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  • Articles  (10,453)
  • Springer  (10,364)
  • Annual Reviews  (89)
  • American Geophysical Union (AGU)
  • 1995-1999  (10,453)
  • 1980-1984
  • 1935-1939
  • 1995  (10,453)
  • Mathematics  (7,137)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition  (3,316)
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  • Articles  (10,453)
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  • 1995-1999  (10,453)
  • 1980-1984
  • 1935-1939
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  • 1
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 23-34 
    ISSN: 0199-9885
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 2
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 57-92 
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  • 3
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 1-21 
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  • 4
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. xiii 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 35-55 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 1-23 
    ISSN: 0066-4286
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 23-35 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 37-67 
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  • 9
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 69-102 
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    Annual Review of Phytopathology 33 (1995), S. 103-118 
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    Annual Review of Phytopathology 33 (1995), S. 119-144 
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  • 12
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 145-172 
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  • 13
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 173-197 
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  • 14
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 199-221 
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  • 15
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 223-249 
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    Annual Review of Phytopathology 33 (1995), S. 251-274 
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  • 17
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 275-297 
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  • 18
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    Annual Review of Phytopathology 33 (1995), S. 299-321 
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  • 19
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    Annual Review of Phytopathology 33 (1995), S. 323-343 
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    Annual Review of Phytopathology 33 (1995), S. 369-391 
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  • 21
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 345-368 
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    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 22
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 429-443 
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  • 23
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 393-427 
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    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 24
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 445-466 
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  • 25
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 489-528 
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  • 26
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Phytopathology 33 (1995), S. 529-564 
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    Annual Review of Phytopathology 33 (1995), S. 467-488 
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    Annual Review of Nutrition 15 (1995), S. 93-110 
    ISSN: 0199-9885
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    Annual Review of Nutrition 15 (1995), S. 111-132 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 191-211 
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  • 31
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 133-159 
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    Annual Review of Nutrition 15 (1995), S. 161-189 
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    Annual Review of Nutrition 15 (1995), S. 213-238 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nutrition 15 (1995), S. 239-261 
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    Annual Review of Nutrition 15 (1995), S. 353-377 
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    Annual Review of Nutrition 15 (1995), S. 293-322 
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    Annual Review of Nutrition 15 (1995), S. 323-352 
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    Annual Review of Nutrition 15 (1995), S. 263-291 
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    Annual Review of Nutrition 15 (1995), S. 379-397 
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    Annual Review of Nutrition 15 (1995), S. 399-417 
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    Annual Review of Nutrition 15 (1995), S. 419-440 
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    Annual Review of Nutrition 15 (1995), S. 473-493 
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    Annual Review of Nutrition 15 (1995), S. 441-471 
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    Annual Review of Nutrition 15 (1995), S. 495-518 
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    Bulletin of mathematical biology 57 (1995), S. 1-20 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the framework of the neural network theory effects similar to hypnotic displays are constructed. They are based on the associative paradigm involving non-linear interaction of excitatory and inhibitory channels with synaptic memory. The non-linearity of long-term memorizing processes may cause effects exhibited by blind spots, which are interpreted as the first stage of hypnosis. More complicated phenomena are discussed in terms of a two-layer network.
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  • 46
    ISSN: 1522-9602
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    Notes: Abstract Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of repliator-type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems —n=2, 3 and 4 — are discussed and complete qualitative analysis is presented. Error thresholds known from simple replication-mutation kinetics with frequency independent replication rates occur here as well. Instead of cooperative transitions or higher order phase transitions the thresholds appear here as supercritical or subcritical bifurcations being analogous to first-order phase transitions.
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    Bulletin of mathematical biology 57 (1995), S. 63-76 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The non-linear behavior of a differential equations-based predator-prey model, incorporating a spatial refuge protecting a consant proportion of prey and with temperature-dependent parameters chosen appropriately for a mite interaction on fruit trees, is examined using the numerical bifurcation code AUTO 86. The most significant result of this analysis is the existence of a temperature interval in which increasing the amount of refuge dynamically destabilizes the system; and on part of this interval the interaction is less likely to persist in that predator and prey minimum population densities are lower than when no refuge is available. It is also shown that increasing the amount of refuge can lead to population outbreaks due to the presence of multiple stable states. The ecological implications of a refuge are discussed with respect to the biological control of mite pests.
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    Bulletin of mathematical biology 57 (1995), S. 99-107 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In many applications of control theory on plant growth models biomass maximization is postulated to avoid analytically unsolvable problems while fruit maximization is commonly considered to be a more realistic criterion. In a special case, we are able to compare these criteria. Iwasa and Roughgarden (1984,Theor. Pop. Biol. 25, 78–105) have investigated a certain class of plant growth models using a fruit maximization criterion. They proved that, in the vegetative growth period, the organs follow a certain path of balanced growth. We show that this path remains optimal when biomass maximization is postulated. This underlines the importance of the balanced growth path found by Iwasa and Roughgarden. Furthermore, our result suggests that in the vegetative growth period the biomass maximization criterion is a good approximation of fruit maximization. In another theoretical control investigation, Schultzeet al. (1983,Oecologia 58, 169–177) derived a different type of balanced growth path. We apply the theory of Iwasa and Roughgarden to an improved version of the model of Schulzeet al. This leads to a new description of balanced growth between root and shoot that reflects non-linearities in the water uptake process and constitutes an interesting hypothesis for further experimental testing.
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    Bulletin of mathematical biology 57 (1995), S. 77-98 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Laiet al. (1990,Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myerset al. (1984,ASME J. biomech. Engng,106, 151–158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to acount for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility, of approximate analytic solutions in certain cases.
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    Bulletin of mathematical biology 57 (1995), S. 109-136 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Many models of immune networks have been proposed since the original work of Jerne [1974,Ann. Immun. (Inst. Pasteur) 125C, 373–389]. Recently, a limited class of models (Weisbuchet al., 1990,J. theor. Biol. 146, 483–499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e. their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.
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    Bulletin of mathematical biology 57 (1995), S. 137-156 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restriced inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the present paper a kinetic study is made of the behaviour of a Michaelis-Menten enzyme-catalysed reaction in the presence of irreversible inhibitors rendered unstable in the medium by their reaction with the product of enzymatic catalysis. A general mechanism involving competitive, non-competitive, uncompetitive and mixed irreversible inhibition with one or two steps has been analysed. The differential equation that describes the kinetics of the reaction is non-linear and computer simulations of its dynamic behaviour are presented. The results obtained show that the systems studied here present kinetic co-operativity for a target enzyme that follows the simple Michaelis-Menten mechanism in its action on the substrate, except in the case of an uncompetitive-type inhibitor.
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    Bulletin of mathematical biology 57 (1995), S. 169-173 
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    Bulletin of mathematical biology 57 (1995), S. 191-203 
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    Notes: Abstract The relative contributions of mitochondrial β-oxidation and peroxisomal β-oxidation and peroxisomal ω-oxidation to the oxidation of a given fatty acidin vivo can be quantitated by an isotopic method. The approach requires infusion of a fatty acid labelled on two specific carbon atoms (e.g. [1-14C] and [11-14C] palmitate) to an isotopic steady state, with subsequent isolation and degradation of an acetylated conjugate as a product of the liver cytosolic acetyl CoA pool and of ketone bodies as a product of the liver mitochondrial acetyl CoA pool.
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    Bulletin of mathematical biology 57 (1995), S. 229-246 
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    Notes: Abstract Pancreatic β-cells in intact islets of Langerhans perfused with various glucose concentrations exhibit periodic bursting electrical activity (BEA) consisting of active and silent phases. The fraction of the time spent in the active phase is called the plateau fraction and appears to be strongly correlated with the rate of release of insulin from islets as glucose concentration is varied. Here this correlation is quantified and a theoretical development is presented in detail. Experimental rates of insulin release are correlated with “effective” plateau fractions over a range of glucose concentrations. There are a number of different models for BEA in pancreatic β-cells and a method is developed here to quantify the dependence of a glucose dependent parameter on glucose concentration. As an example, the plateau fractions computed from the Sherman-Rinzel-Keizer model are matched with experimental plateau fractions to obtain a relationship between the model's glucose-dependent parameter, β, and glucose concentration. Knowledge of the relationships between β and glucose concentration and between experimental measurements of rates of insulin release and plateau fractions permits the determination of theoretical rates of insulin release from the model.
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    Bulletin of mathematical biology 57 (1995), S. 299-344 
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    Notes: Abstract When a suspension of bacterial cells of the speciesBacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development whenN andC depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.
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    Bulletin of mathematical biology 57 (1995), S. 413-439 
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    Notes: Abstract We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (inMathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.
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    Bulletin of mathematical biology 57 (1995), S. 499-506 
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    Bulletin of mathematical biology 57 (1995), S. 461-486 
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    Notes: Abstract To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.
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    The journal of Fourier analysis and applications 2 (1995), S. 29-48 
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    Notes: Abstract We investigate the $L_p$ -error of approximation to a function $f\in L_p({\Bbb T}^d)$ by a linear combination $\sum_{k}c_ke_k$ of $n$ exponentials $e_k(x):= e^{i\langle k,x\rangle}=e^{i(k_1x_1+\cdots+k_dx_d)}$ on ${\Bbb T}^d,$ where the frequencies $k\in {\Bbb Z}^d$ are allowed to depend on $f.$ We bound this error in terms of the smoothness and other properties of $f$ and show that our bounds are best possible in the sense of approximation of certain classes of functions.
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    The journal of Fourier analysis and applications 2 (1995), S. 237-259 
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    Notes: Abstract Let $L[\,\cdot\,]$ be a nondivergent linear second-order uniformly elliptic partial differential operator defined on functions with domain $\Omega.$ Consider the question, "When is a function u a solution of $L[u] = 0$ on $\Omega$ ?" The naive answer, "u is a solution of $L[u] = 0$ on $\Omega$ if $u\in C^2(\Omega)$ and $L[u](x) = 0$ for all $x\in\Omega,$ " is clearly too limited. Indeed, if the coefficients of L are in $W^{1,2}\cap L^{\infty},$ then L can be rewritten in divergence form for which the notion of a "weak" solution can be applied. In this case there could be infinitely many functions that are "weak" but not classical solutions. More importantly, even if the coefficients of L are just bounded and measurable, the recent results of Krylov permit us to construct "solutions" of $L[u] = 0$ on $\Omega,$ and these "solutions" are generally no better than continuous; the "weak" solutions previously mentioned can be obtained by this construction, too. The preceding discussion provides us with an adequate extrinsic definition of solution (i.e., given a function u we either prove that it is or is not the result of such a construction) that has been used by several authors, but one that is not particularly satisfying or illuminating. Our major contribution in this paper is to show the following. I. There is an intrinsic definition of solution that is equivalent to the extrinsic one. II. Furthermore, the intrinsic definition is just the (now) well-known Crandall-Lions viscosity solution, modified in a natural way to accommodate measurable coefficients.
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    The journal of Fourier analysis and applications 2 (1995), S. 397-406 
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    Notes: Abstract We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth. It can be used to study the weighted average of the form $(T^\alpha (\hbox {ln }T)^\beta)^{-1}\int _0^T h(t) \, dt.$
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    Bulletin of mathematical biology 57 (1995), S. 205-227 
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    Notes: Abstract The formation of neuronal networks requires axonal growth towards target neutons. A simple set of grammar rules is introduced to describe axonal growth towards target cells situated both at short and long distances from the growing neuron. Growth for short distances is descrbed by growth following the highest gradient of a chemical compound (which is spread by diffusion from the targets). This approach fails to describe long-distance growth, which is addressed by adopting a graph grammar theory for growing trees. With these rules a flexible tool to draw network of neurons by computer can be developed.
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    Bulletin of mathematical biology 57 (1995), S. 345-366 
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    Notes: Abstract A pair of growth control triads are used to describe coincident tumor growth and liver regeneration after partial hepatectomy. The models are extensions of previous growth control models which describe tumor growth in an unperturbed host (Michelson and Leith, 1991,Bull. math. Biol. 53, 639–656; idem, 1992, Proceedings of the Third International Conference on Communications and Control, Vol. 2, pp. 481–490; idem, 1992,Bull. math. Biol. 55, 993–1011; idem,J. theor. Biol. 169, 327–338). The linkage between the two triads depends upon systemic signals carried by soluble factors, and mathematical descriptors based upon biological first principals are proposed. The sources of the growth factors, their targets and the processing of their signals are investigated. Analyses of equilibrium in the constant coefficients case and simulated growth curves for the dynamic system are presented, and the effects of growth factor-induced mitogenesis and angiogenesis are discussed in particular. A case is made for early and late responses in the coupled control system. The biology of the signal processing paradigm is placed within a new theoretical context and discussed with regard to tumor adaptation, liver differentiation and the development of a tumor hypoxic fraction.
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    Bulletin of mathematical biology 57 (1995), S. 381-399 
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    Notes: Abstract We consider the problem of optimal stabilization and control of populations which follow the Leslie model dynamics, within state space and control systems theory and methodology. Various types of culling strategies are formulated and introduced into the Leslie model as control inputs, and their effect on global asymptotic stability is investigated. Our new approach provides answers to several unexplored problems. We show that in general it is possible to achieve a desired stable equilibrium population level, through the design of a class ofshifted-proportional stabilizing culling policies. Further, we formulate general non-linear constrained opitmization problems, for obtaining the cost-optimal policy among this generally infinite class of such stabilizing policies. The theoretical findings are illustrated through the solution of the problem over an infinite planning horizon for a numerical example. A comparative study of the costs and dynamic effects of various culling strategies also supports the mathematical results.
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    Bulletin of mathematical biology 57 (1995), S. 593-617 
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    Notes: Abstract A new approach for data assimilation, which is based on the adjoint method, but allows the computer code for the adjoint to be constructed directly from the model computer code, is described. This technique is straightforward and reduces the chance of introducing errors in the construction of the adjoint code. Implementation of the technique is illustrated by applying it to a simple predator-prey model in a model fitting mode. A series of identical twin numerical experiments are used to show that this data assimilation approach can successfully recover model parameters as well as initial conditions. However, the ease with which these values are recovered is dependent on the form of the model equations as well as on the type and amount of data that are available. Additional numerical experiments show that sufficient coefficient and parameter recoveries are possible even when the assimilated data contain significant random noise. Thus, for biological systems that can be described by ecosystem models, the adjoint method represents a powerful approach for estimating values for little-known biological parameters, such as initial conditions, growth rates, and mortality rates.
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    Notes: Abstract The effect of group size on behavioral parameters of the Oriental hornet,Vespa orientalis, was assessed experimentally under laboratory conditions. Hornet groups of various sizes (ranging from 1 to 100 individuals per group) comprised of young individuals (0–24 hr of age) devoid of a queen were placed in artificial breeding boxes (ABBs). The following three quantitative parameters were evaluated: the amount and rate of building as a function of the number of hornets in the group, the rate of oviposition as, related to group size and the longevity of hornets as a function of their group size. The probability for the occurrence of these events was similarly considered and additional behavioral parameters were only assessed qualitatively. Results of this investigation revealed a relation between the three mentioned quantitative behavioral parameters and the number of hornets per group. The number of hornets per group was positively related to the extent of building, the number of cells built by a group is $$2\pi \sqrt {group size} $$ , but negatively related to the rate of building. As for the delay of building, a non-monotone relation was found. The relation between number of hornets per group and the oviposition delay was found to be non-monotone; the number of hornets per group and their longevity were found to be inversely related. Discrepanices were recorded on the very small (1–2 individuals) or very large (100 individuals) hornet groups.
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    Bulletin of mathematical biology 57 (1995), S. 527-537 
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    Notes: Abstract A new method for reconstructing evolutionary relationship among bacteria by use of rRNA sequence data is proposed. The method is based on the concept of fuzzy classification of probabilitiesp(i), p(i/j) andp(i/j*) (i=A,G,C,U) of each sequence. The resulting partition tree shares common features of previous works but has some new peculiarities.
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    Bulletin of mathematical biology 57 (1995), S. 619-630 
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    Bulletin of mathematical biology 57 (1995), S. 631-650 
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    Notes: Abstract We describe the behaviour of motile microorganisms (e.g. flagellates) attracted by “gyrotaxis” to a sinking, non-motile particle (e.g. an algal cell). The model is based on the application of Stokes' solution for the flow field around the settling cell. The volume within which the flagellate is attracted to the sinking particle is determined from the trajectories of the flagellate. The model of gyrotaxis has several applications; these include the colonization of sinking marine snow particles with motile microoganisms and suspension feeding by protozoa.
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    Bulletin of mathematical biology 57 (1995), S. 507-526 
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    Notes: Abstract The effect of varying habitat dimensionality on the dynamics of a model predator-prey system is examined using an individual-based simulation. The general results are that in one dimension fluctuations in abundance of prey and predators occur over a large range of spatial scales (extinctions occur over many spatial scales). In two dimensions (and low mobilities of prey and predators) the dynamics become more predictably periodic at local scales and constant at larger scales due to statistical stabilization. In three dimensions, the model can become “phase-locked” with prey and predators displaying oscillations in abundance over large spatial scales.
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    Bulletin of mathematical biology 57 (1995), S. 557-568 
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    Notes: Abstract A rather complete model of the gluconeogenic pathway was used, with the known separate pools of mitochondrial and cytosolic oxalacetate, malate and aspartate. The fumarase, malate dehydrogenase and glutamate oxalacetate transaminase reactions were assumed to be isotopically actively reversible, but none at isotopic equilibrium. Malate was assumed to exchange actively between the mitochondrial and cytosol, while aspartate exchange was more limited, in agreement with the known electrogenic nature of aspartate export from the mitochondria. This model was fit to14C data obtained in hepatocyte studies, and to the whole rat14C data obtained by Heath and Rose (Biochem J. 227, 851–876, 1985). The latter data were easily fit to our model, when a single mitochondrial oxalacetate pool was assumed. However, invoking two mitochondrial oxalacetate pools, as proposed by Heath and Rose, with the oxalacetate formed via pyruvate carboxylase preferentially channelled to gluconeogenesis, could not be fit with the known differences in scrambling in glucose and glutamate produced from L[3-14C]lactate.
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    Bulletin of mathematical biology 57 (1995), S. 569-591 
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    Notes: Abstract Oscillatory secretion of insulin has been observed in many different experimental preparations ranging from pancreatic islets to the whole pancreas. Here we examine the mathematical features underlying a possible model for oscillatory secretion from the perifused, insulin-secreting cell line, HIT-15. The model includes the kinetics of uptake of glucose by GLUT transporters, the rate of glucose metabolism within the cell, and the effect of glucose on the rate of insulin secretion. Putative feedback by insulin on the rate of glucose transport into the cells is treated phenomenologically and leads to insulin oscillations similar to those observed experimentally in HIT cells. The resulting set of ordinary differential equations is simplified by time-scale analysis to a two-variable set of ordinary differential equations. Because of this simplification we can explore, in great detail, the characteristics of the oscillations and their sensitivity to parameter variation using phase plane analysis.
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    Bulletin of mathematical biology 57 (1995), S. 679-699 
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    Notes: Abstract The fluid dynamics of sperm motility near both rigid and elastic walls is studied using the immersed boundary method. Simulations of both single and interacting organisms are presented. In particular, we find that nearby organisms originally undulating with a 90° phase shift may adjust their relative swimming velocities and phase-lock. Comparisons with previous analytical results are also discussed. The tendency of a near-wall to attract organisms is demonstrated.
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    Bulletin of mathematical biology 57 (1995), S. 713-731 
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    Notes: Abstract The secondary immune response is one of the most important features of immune systems. During the secondary immune response, the immune system can eliminate the antigen, which has been encountered by the individual during the primary invasion, more rapidly and efficiently. Both T and B memory cells contribute to the secondary response. In this paper, we only concentrate on the functions of memory B cells. We explore a model describing the memory contributed by the specific long-lived clone which is maintained by continued stimulation with a small amount of antigens sequestered on the surfaces of the follicular dendritic cells (FDC). The behavior of the secondary response provided by the model can be compared with experimental observations. The model shows that memory B cells indeed play an important role in the secondary response. It is found that a single memory cell in a long-lived clone may not be long-lived. In the present note, the influences of relevant parameters on the secondary response are also explored.
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    Bulletin of mathematical biology 57 (1995), S. 749-782 
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    Notes: Abstract A biological system consisting of a population of cells suspended in a liquid substrate is considered. The general problem addressed in the paper is the derivation of the kinetic pattern of population growth as a statistical effect of a very large number of elementary interactions between a single cell and the molecules of nutrient in substrate. Solution of the problem is obtained in the form of equation expressing the population growth ratec as a function of substrate concentration,C s. The analytical expression derived is applied to a real bacterial population (Escherichi coli) and kinetic patterns are theoretically computed. The major findings, expressed roughly, without nuances, are: (i) the concentration of nutrient at the cell membrane,C c, can only be equal to either 0 (for theC s below some threshold valueC *) orC s (forC s〉C *); (ii) the Michaelis-Menten-Monod kinetics observed in experiments is an artifact: the pure (not contaminated by foreign factors) dependence ofc onC s is actually such that the functionc=c(C s) has practically linear increase whenC s〈C *, and is constant,c=c(C *)=const, whenC s〉C *; (iii) the Liebig principle is strictly fulfilled: up to a feasible accuracy of observation, under no circumstances can population growth be limited (controlled) by more than one substrate component—replacement of a limiting component for another one is an instant event rather than a gradual process.
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    Bulletin of mathematical biology 57 (1995), S. 841-881 
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    Notes: Abstract We study the equilibrium properties of idiotypically interacting B cell clones in the case where only the differentiation of B cells is affected by idiotypic interactions. Furthermore, we assume that clones may recognize and be stimulated by self antigen in the same fashion as by antiantibodies. For idiotypically interacting pairs of non-autoreactive clones we observe three qualitatively different dynamical regimes. In the first regime, at small antibody production an antibody-free fixed point, the virgin state, is the only attractor of the system. For intermediate antibody production, a symmetric activated state replaces the virgin state as the only attractor of the system. For large antibody production, finally, the symmetric activated state gives way to two asymmetric activated states where one clone suppresses the other clone. If one or both clones in the pair are autoreactive there is no virgin state. However, we still observe the switch from an almost symmetric activated state to two asymmetric activated states. The two asymmetric activated states at high antibody production have profoundly different implications for a self antigen which is recognized by one of the clones of the pair. In the attractor characterized by high autoantibody concentration the self antigen is attacked vigorously by the immune system while in the opposite steady state the tiny amount of autoantibody hardly affects the self antigen. Accordingly, we call the first state the autoimmune state and the second the tolerant state. In the tolerant state the autoreactive clone is down-regulated by its anti-idiotype providing an efficient mechanism to prevent an autoimmune reaction. However, the antibody production required to achieve this anti-idiotypic control of autoantibodies is rather large.
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    Bulletin of mathematical biology 57 (1995), S. 899-929 
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    Notes: Abstract It is widely believed, following the work of Connor and Stevens (1971,J. Physiol. Lond. 214, 31–53) that the ability to fire action potentials over a wide frequency range, especially down to very low rates, is due to the transient, potassium A-current (I A). Using a reduction of the classical Hodgkin-Huxley model, we study the effects ofI A on steady firing rate, especially in the near-threshold regime for the onset of firing. A minimum firing rate of zero corresponds to a homoclinic bifurcation of periodic solutions at a critical level of stimulating current. It requires that the membrane's steady-state current-voltage relation be N-shaped rather than monotonic. For experimentally based genericI A parameters, the model does not fire at arbitrarily low rates, although it can for the more atypicalI A parameters given by Connor and Stevens for the crab axon. When theI A inactivation rate is slow, we find that the transient potassium current can mediate more complex firing patterns, such as periodic bursting in some parameter regimes. The number of spikes per burst increases asg A decreases and as inactivation rate decreases. We also study howI A affects properties of transient voltage responses, such as threshold and firing latency for anodal break excitation. We provide mathematical explanations for several of these dynamic behaviors using bifurcation theory and averaging methods.
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    Bulletin of mathematical biology 57 (1995), S. 939-941 
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    Bulletin of mathematical biology 57 (1995), S. 945-946 
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    The journal of Fourier analysis and applications 2 (1995), S. 65-107 
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    Notes: Abstract Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in ℂn and on domains of finite type in ℂ2. Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.
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    The journal of Fourier analysis and applications 2 (1995), S. 181-189 
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    Notes: Abstract As a particular wavelet subspace, the Paley-Wiener space $B_{\pi}$ has both regular and irregular sampling theorems. A regular sampling theorem in general wavelet subspaces has been established for several years. In this paper, we discuss the irregular sampling problem in wavelet subspaces.
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    The journal of Fourier analysis and applications 2 (1995), S. 217-225 
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    Notes: Abstract The Adler-Konheim theorem [Proc. Amer. Math. Soc. 13 (1962), 425-428] states that the collection of nth-order autocorrelation functions ${\cal M} = \{M^n(\cdot): n=1,2,\dots\}$ is a complete set of translation invariants for real-valued L1 functions on a locally compact abelian group. It is shown here that there are proper subsets of ${\cal M}$ that also form a complete set of translation invariants, and these subsets are characterized. Specifically, a subset is complete if and only if it contains infinitely many even-order autocorrelation functions. In addition, any infinite subset of $\cal M$ is complete up to a sign. While stated here for functions on $\cal R,$ the proofs presented hold for functions on any locally compact abelian group that is not compact, in particular, on ${\cal R}^n$ and the integer lattice ${\cal Z}^n.$
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    The journal of Fourier analysis and applications 2 (1995), S. 49-64 
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    Notes: Abstract For $k \in {\Bbb N}, k \not= 0,$ define ${\cal F}_kf(\gamma) = \int_{{\Bbb R}^n} f(t)R_k(-2i \pi \gamma.t) \, dt, n\geq 1,$ where $R_k(i\lambda) = e^{i\lambda} - \sum^{k-1}_{j=0} \left(i \lambda \right)^{j} / \left(j~!\right).$ Pointwise estimates and weighted inequalities describing the local Lipschitz continuity of ${\cal F}_kf$ are established. Sufficient conditions are found for the boundedness of ${\cal F}_k$ from $L^p_v$ into $L^q_\mu,$ and a spherical restriction property is proved. A study of the moment subspaces of $L^p_v$ is next developed in the one-variable case, for $1 〈 p 〈 \infty, v$ locally integrable, $v 〉 0$ a.e. It includes a decomposition theorem and a complete classification of all possible sequences of moment subspaces in $L^p_v.$ Characterizations are also given for each class. Applications related to the approximation and decomposition of ${\cal F}_k$ are discussed.
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    The journal of Fourier analysis and applications 2 (1995), S. 135-159 
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    Topics: Mathematics
    Notes: Abstract Often, the Dyadic Wavelet Transform is performed and implemented with the Daubechies wavelets, the Battle-Lemarie wavelets, or the splines wavelets, whereas in continuous-time wavelet decomposition a much larger variety of mother wavelets is used. Maintaining the dyadic time-frequency sampling and the recursive pyramidal computational structure, we present various methods for constructing wavelets ψwanted, with some desired shape and properties and which are associated with semi-orthogonal multiresolution analyses. We explain in detail how to design any desired wavelet, starting from any given multiresolution analysis. We also explicitly derive the formulae of the filter bank structure that implements the designed wavelet. We illustrate these wavelet design techniques with examples that we have programmed with Matlab routines.
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    The journal of Fourier analysis and applications 2 (1995), S. 191-215 
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    Topics: Mathematics
    Notes: Abstract This paper studies a class of linear operators on spaces of functions of one real variable, which correspond to multiplication by a measurable function under the Weil transform $\Theta.$ These operators are called Weil multipliers, and arise out of the authors' study of Gabor series and radar ambiguity functions. Representation theory provides a natural class of Weil multipliers: the set of doubly periodic functions with absolutely convergent Fourier series, ${\bf A}({\bf T}^2).$ It will be proved that functions in ${\bf A}({\bf T}^2)$ are $L^p$ multipliers for all $1 \leq p \leq 2$ and, therefore, define bounded linear endomorphisms of ${\bf L}^p({\bf R}).$ Also, we record the fact that the Wiener lemma tells us something about the orbit structure of these multipliers acting on function spaces on the Heisenberg nilmanifold. Linear maps that correspond to multiplication by a function under a unitary conjugacy have a particularly simple spectral decomposition, which yields an approximation theory for these operators and provides insight into the foundation of the authors' previous work on approximate orthonormal bases. Finally, the problem of inversion of a multiplier will be analyzed for smooth functions that have a specified structure near their zeros.
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    The journal of Fourier analysis and applications 2 (1995), S. 227-235 
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    Notes: Abstract Let $\Omega$ be a smooth domain in R2 containing a polygon D. The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered. We show that D is uniquely determined from boundary measurements corresponding two appropriately chosen Neumann datas.
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    The journal of Fourier analysis and applications 2 (1995), S. 1-14 
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    Notes: Abstract K.-H. Grochenig and A. Haas asked whether for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn. They proved that this is the case when the dimension n = 1. This article shows that this is also the case when the dimension n = 2.
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    The journal of Fourier analysis and applications 2 (1995), S. 15-28 
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    Topics: Mathematics
    Notes: Abstract Let $1 〈 p 〈 \infty, h \in L_p ({\Bbb R}),$ and $f \in L_{p^\prime} ({\Bbb R}).$ Under certain conditions on $h,$ we shall prove that $\int_y^\infty (h_t \ast f)(x)\,dt/t$ converges nontangentially to $f(x_0)$ at $(x_0,0)$ for $a.a.\, x_0.$
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    Bulletin of mathematical biology 57 (1995), S. 487-498 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract This paper deals with the relative growth of three different fruit tissues. Their morphogenetic periods and the mathematical constraints involved are described, and more precisely, the paper shows an allometric relationship (Y=nX m ) between the widths (X, Y) of the main tissues in stone fruits such as cherries, peaches and prunes. The mathematical relationships between the growth of the mesocarp and of the endocarp of somePrunus fruits are described, and it is proved that before the formation of the embryo, growth is allometric, in agreement with conclusions drawn from some experimental data. However, according to another study, the growth of the mesocarp and of the endocarp are ruled by autocatalytic and monomolecular functions, before as well as after the formation of the embryo. In this case, it is proved that if allometry exits in stone fruits, it can only be anantiometry (m=−1). To solve the dilemma, two main alternatives are proposed and discussed. We conclude that, while allometry is established on reasonable grounds before the formation of the embryo, after the formation of the embryo the mesocarp and endocarp evolve independently since a center for the coordination of growth no longer exists, and each tissue can grow according to its own independent rules.
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    Bulletin of mathematical biology 57 (1995), S. 539-556 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract In many organisms, a reliable number of segments is produced even though important properties of the region involved, especially its size at the time of pattern formation, are apparently not specified with sufficient precision. We show that this can be readily accomplished if segmentation occurs through a sequence of bifurcations rather than all at once, and we provide evidence from developmental studies that indicates that this is typically what actually occurs. Our results strongly suggest that where patterns are formed reliably, this generally happens in stages rather than by the setting up in advance of a complete prepattern.
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    The journal of Fourier analysis and applications 2 (1995), S. 287-301 
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    Topics: Mathematics
    Notes: Abstract Estimates from below for the norms of linear means of multiple Fourier series are obtained. These means are given by some function λ and generalize the well-known Bochner-Riesz means. Sharpness of these estimates is established. The assumptions on λ are rather weak and of local character. Our results contain as particular cases a number of earlier published results. Proofs are based on the authors' new results on asymptotics of the Fourier transform of piecewise-smooth functions. Some applications of the results obtained are given, namely, orders of growth of the Lebesgue constants for "ovals" and "hyperbolic crosses" are evaluated and sharp conditions on the modulus of smoothness of a function are given, for this function to be approximated by the linear means.
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    The journal of Fourier analysis and applications 2 (1995), S. 415-426 
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    Topics: Mathematics
    Notes: Abstract For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the time-frequency windows tend to infinity as n → ∞. This class includes those of Battle-Lemarie and Daubechies. In addition, if the scaling functions have at least asymptotic linear phase, then we prove that they converge to the "sinc" function and their corresponding orthonormal wavelets converge to the "difference" of two sinc functions.
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    The journal of Fourier analysis and applications 2 (1995), S. 435-452 
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    Topics: Mathematics
    Notes: Abstract It is shown that a function $f\in L^p[-R,R], 1\le p〈\infty,$ is completely determined by the samples of $\hat f$ on sets $\Lambda=\cup_{i=1}^m\{n/2r_i\}_{n\in{\bf Z}}$ where $R=\sum r_i,$ and $r_i/r_j$ is irrational if $i\ne j,$ and of $\hat f^{(j)}(0) \mbox{ for } j=1,\ldots,m-1.$ If $f\in C^{m-2-k}[-R,R],$ then the samples of $\hat f$ on $\Lambda$ and only the first k derivatives of $\hat f$ at 0 are required to determine f completely. Higher dimensional analogues of these results, which apply to functions $f\in L^p[-R,R]^d$ and $C^{m-2-k}[-R,R]^d,$ are proven. The sampling results are sharp in the sense that if any condition is omitted, there exist nonzero $f\in L^p[-R,R]^d$ and $C^{m-2-k}[-R,R]^d$ satisfying the rest. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials that are not Riesz bases for $L^2[-R,R].$ A signal processing application in which such sampling sets arise naturally is described in detail.
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    The journal of Fourier analysis and applications 2 (1995), S. 487-505 
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    Topics: Mathematics
    Notes: Abstract We provide a direct computational proof of the known inclusion ${\cal H}({\bf R} \times {\bf R}) \subseteq {\cal H}({\bf R}^2),$ where ${\cal H}({\bf R} \times {\bf R})$ is the product Hardy space defined for example by R. Fefferman and ${\cal H}({\bf R}^2)$ is the classical Hardy space used, for example, by E.M. Stein. We introduce a third space ${\cal J}({\bf R} \times {\bf R})$ of Hardy type and analyze the interrelations among these spaces. We give simple sufficient conditions for a given function of two variables to be the double Fourier transform of a function in $L({\bf R}^2)$ and ${\cal H}({\bf R} \times {\bf R}),$ respectively. In particular, we obtain a broad class of multipliers on $L({\bf R}^2)$ and ${\cal H}({\bf R}^2),$ respectively. We also present analogous sufficient conditions in the case of double trigonometric series and, as a by-product, obtain new multipliers on $L({\bf T}^2)$ and ${\cal H}({\bf T}^2),$ respectively.
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    The journal of Fourier analysis and applications 2 (1995), S. 583-596 
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    Notes: Abstract Given an n × n matrix B, positive definite and symmetric, let LB be the differential operator in Rn given by $L_B=\frac{1}{2}\Delta -Bx\cdot \mbox{grad}_x.$ A class of higher Riesz transforms associated with LB is defined by means of higher gradients of order k. It is shown that these transformations are bounded in the space $L^p,\ 1〈p〈\infty,$ with respect to the measure that makes LB selfadjoint. The constants obtained are independent of the dimension n and depend only on k,p, and the number of different eigenvalues of the matrix B. The proof of the results uses an extension of the Littlewood-Paley-Stein theory of square functions to the vector-valued case and inequalities previously proved by one of the authors in the context of the Riesz transforms of order one.
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    The journal of Fourier analysis and applications 2 (1995), S. 473-486 
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    Topics: Mathematics
    Notes: Abstract Let $Mf(x) = \sup(1/2r)\int^{x+r}_{x-r} |f(t)|\;dt$ be the centered maximal operator on the line. Through a numerical search procedure, we have conjectural best constants for the weak-type 1-1 estimate (3/2) and the Lp estimate (the constant B(p,1) such that $M(|x|^{-1/p}) = B(p,1)|x|^{-1/p}).$ We prove that these constants are lower bounds for the best constants and discuss the numerical evidence for the conjectures.
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    The journal of Fourier analysis and applications 2 (1995), S. 507-517 
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    Notes: Abstract The Cauchy problem and global well-posedness for a mathematical model of the strong interaction of two-dimensional, long, internal gravity waves propogating on neighboring pycnoclines in a stratified fluid have been studied by Bona, Ponce, Saut, Tom, and others. We show that global well-posedness occurs even when the initial data is rough.
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    The journal of Fourier analysis and applications 2 (1995), S. 109-133 
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    Topics: Mathematics
    Notes: Abstract In this paper we discuss smooth local trigonometric bases. We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases. These allow natural representations of constant and, sometimes, linear components. We study and compare their approximation properties and applicability in data compression. This is illustrated with numerical examples.
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    The journal of Fourier analysis and applications 2 (1995), S. 161-180 
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    Topics: Mathematics
    Notes: Abstract In this paper we derive rates of approximation for a class of linear operators on $C_B({\bf R}^d)$ associated with a multiresolution analysis $\{ V_n\}_{n\in{\bf Z}}.$ We show that for a uniformly bounded sequence of linear operators $\{T_n\}_{n\in{\bf Z}}$ satisfying $T_n f\equiv f$ on the subspace $V_n\cap C_B({\bf R}^d),$ a lower bound for the approximation order is determined by the number of vanishing moments of a prewavelet set. We consider applications to extensions of generalized projection operators as well as to sampling series.
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