A new dimension in thermal analysis

Summary An enormous development has taken place within the last five years in synchronous teaching over the Internet, i.e. both the teacher and the students are simultaneously in direct communication with each other as in a normal class-room or auditorium. With this concept it is possible to communicate orally, to exchange Power Point Presentations, documents, programmes and live web-camera pictures. It is even possible to use an electronic black board on which both the teacher and the students can work simultaneously. The great advantage with this type of teaching is that it is not restricted to a single class-room/auditorium with limited access, but in a virtual room accessible to everybody in principle all over the world, and which certainly open up new possibilities in teaching. The purpose of this paper is to present and to discuss the concept of virtual class-room teaching, how the system operates in practice, its advantages and, finally, how its inherent limitations can be overcome.     

Monitoring powder blending by NIR spectroscopy

A strategy is proposed for the monitoring of powder blending. Samples are taken throughout the blender vessel and scanned by diffuse reflectance spectroscopy in the NIR range. The NIR spectra are first subjected to the Standard Normal Variate transformation (SNV). The first approach consists of overlaying the transformed spectra taken from different locations at each time. To quantify the differences between the spectra, the standard deviation spectrum at each time is calculated and the mean standard deviation value is plotted as a function of time. This plot indicates the time at which the blend is most homogeneous. Each individual spectrum can be compared with the mixture spectrum, which is an approximation of the spectrum of a true homogeneous sample. For that purpose several approaches, i.e. determination of the dissimilarity, Principal Component Analysis, are proposed. As an alternative approach to monitoring the blending the use of SIMPLISMA is recommended.Dedicated to Professor Dr. h.c. mult. J.F.K. Huber on the occasion of his 70th birthday     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum-group-acceleration matching

We demonstrate how the gradient of the tapering in a tapered fiber can significantly affect the trapping and blueshift of dispersive waves (DWs) by a soliton. By modeling the propagation of a fundamental 10?fs soliton through tapered fibers with varying gradients, it is shown that the soliton traps and blueshifts an increased fraction of the energy in its DW when the gradient is decreased. This is quantified by the group-acceleration mismatch between the soliton and DW at the entrance of the taper. These findings have direct implications for the achievable power in the blue edge of a supercontinuum generated in a tapered fiber and explain observations of a lack of power in the blue edge.     

Spectral Properties for Matrix Algebras

We consider Banach algebras of infinite matrices defined in terms of a weight measuring the off-diagonal decay of the matrix entries. If a given matrix $A$ is invertible as an operator on $\ell ^2$ we analyze the decay of its inverse matrix entries in the case where the matrix algebra is not inverse closed in ${\mathcal B} (\ell ^2),$ the Banach algebra of bounded operators on $\ell ^2.$ To this end we consider a condition on sequences of weights which extends the notion of GRS-condition. Finally we focus on the behavior of inverses of pseudodifferential operators whose Weyl symbols belong to weighted modulation spaces and the weights lack the GRS condition.     

Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus

We study continuity properties for a family {s_p}_p?1 of increasing Banach algebras under the twisted convolution, which also satisfies that a∈s_p, if and only if the Weyl operator a^w(x,D) is a Schatten-von Neumann operator of order p on L². We discuss inclusion relations between the s_p-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on s_p for dilated convolution. As an application we prove that f(a)∈s₁, when a∈s₁ and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators.     

Thin film lithium aluminium negative plate material

LiAl thin film electrodes were formed by cathodic conversion of the surface of a 50 micron Al foil in a propylene carbonate based electrolyte. The films were cycled both in Li-doped poly(ethylene oxide) and propylene carbonate. On charging, an overpotential of 40 mV was required to sustain growth of the LiAl phase, but the diffusional overpotential was minimal. A simple diffusional model for the discharge predicted serious rate limitation due to slow diffusion in the α phase. However, measurements of the diffusion coefficient gave values many orders higher than previously reported and even greater values were required to explain the discharge rates. Cycling behaviour showed that the electrode degradation was less severe in the polymeric electrolyte than in propylene carbonate.     

Schatten classes for Toeplitz operators with Hilbert space windows on modulation spaces

We prove that if ω, ω₁, ω₂, v₁, v₂ are appropriate, , j=1,2, and ωa∈Lp, then the Toeplitz operator Tph₁,h₂(a) from to belongs to the Schatten-von Neumann class of order p. From this property we prove convolution properties between weighted Lebesgue spaces and Schatten-von Neumann classes of symbols in pseudo-differential calculus.