Theoretical analysis of an optimal control problem of conductive–convective–radiative heat transfer

The problem of optimal heat removal from a three-dimensional domain is considered. The specific of the study consist in accounting for the radiative heat transfer. The so-called P₁ approximation of the radiative heat transfer equation is used, which reduces the model to a nonlinear elliptic system. A problem of optimal boundary control of this system is considered. The solvability of the control problem is proved, and necessary optimality conditions of first order are derived. Examples of non-singularity of these conditions are given.     

Big elements in irreducible linear groups

Let V be a linear space over a field K of dimension n > 1, and let \({G \leq {\rm GL}(V)}\) be an irreducible linear group. In this paper we prove that the group G contains an element g such that rank \({(g - \alpha E_{n}) \geq \frac{n}{2}}\) for every \({\alpha \in K}\) , where E _n is the identity operator on V. This estimate is sharp for any \({n = 2^{m}}\) . The existence of such an element implies that the conjugacy class of G in GL(V) intersects the big Bruhat cell \({B\dot{w}_{0}B}\) of GL(V) non-trivially (here B is a fixed Borel subgroup of G). The latter fact is equivalent to the existence of a complete flag \({\mathfrak{F}}\) such that the flags \({g(\mathfrak{F}), \mathfrak{F}}\) are in general position for some g ∈ G.     

The first one-pot ‘alkane-like’ reactions of carbonyl-containing adamantanes

A novel ‘alkane-like’ methodology for the direct and very simple one-pot functionalization of amides and an ester of 1-adamantanecarboxylic acid provides access to new and synthetically challenging 1,3-dicarbonyl-containing adamantanoid compounds with the same or different functional groups.     

Boron trifluoride–etherate mediated synthesis of 3-desoxyanthocyanidins including a total synthesis of tricetanidin from black tea

The synthesis of a series of 3-desoxyanthocyanidins via a BF₃·Et₂O-mediated aldol condensation between a substituted acetophenone and salicylaldehyde derivatives is described. Using this new synthetic methodology the synthesis of tricetanidin, a natural pigment isolated from black tea, was accomplished.     

Fusion of 2-D SIMS Images Using the Wavelet Transform

 Secondary ion mass spectroscopy (SIMS) is a powerful method for element distribution examination of conducting and semi-conducting surfaces at high spatial resolution and with a high sensitivity. Routine surface analysis produces about 8 to 15 images in a short time, each of which displays the intensity distribution of one mass, thus generating a multispectral SIMS image. Formation of occlusions, segregations, and the overall location of the elements relative to each other, are difficult to recognise when looking at n separate 2-D images. Image fusion is a process whereby images obtained from various sensors, or at different moments of time, or under different conditions, are combined together to provide a more complete picture of the object under investigation. The process of combining SIMS images may be viewed as an attempt to compensate for the inherent effect of SIMS to channel the information obtained from the sample into different images, corresponding to different element phases. The wavelet transform is a powerful method for fusion of images. This work covers the use of wavelet based fusion algorithms on multispectral SIMS images, evaluating the performance of different wavelet based fusion rules on different type of image systems and comparing the results to conventional fusion techniques. An aim of this study is to increase the information, i.e. the number of masses, which can be merged into one image in order to enhance the perception and interpretation of the SIMS surface images.     

The modes of combustion of copper nanopowders

It was shown that the synthesis of Cu nanopowder by thermal decomposition afforded chemically purer (without oxides) and finer (specific surface value ～45 m2 g^?1) product than the synthesis by chemical reduction. The latter method leads to pyrophoric nanopowders containing detectable amounts of copper oxides.