Regularizing effect and local existence for non-cutoff Boltzmann equation

The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo differential operators, we prove the regularizing effect in all (time, space and velocity) variables on solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and Maxwellian type decay in velocity variable, there exists a unique local solution with the same regularity, so that this solution enjoys the $C^\infty$ regularity for positive time

Cyclotron radiation and emission in graphene

Peculiarity in the cyclotron radiation and emission in graphene is theoretically examined in terms of the optical conductivity and relaxation rates to propose that graphene in magnetic fields can be a candidate to realize the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf 48}, 559 (1986)].Comment: 4 pages, 3 figure

Effect of the atmosphere on the classification of LANDSAT data

The author has identified the following significant results. In conjunction with Turner's model for the correction of satellite data for atmospheric interference, the LOWTRAN-3 computer was used to calculate the atmospheric interference. Use of the program improved the contrast between different natural targets in the MSS LANDSAT data of Brasilia, Brazil. The classification accuracy of sugar canes was improved by about 9% in the multispectral data of Ribeirao Preto, Sao Paulo

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem

Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.Comment: 29 page

Understanding the Social Science Effect: An Intervention in Life Course Generosity

Does interacting with social science data in early adulthood promote generosity? To investigate this question from a life course development perspective, two distinct samples were drawn for a survey with an embedded experimental design. The first sample is of emerging adult college students (n = 30, median age = 20 years). The second sample is of young adults who were selected to participate based on their prior participation in a nationally representative and longitudinal study (n = 170, median age = 31 years). Toward the end of the survey, participants were randomly selected into a website interaction with either: (a) data on charitable giving, (b) data on social inequality, or (c) data about weather (a control condition). The key outcome of interest is a behavioral measure of generosity: whether participants elected to keep their study incentive or donate their incentive to a charitable organization. The donation decision occurred after the randomly selected website interaction. Interacting with charitable giving data resulted in greater generosity than interacting with weather data, across both samples. Interacting with social inequality data had mixed results. Moreover, emerging adult college students gave at a considerably higher rate overall than the national sample of young adults, net of treatment type. Implications are discussed

Influence of Magnetic Moment Formation on the Conductance of Coupled Quantum Wires

In this report, we develop a model for the resonant interaction between a pair of coupled quantum wires, under conditions where self-consistent effects lead to the formation of a local magnetic moment in one of the wires. Our analysis is motivated by the experimental results of Morimoto et al. [Appl. Phys. Lett. \bf{82}, 3952 (2003)], who showed that the conductance of one of the quantum wires exhibits a resonant peak at low temperatures, whenever the other wire is swept into the regime where local-moment formation is expected. In order to account for these observations, we develop a theoretical model for the inter-wire interaction that calculated the transmission properties of one (the fixed) wire when the device potential is modified by the presence of an extra scattering term, arising from the presence of the local moment in the swept wire. To determine the transmission coefficients in this system, we derive equations describing the dynamics of electrons in the swept and fixed wires of the coupled-wire geometry. Our analysis clearly shows that the observation of a resonant peak in the conductance of the fixed wire is correlated to the appearance of additional structure (near $0.75\cdot$ or $0.25\cdot 2e^2/h$) in the conductance of the swept wire, in agreement with the experimental results of Morimoto et al

Probing the microscopic structure of bound states in quantum point contacts

Using an approach that allows us to probe the electronic structure of strongly pinched-off quantum point contacts (QPCs), we provide evidence for the formation of self-consistently realized bound states (BSs) in these structures. Our approach exploits the resonant interaction between closely-coupled QPCs, and demonstrates that the BSs may give rise to a robust confinement of single spins, which show clear Zeeman splitting in a magnetic field