Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

TiC-MgO composite: an X-ray transparent and machinable heating element in a multi-anvil high pressure apparatus

ABSTRACT

TiC-MgO composite was developed as a heating element for X-ray study in the multi-anvil high pressure apparatus. We synthesized TiC-MgO blocks (50–70 wt.% of TiC) by compression in a cold isostatic press followed by baking in a gas flow furnace. Heaters of tubular shape were manufactured from the synthesized blocks either by lathe or numerically controlled milling machine. The so-produced heating elements have been proved to generate temperatures up to 2250?K at 10?GPa, condition where classical graphite heaters are not suitable anymore due to graphite-diamond transition. These new heaters have been successfully used for in situ X-ray radiography and diffraction measurements on liquid Fe alloys, exploiting excellent X-ray transparency.     

Bis-amino methylation for the synthesis of spiro-fused piperidines using iron(III) trifluroacetate in aqueous micellar medium

An environmentally benign, multicomponent integrated chemical process has been developed for the synthesis of 3,5-dispirosubstituted piperidines by cyclo-condensation reaction of amines, formaldehyde, and dimedone using iron(III) trifluroacetate [Fe(F₃CCO₂)₃] Lewis acid in aqueous micellar medium at ambient temperature (25–30 °C). The heterogeneous solid acid catalyst conveniently promotes this double amino methylation reaction in which six molecules condense in one pot to form six new covalent bonds. The synthesized 3,5-dispirosubstituted piperidines have been screened for their in vitro antibacterial activity using agar well method. Many of these compounds showed satisfactory antibacterial activity as compared to standard drugs against all the bacteria tested.     

The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.     

Monitoring fuel quality: a case study for quinizarin marker content of unleaded petrol marketed in Greece

Fuel adulteration and cross-contamination lead to low-quality fuel products, which may cause increased environmental pollution, loss of taxes and engine problems. An establishment of a quality monitoring mechanism based on laboratory measurements may reveal problematic areas of the fuel supply chain. For the purposes of this work, 97 unleaded petrol samples were measured in order to quantify mass concentration of quinizarin, a substance used in Greece to easily mark the presence of 95 Research Octane Number unleaded petrol in other types of automotive fuels. The samples were obtained from petroleum retail stations selling different brands of fuels and located in different geographic regions of Greece. Statistical analysis of the results revealed quinizarin mass concentrations below the 3 mg L^?1 legislation specification limit and significant differences between brands and geographic regions, which may attributed to the structure of the fuel supply chain in Greece in combination with quinizarin properties and way of handling. Moreover, certain approaches were used for the calculation of decision limits for assessing compliance or non-compliance. These approaches take measurement reproducibility or estimated in-house uncertainty into account, in order to minimize the probability of false rejection.