On L∞L^\infty estimates for Monge-Amp\`ere and Hessian equations on nef classes

The PDE approach developed earlier by the first three authors for $L^\infty$ estimates for fully non-linear equations on K\"ahler manifolds is shown to apply as well to Monge-Amp\`ere and Hessian equations on nef classes. In particular, one obtains a new proof of the estimates of Boucksom-Eyssidieux-Guedj-Zeriahi and Fu-Guo-Song for the Monge-Amp\`ere equation, together with their generalization to Hessian equations

Research on surface roughness of circular arc cut by ASJ

Izrađen je potpuni faktorijalni plan eksperimenata za istraživanje učinaka tlaka mlaza, reznog posmaka i polumjera kružnog luka na površinsku hrapavost kružnog luka rezanog mlazom abrazivne otopine - abrasive suspension jet (ASJ). Ortogonalnim planom eksperimenata analizirala se veličina djelovanja parametara na hrapavost rezne površine na različitim dubinama. Smanjivanje brzine prijelaza je najučinkovitija metoda za smanjenje površinske hrapavosti. Uz to, usporedbom topografije rezne površine s onom pomoću AWJ, ustanovilo se da je površina sastavljena od četiri zone: inicijalna zona, glatka zona, prijelazna zona i gruba zona. Konačno, primijenjena je metoda multipne linearne regresije za postavljanje modela hrapavosti površine na različitim dubinama, što se eksperimentima potvrdilo kao pouzdano. Zaključci mogu poslužiti kao teorijski vodič za poboljšanje učinkovitosti rezanja pomoću ASJ.Full factorial design of experiments was developed in order to investigate the effects of jet pressure, cutting feed, and circular arc radius upon the one response variable surface roughness of circular arc cut by abrasive suspension jet (ASJ). And orthogonal design of experiments was used for analysing the magnitude of effects of parameters on roughness of the cutting surface at different depths. Slowing down the traverse speed is the most effective method to reduce the surface roughness. In addition, comparing the topography of the cutting surface with that by AWJ, it is found that the surface also consists of four zones: initial zone, smooth zone, transition zone and rough zone. Finally, the multiple linear regression was employed to establish the model of cutting surface roughness at different depths, which was proved to be reliable by experiments. The conclusions can provide theoretical guidance for improving the cutting efficiency of ASJ

Effects of Velocity Profiles on Measuring Accuracy of Transit-Time Ultrasonic Flowmeter

Ultrasonic wave carries the information for flowing velocity when it is propagating in flowing fluids. Flowrate can be obtained by measuring the propagation time of ultrasonic wave. The principle of transit-time ultrasonic flowmeters used today was based on that the velocity is uniform along the propagation path of the ultrasonic wave. However, it is well known that the velocity profiles in a pipe are not uniform both in laminar flow and turbulent flow. Emphasis on the effects of velocity profiles across the pipe on the propagation time of ultrasonic wave, theoretical flowrate correction factors considering the real velocity profile were proposed for laminar and turbulent flow to obtain higher accuracy. Experiment data of ultrasonic flowmeter and weighting method are compared to verify the proposed theoretical correction factors. The average relative error of proposed correction factor is determined to be 0.976% for laminar flow and 0.25% for turbulent flow.</jats:p

Effects of Velocity Profiles on Measuring Accuracy of Transit-Time Ultrasonic Flowmeter

Ultrasonic wave carries the information for flowing velocity when it is propagating in flowing fluids. Flowrate can be obtained by measuring the propagation time of ultrasonic wave. The principle of transit-time ultrasonic flowmeters used today was based on that the velocity is uniform along the propagation path of the ultrasonic wave. However, it is well known that the velocity profiles in a pipe are not uniform both in laminar flow and turbulent flow. Emphasis on the effects of velocity profiles across the pipe on the propagation time of ultrasonic wave, theoretical flowrate correction factors considering the real velocity profile were proposed for laminar and turbulent flow to obtain higher accuracy. Experiment data of ultrasonic flowmeter and weighting method are compared to verify the proposed theoretical correction factors. The average relative error of proposed correction factor is determined to be 0.976% for laminar flow and 0.25% for turbulent flow