Halmazelmélet; Partíció kalkulus, Végtelen gráfok elmélete = Set Theory; Partition Calculus , Theory of Infinite Graphs

Előzetes tervünknek megfelelően a halmazelmélet alábbi területein végeztünk kutatást és értünk el számos eredményt: I. Kombinatorika II. A valósak számsosságinvariánsai és ideálelmélet III. Halmazelméleti topológia Ezek mellett Sági Gábor kiterjedt kutatást végzett a modellelmélet területén , amely eredmények kapcsolódnak a kombinatorikához is. Eredményeinket 38 közleményben publikáltuk, amelyek majdnem mind az adott terület vezető nemzetközi lapjaiban jelentel meg (5 cikket csak benyújtottunk). Számos nemzetközi konferencián is résztvettünk, és hárman közűlünk (Juhász, Sádi, Soukup) plenáris/meghívott előadók voltak számos alkalommal. | Following our research plan, we have mainly done research -- and established a number of significant results -- in several areas of set theory: I. Combinatorics II. Cardinal invariants of the continuum and ideal theory III. Set-theoretic topology In addition to these, G. Sági has done extended research in model theory that had ramifications to combinatorics. We presented our results in 38 publications, almost all of which appeared or will appear in the leading international journals of these fields (5 of these papers have been submitted but not accepted as yet). We also participated at a number of international conferences, three of us (Juhász, Sági, Soukup) as plenary and/or invited speakers at many of these

On the existence of a cyclic near-Rrsolvable (6n+4)-cycle system of 2K12n+9

In this article, we prove the existence of a simple cyclic near-resolvable - cycle system of for by the method of constructing its starter. Then, some new properties and results related to this construction are formulated

Planetary magnetic fields

As a consequence of the smallness of the electronic fine structure constant, the characteristic time scale for the free diffusive decay of a magnetic field in a planetary core is much less than the age of the Solar System, but the characteristic time scale for thermal diffusion is greater than the age of the Solar System. Consequently, primordial fields and permanent magnetism are small and the only means of providing a substantial planetary magnetic field is the dynamo process. This requires a large region which is fluid, electrically conducting and maintained in a non-uniform motion that includes a substantial RMS vertical component. The attributes of fluidity and conductivity are readily provided in the deep interiors of all planets and most satellites, either in the form of an Fe alloy with a low eutectic temperature (e.g. Fe-S-O in terrestrial bodies and satellites) or by the occupation of conduction states in fluid hydrogen or 'ice' (H2O-NH3-CH4) in giant planets. It is argued that planetary dynamos are almost certainly maintained by convection (compositional and/or thermal)

Chip-scale atomic magnetometer based on free-induction-decay

This thesis describes the implementation of an optically pumped caesium magnetometer containing a 1:5mm thick microfabricated vapour cell with nitrogen buffer gas, operating in a free-induction-decay configuration. This allows us to monitor the free Larmor precession of the spin coherent Cs atoms by separating the pump and probe phases in the time domain. A single light pulse can sufficiently polarise the atomic sample;however, synchronous modulation of the light field actively drives the precession and maximises the induced spin coherence. Both amplitude- and frequency-modulation have been adopted producing noise floors of 3.4 pT / √Hz and 15.6 pT/√Hz, respectively,within a Nyquist limited bandwidth of 500 Hz in a bias field comparable to the Earth's (~50 μT). We investigate the magnetometers capability in reproducing time-varying magnetic signals under these conditions, including the reconstruction of a 100 pT perturbation using signal averaging.Additionally, we discuss a novel detection mode based on free-induction-decay that observes the spin precession dynamics in-the-dark using Ramsey-like pulses. This aids in suppressing the systematic effects originating from the light-atom interaction during readout, thus vastly improving the accuracy of the magnetometer whilst maintaining a sensitivity that is competitive with previous implementations. This detection technique was implemented further to measure the spin relaxation properties intrinsic to the sensor head, useful in determining the optimal buffer pressure that extends the spin lifetime and improves the sensor's sensitivity performance.This thesis describes the implementation of an optically pumped caesium magnetometer containing a 1:5mm thick microfabricated vapour cell with nitrogen buffer gas, operating in a free-induction-decay configuration. This allows us to monitor the free Larmor precession of the spin coherent Cs atoms by separating the pump and probe phases in the time domain. A single light pulse can sufficiently polarise the atomic sample;however, synchronous modulation of the light field actively drives the precession and maximises the induced spin coherence. Both amplitude- and frequency-modulation have been adopted producing noise floors of 3.4 pT / √Hz and 15.6 pT/√Hz, respectively,within a Nyquist limited bandwidth of 500 Hz in a bias field comparable to the Earth's (~50 μT). We investigate the magnetometers capability in reproducing time-varying magnetic signals under these conditions, including the reconstruction of a 100 pT perturbation using signal averaging.Additionally, we discuss a novel detection mode based on free-induction-decay that observes the spin precession dynamics in-the-dark using Ramsey-like pulses. This aids in suppressing the systematic effects originating from the light-atom interaction during readout, thus vastly improving the accuracy of the magnetometer whilst maintaining a sensitivity that is competitive with previous implementations. This detection technique was implemented further to measure the spin relaxation properties intrinsic to the sensor head, useful in determining the optimal buffer pressure that extends the spin lifetime and improves the sensor's sensitivity performance

Particle Streak Velocimetry: A Diagnostic for High Speed Flows

This work describes the development and implementation of a novel velocimetry technique to probe the exhaust flow of a cold gas thruster. The diagnostic combines the advantages of standard particle velocimetry techniques and the ultra-fast imaging capabilities of a streak camera to probe high speed flows near continuously with improved spatial and velocity resolution compared to Particle Image Velocimetry. This “Particle Streak Velocimetry” technique tracks illuminated seed particles at up to 4.2 GHz allowing time-resolved measurement of one-dimensional flows exceeding 2000 m/s as are found in rocket nozzles and many other applications (US Provisional Patent filed 05/19/16). Single frame images containing multiple streaks are analyzed to find the slope of each incident particle. Tests with inert gas have been performed to validate and develop the technique in supersonic flows without background noise due to combustion. Exhaust centerline flow velocities of a cold gas nozzle flowing pure nitrogen have been probed with 300 nm titanium dioxide seed particles and a 450 nm, continuous-wave laser diode. Measured velocities on the order of 500 m/s were validated against schlieren images of the plume and stagnation temperature measurements, which can also be correlated to velocity for known flow compositions. Further tests using a mixture of helium and nitrogen have been performed with measured velocities of over 1100 m/s that are shown to agree with predicted behavior from isentropic flow analyses