Introduction to the Chemistry of Foods and Forages János Csapó Introduction to the Chemistry of Foods and Forages



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Fatty acids are monocarboxylic acids, constituents of saponifiable lipids. Unbranched molecules with an even number of carbon atoms are dominant. Lipids contain mostly fatty acids with carbon number equal or more than 14, but the amount of short-chain, low molecular weight fatty acids is notable in milk fat and in the oils of palm seed and coconut. Fatty acids with high molecular weight (>18:0) can be found in legumes (e.g. peanut) and in fish oil. Fatty acids with odd carbon number, branched-chain or isoprenoid acids are also occur in traces in some food. They are called minor fatty acids.

In the group of unsaturated fatty acids the double bonds are usually in the isolated position and have cis configuration. Some minor part of the polyunsaturated fatty acids does not have these features. Conjugated linoleic acids (CLA) are fatty acids with 18 carbon and two double bonds which differ in position and geometry. The configuration of the double bonds can be both cis and trans. CLA are formed during the biological hydrogenation of unsaturated fatty acids in the rumen. The milkfat and meat of ruminants contain the highest amount of this unique group of fatty acids. Several health promoting effect (e.g. anticarcinogenic effect) are attributed to these molecules. The nature and degree of biological impact of CLA-isomers can be different.



Unsaturated fatty acids with trans-double bond (e.g. elaidic acid 18:1 ω9t) are artifacts of the industrial processing of oil or fat with the change of the configuration of cis double bond that is originally present (e.g. in oleic acid 18:1 ω9c). They have been shown to be hazardous for human health. The main processes that can be accounted for this phenomenon are partial hydrogenation of plant oils and excess heat treatment of fat and oils.

Most of the unsaturated fatty acids belong to three family groups: ω3 (linolenic type), ω6 (linoleic type) and ω9 (oleic acid type fatty acids). The nomination is based on the position of the double bond from the methyl end of the chain. The occurrence of some omega fatty acids is characteristic for a given group of species e.g. erucic acid (20:1 ω9) can be present in the mustard family of seeds (Brassicaceae). Fish lipids are good source of fatty acids having 20-22 carbons and 5-6 double bonds. Arachidonic acid (20:4 ω6) is present in meat, liver and chicken eggs lipids. Linoleic acid (18:2 ω6) and arachidonic acid are essential fatty acids that must be taken by food while α-linolenic acid (18:3 ω3) is semiessential.

Fatty acids have an important role in the organoleptic properties of fats and oils. Though triacyl glycerides are tasteless in an aqueous emulsion, free fatty acids can be aroma compounds and they can be deliberated from saponifiable lipids both enzimatically or via chemical reactions without enzymes. The aroma threshold values of different fatty acids increase with the carbon number and depends on the matrix of food (Table 3.). The aroma threshold decreases remarkably with lower pH-values because solely undissociated fatty acid molecules are aroma active. The mixture of free fatty acids with carbon number 4−12 has a rancid soapy taste and musty rancid odor in creams. The taste of unsaturated fatty acids emulsified in water is bitter. Mostly α-linolenic acid is responsible for this effect.

The acylglycerols are the mono-, di- or triesters of glycerol with fatty acids. Triacylglycerols have a chiral center when the acyl residues in the first and the third positions are different. Their melting properties depends not only the composition but also the distribution of the fatty acids within the glyceride molecule. Mono-, di- and triglycerides are polymorphic. The different crystal modifications differ in their melting points and crystallographic properties.



Phospho- glyco- and sphingolipids have both hydrophilic and hydrophobic moieties. They belong to the main constituents of biological membranes, therefore occur in all foods of animal and plant origin.

Tocopherols, carotenoids and steroids are unsaponifiable compounds of fats and oils. They are usually present in low concentration 0.2–1.5% in edible oils and fats. Some of them is suitable as an indicator for the identification of a fat or an oil e.g. the ratio of the individual plant steroids (stigmasterol/campesterol) can be applied to decide whether cocoa butter was adulterated or not. The oxidative degradation of carotenoids can result in aroma compounds . β-ionone and β-damascenone have the lowest odor threshold values among C13-norisoprenoides (Fig 13.). The hydroxylated derivatives of C13-norisoprenoids often occur in plants as glycosides and they can be liberated by enzymatic or acid hydrolysis. The changes of the aroma profile of fruits when heated (e.g. juice or marmalade production) is partially attributed to these processes. Carotenoids proved to be also useful food colorants . Pigments of several plants are used to color margarine, various cheese products, beverages, sauces, meat, and confectionery. Raw, unrefined palm oil is good colorant for margarine owing to its carotenoid content (0.05–0.2%).

The main processes that are responsible for the chemical changes of food lipids are the hydrolysis of saponifiable lipids (lipolysis) and peroxidation of the unsaturated fatty acid residues. The cleavage of ester bonds in acyl lipids is promoted by hydrolases being present in both foods and microorganisms (triacylglicerol hydrolases are called lipases ). When fruits and vegetables are sliced or oil seeds are disintegrated some part of the acyl lipids are hydrolyzed and the released fatty acids can also be oxidized by other enzymes.



Lipolysis is mostly undesirable, e.g. in the case of milk short-chain fatty acids can be released and a rancid aroma defect can be developed. The odor formed can be desirable in other cases e.g. in the build-up of specific cheese aromas. Among long-chain fatty acids free linoleic and linolenic acid have an impact on food flavor giving a bitter-burning sensation. In the free form they are susceptible for autoxidation that can results in the formation of compounds also with an intensive odor.

Microbial lipases are often very heat stable. They cannot be inactivated by pasteurization or ultra high temperature treatment and so their presence can lead to the decrease in quality during storage (e.g. in milk products).

Acyl lipids having one or more allyl groups within the fatty acid molecule are not stable food constituents. They are readily oxidized to hydroperoxides. Lipid peroxidation can be processed through autoxidation (autocatalytic chemical reactions) or via the function of lipoxygenases. The resulting hydroperoxides are prone to decompose into great number of other compounds. Some of them are very potent off-flavors. That is the reason why lipid peroxidation is detected by consumers in cases when only a small portion of lipid was subjected to oxidation and also in foods with unsaturated acyl lipids present as minor constituents. Volatile products formed by the deterioration of hydroperoxides are usually very odorous compounds and can have rancid, metallic, fishy or stale flavor. Nevertheless some of them can contribute to the pleasant aroma of fruits and vegetables if they are present at a level below their off-flavor threshold values.

Autoxidation is a radical-induced chain reaction (Fig 14.). Alkyl radicals formed by initiators can react with molecular oxygen and the resulting peroxi radicals can abstract H-atoms from the methylene groups in an olefin compound. Monohydroperoxide molecules are the main products of the chain propagation reactions and their degradation generated radicals that accelerate the oxidation process autocatalytically.

The autoxidation of unsaturated acyl lipids can lead to the deterioration of food quality, therefore the knowledge of the reactions during the induction period is important: how they trigger the start of autoxidation? In the presence of light plant pigments can convert triplet state oxygen to singlet state which is more susceptible to react with high electron density moieties, e.g. π-electron pairs, initiating reactions between unsaturated alkyl chains and molecular oxygen.

The next groups of reactions (chain branching, i.e. decomposition of hydroperoxides into radicals) is promoted by heavy metal ions or heme(in)-containing molecules. The metal content of food can be originated from raw food, from processing equipment and packaging material. It may happen that traces of heavy metals are solubilized during the processing of fat. Such traces can be inactive physiologically but active as prooxidants. The decomposition rates of hydroperoxides also depend on pH and the moisture content of food. The autoxidation of acyl lipids is high for both dehydrated and high-water-content food and has a minimum at about aw=0.3.

While the primary products of autoxidation i.e. monohydroperoxides are odorless and tasteless the secondary products (formed by their decomposition) affect the odor and flavor of food. The volatile secondary products are mostly odor-active carbonyl compounds (Table 4.), moreover malonic dialdehyde, alkanes and alkenes.



Lipoxygenases are present in many plants and in erythrocytes and leucocytes. They catalyze the oxidation of some unsaturated fatty acids to their corresponding monohydroperoxides. Unlike autoxidation, reactions catalyzed by lipoxygenase are substrate specific (linoleic and linolenic acids preferred for the plant enzyme, arachidonic acid for the animal enzyme), the reaction rate is high at low temperatures (0–20°C) and reduced due to inactivation effects of heat treatment. In legumes, e.g., in peas and soybeans non-specific lipoxygenases are present. They can react with esterified fatty acids and also can degrade carotenoids and chlorophyll pigments to colorless products. Hydroperoxides that are formed by the action of lipoxigenases can be decomposed further enzymatically by glutathione peroxidase (in animal tissue) or hydroperoxide lyase (in plants and mushrooms). Glutathione peroxidase catalyzes a reduction of the fatty acid hydroperoxides to the corresponding hydroxy acids. As a result of reactions catalyzed by hydroperoxide lyase different the aldehydes, acids, oxo-acids and allyl alcohols are formed. In fruits and vegetables C6- and C9-aldehydes are dominated while C8-alcohols in mushrooms. These compounds are odorant which generate the characteristic odor of these food items (fruits, vegetables and mushrooms).

Hydroperoxides can be also decomposed by nonenzymatic reactions . The products of these nonspecific reactions are oxo-, epoxy-, mono-, di- and trihydroxy carboxylic acids and some of them possess bitter odor characteristic. They have a role in the case of foods with high unsaturated fatty acid and protein content e.g. legumes or fish products.

The peroxidation of unsaturated acyl-lipids can be inhibited with the exclusion of oxygen (e.g. vacuum packaging or addition of glucose oxidase). Storing the food at low temperature in the dark reduces the rate of autoxidation. In foods when lipoxygenase is active (e.g. fruits and vegetables) these precautions are not sufficient. The enzymes in these items must be inactivated with a heat treatment called blanching. In order to prevent lipid oxidation natural and synthetic antioxidants are often applied.
Chapter 6. Vitamins

Vitamins are organic compounds that are required in minor quantities as nutrients. The vitamin needs depends on the species and also on age within a certain organism. They essential for the growth, maintenance and functioning of the body. During food processing significant vitamin losses can occur (Table 5.). Vitamins can be conversed through chemical reactions into inactive products or extracted from the raw material (e.g. some part of the water-soluble vitamins is leached during blanching or cooking).

In most cases the vitamin requirement can be adequately supplied with a balanced diet. The cause of vitamin deciency (hypovitaminosis or avitaminosis) is the insufficient vitamin intake by food. Needs are increased owing to diseases or stress or disturbances in resorption via the gastroindustrial tract. The extent of vitamin supply can be assessed with the measurement of the vitamin content in blood plasma or the biological activity can be determined. In the latter case not only presence of the vitamin but also the activities of the relating enzymes influence the results.

Vitamins are traditionally classified according to their solubility. The fat-soluble vitamins are A, D, E and K1 and the water-soluble vitamins are B1, B2, B6, nicotinamide, pantothenic acid, biotin, folic acid, B12 and C.

The biological role of retinol (vitamin A) is to affect the protein metabolism of cells of skin or mucous-coated linings of the respiratory or digestive systems. In the case of insufficient supply the state of the epithelial tissue is negatively affected (e.g. hyperkeratosis) and night blindness is developed. Vitamin A is present only in animal tissue. Plant contains carotenoids which are provitamins of retinol. Carotenoids present in animal tissues are always derived from feed of plant origin. The requirement of this vitamin is provided from both sources. Retinol is stored in the liver in the form of fatty acid esters.

Food processing can cause a loss of 5–40% for vitamin A and carotenoids. Heat treatments in the absence of oxygen (e.g. cooking or food sterilization) can cause isomerization and fragmentation. In the presence of oxygen oxidative decomposition occurs and volatile degradation products are formed. The oxidative deterioration of retinol often parallels acyl lipid oxidation. The intensity of this process is affected not only by partial pressure of oxygen but also the applied temperature and the aw of food.

In animals 7-dehydrocholesterol is present in the skin. This molecule form cholecalciferol (vitamin D3) through photolysis by ultraviolet light. Ergocalciferol (vitamin D2) is formed from ergosterol that is present in yeast, moulds and algae therefore it can serve as an indicator for contamination and tolerance limits are given at certain food items. Vitamin D2 and D3 are hydroxylated first in the liver resulting prohormone 25-hydroxycholecalciferol (calcidiol). The last step is also a hydroxylation but it takes place in the kidney resulting 1α,25-dihydroxycholecalciferol (calcitriol) which is an active hormone. Calcitriol promotes the achievement of the optimal calcium concentration in the kidney and in the bones and involves in the synthesis of proteins in the structure of the bone matrix. The deficiency of vitamin D led to inadequate calcification of cartilage and bones and therefore impacts their formation. Childhood rickets occurs in serious cases. In case of adults vitamin D deficiency causes osteomalacia which resulted in the softening and weakening of the bones.

The most important vitamin D source is fish liver oil. Most natural foods have low quantities of vitamin D but their provitamines 7-dehydrocholesterol and ergosterol are widely distributed. Vitamin D3 and its provitamin are present in animal fat, beef and pork liver, egg yolk, butter and cow’s milk. Ergosterol can be detected in wheat germ oil, cabbage, spinach, yeast and mushrooms. Although the vitamin D content of foods is prone to decomposition in the presence of oxygen and light, its supply is usually adequate in the case of adults.

Tocopherols have been shown to possess antioxidative properties. They contributed to the prevention of lipid oxidation and stabilization of membrane structures and act as natural antioxidants preventing other molecules (e.g., vitamin A, ubiquinone) against oxidative deterioration. The individual tocopherol requirement has been shown to increase when the diet contains a high content of unsaturated fatty acids. Among the various tocopherols differing in the number and position of the methyl groups on the ring α-tocopherol (vitamin E) has the highest biological activity. The main source of tocopherols is vegetable oils (particularly germ oils of cereals). Significant losses occur during plant oil hardening and also in dehydrated or deep fried foods via autoxidation processes.

The K-vitamins have naphthoquinone basic structure with different side chains.



Phytomenadione (vitamin K1, phylloquinone) is participated in the post-translational synthesis of proteins involved in blood clotting (e.g prothrombin). Besides the sources of food origin (green leafy vegetables, veal or pork liver) this vitamin is synthesized by the bacteria present in the large intestine. Vitamin K1 is relative stabile to exposure to heat and atmospheric oxygen but easily decomposed in the presence of light and alkali. Hydrogenation process saturates the double bonds that are present on the side chain and the resulting derivative is less active as the natural form.

Thiamine (vitamin B1) is an important coenzyme in the form of its pyrophosphate and participates in the carbohydrate metabolism therefore the thiamine needs is increased in a carbohydrate-enriched diet. This vitamin is found in plants (cereals, vegetables and shelled fruit), yeasts, and also in animals (eggs, pork, beef, fish, milk). In aqueous solutions its stability is low. The thermal degradation of thiamine yields volatiles that contribute to the formation of meat-like aroma in cooked food. Losses of this vitamin were observed via heat treatments (cooking meat, blanching of cabbage) and storage of canned fruit. Thiamine is in an inactive form in foods when nitrites are present. In a stronger acidic medium (e.g. lemon juice) there was not significant thiamine degradation.

Riboflavin (vitamin B2) has a great importance as a prosthetic group of flavine enzymes. With a normal diet deficiency symptoms are rarely observed. This vitamin is present in vegetables, yeast, meat products and fish. The losses during processing are usually low and do not exceed 10–15% but this vitamin is susceptible to the light that induce photolytic decomposition.

Pyridoxine (pyridoxal, vitamin B6) is also coenzyme of several enzymes. Pyridoxal phosphate is the metabolically active form while the intake is usually in the form of pyridoxal or pyridoxamine. Pyridoxal is the most stable form among the active species (pyridoxine, pyridoxol, pyridoxal and pyridoxamine) therefore this form is used for the fortification of food. The losses of vitamin B6 was observed during cooking of meat and vegetables. Sterilization of milk results in an inactive thiazolidine derivative.

Nicotinamide (niacin) is a building unit of NAD+ and NADP+ that are coenzymes of dehydrogenases. This vitamin is present in the form of nicotinic acid or in the form of nicotinic acid amide. Some tryptophan containing foods help to prevent the deficiency symptoms of nicotinamides (e.g. milk and eggs) because L-tryptophan can substitute for niacin in the body. The most abundant sources are liver, lean meat, cereals, yeast and mushrooms. In the case of nicotinic acid moderate losses of up to 15% were detected during the blanching of vegetables.

Pantothenic acid is a constituent of CoA that carrier of acyl groups in the cell metabolism. Liver, adrenal glands, heart and kidney provide the largest supply and the intake by normal diet usually covers the needs. Pantothenic acid is not very prone to decomposition during the normal food handling processes. Thermal processing of milk was accompanied with a moderate loss and also the cooking of vegetables through leaching.

Biotin is prosthetic group of carboxylating enzymes and mostly present in food in this bound form. Hypervitaminosis rarely occurs. Avidin present in raw egg white might inactivate biotin. This vitamin is not very susceptible to deterioration. Food processing and storage can cause a loss of 10-15%.

Folic acid is cofactor of enzymes which transfer single carbon units. Its deficiency can occur both by inadequate nutrition and malfunction of absorption. The bioavailability of folic acid is low because it occurs in a bound form in food attached to oligo-γ-L-glutamates. In order to avoid deficiency supplementation of cereal products is applied in the USA to prevent number of diseases (e.g. neural tube defect) associated with the folic acid deciency.

The decomposition of folic acid in milk is parallel to that of ascorbic acid through an oxidative process. Folic acid loss can be prevented with the addition of ascorbic acid. Cooking of meat is accompanied with small losses of folic acid but blanching did not reduce its content in vegetables.



Cyanocobalamin (vitamin B12) is formed from cobalamins during the processing of raw materials. Cobalamins are present in the form of adenosylcobalamin (coenzyme B12, participates in rearrangement reactions) or methylcobalamin. Inadequate absorption due to the limited formation of the ’intrinsic factor’ glycoprotein can led to vitamin deficiency. Vitamin B12 exerts a positive effect on growth due to the influence on protein metabolism. The most important food sources are: muscle tissue, liver and kidney. The stability of this vitamin is good between pH 4-6 even at elevated temperatures. Greater losses were detected if the pH is alkaline or reducing agents (e.g. ascorbic acid or SO2) are present.

L-Ascorbic acid (vitamin C) can be reversibly oxidized to dehydroascorbic acid. The activity is lost when the lactone ring of dehydroascorbic acid is irreversibly opened and 2,3-diketogulonic acid formed (Fig 15.). Vitamin C is involved in hydroxylation reactions (e.g., biosynthesis of catecholamines, hydroxyproline and corticosteroids).

The oxidation rate of ascorbic acid depends on several conditions during food processing (e.g. oxygen partial pressure, temperature, pH). If heavy metal ions are present the rate of decomposition is much higher than in case of noncatalyzed spontaneous autoxidation.

C-vitamin conversion to the inactive diketogulonic acid can occur even at anaerobic conditions with maximum reaction rate at pH=4 (Fig 15.).

Ascorbic acid and its degradation products react with amino acids and enter into Maillard-type browning reactions.

The loss of ascorbic acid during preservation, storage and processing of food was thoroughly evaluated. The degradation of this vitamin is often used as an indicator to assess the extent of the loss of other important constituents occurring in food.
Chapter 7. Natural Food Colorants

Nowadays the use of natural colors comes to the front instead of synthetic dyes.



Carotenoids occur solved in the lipids providing yellow, orange, red or violet colors of higher plants. They can be present in many parts of the organisms (e.g. fruits, kernels, leaves, roots or petals). The herbivorous animals take up carotenoids with the feed and some part of is stored in the adipose tissue. Carotenoids contain 40 carbon atoms with conjugated double bonds in trans conformation. They can be classified into two groups, hydrocarbon carotenoids and oxygen containing carotenoids (xantofills). Owing to their unsaturated nature they are prone to oxidation resulting color fading. They are the precursors of vitamin A1 in human. The most important hydrocarbon carotenoids are α-, β-, and γ- carotene occurring e.g. in sugar beet and each chlorophyll containing part of the plants. Lycopene is a constituent of roots and fruits of many higher plants (e.g. tomato). The most important members of the group of oxigen containing carotenoids (xantophylls) are kriptoxantin (e.g. found in citrus, corn and paprika), zeaxanthin (occurring in corn, berries and fish) and lutein (colorant of green leaves and egg yolk together with chlorophyll).

The quinone derivatives are primary distributed in plants. Some of the naftoquinones exert similar effect as vitamin K. The occurrence of anthraquinones is scarce. They can be mostly found in insects and mushrooms. Quinones can be present in food in both free and bound form. In the latter case they can form esters or glycosides or connect with proteins. They can often be found in reduced form as polyphenols . When the cell integrity of fruits is disrupted due to mechanical forces and polyphenol oxidases are released the colorless polyphenols are oxidized to molecules with quinonidal structures (melanins). Melanins have dark color and therefore this process is called enzymatic browning. This process is beneficial during processing e.g. in tea or dried fruits but detrimental to fresh fruit and vegetables.

The most important quinones are methoxy-benzoquinone and 2,6-dimethoxy-benzoquinone (that can be isolated from wheat germ), embelin (in berries), juglone (in green nut shell), and anthraquinones (e.g. alizarin) (Fig 16.).

The main groups of flavonoids are anthoxanthines, antocyanidines, aurones and chalcones. Flavonoids can form complexes with metals in neutral or weakly acidic environment. Their indirect antioxidant effect is attributed to this phenomenon. The resulting flavonoid-metal complexes are usually very colorful compounds that sometimes cause unwanted coloration in the product. The structures of anthoxanthines can be derived from the base structure of phenyl-chromon ring (Fig 17.). The color of anthocyanidins is change with the increasing number of hydroxide groups from orange-red to violet. Proanthocyanidines are colorless compounds that can decompose into colorful compounds during food processing. The chemical structure of antocyanidines is changed due to changes in pH. In an acidic medium the oxonium form is stabile while at higher pHs the quinoidal structure is present having different colors (e.g. red – blue).

The chemical base structure of pyrrole food colorants is ringed or linear tetrapyrrole. Metalfree ringed tetrapyrrole derivatives can be divided into two groups, porphyrins and protoporphyrines, having different substituents on the pirrole rings. The base structure is porphyne (Fig. 18.). Metal bearing ringed tetrapyrrole derivatives can have also porphine or phorbine structures. In the porphine-based molecules iron can be present in the form of Fe2+ in ferro-protoporphyrin (protohem) or in the form of Fe3+ in ferri-protoporphyrin (protohemin). Protohem is the prosthetic group of hemoglobin in blood and myoglobin in muscle. In the presence of oxygen the red myoglobin is oxidized to light red oxymyoglobin. The Fe2+ present in myoglobin can also be oxidized to Fe3+, and the resulting metmyoglobin have brown color that is disadvantageous for the organoleptic properties of meat. In the living tissue metmyoglobin reductase converts it back to myoglobin. The color of fresh meat depends mostly on the presence and the ratio of these three color bearing compounds. However, some other compounds have also an effect on the color e.g. cytochromes, B12 vitamin and flavones. In meat products preserved with nitrate/nitrite (i.e. meat curing) the desirable color of the product is developed through the product of the reaction between myoglobin and nitrogen-oxide (formed from nitrite). The resulting nitroso-myoglobin forms nitroso-myochromogen during cooking that is responsible for the formation of the typical red color of the cured products.

The green colorants of plants called chlorophylls are metal bearing tetrapyrrole derivatives with phorbine base structure (Fig. 19.). Chloroplastine is a complex protein with chlorophyll prostetic group.

Bile colorants (e.g. biliverdin and bilirubin) belong to the group of linear tetrapyrrole derivatives .
Chapter 8. Flavor Compounds

Flavor is an overall sensation during food consumption. It is the interaction of three elements: taste, odor and textural feeling. The compounds that are responsible for taste are usually nonvolatile at room temperature therefore interact only with taste receptors. Molecules that are responsible for odors are called aroma substances and they are volatile. Some compound can provide both sensations.

The number of the known volatile compounds in foods is enormous but only a limited number are important for aroma i.e. compounds that are present in food in concentrations higher than the odor thresholds. Although components with concentrations lower than these thresholds also contribute to aroma if the mixtures of them exceed these thresholds. The most important substances defining the characteristic aroma of a given food are called key odorants (Table 6.). Components that can cause a faulty odor or taste, or both are called off-flavor. The use of this term in the case of a given constituent may depend on the type of the food: the same molecule can contribute to the typical odor or taste of one food while causing an unwanted sensation in another.

The definition and determination of taste intensity is described in Chapter 3.



Kataloq: tartalom -> tamop425
tamop425 -> Rényi, András Művészettörténet. Bevezetés
tamop425 -> Népegészségügyi genomika Tartalom
tamop425 -> Emission transmission
tamop425 -> Elektrodinamika Nagy, Károly Elektrodinamika
tamop425 -> Matematikai geodéziai számítások Ellipszoidi számítások, ellipszoid, geoid és terep metszete Dr. Bácsatyai, László Matematikai geodéziai számítások : Ellipszoidi számítások, ellipszoid, geoid és terep metszete
tamop425 -> A szárazföldi növények evolúciója és rendszertana Vezérfonal egy nem is olyan könnyű tárgy tanulásához Podani, János a szárazföldi növények evolúciója és rendszertana: Vezérfonal egy nem is olyan könnyű tárgy tanulásához
tamop425 -> Botanika III. Bevezetés a növénytanba, algológiába, gombatanba és funkcionális növényökológiába Szerkesztette Tuba, Zoltán, Szerdahelyi, Tibor, Engloner, Attila, és Nagy, János
tamop425 -> Magyarország fa- és cserjefajai dr. Bartha, Dénes Magyarország fa- és cserjefajai
tamop425 -> A magyar irodalom történetei II. 1800-tól 1919-ig Szegedy-Maszák, Mihály a magyar irodalom történetei II.: 1800-tól 1919-ig

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