Langmuir probe and spectroscopic studies of RF generated helium-nitrogen mixture plasma

This paper reports the effect of helium percentage variation in a capacitive RF helium-nitrogen mixture plasma on various plasma parameters and concentration of nitrogen active species (N₂(C³Π _u) and N₂ ⁺(B²Σ _u ⁺)). Langmuir probe is used for determination of electron energy distribution functions, effective electron temperature, plasma potential and electron density. Optical emission spectroscopy is used for determination of electron temperature from Boltzmann's plot of He–I lines and the relative changes in the concentration of active species by measuring the emission intensities of nitrogen (0-0) bands of the second positive and the first negative systems. The results demonstrate that electron temperature, electron density and concentration of active species increase significantly with increase in helium percentage in the mixture and RF power.     

Temperature dependent photoluminescence down to 4.2 K in EuTFC

The temperature dependence of photoluminescence in Europium tris[3-(trifluoro-methylhydroxymethylene)-(+)-camphorate] (EuTFC) embedded in polymer films has been examined from 40 K down to 4.2 K with the goal of preparing sensor films for low-temperature thermal imaging. The behavior of EuTFC showed significant difference when based on polystyrene compared to poly(n-alkyl methacrylate)s. In poly(n-alkyl methacrylate)s prepared by standard methods for imaging applications, the photoluminescence is fully saturated below 30 K, whereas in polystyrene films there is a strong temperature dependence even down to 4.2 K. By optimizing the preparation procedure for films made of poly(butyl methacrylate) (PBMA) and poly(methyl methacrylate), also these polymers became very sensitive down to liquid helium temperature. The maximum temperature sensitivity of EuTFC in PBMA is found to be 1.0%/K at 4.2 K. The problem of delamination and cracking of the polymer film at cryogenic temperature is also avoided by the special preparation method.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

Charge dynamics and optical properties of layered cobaltates

We study the charge dynamics and electronic structure by optical spectroscopy technique. Here we focus on the following four issues: (1) the evolution of optical spectra with Na content; (2) the spectral features specific to different regions in the phase diagram; (3) the c-axis optical response for crystal at the A-type antiferromagnetic region; (4) the optical response of misfit-layered Bi₂M₂Co₂O_y (M=Ba, Sr, Ca) and Ca₃Co₄O_y single crystals.     

Laser absorption spectroscopy for combustion diagnosis in reactive flows: A review

Laser absorption spectroscopy (LAS) has been rapidly developed and widely applied to combustion diagnosis in recent decades. As a cost-effective tool for measuring multiple combustion parameters, LAS provides unique properties in terms of accuracy and sensitivity for understanding the reactions and kinetics in reactive flows. Line-of-sight and tomographic LAS techniques have stimulated numerous applications and been proved to be robust for in situ combustion diagnosis in uniform and non-uniform combustion fields, respectively. This review highlights the breakthroughs in the evolution of LAS techniques from the viewpoints of key principles, sensors and instrumentations developed for combustion diagnosis, with particular emphasis on a series of spatially-resolved LAS techniques with their recent applications on obtaining high-fidelity measurement results with minimal intrusion to the practical combustors. Along the way, we note some challenges and requirements for further development of the LAS-based combustion diagnosis.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's and Dougall's summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

Periodic solutions for a class of superquadratic Hamiltonian systems

We prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second-order Hamiltonian systems by applying condition ^∗(C) to critical point theory, and some new solvability conditions of nontrivial periodic solutions are obtained.     

The algebra of harmonic functions for a matrix-valued transfer operator

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite-dimensional C^∗-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algorithms.     

Curriculum, Classroom Practices, and Tool Design in the Learning of Functions Through Technology-Aided Experimental Approaches

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a ‘transposition’ of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic geometry and spreadsheets. The paper focuses then on the potentialities of classroom use of computer algebra packages that could help to go beyond this shortcoming. It looks at a contradiction: while symbolic calculation is a basic tool for mathematicians, curricula and teachers are very cautious regarding their use by students. The rest of the paper considers the design and experiment of a computer environment Casyopée as means to contribute to an evolution of curricula and classroom practices to achieve the transposition in the domain of algebraic activities linked to functions.     

Ekeland’s variational principle for vectorial multivalued mappings in a uniform space

In this paper, we establish Ekeland’s variational principle and an equilibrium version of Ekeland’s variational principle for vectorial multivalued mappings in the setting of separated, sequentially complete uniform spaces. Our approaches and results are different from those in Chen et al. (2008), Hamel (2005), and Lin and Chuang (2010) [13], [14] and [15]. As applications of our results, we study vectorial Caristi’s fixed point theorems and Takahashi’s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated, sequentially complete uniform space. We also apply our results to study maximal element theorems, which are unified methods of several variational inclusion problems. Our results contain many known results in the literature Fang (1996) [21], and will have many applications in nonlinear analysis.