Examination of the Spatial Distribution of Dyes and Polymers in Thin Films by Two-Photon Microscopy

 Two-photon absorption induced fluorescence microscopy was used as a tool for the examination of the spatial distribution of a thin dye film. The two-photon absorption induced fluorescence signal is essentially the same as that produced by excitation with a single photon of equivalent energy. When femtosecond pulses are focused into a sample there is an intrinsic spatial selectivity of the two-photon emission signal, since it is dependent upon the square of the light intensity. This has tremendous implications in fluorescence microscopy. Since two-photon absorption is confined in a small region at the focal waist of an objective lens, photodamage and photobleaching of the sample are significantly reduced. In addition, the two-photon signal has inherent z-axis spatial resolution, which facilitates the construction of 3-D images. In the present work an application of this technique to a thin film of a dye is presented. The method can generally be applied to thin films made from photonic polymers.     

A Learning Framework for Neural Networks Using Constrained Optimization Methods

Conventional supervised learning in neural networks is carried out by performing unconstrained minimization of a suitably defined cost function. This approach has certain drawbacks, which can be overcome by incorporating additional knowledge in the training formalism. In this paper, two types of such additional knowledge are examined: Network specific knowledge (associated with the neural network irrespectively of the problem whose solution is sought) or problem specific knowledge (which helps to solve a specific learning task). A constrained optimization framework is introduced for incorporating these types of knowledge into the learning formalism. We present three examples of improvement in the learning behaviour of neural networks using additional knowledge in the context of our constrained optimization framework. The two network specific examples are designed to improve convergence and learning speed in the broad class of feedforward networks, while the third problem specific example is related to the efficient factorization of 2-D polynomials using suitably constructed sigma-pi networks.     

A New Efficient Heuristic for the Minimum Set Covering Problem

We solve approximately the minimum set covering problem by developing a new heuristic, which is essentially based on the flow algorithm originally developed by Ford and Fulkerson. We perform a comparative study of the performances (concerning solution qualities and execution times) of the flow algorithm as well as of the natural greedy heuristic for set covering originally studied by Johnson and Lovász.     

Fluorescence of Na2 and K2 excited by a gold vapor laser

The gold vapor laser has been used to irradiate the alkali dimers Li₂, Na₂, K₂, and Rb₂. Significant fluorescence was found only from Na₂ and K₂. Six fluorescent series in the A¹Σ_u⁺-X¹Σ_g⁺ system of Na₂ and three in the B¹Π_u-X¹Σ_g⁺ system of K₂ were assigned, respectively. New spectroscopic constants for the X¹Σ_g⁺ state of ³⁹K₂ are derived, and new RKR potential energy curves for the X¹Σ_g⁺ and B¹Π_u states of ³⁹K₂ are given.     

BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies

A methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works by the development of spectral-element methods on unstructured meshes. The present contribution shows that a certain degree of regularity of the geometry may be exploited in order to build a global stability analysis approach based on a regular spectral rectangular grid in curvilinear coordinates and conformal mappings. The derivation of the stability linear operator in curvilinear coordinates is presented along with the discretisation method. Unlike common practice to the solution of the same problem, the matrix discretising the eigenvalue problem is formed and stored. Subspace iteration and massive parallelisation are used in order to recover a wide window of its leading Ritz system. The method is applied to two external flows, both of which are lifting bodies with separation occurring just downstream of the leading edge. Specifically the flow configurations are a NACA 0015 airfoil, and an ellipse of aspect ratio 8 chosen to closely approximate the geometry of the airfoil. Both flow configurations are at an angle of attack of 18° with a Reynolds number based on the chord length of 200. The results of the stability analysis for both geometries are presented and illustrate analogous features.     

The probabilistic solution of the third boundary value problem for second order elliptic equations

Using standard reflected Brownian motion (SRBM) and martingales we define (in the spirit of Stroock and Varadhan-see [S-V]) the probabilistic solution of the boundary value problem

Sampling from a Mixture of Different Groups of Coupons

A collector samples coupons with replacement from a pool containing g uniform groups of coupons, where "uniform group" means that all coupons in the group are equally likely to occur (while coupons of different groups have different probabilities to occur). For each j=1,..., g, let T_j be the number of trials needed to detect Group j, namely to collect all M_j coupons belonging to it at least once. We first derive formulas for the probabilities P {T₁ < … < T_g} and P {T₁=Λ_j=1^g T_j}. After that, without severe loss of generality, we restrict ourselves to the case g=2 and compute the asymptotics of P {T₁ < T₂} as the number of coupons grows to infinity in a certain manner. Then, we focus on T:=T₁ ∨ T₂, i.e. the number of trials needed to collect all coupons of the pool (at least once), and determine the asymptotics of E[T] and V[T], as well as the limiting distribution of T (appropriately normalized) as the number of coupons becomes large.     

Thermal conductivity of archaeological ceramics: The effect of inclusions, porosity and firing temperature

In former studies on archaeological cooking pots or archaeological pyrotechnical ceramics their thermal conductivity was discussed only in relation with other parameters but, it was never actually determined. In the present study a modified Lees’ disk setup was used in order to determine the thermal conductivity of a series of experimental ceramic disks. As for the manufacture of these disks typical ceramic fabrics were simulated, which can be observed in archaeological cooking pots. In order to assess the effect of production parameters on the thermal conductivity, two different clays, one non-calcareous and one calcareous, were tempered with different amounts of granite or phyllite and were fired at three different temperatures: 550 °C, 850 °C and 1050 °C. The most important parameters emerged as the degree of vitrification and porosity of the ceramic matrix.