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[en] In this paper, we obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.

[en] We determine the precise order of B(G)*, for G=+_iG_i, a bounded abelian 2-group, where G_i is a direct sum of r copies of a cyclic group of order 2ⁿ. The cases r=1 and r=k, for some natural number k, are respectively considered in this paper. (author)

[en] Behaviour of diamagnetic cluster oscillating along the magnetic force lines in a trap with magnetic mirrors has been studied. A periodic shift of the reflection points caused by the cluster is shown to result in the motion synchronization of particles constituting the cluster, which ensures the cluster stability. Under equilibrium conditions faster particles, advancing the cluster, are decelerated until they lag behind and then get accelerated again. At that, the fastest particle transforms to the slowest one, and then it again becomes the fastest one. The average rate of the equilibrium cluster particles should decrease monotonously from its front boundary to the rear one. During the cluster oscillation between the reflection points, simultaneously periodic compression and exteneion of ehte cluster with the period, several times exceeding the bounce-pernod, are observed

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[en] Nonlinear optics are increasingly being exploited in optoelectronic and photonic applications. Third-order nonlinear optical processes are particularly interesting, opening the possibility of all-optical switching due the intensity-dependent refractive index. The main materials considered for these applications have been molecular conjugated materials where the π-electron delocalization is believed to give rise to a high response. In order to maximise the efficiency of third-order nonlinear optical devices using these materials an improved understanding of the microscopic origin of the nonlinearity is necessary. A knowledge of the structure-property relationship would allow synthesis to be used to tune the properties of the molecular materials. This thesis contains a study of the third-order nonlinear optical properties of several conjugated molecules and polymers. The molecular contribution has been isolated by studying dilute solutions. However the macroscopic nature of third-order measurements make concentration studies necessary in order to isolate the response due to the solute. The magnitude of a nonlinear signal is determined by the electronic and two-photon allowed resonances of the medium, as well as the intrinsic response. To compare quantitatively several chemical systems, it is necessary to quantify and separate out the effect of these contributions. The third-order technique that has been used here is frequency domain coherent Raman spectroscopy, specifically Coherent Anti-Stokes Raman Spectroscopy (CARS). The Raman resonant signal is sensitive to the electronic resonances within the medium, manifested by a change in the intensity and lineshape of the coherent Raman signal. The results presented in this thesis probe the intrinsic response of the conjugated materials by separating the resonant and intrinsic terms from the coherent Raman lineshapes. The initial material was the conjugated 11 double bond molecule trans-β-carotene studied using CARS at pump wavelengths in the pre-resonance region of > 600 nm. Spontaneous Raman was also used to give improved linewidths for the fitting of the CARS spectra. Trans-β-carotene has previously been studied by various nonlinear optical techniques and therefore allowed comparison of the present work to that of other workers using alternative χ⁽³⁾ characterisation methods. The effect of shifting to higher absorption energy in conjunction with a shorter electron delocalization length was investigated using the 1,4-Bis(2-methylstyryl)-benzene molecule. The work was then extended to look at the PPV-derived conjugated polymers, MEH-PPV and CN-PPV which have the same phenylenevinylene type sub-unit as the 1,4-Bis(2-methylstyryl)-benzene. These polymers have similar energy absorption to trans-β-carotene. These data allowed us to probe how variation of electron delocalisation length and the position of electronic absorption effect the measurement of χ⁽³⁾. In the samples studied two-photon resonance was found to be important at the pump wavelengths utilised. (author)

[en] The characteristics of quasi-periodic (QP) ELF-VLF emissions with periods of 10--150 s and their relationships to magnetic pulsations are studied by using data obtained from Syowa and Mizuho Stations in Antarctica and at Husafell in Iceland, which is located near the geomagnetic conjugate point of Syowa. From the coherency analysis between QP emissions and Pc 3--4 magnetic pulsations it is found that the coherency between the D component of magnetic pulsations and the intensity fluctuations of QP's is much higher than that between the H component of magnetic pulsations and QP's. It is also found that the propagation time of magnetic pulsations (HM waves) from the interaction region between magnetic pulsations and QP's in the magnetosphere to the ground is 20--30 s. These properties are observed at conjugate-pair stations with good conjugacy. The results strongly suggest that QP emissions are modulated by compressional mode Pc 3--4 magnetic pulsations near the equatorial plane in the outer magnetosphere

[en] A long period (approx.6 min) hydromagnetic wave was observed near Lapprox.4 in the southern hemisphere at both Halley Bay and Siple, Antarctica, to have a substantially larger amplitude than that observed in the northern hemisphere conjugate areas. At Halley Bay, as well as at Siple, the wave appeared quite monochromatic. Data from a station array conjugate to Siple in the northern hemisphere showed the wave to be localized near Lapprox.3.4. Whistler wave determinations of the equatorial electron densities show the wave to occur inside the plasmasphere. The wave period and localization region are no readily reconcilable with a cold, pure hydrogen plasma. The density of heavy ions that would be required within the plasmasphere to explain the observations appears excessive from present understanding of magnetosphere plasmas

[en] The generalized Dido problem is considered - a model of the nilpotent sub-Riemannian problem with the growth vector (2,3,5). The Maxwell set is studied, that is, the locus of the intersection points of geodesics of equal length. A complete description is obtained for the Maxwell strata corresponding to the symmetry group of the exponential map generated by rotations and reflections. All the corresponding Maxwell times are found and located. The conjugate points that are limit points of the Maxwell set are also found. An upper estimate is obtained for the cut time (time of loss of optimality) on geodesics.