Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

Calculating the derivative of piecewise functions

Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

Structure and regulation of type 2 transglutaminase in relation to its physiological functions and pathological roles

This chapter contains sections titled: Introduction Structure and Regulation Physiologic Functions of TG2 Disruption of TG2 Functions in Pathologic Conditions Perspectives for Pharmacologic Interventions Concluding Comments Acknowledgements References

Malmquist indexes using a geometric distance function (GDF):application to a sample of Portuguese bank branches

Traditional approaches to calculate total factor productivity (TFP) change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate TFP change may introduce some bias in the analysis, and therefore we propose a procedure that calculates TFP change through observed values only. Our total TFP change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared. The proposed approach is applied in this paper to a sample of Portuguese bank branches.

Past historic in obituaries: chronicle of a death foretold

The French Past Historic (passé simple: PS), as a perfective past, is ideally suited to the obituary genre narrating the highlights of a life in chronological order. However, 20th century linguists have claimed that this tense has become obsolete. It is, therefore, worth exploring the presence of PS in obituaries. This paper explores three types of variation (diachronic, diastratic and diatopic) on a corpus of diachronic 20th century sources, and contemporary Parisian and regional newspapers. The study has noticed a diachronic diminution of the quantitative use of PS and a lesser decline of its functions as a foregrounded tense, and greater vitality in Western and Southern papers. However the geographical factor was less influential than the distribution. The readership may prove decisive as we have seen the most productive uses in the most conservative papers, the most formulaic in the left-wing paper, and the least developed in the populist paper.

Characterization of tissue transglutaminase 2 in macrophage function

Programmed cell death, apoptosis, is a highly regulated process that removes damaged or unwanted cells in vivo and has significant immunological implications. Defective clearance of apoptotic cells by macrophages (professional phagocytes) is known to result in chronic inflammatory and autoimmune disease. Tissue transglutaminase 2 (TG2) is a Ca2+-dependent protein cross linking enzyme known to play an important role in a number of cell functions. Up-regulation of TG2 is thought to be involved in monocyte to macrophage differentiation and defective clearance of apoptotic cells by TG2 null mice has been described though in this context the role of TG2 is yet to be fully elucidated. Cell surface-associated TG2 is now recognized as being important in regulating cell adhesion and migration, via its association with cell surface receptors such as syndecan-4, ß1 and ß3 integrin, but its extracellular role in the clearance of apoptotic cells is still not fully explored. Our work aims to characterize the role of TG2 and its partners (e.g. syndecan-4 and ß3 integrin) in macrophage function within the framework of apoptotic cell clearance. Both THP-1 cell-derived macrophage-like cells and primary human macrophages were analyzed for the expression and function of TG2. Macrophage-apoptotic cell interaction studies in the presence of TG2 inhibitors (both cell permeable and impermeable, irreversible and active site directed) resulted in significant inhibition of interaction indicating a possible role for TG2 in apoptotic cell clearance. Macrophage cell surface TG2 and, in particular, its cell surface crosslinking activity was found to be crucial in dictating apoptotic cell clearance. Our further studies demonstrate syndecan-4 association with TG2 and imply possible cooperation of these proteins in apoptotic cell clearance. Knockdown studies of syndecan-4 reveal its importance in apoptotic cell clearance. Our current findings suggest that TG2 has a crucial but yet to be fully defined role in apoptotic cell clearance which seems to involve protein cross linking and interaction with other cell surface receptors.

Spatially orthogonal chemical functionalization of a hierarchical pore network for catalytic cascade reactions

The chemical functionality within porous architectures dictates their performance as heterogeneous catalysts; however, synthetic routes to control the spatial distribution of individual functions within porous solids are limited. Here we report the fabrication of spatially orthogonal bifunctional porous catalysts, through the stepwise template removal and chemical functionalization of an interconnected silica framework. Selective removal of polystyrene nanosphere templates from a lyotropic liquid crystal-templated silica sol–gel matrix, followed by extraction of the liquid crystal template, affords a hierarchical macroporous–mesoporous architecture. Decoupling of the individual template extractions allows independent functionalization of macropore and mesopore networks on the basis of chemical and/or size specificity. Spatial compartmentalization of, and directed molecular transport between, chemical functionalities affords control over the reaction sequence in catalytic cascades; herein illustrated by the Pd/Pt-catalysed oxidation of cinnamyl alcohol to cinnamic acid. We anticipate that our methodology will prompt further design of multifunctional materials comprising spatially compartmentalized functions.

Differences in market-oriented behaviour levels across firms' domestic and export marketing operations:a study of antecedents and consequences

Researchers are beginning to recognise that organisations often have different levels of market orientation across different aspects of their operations. Focusing on firms involved in export marketing, this study examines how market-oriented behaviour differs across firms' domestic and export marketing operations. In this respect, the study is the first of its kind since it investigates three main issues: (1) to what extent do differences exist in firms' levels of market-oriented behaviour in their domestic markets (i.e., their domestic market-oriented behaviour) and in their export markets (i.e., their export market-oriented behaviour), (2) what are the key drivers of such differences, and (3) what are the performance implications for firms of having different levels of domestic and export market-oriented behaviour. To shed light on these research questions, data were collected from 225 British exporting firms using a mail questionnaire. Structural equation modelling techniques were used to develop and purify measures of all construct of interest, and to test the theoretical models developed. The results indicate that many of businesses sampled have very different levels of market orientation in their domestic and exporting operations: typically, firms tend to be more market-oriented in their domestic markets relative to their export markets. Several key factors were identified as drivers of differences in market orientation levels across firms' domestic and export markets. In particular, it was found that differences were more pronounced when: (i) interfunctional interactions between domestic marketing and export marketing are rare, (ii) when domestic and export marketing follow asymmetric business strategies, (iii) when mutual dependence between the functions is low, (iv) when one or other of the functions dominates the firm's sales, and (v) when there are pronounced differences in the degree to which the domestic and the export markets are experiencing environmental turbulence. The consequences of differences in market-oriented behaviour across firms' domestic and export markets were also studied. The results indicate that overall sales performance of firms (as determined by the composite of firms' domestic sales and export sales performance) is positively related to levels of domestic market-oriented behaviour under high levels of environmental turbulence in firms' domestic markets. However, as domestic market turbulence decreases, so to does the strength of this positive relationship. On the other hand, export market-oriented behaviour provides a positive contribution to firms' overall sales success under conditions of relatively low export market turbulence. As the turbulence in export markets increases, this positive relationship becomes weaker. These findings indicate that there are numerous situations in which it is sub-optimal for firms to have identical levels of market-oriented behaviour in their domestic and exporting operations. The theoretical and practical implications of these findings are discussed.

Computer aided manufacturing of geometric models

As systems for computer-aided-design and production of mechanical parts have developed, there has arisen a need for techniques for the comprehensive description of the desired part, including its 3-D shape. The creation and manipulation of shapes is generally known as geometric modelling. It is desirable that links be established between geometric modellers and machining programs. Currently, unbounded APT and some bounded geometry systems are being widely used in manufacturing industry for machining operations such as: milling, drilling, boring and turning, applied mainly to engineering parts. APT systems, however, are presently only linked to wire-frame drafting systems. The combination of a geometric modeller and APT will provide a powerful manufacturing system for industry from the initial design right through part manufacture using NC machines. This thesis describes a recently developed interface (ROMAPT) between a bounded geometry modeller (ROMULUS) and an unbounded NC processor (APT). A new set of theoretical functions and practical algorithms for the computer aided manufacturing of 3D solid geometric model has been investigated. This work has led to the development of a sophisticated computer program, ROMAPT, which provides a new link between CAD (in form of a goemetric modeller ROMULUS) and CAM (in form of the APT NC system). ROMAPT has been used to machine some engineering prototypes successfully both in soft foam material and aluminium. It has been demonstrated above that the theory and algorithms developed by the author for the development of computer aided manufacturing of 3D solid modelling are both valid and applicable. ROMAPT allows the full potential of a solid geometric modeller (ROMULUS) to be further exploited for NC applications without requiring major investment in new NC processor. ROMAPT supports output in APT-AC, APT4 and the CAM-I SSRI NC languages.

Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

Some aspects of performance at a psychokinetic task

Psychokinetic phenomena are currently anomalous with respect to physics. They are not generally accepted as genuine nor are their possible physical mechanisms understood. It is argued here that a certain class of psychokinetic phenomena, termed "directly detectable" psychokinetic effects, are likely to yield possibly important insights into the physical mechanisms mediating psychokinetic phenomena generally. The current use within parapsychological research of randomly behaving psychokinetic target systems is criticised on several grounds. They are of limited scope for use in delineation of physical mechanisms involved in psychokinesis, and their intrinsic characteristics prevent subjects from utilising their possible capacity to learn to produce larger magnitude effects. It is argued that instrumented directly detectable psychokinetic tasks have characteristics which may allow subjects to treat their psychokinetic ability as akin to a normal skill which can be improved with continued practice, using an experimental paradigm similar to that used in the biofeedback training of physiological functions. The task used in this work was a microscopic form of psychokinetic metal-bending, whereby subjects produce pulse-like electrical outputs in a ceramic piezoelectric element used as psychokinetic target. Subjects were not allowed to touch the target and many effects were obtained under witnessed conditions with subjects situated several metres from it. One pilot and three principal longitudinal training studies were performed with a total of seventeen subjects. Six of the seventeen subjects showed significant improvement in their psychokinetic performance in the training studies, one showed a non-significant increase. The other ten failed to show any convincing signs of psychokinetic output. Three of the successful subjects did not show convincing signs of voluntary control over their effects, three did. Large individual differences were found including different rates of learning and levels of initial and final ability. This research was performed by Julian David Isaacs in preparation for the degree of Doctor of Philosophy and was submitted in 1984.

The design of a support department simulator for use in the design of manufacturing systems

Manufacturing firms are driven by competitive pressures to continually improve the effectiveness and efficiency of their organisations. For this reason, manufacturing engineers often implement changes to existing processes, or design new production facilities, with the expectation of making further gains in manufacturing system performance. This thesis relates to how the likely outcome of this type of decision should be predicted prior to its implementation. The thesis argues that since manufacturing systems must also interact with many other parts of an organisation, the expected performance improvements can often be significantly hampered by constraints that arise elsewhere in the business. As a result, decision-makers should attempt to predict just how well a proposed design will perform when these other factors, or 'support departments', are taken into consideration. However, the thesis also demonstrates that, in practice, where quantitative analysis is used to evaluate design decisions, the analysis model invariably ignores the potential impact of support functions on a system's overall performance. A more comprehensive modelling approach is therefore required. A study of how various business functions interact establishes that to properly represent the kind of delays that give rise to support department constraints, a model should actually portray the dynamic and stochastic behaviour of entities in both the manufacturing and non-manufacturing aspects of a business. This implies that computer simulation be used to model design decisions but current simulation software does not provide a sufficient range of functionality to enable the behaviour of all of these entities to be represented in this way. The main objective of the research has therefore been the development of a new simulator that will overcome limitations of existing software and so enable decision-makers to conduct a more holistic evaluation of design decisions. It is argued that the application of object-oriented techniques offers a potentially better way of fulfilling both the functional and ease-of-use issues relating to development of the new simulator. An object-oriented analysis and design of the system, called WBS/Office, are therefore presented that extends to modelling a firm's administrative and other support activities in the context of the manufacturing system design process. A particularly novel feature of the design is the ability for decision-makers to model how a firm's specific information and document processing requirements might hamper shop-floor performance. The simulator is primarily intended for modelling make-to-order batch manufacturing systems and the thesis presents example models created using a working version of WBS/Office that demonstrate the feasibility of using the system to analyse manufacturing system designs in this way.