Fatma Ayaz

Solutions of the system of differential equations by differential transform method

In this study, three-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of two and three-dimensional differential transform, exact solutions of linear and non-linear systems of partial differential equations have been investigated. The results of the present method are compared very well with those obtained by decomposition method. Differential transform method can easily be applied to linear or non-linear problems and reduces the size of computational work. With this method exact solutions may be obtained without any need of cumbersome work and it is an useful tool for analytical and numerical solutions.

On the two-dimensional differential transform method

In this paper, two-dimensional differential transform method of solution of the initial value problem for partial differential equations (PDEs) have been studied. New theorems have been added and some linear and nonlinear PDEs solved by using this method. The method can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational work. In this work, additionally, analytical form solutions of two diffusion problems have been obtained and the solutions are compared very well with those obtained by decomposition method.

Applications of differential transform method to differential-algebraic equations

In this paper, numerical solution of linear differential-algebraic equations (DAEs) is considered by differential transform method. Two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions. Differential transform method can easily be applied to DAEs and series solutions are obtained. After the transformation, here, we have formulated series coefficients very simply for the considered problems.

Flow through and particle interception by an infinite array of closely-spaced circular cylinders

Steady two-dimensional laminar flow through an infinite array of parallel circular cylinders is computed numerically for values of the Reynolds number Re, based on oncoming velocity and cylinder diameter, up to 40, and for values of the spacing parameter, W (the ratio of the distance between cylinder axes to the cylinder radius), ranging from 2.3 to 10. The method used is that of Fornberg (1991). Results are presented for the dimensionless drag on a cylinder, D (or, equivalently, the dimensionless permeability of the array, β = W/D) and are compared with previous analytical results for very small Re and either wide or very narrow gaps. Results are also presented for the efficiency with which a filter consisting of such an array would capture spherical particles of radius b by direct interception, assuming that particle centres follow streamlines and that a particle is captured whenever it touches a cylinder. Such results are applicable to the study of filter feeding by small aquatic organisms.

Chemical composition and antimicrobial activity of the essential oil of Conyza canadensis (L.) Cronquist from Turkey

Abstract The essential oils obtained from the aerial parts and the roots of Conyza canadensis (L.) Cronquist (Asteraceae) at the flowering stage, collected from Turkey were simultaneously analysed by GC-FID and GC-MS. Forty-six components comprising 82.8% of the essential oil from the aerial parts and seven components comprising 96.7% of the roots oil were identified. Major constituents of the essential oil of the aerial parts were found to be limonene (28.1%), spathulenol (16.3%) and β-pinene (9.7%), whereas cis-lachnophyllum ester (86.5%), (2Z,8Z)-matricaria ester (3.9%) and β-pinene (2.3%) were identified to be main constituents in the volatiles of the root parts. In addition, antimicrobial activity of the essential oils was screened against Gram-positive and Gram-negative bacteria as well as one strain of fungus by broth microdilution method. Both of the essential oils exhibited antifungal activity against Candida albicans ATCC 10231 with 0.078 μg/ml MIC values. The highest antibacterial activity was observed by aerial parts oil against Escherichia coli RSKK 234 (MIC: 0.039 μg/ml). This is the first report on the chemical composition and antimicrobial activity of the essential oils obtained from C. canadensis growing in Turkey.

Phytotoxicity, Toxicity on Brine Shrimp and Insecticidal Effect of Chrysophthalmum gueneri Aytac & Anderb. Growing in Turkey

Objectives: The aim of this study was to investigate the probable toxicity on brine shrimp, phytotoxicity, and insecticidal activity of Chrysophthalmum gueneri Aytac & Anderb. Materials and Methods: The MeOH (80%) extract obtained from the whole plant of C. gueneri was fractionated through subsequent solvent extractions in increasing polarity with n-hexane, chloroform, and n-butanol. The MeOH (80%) extract and all fractions of C. gueneri were evaluated for their biologic activities using in vitro screening bioassays such as brine shrimp lethality test and phytotoxicity against Lemna minor, as well as insecticidal activity against Rhyzopertha dominica and Tribolium castaneum. Results: The findings showed that the n-hexane and chloroform fractions of the plant had significant phytotoxic activities with 100% growth inhibition (GI) at 1000 μg/mL against L. minor. Moreover, the MeOH (80%) extract (53% GI) and n-butanol fraction (46.6% GI) of the plant had moderate phytotoxic activities at 1000 μg/mL. Otherwise, no samples had toxicity on the brine shrimps. In addition, the remaining water fraction had low insecticidal activity with 20% mortality against T. castaneum. Conclusion: Our results show that the n-hexane and chloroform fractions of C. gueneri had potential phytotoxic effects.

Cytotoxic, Phytotoxic and Insecticidal Activities of Chrysophthalmum montanum (DC.) Boiss.

Objectives: To investigate the in vitro cytotoxic, phytotoxic, and insecticidal activity of Chrysophthalmum montanum (DC.) Boiss. Materials and Methods: The crude methanol (80%) extract of the aerial parts of C. montanum was fractionated to obtain n-hexane, chloroform, n-butanol, and remaining water fractions. The crude extract and subsequent solvent fractions of the plant were evaluated for their biological activities using screening bioassays such as cytotoxicity on brine shrimp lethality, phytotoxicity against Lemna minor L., and insecticidal activity against Rhyzopertha dominica and Tribolium castaneum. Results: The cytotoxicity assay revealed that the crude extract, n-hexane, and chloroform fractions of the plant had positive lethality with LD50 values of 71.51, 126.62, and 75.95 µg/mL, respectively. The extract and its fractions, except for the remaining water fraction, showed phytotoxic activity, which was expressed as percentage growth regulation in a concentration-dependent manner. n-hexane and chloroform fractions in particular had 100% growth inhibition (GI) at 1000 μg/mL, followed by the n-butanol fraction (62.6% GI) and crude extract (40.0% GI) of the plant at the same concentration. Otherwise, all samples had no insecticidal activity against R. dominica and T. castaneum. Conclusion: This study demonstrates that C. montanum contains bioactive compounds related to potential biological activities such as cytotoxic and phytotoxic.

Analysis of the essential oils of subgenus Caropodium from Turkey; Grammosciadium schischkinii (V.M.Vinogr. & Tamamsch.) V.M.Vinogr., G. haussknechtii Boiss., G. pterocarpum Boiss. and G. platycarpum Boiss. & Hausskn. ex Boiss.

Abstract The composition of the hydrodistilled essential oils obtained from aerial parts of Grammosciadium schischkinii (V.M.Vinogr. & Tamamsch.) V.M.Vinogr., G. haussknechtii Boiss., G. pterocarpum Boiss. and G. platycarpum Boiss. & Hausskn. ex Boiss. (Apiaceae) which belong to subgenus Caropodium, growing in Turkey, were simultaneously analyzed by GC and GC-MS. The analysis revealed fifty-seven constituents, accounting 84.3–99.5% of the oils. The essential oil composition of G. schischkinii and G. haussknechtii which are endemic taxa to Turkey, have herein demonstrated for the first time. Moreover, we firstly defined the chemical characterization of the essential oil obtained from G. platycarpum gathered from Turkey. Oil samples showed different chemical compositions with regard to species and locations. Linalool (88.5 and 94.2%) was the main component of the oil samples from G. platycarpum, while hexadecanoic acid (20.6%) was the major in the oil sample of G. haussknechtii. Caryophyllene oxide (45.9 and 20.7%) was defined as the principal constituent in the oil samples of G. schischkinii and G. pterocarpum, respectively. In addition, phytol (19.1%) was determined as the main component in the oil of G. haussknechtii and this compound was first determined in the highest amount among the essential oils of the genus Grammosciadium.