The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.     

The food preservative potential of essential oils: is lemongrass the answer?

Several essential oils of medicinal plants possess proven antimicrobial activity and are suitable for applications on the food industry. The oil from Cymbopogon citratus (lemongrass) has been reported to have a wide range of biological activities. However, there are few controlled studies confirming its antimicrobial activity. The aim of our study was to assess the antimicrobial potential of lemongrass oil against a wide spectrum of food spoilage and pathogenic bacteria and yeast in liquid and vapour phase. The chemical composition of the oil was analyzed by gas chromatography; 14 components were identified and geranial (28.93 %), neral (24.30 %) and myrcene (23.92 %) were the most abundant constituents. Lemongrass oil showed potent antimicrobial activity against Gram positive bacteria and exhibited the strongest antifungal effect against Candida albicans and C. parapsilosis. Minimum inhibitory concentration varied from 0.019 to 1.25 mg mL^?1 for Gram positive bacteria and yeasts, indicating Staphylococcus aureus, S. epidermidis and C. albicans as the most susceptible strains. Moreover, the diameter of inhibition zone (DIZ) increased with increasing essential oil (EO) volume. Considerably superior antimicrobial activity was observed in the vapour phase. The DIZ resulting from the exposure to EO vapour was significantly larger than that from the same volume in the liquid phase. The DIZ varied from 22 to 90 mm for Candida strains. There is growing evidence that EO in vapour phase are effective antimicrobial systems and that they do have advantages over the use of oil in liquid phase. Our results imply that lemongrass oil could be useful for the development of novel types of natural preservatives for food control.     

Improving the time resolution and signal noise ratio of ultrasonic testing of welds by the wavelet packet

In ultrasonic testing of welds, detection of small flaws is often difficult by the superimposed noise due to the grain structure of the material. The scattering of ultrasonic waves from grain boundaries can interfere and introduce disturbance in the received signal that can sometimes mask indications due to a small but potentially dangerous defect. However, to enhance the flaw characterization, methods based on ‘thresholding’ have given good results only when the signal to noise ratio is high, and since bandwidth of the reflected signal as well as its principal frequency is subject to wide variation, it is impossible to create an appropriate band pass filter. So linear filtering does not provide good results, because both, the structure noise and flaw signal concentrate energy in the same frequency band. Non-linear filtering can be used to reduce or suppress the noise from ultrasonic signals. One way out is to use the time frequency transforms, the method is based on the wavelet packet decomposition. The Debauchee function of order 8 [Daubauchee I. Orthogonal bases of capacity wavelets. Commun Pure Appl Math 1998;41] has been chosen as the analyzing function, and each measured ultrasonic signal is analyzed by a filter bank through only three levels of decomposition. This work demonstrates that the following analysis is very efficient with respect to signal recovery from noisy data. The experimental results have shown that the proposed method has excellent performances on SNR enhancements.     

Nominalization,predication and type containment

In an attempt to accommodate natural language phenomena involving nominalization and self-application, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briefly review the main extant proposals, and then develop a new approach, based semantically on Aczel's notion of Frege structure, which implements a version ofsubsumption polymorphism. Nominalization is achieved by virtue of the fact that the types of predicative and propositional complements are contained in the type of individuals. Russell's paradox is avoided by placing a type-constraint on lambda-abstraction, rather than by restricting comprehension.Kamareddine is grateful to the Department of Mathematics and Computing Science, Technical University of Eindhoven, for their financial support and hospitality during the academic year 1991–92.Klein's work has been carried out as part of the research programmes of the dyana project (BR 3175 and BR 6852), funded by CEC esprit Basic Research Division, and of the Human Communication Research Centre, supported by the UK Economic and Social Research Council.