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

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

Nonholonomic constraints in kk-symplectic Classical Field Theories

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.Comment: 27 page

Case study about field trial responses of the zero energy storage system

A low cost ‘Zero Energy Cool Chamber (ZECC)’ has been developed for storing fruits and vegetables by usingpassive evaporative mechanism. This paper presents the results of a survey on the farmer’s opinion regarding the exploitationof zero energy storage system. This survey was conducted at Mymensingh district of Bangladesh from 2011 to 2012 and italso revealed that most of the farmers sell their produce to the middlemen just after the harvest. Lack of transportation facility, shortage of energy supply and lack of investment on storage, lower price of vegetables during the harvesting season, farmers in the rural areas often sell their products to the middleman or in the local market at low prices. They are not even able to get the return of invested money of cultivating vegetables or fruits. As a result, higher percentage of poverty level remains in farmer’s community. They demanded low cost storage system such as zero energy storage system which doesn’t require electricity for operating to store their agricultural produces.Keywords: agricultural produces, storage, farmer’s perception, quality, benefit, Banglades

Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

Strongly Blueshifted Phenomena Observed with {\it Hinode}/EIS in the 2006 December 13 Solar Flare

We present a detailed examination of strongly blueshifted emission lines observed with the EUV Imaging Spectrometer on board the {\it Hinode} satellite. We found two kinds of blueshifted phenomenon associated with the X3.4 flare that occurred on 2006 December 13. One was related to a plasmoid ejection seen in soft X-rays. It was very bright in all the lines used for the observations. The other was associated with the faint arc-shaped ejection seen in soft X-rays. The soft X-ray ejection is thought to be an MHD fast-mode shock wave. This is therefore the first spectroscopic observation of an MHD fast-mode shock wave associated with a flare.Comment: 18 pages, 1 table, 6 figures. ApJ, accepte

L1 transfer in the acquisition of manner and path in Spanish by native speakers of English

In this article the authors argue that L1 transfer from English is not only important in the early stages of L2 acquisition of Spanish, but remains influential in later stages if there is not enough positive evidence for the learners to progress in their development (Lefebvre, White, & Jourdan, 2006). The findings are based on analyses of path and manner of movement in stories told by British students of Spanish (N = 68) of three different proficiency levels. Verbs that conflate motion and path, on the one hand, are mastered early, possibly because the existence of Latinate path verbs, such as enter and ascend in English, facilitate their early acquisition by British learners of Spanish. Contrary to the findings of Cadierno (2004) and Cadierno and Ruiz (2006), the encoding of manner, in particular in boundary crossing contexts, seems to pose enormous difficulties, even among students who had been abroad on a placement in a Spanish-speaking country prior to the data collection. An analysis of the frequency of manner verbs in Spanish corpora shows that one of the key reasons why students struggle with manner is that manner verbs are so infrequent in Spanish. The authors claim that scarce positive evidence in the language exposed to and little or no negative evidence are responsible for the long-lasting effect of transfer on the expression of manner