The statitistical evaluation of the uniaxial compressive strength of the Ruskov andesite

The selection of a suitable model of the statistical distribution of the uniaxial compressive strength is discussed in the paper. The uniaxial compressive strength was studied on 180 specimens of the Ruskov andesite. The rate of loading was 1MPa.s-1. The experimental specimens had a prismatic form with a square base; the slightness ratio of specimens was 2:1. Three sets of specimens with a different length of the base edge were studied, namely 50, 30 and 10 mm. The result of the measurement were three sets with 60 values of the uniaxial compressive strength. The basic statistical parameters: the sample mean, the sample standard deviation, the variational interval, the minimum and maximum value, the sample obliqueness coefficient and the sharpness coefficient were evaluated for each collection. Two types of the distribution which can be joined with the real physical fundamentals of the desintegration of rocks ( the normal and the Weibull distribution ) were tested. The two-parametric Weibull distribution was tested. The basic characteristics of both distributions were evaluated for each set and the accordance of the model distribution with an experimental distribution was tested. The ÷2-test was used for testing. The two-parametric Weibull distribution was selected following the comparison of the test results of both model distributions as a suitable distribution model for the characterization of uniaxial compressive strength of the Ruskov andesite. The two-parametric Weibull distribution showed better results of the goodness-of-fit test. The normal distribution was suitable for two sets; one of the sets showed a negative result of the goodness-of-fit testing. At the uniaxial compressive strength of the Ruskov andesite, a scale effect was registered : the mean value of uniaxial compressive strength decreases with increasing the specimen base edge. This is another argument for using the Weibull distribution as a suitable statistical model of the uniaxial compressive strength distribution. The Weibull distribution unlike the normal distribution enables the physical interpretation of the scale effect influence on uniaxial compressive strength value

A fixed-point approach for decaying solutions of difference equations

A boundary value problem associated to the difference equation with advanced argument \begin{equation} \label{*}\Delta\bigl (a_{n}\Phi(\Delta x_{n})\bigr)+b_{n}\Phi(x_{n+p} )=0,\ \ n\geq1 \tag{$*$} \end{equation} is presented, where $\Phi(u)=|u|^{\alpha}$sgn $u,$ $\alpha>0,p$ is a positive integer and the sequences $a,b,$ are positive. We deal with a particular type of decaying solutions of (\ref{*}), that is the so-called intermediate solutions (see below for the definition) . In particular, we prove the existence of these type of solutions for (\ref{*}) by reducing it to a suitable boundary value problem associated to a difference equation without deviating argument. Our approach is based on a fixed point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future researches complete the paper.Comment: accepted for publication on Philosophical Transactions of the Royal Society A. Issue: Topological degree and fixed point theories in differential and difference equations Editors: Maria Patrizia Pera and Marco Spadin

Características de um motor de trator alimentado com combustíveis mineral e biodisel misturados com óleo de colza

One of the most unfavourable characteristics of crude vegetable oil when used as the fuel is the high viscosity. To improve this weakness, oil can be blended with mineral diesel or biodiesel fuels. This study was designed to evaluate how the use of mineral diesel or biodiesel blend with cold pressed rapeseed (Brassica napus) oil affects the engine power, torque and fuel consumption. A tractor equipped with direct injection, water cooling system and three-cylinder diesel engine was used for the experiment. Fuels used were standard diesel fuel (diesel), rapeseed oil methyl ester - biodiesel (B100) and their mixtures with 10, 30 and 50 vol. % of cold pressed rapeseed oil (RO). Increased portion of RO in diesel fuel blends had almost no effect on the torque measured on the tractor PTO shaft; it however decreased the maximal power. Fuel blends with B100 and rising RO content (up to 50%) gave a positive correlation with maximal torque and power. By increasing the portion of RO from 0 to 50%, the minimal specific fuel consumption increased by 6.65% with diesel and decreased by 2.98% with B100 based fuel.Uma das características mais desfavoráveis dos óleos vegetais crus usados como combustível é a alta viscosidade. Para melhorar este ponto fraco, o óleo pode ser misturado com diesel mineral ou biodiesel. Este estudo foi desenvolvido para avaliar como o uso de diesel mineral ou biodiesel misturado a oleo de colza (Brassica napus) extraído por pressão a frio afeta a potência do motor, o torque e o consumo de combustível, empregando um trator equipado com injeção direta, sistema de refrigeração de água e um motor de três cilindros. Os combustíveis utilizados foram o diesel padrão (diesel), éster metílico de óleo de sementes de colza - biodiesel (B100) e suas misturas com 10, 30 e 50 % vol. de óleo de semente de colza pressionado a frio (RO). Maiores proporções de RO nas misturas de diesel praticamente não tiveram efeito sobre o torque medido na tomada de força do trator; porém diminuíram a potência máxima. Misturas com B100 e conteúdos de RO até 50% apresentaram correlações positivas com torque máximo e com a potência. Aumentando a proporção de RO de 0 a 50%, o consumo mínimo específico aumentou 6.6% com diesel e decresceu 3% com combustível baseado em B100