Theses supervised by Prof. Dr. Mustafa Bayram
22 theses · Yıldız Technical University, Gaziantep University, Tokat Gaziosmanpaşa University
Stokastik diferansiyel denklemlerin bazı tıp ve finans problemlerine uygulanması ve nümerik çözümleri
Bu tez çalışmasında çözümü stokastik süreçler olan stokastik diferansiyel denklemler konusu ve uygulama alanları incelenmiştir. Stokastik diferansiyel denklemlerin varlık tekliklerinden bahsedilip, analitik ve nümerik çözüm yöntemleri anlatıldıktan sonra, ilgili nümerik yöntemlerin kararlılık analizleri üzerinde durulmuştur. Uygulamalar kısmında stokastik diferansiyel denklemler, iki önemli konu olan tümör büyümesi ve hisse senedi tahminleri için kullanıldı. İlk uygulama olarak, 01.01.2005- 01.01.2015 tarihleri arasındaki YAHOO hisse senedi fiyatları, finansal bir stokastik diferansiyel denklem modeli olan Black-Scholes modeli ile yaklaşık olarak hesaplandı. İkinci bir uygulama olarak ise paratiroid tümörünün insan vücudundaki davranışı ve büyümesi üzerine çalışıldı. Bunun için öncelikle Gompertz model tanımlandı ve literatürdeki 41 gerçek hasta üzerinden paratiroid kanserinin zamana göre değişimi deterministik olarak incelendi. Daha sonra hastalar üzerinden elde edilen veriler ile, stokastik modeldeki difüzyon katsayısı belirlendi ve bu katsayı kullanılarak, deterministik Gompertz kurallarının geçerli olduğu stokastik Gompertz model tanımlandı. Tanımlanan bu stokastik model ile tümör büyümesinin zamana göre değişimi yaklaşık olarak hesaplandı. İki modelin de hem analitik çözümleri hem de tanımlanan nümerik yöntemler kullanılarak nümerik çözümleri elde edildi. Elde edilen çözümler gerçek veriler ile kıyaslandı, hata tabloları ve garfikler ile etkinlikleri gösterildi. Anahtar Kelimeler: Stokastik diferansiyel denklemler, maksimum olabilirlik tahmin metodu, non-parametrik tahmin metodu, Black-Scholes model, stokastik Gompertz model.
Kuskus–Maraş tarhana (coustar) üretim tekniğinin geliştirilmesi
Tarhana is a food product with high nutritional value, which was produced by traditional methods at homes in ancient times and reached today. There are many fermented grain products like tarhana in the world. The understanding of the importance of fermented products for human health increased. The trend shows that people do not only choose practical foods but also highly nutritious foods. Couscous is a product of cereal and it is very popular due to its wide range of uses. The nutritional value of couscous is low. People in developed and developing countries want more nutritious foods. This clearly explains the reason behind the use of tarhana while producing couscous, as additional nutrition. In this study, the flour tarhana and Maraş tarhana was transformed into the form of couscous and defined as Coustar. A more functional type of couscous has been developed. In this context, couscous has also been enriched with tarhana properties. Within the scope of the study, FTIR, DSC, texture, pH, titratable acidity, starch amount and moisture (%, wb), protein (%, db), ash (%, db) content, sensory analysis and color values (L *, a *, b *, and YI) were determined. According to TPA analysis and sensory analysis, no significant difference was found in newly produced products (p>0.05). It can be interpreted that this may be a product that is loved and consumed like couscous. According to the results of the analysis, a preferable new type of couscous with higher protein content was produced. Key Words: Tarhana, Couscous, Enrichment, Coustar, Cereal
Ultrasesin gofrete etkisi
The use of ultrasound has recently received significant attention in the food industry due to consumers' conscious and healthy food preferences, developing and changing consumption habits and especially new trends towards functional foods. The aim of this study of the improving the qualitative properties of the wafer sheets and providing the desired structure using ultrasound in wafer batters. Specifically, the aim of this project was to increase the porous texture with the necessary processing and quality properties by observing the effects of different ultrasound frequencies applied in the wafer sheets batter on the baked wafer sheet's structure and thus to obtain a high porous texture with a physical method. In this the study, it was observed that ultrasound application at 25 and 40 kHz changed the wafer properties. While this application caused to decrease in wafer weight with different time (15, 30, 45 and 60 min), batter showed different viscosity value. Applied 40 kHz ultrasound shown better result for stringy-batter texture by the way undesired gluten formation. On the other hand, the hardness of wafer sheet decreased as generally for two different ultrasound applications.
Hububat ürünlerinde patlatma süreç parametrelerinin belirlenmesi
Cereals are important sources of dietary fibre, B vitamins (thiamine, riboflavin, niacin and folic acid) and minerals such as iron, magnesium and selenium. This study aimed that the puffing cereals such as bread, durum and buckwheat, with the desired textural properties by determining the optimum parameters with the help of different pressure (6, 7 and 8 bar) and different water quantities (25, 50 and 75 mL). By determining the optimum pressure and water values for the puffing of bread wheat, durum wheat and buckwheat, it was desired to obtain a product with the desired puffing volume and texture. A product with the desired properties and texture was obtained for bread wheat at 8 bar pressure and 75 mL water. The product with the desired density and textural properties was obtained for durum wheat at 8 bar and 75 mL water. The product with the desired density and textural properties was obtained for buckwheat at 8 bar and 50 mL water.
Diferensiyel cebirsel denklemlerin kuvvet serisi ile çözümü
Bu tezde, mühendislik ve fen bilimlerinde ortaya çı diferensiyel cebirsel denklemkansistemlerini çözmek için bir metot sunuldu. İ olarak, diferensiyel cebirsel denklem sistemilkkeyfi mertebede kuvvet serisine dönüş türüldü, daha sonra nümerik sistem çözüldü. Testmetodumuzda 1-index ile iki farklı problem ele aldı Problemlerin çözümleri tam çözümlerik.ı rı .ile karş tıldılaşAnahtar kelimeler: Diferensiyel cebirsel denklem, kuvvet serileri, index, keyfi mertebe.
Rasyonel interpolasyon yöntemleri ve uygulamaları
Bu tezde, lineer olmayan interpolasyon yöntemlerinden rasyonel interpolasyon yöntemleri incelendi. Bu yöntemler ile interpolasyon polinomlarının elde edilmesi ve rasyonel interpolasyon polinomlarının hesaplanma yöntemleri açıklandı ve bunlarla ilgili algoritmalar verildi. Ayrıca bu rasyonel interpolasyon yöntemlerinden rasyonel Hermite interpolasyon yöntemi kullanılarak açık ve kapalı formüller elde edildi. Bu formüller adi diferansiyel denklemler için başlangıç değer problemine uygulanarak elde edilen yaklaşık çözümler tam çözümler ile karşılaştırıldı.
Diferensiyel cebirsel ve kısmi türevli diferensiyel cebirsel denklemlerin nümerik çözümü
Bu tezde, mühendislik ve fen bilimlerinde ortaya çıkan diferensiyel cebirsel ve kısmi türevli diferensiyel cebirsel denklemleri çözmek için diferensiyel dönüşüm metodu sunuldu. Bu metotla denklem sistemlerinin yaklaşık analitik çözümleri bulundu ve bu çözümler tam çözümlerle karşılaştırıldı. Anahtar kelimeler: Diferensiyel cebirsel denklem, kısmi türevli diferensiyel cebirsel denklem, kuvvet serileri, index, diferensiyel dönüşüm metodu.
Senkronizasyon
Senkronizasyon olgusu günlük yaşamımızın pek çok noktasında mevcuttur. Bu olguyu tanımlamak için n özdeş mekanik veya biyolojik sistemi ele aldık. Daha sonra bu sistem içinde bazı etkileşimlerin olduğunu kabul edip n çiftli özdeş sistem üzerinde çalıştık.Araştırdığımız makalelerde yalnızca lineer çiftlilerin çeşitli tipleri incelenmiştir. Biz bu çalışmada onların elde ettiği sonucu genelleyerek n çiftli özdeş lineer olmayan sistemler için senkronizasyonu ele alacağız.Bu tez aşağıdaki şekilde organize edilmiştir.1. Kısımda senkronizasyon hakkında genel bilgiler verdik. 2. Kısımda dinamik sistemler hakkında bazı tanım ve özellikleri vereceğiz. 3.Kısımda n çiftli özdeş sistemlerin global çözümleri için senkronizasyonu inceleyeceğiz. 4. Kısımda f için kesin yaklaşımlar altında yukardaki sistemin kompakt global etkileyicisinin olduğunu gösterdik. 5. Kısımda elde ettiğimiz analizleri uyguladığımız bir biyolojik model tanımladık.
Impact of acidity, hardness and iron content of cooking water on bulgur quality
The two main raw materials used in making bulgur are wheat and water. In bulgur factories, different water sources are used as water source and the chemical constituents of water affect various properties of bulgur produced. The aim of this study is to use cooking water in bulgur production after adjusting its chemical properties and to examine the quality parameters after cooking (cooked wheat) and drying, tempering, bran separation, grinding operations (bulgur) and to contribute to the production of better quality bulgur. In order to achieve this, pH (3, 5, 7, 9 and 11), hardness (~53 (soft), 129 (hard) and 269 (very hard) mg/L CaCO3) and iron contents (0, 1 and 2 ppm) of the wheat cooking water were adjusted and used in the bulgur production. In the study, some properties of water and wheat were examined during cooking. Wheat, cooked wheat and bulgur samples underwent analyses for pH, moisture, ash, protein, fat, starch, colour, phenolic compounds, antioxidant activity, mineral content and texture profile. Furthermore, FTIR and DSC analyses were performed on wheat and bulgur samples and additional sensory analysis was performed on bulgur samples. As a result of the study, it was determined that the colour of bulgur darkened in bulgur produced with cooking water with a pH ≥11 and that cooking with very hard water negatively affected the colour of bulgur, but the amount of iron did not have a negative effect on the colour. The results of the study showed that the textural properties of bulgur were not statistically significantly affected by the acidity, hardness and iron level (P>0.05) of cooking water.
Determination of optimum enzymes concentrations at reaction step of maltose syrup process
Reaction time and enzyme concentration are important parameters for the maltose syrup production. In this study, two parameter were controlled, which are enzyme and time, also was to determine the optimum starch decomposition reaction period during maltose production. Different concentrations of beta and alpha amylase enzymes (0.10, 0.15, 0.20 and 0.25 ml of β-amylase; 0.03, 0.05, 0.07 and 0.09 ml of α-amylase) were used. The concentration of dextrose, maltose, maltotriose (DP3), high sugars (DPN), pH and Brix were determined. It was found that optimum reaction time was determined as 6.0 hour to reach optimum level for each components. Enzymatic reaction of maltose syrup was optimized using three numerical models which were linear, quadratic and artificial neural network. Input variables of models were alpha amylase enzyme (E2), beta amylase enzyme (E1) and time (t). Output variables of models were the percentage of maltose, dextrose, DP3 and DPN. The results indicated that ANN model has higher performance than quadratic and linear models on sugar profile of maltose syrup. Three inputs, four outputs and one hidden layer with eleven nodes were used. Besides this feature, neural network was designed for reversing the process such that inputs are to be selected as outputs, and outputs become inputs in the first network. Desired product specifications are adjusted due to reversible feature of model. Key words: maltose, maltose syrup, starch, corn, α-amylase, β-amylase
The development of new techniques to increase the performance of germination and new products from germinated wheat and red-lentil
In this study, microwave and ultrasound aided germination operation was investigated as a new technique to produce germinated bulgur (as a new developed product) and red-lentil. During the study, microwave (1, 3 and 5 W/kg of power levels for 1, 3 and 5 mins) and ultrasound (at 40 kHz, 10, 30 and 50 W/kg of power levels for 10, 20 and 30 mins) were carried out during the germination operation (20 hrs at 25 oC, 95 % RH, non-illuminated condition) by applying at each 6-hours intervals to improve the nutritional value and to increase the germination performance of wheat (Triticum durum to produce bulgur) and red-lentil (Lens culinaris). After the germination operation, bulguration (combined cooking and drying operation) was made then milling and sieving were performed to produce bulgur from the germinated wheat. Red-lentil was directly germinated and analyzed. For both final products, yield (%), 1000-kernels weight (g, d.b.), hectolitre-weight (kg/100 L, d.b.), moisture (%, d.b.), ash (%, d.b.), protein (%, d.b.), fat (%, d.b.) and starch (%, d.b.) contents, color values (CIE L*, CIE a*, CIE b* and CIE YI) and water absorption capacities (%, d.b.) were determined. Only for bulgur samples the amount of water-soluble substance (%, g/g) was also determined. For both products, sensory analysis was made. Ultrasound and microwave operations decreased the fat contents of bulgur (P≤0.05) and red-lentil (P≤0.01). Germination increased CIE L* value of bulgur (P≤0.05); however, it decreased the fat and starch contents of wheat and red-lentil significantly.
Prediction of food requirement for future based on calorie demand
In this study, some qualitative and quantitative parameters were taken into account for foresights of the food such as global warming, climate change, environmental conditions, ozone layer and atmospheric impacts, water, culture, change in technology, agriculture, nanotechnology, innovation, bioenergy, calorie requirement, growth rate of population, distribution of age, population amount and energy amount of energy supplying compounds. As a result of this study, it is concluded that World has enough sources to feed every people around the globe in both today and in the years 2050 and 2100 if all the people share the consumption of the calorie amount equally based on their age group and gender. For example, for the year 2050, 1.24 x 109 tones/year cereal is projected to enough for the World based on above situation. To provide this, it is appraised that new type of economic models may be studied.
Solid handling properties of bulgur produced by antep and Karaman/Mut techniques
The interest on bulgur is increasing overall the World due to its nutritional and functional properties. It was one of the traditional product. However, its production has been started to made in modern plants for about 30 years. Due to the lack of the solid handling properties of bulgur in the literature, there are some plant and equipment design problems. The designers and manufacturers need some important solid handling properties. In this study, the solid handling properties of Durum and bread types bulgur were determined at each processing step of Antep and Karaman/Mut bulgur production methods. The sphericity, particle size (mm), packed and loose bulk densities (kg/m3), voidage, angle of repose, sliding angle, particle density, minimum fluidization velocity (m/s), silo discharge capacity, flow regime and size distribution (screen analysis) were measured. Additionally, the moisture (%, w.b.), protein (%, d.b.), ash (%, d.b.) contents and color values (L*, a*, b* and YI) were determined as quality parameters. It was found that the solid handling properties of bulgur during Antep and Karaman/Mut processing significantly (p≤0.05) changed. The changes in raw material, moisture, particle size and shape were very important for the solid handling properties of bulgur. Key Words: bulgur, solid handling property, sphericity, Antep bulgur, Karaman/Mut bulgur, Durum wheat, bread wheat
Future projection for Syrian food industry
Syria is a middle-income developing country with an economy that heavily depends on the food and agricultural sectors. However, with the crisis, which started in March 2011, Syria's food and agricultural industries have been badly affected. While the most of the processing factories and agricultural facilities such as greenhouses, irrigation canals and pumps have been damaged in the conflict areas, this resulted in a huge recession in the agricultural productivity of Syria. It is estimated that this will impact the country to meet the future food requirements as well. In this study the food and energy (nutritional) requirements in Syria for the years 2020, 2030, 2040 and 2050 were calculated by assessing the demand and capacity of the country before the Syrian crisis. The food requirements (ton/year) based on the various sectors and food groups were calculated, which were used to determine the amount of food to feed Syria and investment projections on the food sector. For the enhancement of the agricultural productivity, shortcomings in the sector were identified. It is aimed to provide a guidance on which basic steps should be taken during the rehabilitation period by assessing the agricultural self-sufficiency of Syria. Key Words: Syria; Food; Agriculture; Food Industry; Economy
A research on the usage of rice produced in Turkey to produce sake
Sake has been processed from rice in Japan since the ancient times as a national beverage. It is consumed at the religional and traditional ceremonies. Polishing, washing, soaking, steaming, koji preparation, the preparation of moto as yeast starter and moromi fermentation are the main steps for sake brewing. In the present study, it was aimed to designate features and the techniques of sake using short rice produced in Turkey. In this study, short type rice (Karacadağ and Krasnodarsky-424), which were taken from local rice producers, were soaked in water after the polishing operation about 70 % remain. Then, Aspergillus oryzae was inoculated and solid-fermented starter koji was added. Then, Saccharomyces cerevisiae was inoculated and waited for fermentation for a certain time. Solid-liquid mix, which was obtained from fermentation, was filtered; sake, which was liquid part, was obtained. As a result, 12.65 and 13.8 % alcohol contents were obtained by using Karacadağ and Krasnodarsky-424 type short rice, respectively. When the results of sensory analysis were evaluated, it was observed that sake produced from Karacadağ type rice was acceptable.
Search on the production techniques of wheat and red lentil brans low calorie dietary fiber
Awareness of the importance of healthy and low calorie diets is increasing overall the world due to its nutritional and functional effects on the healthy body. Enrichment dietary products with dietary fibers become common a lot nowadays. In this study, physical and chemical changes of wheat and red lentil dietary fiber were determined for soaking, cooking, microwave and ultrasound treatments. The moisture (%, w.b.), protein (%, d.b.), ash (%, d.b.), fat (%, d.b.), starch (%, d.b.), sugar (%, d.b.), carbohydrates (%, d.b.), total dietary fiber (%, d.b.), calorie and color values (L*, a*, b* and YI) were determined. It was found that the chemical properties of wheat and red lentil brans significantly (p≤0.05) changed based on production methods, soaking, cooking, microwave and ultrasound. According to the results of analyses, the fat content of wheat and red lentil dietary fibers did not change (p< 0.05) in all treatments. The dietary fibers calorie content decreased (p≤0.05) in all different treatments and the dietary fiber content increased (p≤0.05) in all different treatments except soaked wheat bran. Key Words: Wheat Bran, Red Lentil bran, Soaking, Cooking, Microwave, Ultrasound, Physical and Chemical Properties, Dietary Fibers.
Determination of processing properties of Turkish Coffee
In this study, a Brazil orginated Coffee robusta was used to obtain the optimum processing parameters and properties. Green coffee as raw material was analyzed by measuring protein content, fat content, bulk and absolute density, color, moisture content, acidity, soluble solid content, pH and ash content.In order to determine the processing parameters and techniques; three main operations were tested namely, roasting, milling and cooking. Additionally, in order to determine the effect of the storage time for Turkish coffee quality, a storage test was made. For the roasting operations, microwave (350, 490 and 700 W), infrared (600 and 1200 W) and conventional oven (160, 180, 200 and 220oC) were used. Acidity, pH, moisture content and color were measured after roasting method. The coffee was milled by using hammer and cutter type mills. According to the study, microwave roasting at 350 W for 30 min was determined as the best usable technique commercially. In cooking process, electrical and cupper pots were used as a cooking operation at various temperatures with different water softness degrees. The initial water temperature as 4oC provided the best foam volume and stability for Turkish coffee. It was observed that, the foam volume of coffee which cooked with cupper pot and tap water was higher than the other methods.The coffee was also stored at refrigeration (4oC) and room (25oC) temperatures for one month. After one month, pH, acidity, color, foam volume and stability were measured. The foam volume increased and foam stability decreased during the storage at refrigeration temperature.Key words: Turkish coffee, roasting, milling, cooking, storage.
Soğan kabuğundan serbest ve bağlı fenolik bileşik ekstraksiyonunun optimizasyonu, model gıdaların fenolik bileşik biyoyararlılığı üzerine etkisinin İn Vitro gastrointestinal sistemde incelenmesi
Bu çalışmada soğan kabuğundan serbest ve bağlı fenolik bileşik ekstraksiyonunun klasik ve ultrasonik destekli ekstraksiyon (KE ve UDE) teknikleri kullanarak optimizasyonu, optimum koşullar uygulanarak elde edilen soğan kabuğu fenolik ekstraktlarının (SKFE) fitokimyasal ve antimikrobiyal aktivitelerinin yanı sıra biyoyararlılığının in vitro gastrointestinal sistemde farklı gıda (ayçiçek yağı, krema, süt, laktozsuz süt, elma sirkesi, patates püresi, bal) ve gıda bileşenleri (oleik asit, sakkaroz, kazein) ile model sistem oluşturularak belirlenmesi amaçlanmıştır. Ayrıca, SKFE ilavesi ile ekmek ve kefir üretilmesi, ekmek ve buzdolabında depolama (+4 °C) işlemi (1., 7., 14. ve 21. gün) boyunca kefir örneklerinin in vitro biyoyararlanımları ve çeşitli özelliklerinin belirlenmesi amaçlanmıştır. Soğan kabuğundan KE ile serbest fenolik bileşik (%47.94 EtOH konsantrasyonu, 149.88 dk., 64.37 °C) ve bağlı fenolik bileşik (4.98 M NaOH konsantrasyonu, 119.34 dk., 75.80 °C) ekstraksiyonunda toplam fenolik madde (TFM) değerleri sırasıyla 75.10, 26.06 mg GAE/g kuru örnek olarak tespit edilirken, toplam flavonoid (TFL) değerleri sırasıyla 59.23, 17.34 mg KE/g kuru örnek olarak tespit edilmiştir. UDE ile serbest fenolik bileşik (%45.33 EtOH konsantrasyonu, 86.42 dk., 63.84 °C) ve bağlı fenolik bileşik (4.83 M NaOH konsantrasyonu, 87.32 dk., 61.58 °C) ekstraksiyonunda TFM değerleri sırasıyla 78.25, 20.20 mg GAE/g kuru örnek olarak tespit edilirken, TFL değerleri sırasıyla 69.70, 15.16 mg KE/g kuru örnek olarak tespit edilmiştir. Soğan kabuğu TFM değerinin yaklaşık %26'sının bağlı fenolik bileşiklerden oluştuğu belirlenmiştir. Optimum koşullarda elde edilen ekstraktların ABTS (16.36-77.18 mg TE/g kuru örnek), DPPH (5.22-29.11 mg TE/g kuru örnek) ve FRAP (26.92-82.72 mg TE/g kuru örnek) değerleri belirlenmiştir. Ekstraktların kuersetin (1.49-9.61mg/g kuru örnek), kuersetin 3-β-D glikozit (5.29-6.57 mg/g kuru örnek) ve protokateşik asit miktarları (3.18-3.87 mg/g kuru örnek) tespit edilmiştir. Ekstraktların patojen ve starter mikroorganizmalara karşı MİK değerlerinin sırasıyla, 1.563-6.25, 3.125-12.5 mg/mL aralığında değiştiği belirlenmiştir. Ekmeğe ve kefire eklenen SKFE ilavesinin artışına bağlı olarak fenolik bileşik ve antioksidan aktivite değerlerinde artış tespit edilmiştir. Ancak SKFE oranının artmasına paralel olarak ekmeğin hacim ve toplam hacim indeksinde azalma, kabuk kalınlığı ve sertlik özelliklerinde artma; kefirin ise pH değerlerinde artma tespit edilmiştir. Serum diyaliz edilebilir (IN) fazı değerlendirildiğinde TFM ve TFL açısından aktive edici etki süt, krema ve sakkaroz örneklerinde tespit edilmiştir. FRAP açısından aktive edici etki süt, laktozsuz süt, krema, ayçiçek yağı, patates püresi ve bal örneklerinde belirlenirken, ABTS açısından hiçbir kombinasyonda aktive edici etki belirlenememiştir. Bireysel fenolik bileşiklerden protokateşik açısından aktive edici etki süt, laktozsuz süt, krema, ayçiçek yağı, bal, sirke ve oleik asit kombinasyonlarında belirlenirken, kuersetin ve kuersetin 3-β-D glikozit açısından hiçbir kombinasyonda aktive edici etki tespit edilememiştir.
Research on color changes during bulgur production and the development of new systems to obtain yellow bulgur
Bulgur were tempered with two different methods: spray and steam tempering, followed by polishing with four different method: UV/Sun-light treatments, mechanical polisher, microwave/infrared and additives. In the first method, bulgur was exposed the UV/Sun-light simulation for 12, 24, 36, 48, 60 and 72 hours. In the second method, bulgur were polished using electrical heater aided mechanical polisher (EHA-MP) and modified EHA-MP with preheating systems (microwave and infrared) at 40, 60 and 80°C. In the third method, bulgur were applied to microwave with 350, 490 and 700 W for 120, 240, 360, 480 and 600 seconds. In the last method, ascorbic acid, benzoyl peroxide, potassium hydroxide, lutein and riboflavin were added separately at 5 different amounts. After tempering and polishing, moisture content (%, d. b.), ash content (%, d. b.), protein content (%, d. b.), total carotenoid content (TCC, expressed as µg/g lutein equivalent), color values (CIE L*, a*, b* and YI) and energy consumption (kJ/kg) of process were determined. It was found that steam tempering was better method than spray tempering according to CIE b* values. UV-light resulted in a noticeable (P≤0.05) improvement on the color (CIE L* and CIE b*). The strongest relationship between CIE b* (yellowness) and TCC (pigment) were obtained with steam and UV-light applied bulgur (r2=0.62). Additives increased (P≤0.05) yellowness and most of them increased the TCC. EHA-MP, UV-light treatment and microwaving consume less energy than current mechanical polishing method. As a conclusion, steam tempering and UV-light treatments should be preferred instead of current polishing method.
A study of Lebesgue constants in barycentric rational and multivariate polynomial interpolation
The Lebesgue constant is a valuable numerical instrument for linear interpolation, because it indicates how the interpolant of a function compares to the best linear approximant of that function. Furthermore, if the interpolant is computed by making use of the Lagrange basis functions, then the Lebesgue constant also expresses the conditioning of the interpolation problem at hand. Many publications have been devoted to the search for optimal interpolation points, optimal in the sense that these points lead to a minimal Lebesgue constant for interpolation problems on the interval [-1,1]. In this thesis, the best results obtained in univariate polynomial interpolation are generalized to univariate rational interpolation. In addition, this generalization provides a very practical and useful result in the case of barycentric rational interpolation, where simple equidistant interpolation points apparently yield very slowly increasing Lebesgue constants. The literature demonstrates a direct link between the orthogonality of polynomials and optimal interpolation points for polynomial interpolation. In this thesis, this connection is further explored for the case of linear interpolation, using rational functions with a predetermined denominator (preassigned poles) on the one hand and multivariate polynomial functions on the unit disk on the other hand.
A study of Lebesgue constants in barycentric rational and multivariate polynomial interpolation
The Lebesgue constant is a valuable numerical instrument for linear interpolation, because it indicates how the interpolant of a function compares to the best linear approximant of that function. Furthermore, if the interpolant is computed by making use of the Lagrange basis functions, then the Lebesgue constant also expresses the conditioning of the interpolation problem at hand. Many publications have been devoted to the search for optimal interpolation points, optimal in the sense that these points lead to a minimal Lebesgue constant for interpolation problems on the interval [-1,1]. In this thesis, the best results obtained in univariate polynomial interpolation are generalized to univariate rational interpolation. In addition, this generalization provides a very practical and useful result in the case of barycentric rational interpolation, where simple equidistant interpolation points apparently yield very slowly increasing Lebesgue constants. The literature demonstrates a direct link between the orthogonality of polynomials and optimal interpolation points for polynomial interpolation. In this thesis, this connection is further explored for the case of linear interpolation, using rational functions with a predetermined denominator (preassigned poles) on the one hand and multivariate polynomial functions on the unit disk on the other hand.
A study of Lebesgue constants in barycentric rational and multivariate polynomial interpolation
The Lebesgue constant is a valuable numerical instrument for linear interpolation, because it indicates how the interpolant of a function compares to the best linear approximant of that function. Furthermore, if the interpolant is computed by making use of the Lagrange basis functions, then the Lebesgue constant also expresses the conditioning of the interpolation problem at hand. Many publications have been devoted to the search for optimal interpolation points, optimal in the sense that these points lead to a minimal Lebesgue constant for interpolation problems on the interval [-1,1]. In this thesis, the best results obtained in univariate polynomial interpolation are generalized to univariate rational interpolation. In addition, this generalization provides a very practical and useful result in the case of barycentric rational interpolation, where simple equidistant interpolation points apparently yield very slowly increasing Lebesgue constants. The literature demonstrates a direct link between the orthogonality of polynomials and optimal interpolation points for polynomial interpolation. In this thesis, this connection is further explored for the case of linear interpolation, using rational functions with a predetermined denominator (preassigned poles) on the one hand and multivariate polynomial functions on the unit disk on the other hand.