid hydrolysis of glucans A, B, and C has given five linear oligosaccharides consisting of α-(1→6)-bound glucopyranose residues, and their structures have been investigated by reduction, peroxidate oxidation, methylation, mass spectrometry, and13C NMR spectrometry. Chemical structures are proposed for glucans A, B, and C.

The water-soluble polysaccharides and pectin substances from the wastes of vegetable and melon-type crops have been studied and their monosaccharide compositions have been determined. High- and low-methoxyl pectins have been isolated, and the physicochemical characteristics are given.

The physicochemical properties and qualitative and quantitative monosaccharide composition of Acantophyllum knorringianum pectin were determined. It has been found using periodate-nitric-acid oxidation and IR spectroscopy that galacturonan is a polymer consisting of α-1→-4-bonded D-galacturonic acid units. The isolated polysaccharide from roots had immunostimulating activity.

The carbohydrate and lipid compositions of seeds from Gleditsia triacanthos L. cultivated in Uzbekistan are investigated. Water-soluble polysaccharide (galactomannan), pectinic substances, and hemicellulose are isolated. Their physicochemical properties and monosaccharide composition are found. The content and fatty-acid composition of neutral, glyco-, and phospholipids are determined.

Helianthus tuberosus has unlimited potential for multi-faceted application to food, feed, technical, medicinal, and ecological problems. Lipids [1], carbohydrates, and protein constituents of H. tuberosus variety Faiz Baraka that was developed in Uzbekistan were studied earlier [2]. In continuation of this research, we studied carbohydrates and proteins of H. tuberosus variety Muzhiza that was developed at the Uzbekistan Research Institute of Horticulture by individual and mass selection from voucher samples. The starting material of air-dried finely ground tubers was worked up with CHCl3–MeOH (2:1) in order to remove lipophilic substances. Successive extraction of the remaining raw material isolated water-soluble polysaccharides (WSPS) and fructooligosaccharides (FOS) using H2O at room temperature; inulin, hot H2O; pectinic substances (PS), a mixture of oxalic acid and ammonium oxalate solutions; and hemicellulose (HMC), base solution (5%). A light-brown powder was obtained after evaporation of the alcoholic mother liquor and work up with Me2CO. It contained glucose, fructose, and a series of FOS. The homologous series of FOS began with a saccharose of the lowest homolog (for n = 0) that was followed by trisaccharides differing from the previous one by a single fructose residue. The highest homolog of this series was inulin [3]. The contents of FOS and inulin were 35% and 9.1%, respectively. The polysaccharide contents in H. tuberosus tubers of the two studied varieties were compared. The results are given below

The structure of galactomannan from seeds ofGleditsia macracantha is studied by methylation, periodate oxidation, and partial acid hydrolysis. The principal polyglycoside chain consists of β-1→4-bonded mannopyranose units, where the mannose is substituted in the 6-position by single α-D-galactopyranose units.

The dynamics of the accumulation of galactomannans (GMs) in the seeds ofGleditsia macracantha have been studied. Their maximum content was observed during dormancy. It was found that with the development and growth of the fruit the yield and characteristic viscosity of the GMs and the amount of mannose in them increased.

The water-soluble polysaccharides of the seeds of eight species of Gleditsia have been isolated and studied. They are galactomannans with different viscosities, specific rotations, and ratios of galactose and mannose. A study of their chemical transformations and IR spectral data has shown that the monosaccharide residues are pyranoses linked by β-1-4-glycosidic bonds having in the second componentD-galactose with the α-configuration of the glycosidic center and the most probable chair conformation of the pyranose ring.

Water-soluble polysaccharides, pectin substances, and hemicelluloses have been isolated from the epigeal part ofLagochilus zeravschanicus and characterized. The pectins isolated are characterized by a high degree of esterification of the carboxy groups, and their base consists of a fragment constructed from α-1→4-linkedD-galacturonic acid residues.

A mannan has been isolated from the bulbs ofUngernia ferganica Vved., and its qualitative chemical composition, the nature of the bond between the hexose residues, and the form of the molecule have been determined. It has been established that the mannan is a relatively nontoxic compound and exhibits a pronounced hypolipidemic activity both in intact animals and in animals with experimental hyperlipidemia.

Lipids and polysaccharides have been obtained from the leaves ofBrassica oleracea. The qualitative and quantitative compositions of the lipid complex have been studied. The fatty acid compositions of the total neutral lipids and of the phospho- and glycolipids have been determined. The carbohydrate complex of cabbage includes water-soluble polysaccharides, low-methoxyl pectins, hemicelluloses, and free monosugars. The polypeptides have been characterized by their mannoside compositions.

The polysaccharides of three cultivated varieties ofAlthea rosea have been investigated. The amounts of water-soluble polysaccharides and pectin substances in various organs of the plant have been determined. It has been shown that the maximum amount of water-soluble polysaccharides and pectin substances is present in the flowers. Their monosaccharide compositions have been studied. The physicochemical characteristics of the pectin substances are given.

Pectins have been isolated from five species of wild apples and have been characterized. They contain galacturonic acid, galactose, glucose, and arabinose residues. The titrimetric indices of the substances isolated have been determined. It has been shown by IR spectroscopy the pectins isolated are extracted partially in the form of pectic acids.

The dynamics of the accumulation of water-soluble polysaccharides and pectin substances of Aconitum zaravschanicum Steinb over the vegetation periods have been studied. The maximum amounts of polysaccharides have been established and their comparative physicohemical characteristics have been determined.

The partial acid hydrolysis of the homogeneous fraction C of the pectin fromEremurus regelii Vved. leaves has given a galacturonan. Its structure has been established on the basis of the results of periodate-nitric acid oxidation, methylation, and13C NMR spectroscopy.

We studied previously plants of the families Liliaceae [1, 2], Amaryllidacea [3], Malvaceae [4], and Caryophyllaceae [5]. In continuation of work in this area, we studied water-soluble polysaccharides (WSPS) from seeds of higher plants of the family Apiaceae (Umbelliferae). The composition and content and physicochemical characteristics of seeds from representatives of this family have not been reported. Furthermore, many Umbelliferae plants have great economic value as food, drug, feed, and technical plants [6]. Therefore, our goal was to isolate and determine qualitatively and quantitatively WSPS from seeds of 15 plant species of the family Apiaceae. The common determination method for WSPS from all seeds included grinding air-dried seeds (10 g), treatment with EtOH:CHCl3 (1:2, v/v) to remove lipids and pigments, and extraction (3 ) of WSPS with water at room temperature (1:10 ratio). The extracts were evaporated. Polysaccharides were precipitated by alcohol. The precipitate was washed with acetone and dried. The monosaccharide composition of WSPS was established after total acid hydrolysis (H2SO4, 2 N, 100°C, 5 h) and subsequent analysis. GC of aldononitrile acetates [7] was performed on a Chrom-5 instrument with a flame-ionization detector, glass column (250 0.20 mm), 5% Silicone XE-60 on inerton NAW (0.200–0.250 m), 205°C, N2 carrier gas, 30 mL/min. Samples of WSPS were white powders with a cream tint. They did not have reducing power and did not contain starch according to a negative test with iodine. Fehling solution was added to aqueous solutions of the polysaccharides using the principle of selective precipitation of mannose-containing polysaccharide [8]. A precipitate formed for seeds of Angelica ternata, Coriandrum sativum, Heraclim lehmannianum, Ferula tenuisecta, F. diversivittata, Foeniculum vulgare, and Mediasia macrophylla. Polysaccharides of the mannan type were probably present in the isolated WSPS. Table 1 shows that the studied polysaccharides were obtained in different yields from the seeds. The WSPS content was 0.38-5.96% and was greater in seeds of Anethum graveolens, Daucus carota L., Ferula tschimganica (>4%); and in Foeniculum vulgare (5.6%) and Mediasia macrophylla (5.96%). The hydrolysis products of the WSPS contained from two to five monosaccharides. Rhamnose was present in all studied polysaccharides from plant seeds. The principal components were rhamnose, arabinose, glucose, and galactose. This indicated that the polysaccharide fractions contained rhamnoarabinogalactan, rhamnoxylogalactan, glucan, and rhamnoglucan. Thus, screening of seeds from 15 plant species of the family Apiaceae found that the isolated WSPS differed in quantitative content of WSPS and monosaccharide composition. Some WSPS (A. ternata, C. sativum, H. lehmannianum, F. tsehimganica, F. diversivittata, F. vulgare, M. macrophylla) contained mannan-type polysaccharides. As stated above, polysaccharides affect the physiological activity of many food additives [9]. In this respect, screening of WSPS from seeds of Anethum graveolens, C. sativum, Ferula, Foeniculum vulgare, and M. macrophylla are interesting for further medical and biological testing.

Curcuma longa L. is a perennial herbaceous plant of the family Zingiberaceae and is indigenous to South Asia, tropical Australia, etc. The principal raw material of C. longa is the rhizomes, yellowish-gray on the outside, golden-yellow in cross section. The pear-shaped or egg-shaped I order rhizomes or cylindrical side runner II order rhizomes are used commercially. Rhizome powder is widely used as a spice to improve the taste of food, to give it a yellow color, and to improve digestion. It exhibits cholegogic, diuretic, and stimulant activity [1–4]. Our goal was to study the content and composition of the carbohydrates depending on the introduction site, in particular, under Tashkent oasis conditions. We studied air-dried powdered I and II order rhizomes, roots, and leaves. Lipophilic compounds were isolated from raw material by treatment with CHCl3:EtOH (2:1, v/v). Then sugar soluble in alcohol (SSA) was isolated by EtOH (82%). The SSA content was dominant in II order rhizomes (11.8%). The SSA composition was analyzed by descending PC on FN-13 paper using n-BuOH:Py:H2O (6:4:3). Sugars were identified using anilinium acid phthalate (hexoses) and alcoholic urea (5%, ketoses). The SSA contained arabinose, glucose, and fructose. The raw material remaining after SSA isolation was extracted exhaustively with water at room temperature, oxalic acid and ammonium oxalate (1:1) solutions (0.5%) at 70°C, and aqueous base (5%). The aqueous and acidic extracts were condensed and precipitated by EtOH to afford the corresponding water-soluble polysaccharides (WSPS) and pectinic compounds (PC). The basic extract was neutralized with CH3COOH, dialyzed against tapwater, evaporated, and treated with alcohol (three times the volume) to isolate hemicellulose (HC). The monosaccharide compositions of the polysaccharide fractions were determined after acid hydrolysis (H2SO4, 2 N, 100°C, 5–12 h). The hydrolysates were treated with BaCO3 until neutral, filtered, evaporated, and analyzed by PC and GLC. Sugars were identified using markers. GLC scans were recorded on a Chrom-5 chromatograph with a flame-ionization detector, glass column (250 0.20 mm), 5% Silicone XE-60 on inerton, super-grain (0.16–0.20 mm), 205°C, N2 carrier gas, 30 mL/min. Sugars were analyzed as aldononitrile acetates [5]. Table 1 presents the polysaccharide (PS) content and its monosaccharide composition. It can be seen that PS were distributed differently in various plant organs. There were more PS in I-II order rhizomes than in roots and leaves. The dominant PS in all plant organs were base-soluble PS, i.e., HC. The WSPS content in various organs was 0.86–2.6%; in roots, traces. The principal WSPS monosaccharide of I order rhizomes and leaves was glucose. Mainly xylose, mannose, and glucose were detected in the WSPS hydrolysate of II order rhizomes. WSPS of rhizomes were a friable white powder with a yellow tint that was soluble in water to form a slightly cloudy solution. The aqueous solution of PS gave a positive test with iodine. This suggested that the PS were glucans. Glucose dominated in the hydrolysate. Table 1 shows that PC accumulated in rhizomes. Their principal monosaccharide was glucose. There were less PC in roots and leaves. Glucose also dominated. This was consistent with the presence of starch (positive test with iodine). The isolated PC were a white powder with a yellow tint that dissolved with heating in water and formed viscous solutions. The PC differed from each other qualitatively and quantitatively. Galacturonic acid, arabinose, xylose, and glucose were detected in the PC hydrolysates.

Free and bound lipids from Helianthus tuberosus tubers were investigated. Neutral, glyco-and phospholipid classes and their fatty-acid compositions were determined. The composition of unsaponified substances was established.

The class composition and fatty-acid composition of the neutral lipids of kenaf processing wastes have been studied. The presence of acetates of triterpene alcohols and of free triterpenols has been established by physicochemical methods of analysis in the neutral lipids of kenaf. Hemicelluloses and cellulose predominate in the polysaccharide complex of kenaf chaff. Among the hemicelluloses, the xylans predominate.