Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.     

On multiple integrals of special form

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.     

Mixing methodologies to enhance the implementation of healthcare operational research

Healthcare Operational Research (OR) has had limited success in achieving a sufficient level of stakeholder acceptance to lead to implementation of results. This research study is aimed at combining OR methodologies to achieve greater acceptance of results for organizational change. Patient flow delays in the Paediatric intensive care unit (PICU) at Children's Hospital of Wisconsin were identified using case studies. Patient flow was modelled using hard OR (simulation) using case study findings, with active stakeholder participation, and enhanced with outcomes research. Outcomes research allowed achieving greater clinical relevance of OR findings. Results from hard OR, particularly for politically sensitive issues, were persuasive but inadequate to result in change. Soft OR (cognitive mapping) was used to identify new issues and enhance results. Consequently, the planned PICU expansion was deferred, and resources focused on improving staffing strategies identified independently from both hard and soft OR. These findings suggest that: (1) Outcomes research can play a unique role to enhance results in healthcare OR. (2) After obtaining a holistic understanding of the system using hard and soft OR, stakeholders are willing to implement results from each independently, supporting the development of a common form of knowledge, which is consistent with Mixed-Mode Modelling. (3) Hard OR, enhanced with outcomes research, with active stakeholder participation, and combined with soft OR, results in greater acceptance and sustained organizational change.     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

A real time method for surface cleanliness measurement

The measurement of surface cleanliness is a significant problem in many industrial and technological processes. Existing methods are based on laboratory procedures, that are not performed in real time, can not be automated, and usually are restricted to a small portion of the sample. In this study we describe a new method for real time measurement of the amount of surface dirt or contamination deposited on a surface. It relies on the ablation of the surface dirt film by means of a short laser pulse, and the subsequent measurement of the emitted sound. The intensity of the sound is proportional to the amount of surface dirt and provides a direct measurement of the cleanliness of the surface. We also developed a reference sample for calibration, based on a uniform distribution of dots printed on white paper. The density and the dot size can be easily modified providing a homogeneous, uniform and reproducible standard for the measurement. Based on this method, we designed, developed and patented the first industrial instrument for on-line determination of the degree of cleanliness of manufactured cold rolled steel plate bobbins. PACS 79.20.D; 81.70.C; 42.62.     

Analysis of some medicinal plants in South-western Nigeria using PIXE

Summary Analysis of thirteen medicinal plants of various biological activities commonly used in South-western Nigeria was carried out using PIXE technique. Nine of these plants are anti-cancer while four are antimicrobial. PIXE measurements were carried out using collimated proton beams delivered by the 2. 5 MV AN 2000 Van de Graaff accelerator at the Istituto Nazionale di Fisica Nucleare (INFN), (LNL) Legnaro, (Padova), Italy. The results showed the presence of twenty three different elements in the plants and none of them contains any toxic heavy metals. Only Chenopodium ambrosioides showed detectable levels of selenium which is considered important in cancer prevention.     

BF3-doped polyaniline: A novel conducting polymer

We review the unusual structural, transport and magnetic properties of highly conducting polyaniline, doped with boron trifluoride. Our studies establish the unique conducting state of this system, which is in distinct contrast with the conventional proton-doped polyaniline samples.     

Solution and solid-state NMR characterization of poly(p-phenylene terephthalamide)

NMR spectroscopy has been used to characterize poly(p-phenylene terephthalamide) in the solid state and in solution in sulfuric acid. Solid-state ¹³C NMR spectra illustrate that the chain structure is highly ordered in the solid state and is of lower symmetry than in solution. Solid-state ¹³C and ¹H NMR results show that only very limited motion takes place over the temperature range of ?170 to +200°C. High-resolution NMR spectra can be observed only in very dilute isotropic solutions because it is the overall rotational motion of the polymer, not segmental motion, that averages the nuclear spin interactions to their isotropic values. These results demonstrate that previous solution NMR studies that were interpreted as reflecting the presence of isotropic and anisotropic high-molecular-weight polymer phases over a wide range of concentrations actually are representative of polymer degradation.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Generalized second law of thermodynamics in quintom dominated universe

In this Letter we will investigate the validity of the generalized second law of thermodynamics for the quintom model of dark energy. Reviewing briefly the quintom scenario of dark energy, we will study the conditions of validity of the generalized second law of thermodynamics in three cases: quintessence dominated, phantom dominated and transition from quintessence to phantom will be discussed.