Real Continuum Research Articles

Molecular subtypes of bladder cancer: Jekyll and Hyde or chalk and cheese?

Cancer of the bladder shows divergent clinical behaviour following diagnosis and it has been proposed that two major groups of tumours exist that develop via different molecular pathways. Low-grade, non-invasive papillary tumours recur frequently, but patients with these tumours do not often suffer progression of disease to muscle invasion. In contrast, tumours that are invading muscle at diagnosis are aggressive and associated with significant mortality. Molecular studies have identified distinct genetic, epigenetic and expression changes in these groups. However, it is not yet clear whether there is direct progression of low-grade superficial tumours to become invasive (a Jeckell and Hyde scenario) or whether in those patients who apparently progress from one form of the disease to the other, different tumour clones are involved and that the two tumour groups are mutually exclusive ('chalk and cheese'). If the latter is true, then attempts to identify molecular markers to predict progression of low-grade superficial bladder tumours may be fruitless. Similarly, it is not clear whether other subgroups of tumours exist that arise via different molecular pathways. There is now a large amount of molecular information about bladder cancer that facilitates examination of these possibilities. Some recent studies provide evidence for the existence of at least one further group of tumours, high-grade superficial papillary tumours, which may develop via a distinct molecular pathway. Patients with such tumours do show increased risk of disease progression and for these there may exist a real progression continuum from non-invasive to invasive. If this is the case, definition of the molecular signature of this pathway and improved understanding of the biological consequences of the events involved will be pivotal in disease management.

La neurogénèse dans le cerveau adulte : de l’effondrement des dogmes vers de nouvelles thérapies ?

Since the early sixties, many concepts concerning neurogenesis have been progressively ruled out. Proof of the persistence of a physiological neurogenesis in adult mammals, including humans, raised the concept of a unique precursor cell giving birth to neurons and glial cells. According to this concept, a real continuum between neuroepithelial cells, radial glia and astrocytes exists from the embryonic period to adult age and generates both neurons and glial cells. Different factors, either secreted in situ or transported by blood, can influence this physiological neurogenesis process. The targets and role of newborn neurons are not clearly understood. In pathological conditions (ischemia, epilepsy, lesions), the physiological neurogenesis process is enhanced; however the significance of this neurogenesis excess (beneficial or deleterious) is not completely known. Advances in understanding the regulation of neurogenesis in these different conditions represent hopes of new therapeutic procedures, not only by improving the control of differentiation and survival of transplanted stem cells, but also by the possibility of modifying the processes of "endogenous neurogenesis".

The structure of H$\mathsf{_{2}}$O shells in Mira atmospheres

Dynamic models of M-type Mira variables predict the occurrence of water "shells", i.e. of zones of high H2O density and high H2O absorption inside the stellar atmosphere. The density, position and width of these shells is closely correlated with different types of two-component shapes of the intensity distribution on the disk in the H, K and L near-continuum bandpasses. We investigate these correlations and highlight the role of a spectrophotometric H2O index that warns against serious complications in diameter measurements in the case of substantial water contamination of the bandpass of observation. Simultaneous spectrophotometric and interferometric measurements may allow observers to estimate real continuum diameters more precisely.

On possible non-homeomorphic substructures of the real line

We consider the problem, raised by Kunen and Tall, of whether the real continuum can have non-homeomorphic versions in different submodels of the universe of all sets. This requires large cardinals, and we obtain an exact consistency strength: Theorem 1. The following are equiconsistent: (i) ZFC + ∃κ a Jonsson cardinal; (ii) ZFC + 3M a sufficiently elementary submodel of the universe of sets with R M not homeomorphic to R. The reverse direction is a corollary to: Theorem 2. c is Jdnsson ⇔ ∃M < H(c + )∃X M hereditarily separable, hereditarily Lindelof, T 3 with X ¬= X M . We further consider the large cardinal consequences of the existence of a topological space with a proper substructure homeomorphic to Baire space.

Eliminating the ‘hard’/‘soft’ real-time dichotomy

A brief and informal overview is given of a new framework which permits timeliness to be expressed and enforced for the whole real time continuum in a well defined and general way. The framework has been successfully implemented and used experimentally. The new model of timeliness which was created is called the benefit accrual model. It is a framework for expressing timeliness requirements across a wide spectrum of real time hardness and softness in a unified and well defined manner-timeliness is a continuum of softness, in which &apos;hard&apos; is one end point. This model is a generalisation of the earlier time value functional model (E.D. Jensen et al., 1985) in the Alpha kernel. The framework is based on three orthogonal functions for specifying timeliness: the time constraint for individual computations; the collective timeliness of a set of computations; and the acceptability of collective timeliness of a set of computations. First, the author introduces the idea of timeliness as a scoped attribute of a computation.

Computational Machining of Titanium Alloy—Finite Element Modeling and a Few Results

A Finite element modeling was developed for the computational machining of titanium alloy Ti-6Al-4V. The chip formation in metal cutting is one of the large deformation problems, thus, in the formulation of the elastic-plastic deformation analysis, geometrical nonlinearity due to the large shape change of the finite elements was taken into account and the over-constraint of incompressibility on the deformation of ordinary finite elements in the plastic range was relaxed to make the elements deformable as a real continuum. A ductile fracture criterion on the basis of strain, strain rate, hydrostatic pressure and temperature was applied to the crack growth during the chip segmentation. The temperature field in the flowing chip and workpiece and the fixed tool was calculated simultaneously by an unsteady state thermal conduction analysis and the remeshing of tool elements. The serrated chips predicted by the computational machining showed striking resemblances in the shape and irregular pitch of those obtained by actual cutting. The mean cutting forces and the amplitude of cutting force vibration in the computational machining were in good agreement with those in the actual machining.

三次元切削の有限要素法シミュレーション 工具食付き過程の大変形問題の解析

Tool entry process in three dimensional cutting is simulated by finite element method. Since the chip forming process is one of large deformation problems, geometrical nonlinearity due to the change of shape is introduced into finite element formulation. Constant strain tetrahedra element is used and over-constraint of incompressibility on the deformation of the finite elements in plastic region is relaxed using Nagategaal-Rice functional to make the elements as deformable as real continuum. The chip formation from tool entry to steady state is realized in the analysis and stress and strain distributions in chip and machined surfaces are also obtained. Lower shear angle at side surface of the work, side flow and chip flow direction predicted are in good agreement with experimental results of cutting of plasticine.

チタン合金（Ｔｉ‐６Ａｌ‐４Ｖ）の鋸歯状切りくず生成のＦＥＭシミュレーション 第１報 解析手法の定式化と一二の適用例

A finite element modelling, which consists of elastic-plastic deformation analysis and unsteady state thermal conduction analysis, has been developed to simulate the serrated chip formation of titanium alloy Ti-6Al-4V. Since the chip formation in metal cutting is one of the large deformation problems, geometrical nonlinearity due to the change of shape is introduced into finite element formulation and over-constraint of incompressibility on the deformation of finite elements in plastic range is relaxed to make the elements deformable as real continuum. A strain criterion for ductile fracture, which is modified using hydrostatic pressure, temperature and strain rate, is applied to the crack growth in the segmentation of the chip. The serrated chips obtained through the simulation shows a striking resemblance in their shape and irregular pitch to those by actual cutting. Maximum temperature does not locate on the rake face but in the chip close to cutting edge because of the low thermal conductivity and low specific heat of titanium alloy.

Non-universal elasticity exponent for three-dimensional continuum percolation systems

Abstract The measured Young's moduli of three real continuum systems (sintered glass beams, sintered Al2O3 ceramics, and gel-derived porous silica) with the volume fraction p occupied by solid phase are analyzed in terms of percolation theory. The elasticity critical exponents for the three systems, measured in the range 0.058 ⩽ (p−p c ) ⩽ 0.35 , are about 1–3, less than recent theory and numercial simulation values for lattice and continuum elastic models. The differences show that a non-universal elasticity exponent can be obtained in real continuum percolation systems.

Continuum and emission-line variability of the Seyfert galaxy Arakelian 120 - Analysis of a large database

New spectrophotometric observations are combined with observations from earlier papers to construct a homogeneous data base of 107 optical continuum measurements and 75 H-beta flux measurements of the Seyfert 1 galaxy Akn 120. Statistical analysis of these data reveals that: (1) the individual measurements are apparently accurate to better than about 10 percent; (2) there is no reliable evidence for real continuum or emission-line variations on timescales shorter than about 20 days; and (3) there is substantial evidence for real variations in both the line and the continuum on timescales in the range of about 20-40 days. Indeed, large-amplitude (nearly a factor of 2) emission-line changes have been detected on several occasions over intervals shorter than two months. The correlation between the continuum and emission-line changes is consistent with the earlier claim that the broad-line region is quite small in this galaxy. 24 refs.

Resonances and background: A decomposition of scattering information.

An analytic representation of the full Green's function including bound states, resonances, and remaining contributions has been obtained for a class of dilatation analytic potentials, including the superimposed Coulomb potential. It is demonstrated how to obtain the locations and residues of the poles of the Green's function as well as the associated generalized spectral density. For a model potential which has a barrier and decreases exponentially at infinity we have found a certain deflation property of the generalized spectral density. A qualitative explanation of this phenomenon is suggested. This constitutes the motivation for an approximation that explicitly shows a decomposition of the (real) continuum, corresponding to scattering data, into resonances and background contributions. The present representation is also shown to incorporate the appropriate pole-background interferences. Numerical residue strings are computed and analyzed. Results for the Coulomb potential plus the above-mentioned model potential are reported and compared with the previous non-Coulomb case. A similar deflation effect is seen to occur, as well as basically the same pole- and residue-string behavior. The relevance of the present analysis in relation to recently planned experiments with electron-cooled beams of highly charged ions is briefly discussed.

Bright threads in the inner wing of solar Ca II K line

On spectrograms of the K line at quiet regions of the Sun, bright threads visible in the real continuum due to the granulations are also seen in the outer wing as far as ¦Δλ¦ ∼ 3 A from the line centre. At the inner wing (3 A ≳ ¦Δλ¦ ≳ 0.5 A) bright threads are also seen, but their spatial distribution is different from the former ones. The threads at the inner wing appear at intergranular regions, and many of them are seen inside the supergranulation. Their size and number density are about the same as those of the granulation. These facts reflect that the penetration of the granular high temperature layer stops at a certain height in the photosphere, and that the intergranular bright threads at the inner wing are due to a hotter temperature layer, located at a considerably higher photospheric layer than the granulation.

A general Laguerre transform and a related distance between probability measures

A Laguerre transform will be exhibited which maps both functions in L2( x1, x) and finite signed measures into two-sided square summable sequences, extending previous results of Keilson, Nunn, and Sumita [4, 5. 141. The norm natural to the associated Hilbert space will be shown to provide a theoretically simple and numerically quantifiable measure for the distance between two probability distributions. A practical tool for measuring the convergence of iterative procedures. and a stopping criteria for such procedures are thereby obtained. In previous papers [4, 5, 143 an algorithmic framework was developed for the computer evaluation of repeated combinations of multiple convolutions, differentiation, integration, multiplication by polynomials, and other operations on the full real continuum R. The procedure enables one to evaluate distributions of interest in engineering, statistics, applied probability, and operations research, which have been available only formally behind the “Laplacian curtain.” The power and precision of the procedure have been demonstrated through a variety of applications [4, 5. 6, 7, 8, 9, 12, 13, 14, 15-j. The success of the procedure rests in large part on the availability of operational properties mapping the continuum operations into Lattice operations, and vice versa. The transform based on generalized Fourier series employs as a basis the union of the set of Laguerre functions I,(x) =e-1!2”L,(x) on the positive continuum, and a complementary set for the negative continuum. Here L,(x) is the Laguerre polynomial of degree n defined, for example, by Rodrigues’ formula L,(x) = (l/n!) e”(d/dx)“(x”e-” ). A brief description of the procedure and notation is given in the Appendix. That notation will be employed throughout the paper. The restriction of the domain of the Laguerre transform to functions in L,( c~j, a) has limited, to some extent, the easy applicability of the 288 0022-247X/86 $3.00

Fuzzy pretopological spaces and their representation

Today it is obvious that topology and uniformity and the many related theories, have and will have a fundamental play in applied sciences. Every representation of real entities in a mathematical language necessarily implies a topological study of its goodness; it is a problem of linguistic translation continuity, as defined by Hammer [ 71 (this translation must preserved some important features of the original). The power of actual digital computers enables us to use new ways in automatic pattern recognition, but at the same time it shows us the many difficulties we encounter in searching a proper formulation of the topological concepts that everyone has in mind and uses in a naturally and more or less conscientious fashion. One of the first axiomatisations of the concept of topological space was done by Hausdorff, and it is not so old. It is only recently that some authors have thought if necessary to generalize these concepts and have obtained practical applications, for instance, Appert [ 11, Hammer [6, 71, Brissaud [3], Mougeot Auray Duru [2]. This has been especially motivated by the necessity of finding new concepts which well apply to finite sets and approx- imations, as Hammer remarks: “Topologists actually had one model in ind, the real continuum and its generated Euclidean spaces but not approximation and certainly not finite sets.” We think that the effort of interpretation and application to many fields, such as linguistics, system theory, and education, made by Hammer is of great importance ([7] and its references). An important discovery in system theory, which has been inforpally stated as a principle by Zadeh [ 111, is: “As the complexity of a system increases our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision and significance become almost mutually exclusive characteristics.” This principle is very close to limit problems and paradoxes encountered by physicians, in particular, the similitude with the Heisenberg uncertainty prin- ciple is clear. It is certainly a motivation for the use of fuzzy set theory. But these two aspects (pretopology or extended topology as named by Hammer,

Non-Euclidean Geometries

THE ordinary theory of analytical geometry may be extended by analogy as follows: Let Xl, X2,... Xn be independent variables, each ranging over the complete real (or ordinary complex) continuum. Any particular set (Xl, X2,... Xn), in that order, is said to be a point, the co-ordinates of which are these Xi; and the aggregate of these points is said to form a point-space of n dimensions (Pn). Taking r<n, a set of r equations φ1=o, φ2=o,... φr=o, connecting the co-ordinates, will in general define a space Pn-r contained in Pn. Theorems about loci, contact, envelopes, and the principle of duality all hold good for this enlarged domain, and we also have a system of projective geometry analogous to the ordinary one.