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  • 1
    Electronic Resource
    Electronic Resource
    The vacuum and Bach equations in terms of light cone cuts (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 3704-3721 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Light cone cuts are the intersection of the light cones of space–time events with an initial data surface which is usually taken to be null infinity. These are determined by a "cut function,'' a function of the space–time coordinates and the sphere of generators of null infinity. The Bach equations and the conformal vacuum equations are shown to lead to a single scalar "main'' equation on the cut function. In simplified cases, i.e., when the Weyl curvature is either small or self-dual, this equation can be integrated to give a simple scalar conformally invariant elliptic equation on the sphere of null directions. It has the remarkable property that the general solution of the Einstein vacuum equations in these cases can be derived from the solution to this auxiliary equation in two dimensions. In general, it will not be possible to reduce it to an auxilliary equation on the sphere. Nevertheless, the main equation is still a necessary condition and it is conjectured that it is also sufficient to imply the Bach equations in general and supporting arguments are given. It is also shown how to extend the Kozameh–Newman framework to the case of light cone cuts of a spacelike Cauchy hypersurface. The analogous procedures for Yang–Mills are also discussed. A conformally invariant formalism for calculations on null infinity is described in an Appendix. This is used for all the calculations which are only described in brief form in the main text. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530992
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  • 2
    Electronic Resource
    Electronic Resource
    A connection between the Einstein and Yang-Mills equations (1989)
    Springer
    Communications in mathematical physics 121 (1989), S. 659-668 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unifield equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie-algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie algebra as that of the volume preserving 3-dimensional diffeomorphisms.) When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einsteinvacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of anSO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01218161
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  • 3
    Electronic Resource
    Electronic Resource
    The Landau-Lifshitz equation, elliptic curves and the Ward transform (1993)
    Springer
    Communications in mathematical physics 154 (1993), S. 25-47 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters λ1, λ2, λ3 that live on an elliptic curve Σ. The crucial role of the groupK ≃ ℤ2 × ℤ2 of translations by the half-periods of Σ and its non-trivial central extension $$\tilde K$$ is brought out and an analogue of Birkhoff factorisation for $$\tilde K$$ -equivariant loops in Σ is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over Σ. Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over Σ and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC ∞(S 1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096830
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  • 4
    Electronic Resource
    Electronic Resource
    On the density of the Ward ansätze in the space of anti-self-dual Yang Mills solutions (1990)
    Springer
    Communications in mathematical physics 130 (1990), S. 139-155 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A general patching matrixP for the twistor construction of antiself-dual Yang-Mills fields is approximated by a terminating Laurent series. The approximate patching matrixP(m) is triangularized (so that it becomes one of the Ward ansätze) and the associated Riemann-Hilbert problem is solved, thereby generating an anti-self-dual solution of the Yang-Mills equations. The approximate patching matrices and the associated (exact) anti-self-dual Yang-Mills solutions are then shown to converge onP and its corresponding solution so that the Ward ansätze forms a dense subset in the solution space in the Weierstrass sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099879
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  • 5
    Electronic Resource
    Electronic Resource
    The Landau-Lifshitz equation, elliptic curves and the ward transform (1993)
    Springer
    Communications in mathematical physics 158 (1993), S. 215-215 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02097238
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  • 6
    Electronic Resource
    Electronic Resource
    The twistor theory of equations of KdV type: I (1994)
    Springer
    Communications in mathematical physics 166 (1994), S. 191-218 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This article is the first of two concerned with the development of the theory of equations of KdV type from the point of view of twistor theory and the self-dual Yang-Mills equations. A hierarchy on the self-dual Yang-Mills equations is introduced and it is shown that a certain reduction of this hierarchy is equivalent to then-generalized KdV-hierarchy. It also emerges that each flow of then-KdV hierarchy is a reduction of the self-dual Yang-Mills equations with gauge group SL n . It is further shown that solutions of the self-dual Yang-Mills hierarchy and their reductions arise via a generalized Ward transform from holomorphic vector bundles over a twistor space. Explicit examples of such bundles are given and the Ward transform is implemented to yield a large class of explicit solutions of then-KdV equations. It is also shown that the construction of Segal and Wilson of solutions of then-KdV equations from loop groups is contained in our approach as an ansatz for the construction of a class of holomorphic bundles on twistor space. A summary of the results of the second part of this work appears in the Introduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099306
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  • 7
    Electronic Resource
    Electronic Resource
    Effects of scale insect herbivory and shading on net gas exchange and growth of a subtropical tree species (Guaiacum sanctum L.) (1990)
    Springer
    Oecologia 84 (1990), S. 468-473 
    Details
    ISSN: 1432-1939
    Keywords: Toumeyella sp. ; Insect-plant interaction ; Photosynthesis ; Chlorophyll ; Nitrogen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The scale insect, Toumeyella sp., feeds exclusively on the subtropical hammock tree lignum vitae (Guaiacum sanctum L.). The combined effects of scale herbivory and shading on leaf gas exchange characteristics and growth of lignum vitae trees were studied using a factorial design. Trees grown in full sun or in 75% shade were manually infested with scale or left noninfested. Beginning 4 weeks after infestation, net CO2 assimilation, stomatal conductance, transpiration, internal partial pressure of CO2, and water-use efficiency were determined on single-leaves at 4-week intervals for trees in each treatment. At the end of the experiment, net CO2 assimilation was determined for whole plants. Total leaf area, leaf, stem, and root dry weights, and leaf chlorophyll and nitrogen concentrations were also determined. Scale infested trees generally had lower net CO2 assimilation, stomatal conductance, and transpiration rates as well as less leaf area, and root, stem, and leaf dry weights than noninfested trees. Twenty four weeks after the shade treatment was imposed, sun-grown trees had approximately twice the leaf area of shade-grown trees. Shade-grown trees compensated for the reduced leaf area by increasing their photosynthetic efficiency. This resulted in no difference in light saturated net CO2 assimilation on a whole plant basis between sun-grown and shade-grown trees. Chlorophyll and nitrogen concentrations per unit leaf area were greater in leaves of shade-grown trees than in leaves of sun-grown trees. Shading and herbivory by Toumeyella sp. each resulted in decreased growth of Guaiacum sanctum. Scale insect herbivory did not result in greater detrimental effects on leaf gas exchange characteristics for shade-grown than for sun-grown trees. Herbivory by Toumeyella resulted in a greater decrease in tree growth for sun-grown than for shade-grown trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00328162
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  • 8
    Electronic Resource
    Electronic Resource
    Sampling range of male sweetpotato weevils (Cylas formicarius elegantulus) (Summers) (Coleoptera: Curculionidae) to pheromone traps: Influence of pheromone dosage and lure age (1990)
    Springer
    Journal of chemical ecology 16 (1990), S. 2493-2502 
    Details
    ISSN: 1573-1561
    Keywords: Cylas formicarius elegantulus (Summers) ; Coleoptera ; Curculionidae ; sex pheromone ; sweetpotato weevil ; mark-release-recapture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract Studies were conducted to determine the effects of sex pheromone dosage and lure age on movement of male sweetpotato weevils (SPW),Cylas formicarius elegantulus (Summers), using mark-release-recapture techniques. SPW trap counts from various downwind distances were compared for dosages ranging from 0.01 to 10.0 μg and lure ages ranging from fresh (0 days old) to 64 days old. The percentages of male SPW recaptured decreased with an increase in release distance and decreased with a decrease in dosage at each corresponding distance. Most SPW were caught within the first 16-hr period. Slopes of percent recapture vs. release distance for the two higher dosages (10 μg and 1.0 μg) differed from those of the two lower dosages (0.1 and 0.01 μg) but did not differ from each other. Intercepts were similar among the three higher dosages. Slopes did not differ among the five lure ages examined. Intercepts differed between fresh (0 days old) and 24-day-old septa at 16 hr and between fresh (0 days old) and 34-day-old septa at 40 hr. Previous exposure to pheromone (conditioning) did not increase percentages of SPW recaptured. Results indicate that male SPW are capable of traversing distances of at least 280 m in 16 hr. The pheromone tested in this study appears to be effective at dosages lower than any other coleopteran sex-pheromone system. Incorporation of this pheromone into a SPW management system may effectively reduce the use of insecticides.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01017472
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  • 9
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    Synergy between anti-CD4 and anti-tumor necrosis factor in the amelioration of established collagen-induced arthritis. (1994)
    National Academy of Sciences
    Details
    Publication Date: 1994-03-29
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
    Published by National Academy of Sciences
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  • 10
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    The vacuum and Bach equations in terms of light cone cuts (1995)
    American Institute of Physics
    Details
    Publication Date: 1995-07-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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