Solving non-linear elliptic difference equations by extendable sparse factorization procedures

New extendable LU sparse factorization procedures are presented for the solution of non-linear elliptic difference equations. The derived iterative methods are shown to be both competitive and computationally efficient in comparison with existing schemes. Application of the methods on non-linear elliptic boundary value problems both in two and three space dimensions are discussed and numerical results are given.     

Some basic results on M-matrices in connection with the Accelerated Overrelaxation (AOR) method

This paper extends some recent results by Varga concerning the theory of M-matrices, in connection with the well known iterative methods of Jacobi, of Extrapolated Jacobi and of Successive Over-relaxation, in two directions: i) The iteration matrix of the iterative scheme considered is more general than that of the aforementioned methods and may include a diagonal part and ii) the theory is presented in such a way that the number of equivalent statements given in the text covers the Accelerated Overrelaxation (AOR) method introduced by the present author not long ago.     

Numerische Lösung gewöhnlicher Differentialgleichungen mit Splinefunktionen

In this paper a general procedure to obtain spline approximations for the solutions of initial value problems for ordinary differential equations is presented. Several well-known spline approximation methods are included as special cases. It is common practice to partition the interval for which the initial value problem is defined into equidistant subintervals and to construct successively the spline approximation; thereby the spline function has to satisfy certain conditions at the knots. In the general procedure presented here additional knots are admitted in every subinterval. At these points which need not be equally spaced the spline approximation has to fulfill analogous conditions as at the original knots. Convergence and divergence theorems are proved; especially the influence of the additional knots on convergence and divergence of the method is investigated.     

Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter

Let the space curveL be defined implicitly by the (n, n+1) nonlinear systemH(u)=0. A new direct Newton-like method for computing turning points ofL is described that requires per step only the evaluation of one Jacobian and 5 function values ofH. Moreover, a linear system of dimensionn+1 with 4 different right hand sides has to be solved per step. Under suitable conditions the method is shown to converge locally withQ-order two if a certain discretization stepsize is appropriately chosen. Two numerical examples confirm the theoretical results.     

On real factorizations of symmetric circulant sparse matrices

For the matricesA mentioned in the headline we determine the limit points up to which there is possible a real factorization of the formA=QQ ^T . HereQ=(q _ij ) is a circulant matrix, where from the elementsq _ij andq _ji withi≠j always one element is vanishing.     

Food safety education makes the difference: food safety perceptions, knowledge, attitudes and practices among Turkish university students

This study evaluated the influence of food safety education on the food safety perceptions, knowledge, attitudes, and practices among Turkish university students. Structured questionnaires were applied to 275 students majoring in “health or food” and 570 students majoring in “non-health or non-food” on a face-to-face basis. Food has positive connotations since associated primarily with taste and hunger in both groups. Freshness of the food product was the most important factor for the “health or food major” group, which was stated as quality for the “non-health or non-food major” group, when shopping for food (p < 0.05). Food poisoning was the main risk associated with foods in the “health or food major” group whereas fats was the most popular choice for the same question in the other group (p < 0.05). Positive influence of food safety education was clear from the results since a significant difference existed between the mean scores of knowledge, attitudes, and practices according to major discipline (p < 0.05). However, persistent food safety attitudes and practices showed little improvement with education. Although a significant difference existed between the disciplines, students in both groups did not have knowledge on the risk of raw white cheese consumption (p < 0.0001). High number of students shared their bowls with other people, consumed raw eggs and raw meat, and ate cooked foods left at room temperature more than 6 h if covered. Scientists and doctors were more trusted sources of information about serious food risks (p < 0.05). Trust in governmental agencies was significantly less in both groups.     

Capability of the rosemary (Rosmarinus officinalis) extract on the oxidative stability of cooked sea bream (Sparus aurata) during frozen storage

The effects of rosemary extract addition on oxidative stability of cooked sea bream during frozen storage period were investigated. Sea bream fillets were fried, oven baked and grilled. Three groups with rosemary extract were also cooked by the same methods and cooked samples (with and without rosemary extract) were stored in ?18?°C for 4?months. After cooking procedures, the FFA formation was quite similar in fresh-raw and fried sea bream fillets, but significantly increased oven baked (0.31?C0.33% oleic acid) and grilled fillets (0.39?C0.40% oleic acid). The highest value of PV was also obtained from grilled fillets (1.18?C1.58?meq/kg). However, TBA values (1.92?mg MA/kg for fresh-raw fillet) did not increase in sea bream fillets after the frying and grilling procedure except oven baking without rosemary extract (2.41?mg MA/kg). A considerable increase in the FFA, PV and TBA was observed in all cooked groups during frozen storage period. The treated samples with rosemary extract generally showed slower PV and TBA formation than those of the untreated samples. However, the additions of rosemary extract have positive effect on sensory quality of baked sea bream.     

Fire performance and decay resistance of solid wood and plywood treated with quaternary ammonia compounds and common fire retardants

In this study, the fire performance and decay resistance of solid wood and plywood treated with quaternary ammonia compounds (didecyl dimethyl ammonium chloride (DDAC) and didecyl dimethyl ammonium tetrafluoroborate (DBF)) were compared with the performance of untreated control specimens and specimens treated with common fire retardants ((monoammonium phosphate (MAP), diammonium phosphate (DAP) and ammonium sulphate (AS)). Test specimens were treated with 1% and 4% (% m/v) aqueous solutions of the chemicals. The fire performance tests were the fire tube test (ASTM E 69) which measures mass losses in the specimens and the cone calorimeter test (ASTM E 1354) which measures mass loss, heat release rate, time for sustained ignition, effective heat of combustion, and specific extinction area. The results from the cone calorimeter tests were used to estimate the flame spread index (FSI) in the Steiner tunnel test (ASTM E 84). Heat release rates of the specimens treated with MAP, DAP, and AS were lower than those of both DDAC and DBF-treated specimens and the untreated control specimens. Compared with the untreated specimens, higher heat release rates were observed for the specimens treated with the quaternary ammonia compounds, DDAC and DBF. The estimates for the FSI for DDAC and DBF were for values equal to or higher than for the untreated control specimens. At higher concentration levels, MAP, DAP and AS were effective in decreasing initial contribution of heat release to potential fire. Decay resistance tests were done according to AWPA E 10 standard method using one brown-rot fungus and one white rot-fungus. Decay resistance tests revealed that solid wood specimens treated with DDAC and DBF showed resistance against the fungi tested, however, MAP, DAP and AS did not provide complete protection. While DBF and DDAC increased resistance of plywood specimens, high mass losses in plywood specimens treated with MAP, DAP and AS were obtained.     

Untersuchungen zum Transfer pharmakologisch wirksamer Substanzen aus der Nutztierhaltung in Porree und Weißkohl

Investigation on the transfer of pharmacologically active substances used in animal husbandry into leek and cabbage. The potential of leek and cabbage for uptake of highly prescribed veterinary drugs (antibiotics) was tested in hydroponically grown plants. For this purpose the antibiotics sulfadiazine (SFD), enrofloxacine (ENR), tetracycline (TC), chlortetracycline (CTC) and monensine (MON) were chosen. A further aim was to gain data on the situation of vegetables grown in agricultural practise with regard to antibiotic residues. The evident effects of the antibiotics on plants grown hydroponically (each antibiotic was administered at 5 μmol/l nutrient solution) were greatly different: With regard to leek there were no visible effects (MON, SFD), a weak bleaching of the younger leaf sections (CTC), and strong effects of ENR. The (phytotoxic) effects of antibiotics on cabbage were much more distinct. CTC caused a yellowing of the plant vasculature in cabbage. MON induced lesions on some leaves and finally led to leaf wilting. With administration of ENR a nearly complete bleaching of young leaves was observed. Using LC-MS/MS-methods (low-resolution and high-resolution MS) the administered antibiotics, as well as conversion products and metabolites, were separately identified and quantified in various organs of leek (roots, young and old sections of leaves) and cabbage (roots, stalks, young and old leaves). Depending on the type of antibiotic, vegetable species, and plant organ, the detected concentrations of antibiotic residues comprised several orders of magnitude ranging from μg/kg to mg/kg of fresh weight (fw). The highest concentrations of antibiotics were found in roots of both vegetable species: CTC and TC were detected at approximately 10 mg/kg fw in cabbage roots and at approximately 20 mg/kg fw in leek roots and ENR was determined at approximately 12 mg/kg fw in cabbage roots. Low amounts of ENR were metabolised to ciprofloxacine (CIP). ENR occurred at similar concentrations of approximately 7 mg/kg fw in roots and old leaves of cabbage, indicating a high transport rate of this antibiotic in the cabbage plant. In stalks, young and old leaves of cabbage and in young and old leaf sections of leek all administered antibiotics were detected. Within these antibiotics, ENR and CTC and their conversion products, e. g. demeclocycline (DMC) and TC, occurred at the highest concentrations. SFD and MON were found in considerably lower concentrations (<100 μg/kg fw). The results of our experiments in hydroponic cultures, using defined concentrations of antibiotics in the nutrient solution, evidently demonstrate that cabbage and leek have a very high potential for uptake of a number of veterinary antibiotic drugs, especially for tetracycline and ENR.