Mononuclear iron(III) piperazine-derived complexes and application in the oxidation of cyclohexane

Oxygenated products from selective hydrocarbon oxidation have high commercial value as industrial feedstocks. One of the most important industrial processes is the cyclohexane oxidation to produce cyclohexanol and cyclohexanone. These organic substances have special importance in the Nylon manufacture as well as building blocks for a variety of commercially useful products. In this work we present the synthesis and characterization of a new mononuclear piperazine-derived series of iron(III) complexes and their catalytic activity towards cyclohexane oxidation essays. All complexes present octahedral high-spin iron(III) center according to elemental analysis, FTIR, UV-VIS and Mössbauer spectroscopy characterization. The cyclohexane oxidation resulted in cyclohexanol, cyclohexanone and cyclohexyl hydroperoxide as products, with yields up to 39 %. The best results were obtained with the complex (NH4)[Fe(BPPZ)Cl2] (BPPZ: lithium 1,4-bis-(propanoate) piperazine) and with hydrogen peroxide as oxidant. The reactions were carried out at room temperature and atmospheric pressure, which incomes a great advantage over the current industrial process of cyclohexane production.

EFFECT OF THE DENSITY OF INUNDATION WATER ON TSUNAMI RUN-UP

Aiming for the advancement of historical and/or prospective tsunami scale evaluations, and focusing on the tsunami run-up, series solutions to the tip position a(t), velocity U (=da/dt) and acceleration d2a/dt2 in the tip region of inundation flow (unsteady flow) with sediment over a uniformly sloping bottom under the condition that the friction factor K is not linked to the density of inundation water, and analytical solutions to a(t), U(t), d2a/dt2, the maximum run-up distance a_m and height Rm under the condition that K is linked to density are derived, and effects of density on them and run-up process are theoretically examined. It is indicated that (1) in the run-up analysis (including numerical simulation) of tsunami with sediment under the condition of a constant K, even if a_m and Rm can be predicted accurately, there is a possibility of evaluating the run-up duration time inaccurately and vice versa, and (2) linking K to density is necessary to solve this matter. An expression for the relationship between K and is also presented. Moreover, it is verified that the derived series and analytical solutions are useful to discuss the effects of density on the run-up of tsunami with sediment through a comparison between the experimental and theoretical maximum run-up distances.

Sequential modelling of the Earth magnetic field

<p>Geomagnetic field models derived from satellite data cover now more than twenty years and are obtained through the processing and analyses of a massive amount of vector magnetic data. As our understanding of the geomagnetic field progresses, these models have to describe contributions of more and more sources with rather complex mathematical representation. In order to handle this increasing complexity and amount of available data, we use a sequential modelling approach (a Kalman filter), combined with a correlation based modelling step (Holschneider et al; 2016). In order to reach high temporal resolution for the core field, a sequence of snapshot models, 3-months apart, has been built. The main characteristics of the derived series of Gauss coefficients are the same as those of recently released field models based on classic modelling techniques. The results we obtained show the importance of a careful calibration of the Kalman prediction steps as well as applying Kalman smoother at the end of the modelling. We identify also the induced fields as the main limitation for an increase resolution of the core field. We will present how these induced fields have been handle in a recent version of the model and future steps to progress further in the representation of the different sources of the geomagnetic field.</p>

Geocenter coordinates and Earth rotation parameters from GPS-only, GLONASS-only, Galileo-only, and the combined GPS+GLONASS+Galileo solutions

<p>The European GNSS – Galileo can be considered as fully serviceable with 24 active satellites in space since late 2018. Galileo satellites have a different revolution period than that of GPS and GLONASS, and moreover, two additional Galileo satellites are orbiting in an eccentric orbit which helps to decorrelate some global geodetic parameters.</p><p>This contribution shows the results from Galileo-only, GPS-only, GLONASS-only, and the combined multi-GNSS solutions with a focus on Earth rotation parameters and geocenter coordinates based on the 3-year solution. We discuss the system-specific issues in individual GNSS-derived series and resonances between satellite revolution periods and Earth rotation. We found that the Galileo-based and GLONASS-based parameters are inherently influenced by the spurious signals at the frequencies which arise from the combination of the satellite revolution period and the Earth’s rotation, e.g. 3.4 days for Galileo and 3.9 days for GLONASS. On the other hand, we observe a systematic drift of GPS-based UT1-UTC values with a magnitude of 8.1 ms/year which is due to the revolution period of the GPS satellites which is equal to half of the sidereal day and causes a deep resonance. For Galileo, the UT1-UTC drift is sixteen times smaller than that of GPS and equals just 0.5 ms/year. GLONASS-derived pole coordinates and geocenter coordinates show large spurious offsets with respect GPS and Galileo solutions, as well as with respect to the IERS-C04-14 series and Satellite Laser Ranging data. GLONASS-specific problems can be partially reduced by applying a box-wing orbit model and by reducing the number of estimated empirical orbit parameters. The quality of Galileo-derived geocenter coordinates is comparable to the GPS-based results. The Galileo-derived polar motion is affected by systematic errors in receiver and satellite antenna offsets. The best results of geocenter coordinates and Earth rotation parameters can be obtained from the combined GPS+Galileo+GLONASS solutions, however, some system-specific issues still remain in the combination.</p><p> </p>

On the structure of virtually nilpotent compact p-adic analytic groups

LetGbe a compactp-adic analytic group. We recall the well-understood finite radical{\Delta^{+}}and FC-centre Δ, and introduce ap-adic analogue of Roseblade’s subgroup{\mathrm{nio}(G)}, the unique largest orbitally sound open normal subgroup ofG. Further, whenGis nilpotent-by-finite, we introduce the finite-by-(nilpotentp-valuable) radical{\mathbf{FN}_{p}(G)}, an open characteristic subgroup ofGcontained in{\mathrm{nio}(G)}. By relating the already well-known theory of isolators with Lazard’s notion ofp-saturations, we introduce the isolated lower central (resp. isolated derived) series of a nilpotent (resp. soluble)p-valuable group, and use this to study the conjugation action of{\mathrm{nio}(G)}on{\mathbf{FN}_{p}(G)}. We emerge with a structure theorem forG,1\leq\Delta^{+}\leq\Delta\leq\mathbf{FN}_{p}(G)\leq\mathrm{nio}(G)\leq G,in which the various quotients of this series of groups are well understood. This sheds light on the ideal structure of the Iwasawa algebras (i.e. the completed group ringskG) of such groups, and will be used in future work to study the prime ideals of these rings.

FREE CENTRE-BY-NILPOTENT-BY-ABELIAN LIE RINGS OF RANK 2

We study the free Lie ring of rank $2$ in the variety of all centre-by-nilpotent-by-abelian Lie rings of derived length $3$. This is the quotient $L/([\unicode[STIX]{x1D6FE}_{c}(L^{\prime }),L]+L^{\prime \prime \prime })$ with $c\geqslant 2$ where $L$ is the free Lie ring of rank $2$, $\unicode[STIX]{x1D6FE}_{c}(L^{\prime })$ is the $c$th term of the lower central series of the derived ideal $L^{\prime }$ of $L$, and $L^{\prime \prime \prime }$ is the third term of the derived series of $L$. We show that the quotient $\unicode[STIX]{x1D6FE}_{c}(L^{\prime })+L^{\prime \prime \prime }/[\unicode[STIX]{x1D6FE}_{c}(L^{\prime }),L]+L^{\prime \prime \prime }$ is a direct sum of a free abelian group and a torsion group of exponent $c$. We exhibit an explicit generating set for the torsion subgroup.

Relation of the Cyclotomic Equation with the Harmonic and Derived Series

We associate some (old) convergent series related to definite integrals with the cyclotomic equationxm-1=0, for several natural numbersm; for example, form=3,x3-1=(x-1)(1+x+x2)leads to∫01dx(1/(1+x+x2))=π/(33)=(1-1/2)+(1/4-1/5)+(1/7-1/8)+⋯. In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrarymare well defined but do imply integrals and/or series summations rather involved.

On the length of the shortest non-trivial element in the derived and the lower central series

We provide upper and lower bounds on the length of the shortest non-trivial element in the derived series and lower central series in the free group on two generators. The techniques are used to provide new estimates on the nilpotent residual finiteness growth and on almost laws for compact groups.