Root multiplicities and number of nonzero coefficients of a polynomial

It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial over a field of characteristic zero is larger than the multiplicity of any of its nonzero roots. We extend this result to an appropriate statement in positive characteristic. Furthermore, we present a new proof of the original result, which produces also the exact number of monic polynomials of a given degree for which the bound is attained. A similar argument allows us to determine the number of monic polynomials of a given degree, multiplicity of a given nonzero root, and number of nonzero coefficients, over a finite field of characteristic larger than the degree.Comment: 6 pages. Minor change from previous version: added Example 6, illustrating the difficulties arising when one tries to relax the hypothesis n<p of Theorem

Syntactic Analysis Based on Matrix Grammar

Tato bakalářská práce se zabývá syntaktickou analýzou založenou na maticových gramatikách. V teoretické části nejdříve přináší několik různých pohledů na tento typ řízených gramatik a zkoumá podobnosti s klasickými bezkontextovými gramatikami. Z těchto podobností se poté v praktické části snaží vycházet při návrhu modelu prediktivní syntaktické analýzy pro některé kontextové jazyky, ke kterým můžeme sestrojit odpovídající maticové gramatiky, které je generují. V práci jsou rovněž prezentovány některé experimentální algoritmy a návrh řešení, které by se daly spíše využít při dalším vývoji projektu.The subject of this thesis is to develop a method of syntactic analysis based on matrix grammar s. In its theoretical part we provide various analytical aspects for this type of regulated grammar in order to reveal the common background as well as search for similarities with the classical context-free grammars which we will then be able to benefit from in the practical part. Our goal is to extend the well-known predictive method of syntactic analysis to further accept a wider spectrum of formal languages - some of the context-sensitive ones which we are able to generate using our matrix grammars. Besides this main effort we also present some experimental algorithms and suggestions hich could be used in further research of this project.

Covering theorems for Artinian rings

The covering properties of Artinian rings which depend on their additive structure only, are investigated

Solvation, Structure and Organization at Liquid Surfaces

This dissertation presents the results of nonlinear spectroscopic studies whose goal is to understand how the asymmetric nature of interfaces and intermolecular interactions give rise to interfacial solvation properties and solvent structure. The first part of this thesis uses resonance enhanced second harmonic generation to examine the polarity and hydrogen bonding opportunities at interfaces formed between hydrophilic silica and both weakly and strongly associating organic liquids. Measuring interfacial electronic spectra of probe molecules that exhibit solvatochromic sensitivity to polarity and hydrogen bonding, we saw that small changes in solvent structure affect interfacial polarity, and strongly associating alcohols solvents create a region of heterogeneous polarity at the interface. Silica appears to donate hydrogen bonds to adsorbates no matter what solvent (protic or aprotic) was chosen. The second part of this dissertation uses another nonlinear spectroscopic technique, vibrational sum frequency generation, to determine the structure and orientation of solvent molecules adsorbed to silica/vapor, silica/liquid, and neat liquid/vapor interfaces. By comparing spectral features appearing under different experimental polarization conditions, we have determined average solvent orientations and degree of organization. Our initial studies of alkanes adsorbed to the silica/vapor interface show that despite strong substrate-adsorbate interactions, molecules at the interface show some degree of long range order and organization. In order to examine how the strength of intermolecular forces between adsorbates and either the substrate or neighboring molecules affect interfacial organization, we measured vibrational spectra of octanol isomers as well as different functional group containing n-alkyl molecules at silica/vapor and silica/liquid interfaces. The octanol studies show that strongly associating molecules form ordered monolayers at the silica/vapor interface, but that strength of lateral interactions is important for preserving that order when the liquid is brought into contact. Branched isomers appeared very disordered at solid/liquid interfaces. Further examining this change in order between solvents at silica/vapor and silica/liquid interfaces using equal length but different functional group containing solvents, we see that the energetics of adsorption and solvation are likely to be responsible for the degree of order both at the solid/vapor surface (adsorption) and solid/liquid interface (both adsorption and solvation)

On the Catalan equation over algebraic number fields

L

Morphological and antioxidant characteristics of quince (Cydonia oblonga Mill.) and chinese quince fruit (Pseudocydonia sinensis Schneid.)

Quince (Cydonia oblonga Mill.) is a fruit species, whose fruits have a high therapeutic value and therefore are used in many countries in traditional medicine. Chinese quince (Pseudocydonia sinensis Schneid.) is a lesser used species, although it is a relative of quince. The aim of the study was to evaluate some morphological characters of both kinds of fruit and antioxidant activity of morphological parts of the fruit. For these experiments, two genotypes were used from each species growing in the Arboretum Mlyňany (Slovakia). We determined the antioxidant activity of different parts by the DPPH method. In the genotypes from the evaluated species C. oblonga/P. sinensis we determined the average weight of the fruit in the fresh condition to be in the range 147.61 - 253.27 g / 197.85 - 466.38 g, the exocarp weight 28.50 - 43.89 g / 24.85 - 45.10 g, the mesocarp weight 116.36 - 204.99 g / 160.30 - 389.80 g, the seed weight 1.05 - 1.54 g / 9.22 - 17.42 g, the height of fruit 74.09 - 80.88 mm / 98.06 - 124.48 mm, average of fruit 60.11 - 81.51 mm / 62.33 - 88.64 mm. In aqueous extracts we determined antioxidant activity of the species C. oblonga / P. sinensis in dry exocarp in the range 43.52 - 67.73% / 52.76 - 82.20%, in fresh mesocarp 7.36 -14.78% / 15.30 - 23.50%, in dry mesocarp 30.92 - 41.30% / 41.68 - 50.15% and dry endocarp 55.19 - 76.44% / 91.20 - 92.72%. We determined antioxidant activity in methanolic extracts of the species C. oblonga / P. sinensis in dry exocarp in the range 93.29 - 93.32% / 91.87 - 93.25%, in fresh mesocarp 10.29 - 36.0% / 17.10 - 17.11%, in dry mesocarp 54.55 - 74.11% / 80.39 - 84.11% and in dry endocarp 95.14 - 95.39% / 94.97 - 95.62%. Results document that the fruits of both species can be practically used in the preparation of many dishes, while they can be used as raw material for pharmaceutical and cosmetic use

Redistribution of mineral elements in wheat grain when applying the complex enzyme preparations based on phytase

Biogenic minerals play an important role in the whole human nutrition, but they are included in the grain of the phytates that reduces their bioavailability. Whole wheat bread is generally considered a healthy food, but the presence of mineral elements in it is insignificant, because of weak phytate degradation. From all sources of exogenous phytase the most productive are microscopic fungi. To accelerate the process of transition hard mineral elements are mobilized to implement integrated cellulolytic enzyme preparation based on the actions of phytase (producer is Penicillium canescens). Phytase activity was assessed indirectly by the rate of release of phosphate from the substrate. It has been established that the release rate of the phosphoric acid substrate is dependent on the composition of the drug and the enzyme complex is determined by the presence of xylanase. The presented experimental data shows that a cellulase treatment of the grain in conjunction with the β-glucanase or xylanase leading to an increase in phytase activity could be 1.4 - 2.3 times as compared with the individual enzymes. As a result of concerted action of enzymes complex preparation varies topography grain, increase the pore sizes in seed and fruit shells that facilitate the penetration of the enzyme phytase in the aleurone layer to the site of phytin hydrolysis and leads to an increase in phytase activity. In terms of rational parameters of enzymatic hydrolysis, the distribution of mineral elements in the anatomical parts of the grain after processing complex enzyme preparation with the help of X-ray detector EMF miniCup system in a scanning electron microscope JEOL JSM 6390 were investigated. When processing enzyme preparation wheat trend in the distribution of mineral elements, characteristic of grain - the proportion of these elements in the aleurone layer decreases, and in the endosperm increases. Because dietary fiber and phytate found together in the peripheral layers of fiber-rich grains, it is difficult to separate the effects of degradation processes nonstarch polysaccharides and fiberphytate redistribution of polyvalent metal ions. However, studies have shown that phytase - an effective mechanism for regulating mineral nutrient diet. Application of phytase in grain bakery technology will increase the biological value of the product.  

Morphological characteristics for fruits of aronia mitschurinii A.K. Skvortsov & Maitul.

The aim of this study was to determine morphometric characteristics of fruits within some phenotypes of Aronia mitschurinii A.K. Skvortsov &amp; Maitul. Their morphometric parameters were following: weight from 0.75 g (AM-03) to 1.52 g (AM-04), length from 9.46 mm (AM-03) to 12.73 mm (AM-04), diameter from 10.49 mm (AM-03) to 13.73 mm (AM-04), fruits number in the corymb from 11.33 (AM-07) to 20.13 (AM-03), cumulative weight of fruits in the corymb from 10.42 g (AM-07) to 21.73 g (AM-04), volume of fruits from 0.55 (AM-03) to 1.26 (AM-04) cm3. The shape index of the fruits was found in the range of 0.87 (AR-01, AR-05, AR-07) to 0.93 (AM-02). The analysis of coefficient of variation showed the difference of variability in morphological characteristics between Aronia mitschurinii samples. Data showed that the most variability of important selection characteristics are the average cumulative mass of fruits in a сorymb - from 12.34 (AM-03) to 38.61 (AM-02) % and fruit number of fruits in the сorymb - from 14.56 (AM-03) to 36.88 (AM-02) %. The other characteristics are more or less stable. The introduction population of the Aronia mitschurinii, was created in the M.M. Gryshko National Botanical Garden in Kyiv, has a sufficient potential for successful selection work

МОРФОЛОГІЧНА ХАРАКТЕРИСТИКА БДЖОЛИНОГО ОБНІЖЖЯ ОДЕРЖАНОГО З BRASSICA NAPUS L.

The purpose of this work was to research the morphological characteristics of monofloral bee pollen obtained from Brassica napus L.&nbsp;The formulated goals were: determine the period of bee pollen receiving; implement the selection of bee pollen samples during blooming period of species; establish the monoflorality&nbsp;ratio of the total pollen collection; explore the morphometric indicators of bee pollen by the parameters of pollen lump, shaping level and weight. Bee pollen collection was carried out in Skvyra district of Kyiv region from local population of Apis mellifera&nbsp;L. families.&nbsp;Morphometric measurements were performed in the Institute of Biodiversity Conservation and Biosafety, Slovak University of Agriculture in Nitra.&nbsp;Here were determined the&nbsp;amount&nbsp;of&nbsp;bee&nbsp;pollen&nbsp;per&nbsp;one&nbsp;day&nbsp;brought by one&nbsp;family:&nbsp;from&nbsp;&nbsp;27.04 to 03.05.16 is&nbsp;50.8 ± 2.25&nbsp;g;&nbsp;from 04.05 to 06.05.16 –&nbsp;100.0 ± 3.33&nbsp;g; from&nbsp;07.05 to 17.05.16 –&nbsp;270.7 ± 11.79&nbsp;g;&nbsp;from 18.05 to 22.05.16 –&nbsp;100.5 ± 3.028&nbsp;g; from&nbsp;23.05 – 25.05.16 –&nbsp;39.8&nbsp;±&nbsp;2.74&nbsp;g.&nbsp;Here were defined the morphological parameters of bee pollen lump from B. napus:&nbsp;length is in the range&nbsp;from&nbsp;3.40 ± 0.061&nbsp;mm to 3.66 ± 0.048&nbsp;mm; width is in the range&nbsp;from&nbsp;2.88 ± 0.059&nbsp;mm to 3.26 ± 0.067&nbsp;mm; weight is in the range&nbsp;from&nbsp;8.65 ± 0.317 mg to 11.31 ± 0.241 mg; shaping level of bee pollen is in the range 4.62 – 4.96 points. The total monoflorality ratio constitutes from 79.94 ± 0.619&nbsp;% to 98.00 ± 0.202&nbsp;%.&nbsp;The obtained results confirmed that the activity of bee flying depends on the blooming period and intensity of the nectar secretion, on the collection of protein feed&nbsp;from&nbsp;B. napus.&nbsp;Pollen lumps from Brassica napus&nbsp;L. bee pollen&nbsp;were large, dense, regular shape without splits, which specified the possibility of its use for the producing on a commercial scale. &nbsp;Целью работы было исследование морфологической характеристики монофлорной пчелиной обножки полученной из Brassica napus L. Поставленные задачи: установить период получения пчелиной обножки; осуществить отбор пчелиной обножки течение цветения вида; установить монофлорность общего сбора обножки; исследовать морфометрические показатели обножки по параметрам пыльцевого комочка, сформированности и массы. Отбор обножки осуществляли в Сквирском районе Киевской области от семей Apis mellifera L. местной популяции. Морфометрические измерения проводили в Институте сохранения агробиоразнообразия и биологической безопасности, при Словацком аграрном университете в Нитре. Установили, количество принесенной обножки в сутки одной семьей: с 27.04 по 03.05.16 г. – 50,8 ± 2,25 г.; с 04.05 по 06.05.16 г. – 100,0 ± 3,33 г.; с 07.05 по 17.05.16 г. – 270,7 ± 11,79 г.; с 18.05 по 22.05.16 г. – 100,5 ± 3,028 г.; с 23.05 по 25.05.16 г. – 39,8 ± 2,74 г. Определили морфологические параметры пыльцевого комочка обножки с Brassica napus L.: длина в пределах от 3,40 ± 0,061 мм до 3,66 ± 0,048 мм; ширина в пределах от 2,88 ± 0,059 мм до 3,26 ± 0,067 мм; масса в пределах от 8,65 ± 0,317 мг до 11,31 ± 0,241 мг; сформированность в пределах от 4,62 – 4,96 баллов. Степень монофлорности составлял от 79,94 ± 0,619 % до 98,00 ± 0,202 %. Полученные результаты подтверждают, что активность лета пчел на сборе белкового корма из B. napus зависит от периода его цветения и интенсивности выделения нектара. Пыльцевые комочки обножки с B. napus крупные, плотные, правильной формы, без надколов, что указывает на возможность использовать их для производства в промышленных объемах.Метою&nbsp;роботи було дослідження морфологічної характеристики монофлорного бджолиного обніжжя одержаного з&nbsp;Brassica&nbsp;napus&nbsp;L. Поставлені завдання: встановити період одержання бджолиного обніжжя; здійснити відбір бджолиного обніжжя продовж цвітіння виду; встановити монофлорність загального збору обніжжя; дослідити морфометричні показники обніжжя за параметрами пилкової грудочки, сформованістю та масою. Відбір обніжжя здійснювали у Сквирському районі Київської області від сімей Apis mellifera&nbsp;L. місцевої популяції. Морфометричні вимірювання проводили в&nbsp;Інституту збереження агробіорізноманіття та біологічної безпеки, при Словацькому аграрному університеті в Нітрі. Встановили, кількість принесеного обніжжя за добу однією сім’єю: з 27.04 по 03.05.16&nbsp;р. –&nbsp;50,8 ± 2,25&nbsp;г;&nbsp;з 04.05 по 06.05.16&nbsp;р. –&nbsp;100,0 ± 3,33&nbsp;г; з&nbsp;07.05 по 17.05.16&nbsp;р. –&nbsp;270,7 ± 11,79&nbsp;г;&nbsp;з 18.05 по 22.05.16&nbsp;р. –&nbsp;100,5 ± 3,028&nbsp;г; з&nbsp;23.05 – 25.05.16&nbsp;р. –&nbsp;39,8 ± 2,74&nbsp;г. Визначили морфологічні параметри&nbsp;пилкової грудочки&nbsp;обніжжя з&nbsp;Brassica&nbsp;napus&nbsp;L.: довжина у межах від 3,40 ± 0,061&nbsp;мм до 3,66&nbsp;±&nbsp;0,048&nbsp;мм; ширина у межах від 2,88 ± 0,059&nbsp;мм до 3,26 ± 0,067&nbsp;мм; маса у межах від 8,65 ± 0,317&nbsp;мг до 11,31 ± 0,241&nbsp;мг; сформованість у межах від 4,62 – 4,96 балів. Ступінь монофлорності становив від 79,94&nbsp;±&nbsp;0,619% до 98,00 ± 0,202%. Отримані результати підтверджують, що активність льоту бджіл на зборі білкового корму&nbsp;з&nbsp;B.&nbsp;napus&nbsp;залежить від періоду його цвітіння та інтенсивності виділення нектару. Пилкові грудочки обніжжя з&nbsp;B.&nbsp;napus&nbsp;великі, щільні, правильної форми, без надколів, що вказує на можливість використовувати їх для виробництва у промислових обсягах. &nbsp