Solution of fractional differential equations by using differential transform method

In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley–Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.     

Hepatic nodules in liver transplantation candidates: MR imaging and underlying hepatic disease

OBJECTIVE: To assess by MR imaging the frequency of hepatic nodules in patients waiting on the liver transplant list and to determine whether certain underlying hepatic diseases were more often associated with the development of such hepatic nodules. MATERIAL AND METHODS: We reviewed the MR and clinical records in all patients seen by the liver transplant service at our center since its inception in January 1998 until September 2002. A total of 371 patients (207 men and 164 women, age range 18-68 years, mean 45 years) were included in the study. The presence of hepatic nodules, size, number and underlying hepatic diseases were determined in all patients. Magnetic resonance imaging was performed on a 1.5-T MR imager using T1-weighted, T2-weighted and multi-phase gadolinium-enhanced sequences. Odds ratio (OR) and 95% confidence intervals (CIs) were computed to evaluate the association between the underlying hepatic disease and the development of hepatic nodule. RESULTS: Among 371 liver transplantation candidates, the most common underlying hepatic disease was hepatitis C virus (HCV) infection, either alone (n=93; 25%) or associated with other hepatic diseases (n=40; 10.8%). Of all patients, 33 (8.9%) had regenerative nodules (RNs), 40 (10.7%) dysplastic nodules (DNs) and 57 (15.3%) hepatocellular carcinomas (HCCs). Hepatocellular carcinoma was observed in 35.3% of patients with HCV infection and alcohol abuse combined, 24.5% with cryptogenic cirrhosis, 25% with hemochromatosis and 19% with alcohol abuse. Patients who had either DNs or HCC were 2.5 times more likely to have either alcohol abuse or HCV, alone or combined, as the substrate of their liver disease (OR 2.54, 95% CI 1.56-4.13). Our data suggest a supra-additive interaction between HCV infection and ethanol in their association with MR imaging detected lesions. CONCLUSION: Patients with cryptogenic cirrhosis, alcohol abuse, HCV infection (alone or combined) and hemochromatosis had the greatest likelihood of having HCC, with the combination of HCV infection and alcohol abuse having the highest of all.     

Seed Oils of Fifteen Ebenus Taxa Growing in Turkey

Oil yields and compositions from seeds of 15Ebenustaxa growing in Turkey were investigated. The yields were found between 4.0% and 13.0%. The seeds ofE. Barbigerashowed the highest whileE. Plumosavar.plumosashowed the lowest yield of oil among the 15 taxa investigated. GC/MS showed that linoleic acid (42.8-55.6%), palmitic acid (13.8-23.6%), and oleic acid (15.9-23.6%) are the main fatty acid components of all the species     

Synthesis of pyrene end‐capped A6 dendrimer and star polymer with phosphazene core via “click chemistry”

Novel hexa‐armed and pyrene (Pyr) end‐capped phosphazene dendrimer [N₃P₃‐(Pyr)₆] and star polymer with poly(ε‐caprolactone) (PCL) arms [N₃P₃‐(PCL‐Pyr)₆] were prepared via two series of reactions. In these series, core‐first approach was used starting from a hexa‐hydroxy functional phosphazene derivative (N₃P₃‐(OH)₆). It was used as an initiator in the ring‐opening polymerization of ε‐caprolactone to prepare a hexa‐armed PCL star polymer (N₃P₃‐(PCL‐OH)₆). Hydroxyl functionalities of N₃P₃‐(OH)₆ and N₃P₃‐(PCL‐OH)₆ were then successfully converted into bromide and azide, in turn. Further end‐group modifications of azide functional dendrimer precursor (N₃P₃‐(N₃)₆) and star polymer (N₃P₃‐(PCL‐N₃)₆) were achieved quantitatively via the Cu(I) catalyzed click reaction between azide functional groups and 1‐ethynyl pyrene in the final step. Moreover, the pyrene end‐capped phosphazene dendrimer and star polymer were used in noncovalent functionalization of multiwalled carbon nanotubes. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Synthesis,photopolymerization, and adhesive properties of hydrolytically stable phosphonic acid‐containing (meth)acrylamides

Three novel dental monomers containing phosphonic acid groups ( 1a and 2a , based on diethyl amino(phenyl)methylphosphonate and 3a based on diethyl 1‐aminoheptylphosphonate) were synthesized in two steps: the reaction of α‐aminophosphonates with acryloyl chloride (for monomers 1a and 3a ) or methacryloyl chloride (for 2a ) to give monomers with phosphonate groups, and the hydrolysis of phosphonate groups by using trimethyl silylbromide. Their (and the intermediates') structures were confirmed by FTIR, ¹H, ¹³C, and ³¹P NMR spectroscopy. All the monomers dissolve well in water (1<pH<2) and are hydrolytically stable. Their homo‐ and copolymerizations with 2‐hydroxyethyl methacrylate (HEMA) and HEMA/glycerol dimethacrylate were investigated with photo‐DSC. Thermal polymerization of the new monomers in water or in ethanol/water solution was investigated, giving polymers in good yields. X‐ray diffraction results showed only dicalcium phosphate dehydrate formation upon interaction of 1a ‐ 3a with hydroxyapatite indicating its strong decalcification and that monomer‐Ca salts are highly soluble. Some results were also compared to those with a bisphosphonic acid‐containing methacrylamide ( 4a ) previously reported; and the influence of monomer structure on polymerization/adhesive properties is discussed. These properties, especially hydrolytic stability and good rates of polymerization, make these new monomers suitable candidates as components of dental adhesive mixtures. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 511–522     

Highly Efficient Method Towards In Situ Immobilization of Invertase Using Cryogelation

A novel method was developed for the immobilization of Saccharomyces cerevisiae invertase within supermacroporous polyacrylamide cryogel and was used to produce invert sugar. First, the cross-linking of invertase with soluble polyglutaraldehyde (PGA) was carried out prior to immobilization in order to increase the bulkiness of invertase and thus preventing the leakage of the cross-linked enzyme after immobilization by entrapment. And then, in situ immobilization of PGA cross-linked invertase within cryogel synthesis was achieved by free radical polymerization in semi-frozen state. The method resulted in 100 % immobilization and 74 % activity yields. The immobilized invertase retained all the initial activity for 30 days and 30 batch reactions. Immobilization had no effect on optimum temperature and it was 60 °C for both free and immobilized enzyme. However, optimum pH was affected upon immobilization. Optimum pH values for free and immobilized enzyme were 4.5 and 5.0, respectively. The immobilized enzyme was more stable than the free enzyme at high pH and temperatures. The kinetic parameters for free and immobilized invertase were also determined. The newly developed method is simple yet effective and could be used for the immobilization of some other enzymes and microorganisms.     

Differential Pulse Voltammetric Determination of Montelukast in Tablets and Human Plasma by Using Chitosan Modified Carbon Paste Electrode

Electrochemical reduction and determination of montelukast (MKS) was studied in methanol – 0.1 M HCl solution (1 : 1, v/v) by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) at chitosan modified carbon paste electrode. The linear range was 1.70×10^?7–1.83×10^?5 M for DPV analysis. Limit of detection (LOD) and limit of quantification (LOQ) were 5.32×10^?8 M and 1.61×10^?7 M, respectively. The developed method was successfully applied to the determination of MKS in tablets and spiked human plasma. The results obtained were in good agreement with those obtained using a reported spectrofluorimetric technique.     

Design,Synthesis, and Biological Evaluation of Pyridazinones Containing the (2-Fluorophenyl) Piperazine Moiety as Selective MAO-B Inhibitors

Twelve pyridazinones (T1–T12) containing the (2-fluorophenyl) piperazine moiety were designed, synthesized, and evaluated for monoamine oxidase (MAO) -A and -B inhibitory activities. T6 was found to be the most potent MAO-B inhibitor with an IC₅₀ value of 0.013 µM, followed by T3 (IC₅₀ = 0.039 µM). Inhibitory potency for MAO-B was more enhanced by meta bromo substitution (T6) than by para bromo substitution (T7). For para substitution, inhibitory potencies for MAO-B were as follows: -Cl (T3) > -N(CH₃)₂ (T12) > -OCH₃ (T9) > Br (T7) > F (T5) > -CH₃ (T11) > -H (T1). T6 and T3 efficiently inhibited MAO-A with IC₅₀ values of 1.57 and 4.19 µM and had the highest selectivity indices (SIs) for MAO-B (120.8 and 107.4, respectively). T3 and T6 were found to be reversible and competitive inhibitors of MAO-B with K_i values of 0.014 and 0.0071, respectively. Moreover, T6 was less toxic to healthy fibroblast cells (L929) than T3. Molecular docking simulations with MAO binding sites returned higher docking scores for T6 and T3 with MAO-B than with MAO-A. These results suggest that T3 and T6 are selective, reversible, and competitive inhibitors of MAO-B and should be considered lead candidates for the treatment of neurodegenerative disorders like Alzheimer’s disease.     

Evaluating students’ conceptual and procedural understanding of sampling distributions

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their understanding of sampling distributions, students should have a strong conceptual foundation that is balanced with procedural knowledge. To address this issue, this study was designed to examine the relationship between college students’ procedural and conceptual knowledge of sampling distributions. With this aim in mind, an achievement test consisting of two sections – procedural and conceptual knowledge – was prepared. In answering the questions related to procedural knowledge, the participants were more successful in identifying the relationship between standard deviation of a population and sample means. However, they lacked theoretical knowledge about statements that they had heard or knew intuitively. Simulation activities provided in statistics courses may support students in developing their conceptual understanding in this regard.