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Interesting Example (interesting + example)
Selected AbstractsHeavy Metals in Matrices of Food Interest: Sequential Voltammetric Determination at Trace and Ultratrace Level of Copper, Lead, Cadmium, Zinc, Arsenic, Selenium, Manganese and Iron in MealsELECTROANALYSIS, Issue 18 2004Clinio Locatelli Abstract The voltammetric methods are very suitable and versatile techniques for the simultaneous metal determination in complex matrices. The present work, regarding the sequential determination of Cu(II), Pb(II), Cd(II), Zn(II) by square-wave anodic stripping voltammetry (SWASV), As(III), Se(IV) by square-wave cathodic stripping voltammetry (SWCSV) and Mn(II), Fe(III) by square-wave voltammetry (SWV) in matrices involved in foods and food chain as wholemeal, wheat and maize meal, are an interesting example of the possibility to sequentially determine each single element in real samples. Besides the set up of the analytical method, particular attention is aimed either at the problem of possible signal interference or to show that, using the peak area Ap as instrumental datum, it is possible to achieve lower limits of detection. The analytical procedure was verified by the analysis of the standard reference materials: Wholemeal BCR-CRM 189, Wheat Flour NIST-SRM 1567a and Rice Flour NIST-SRM 1568a. Precision, as repeatability, and accuracy, expressed as relative standard deviation and relative error, respectively, were lower than 6% in all cases. In the presence of reciprocal interference, the standard addition method considerably improved the resolution of the voltammetric technique. Once set up on the standard reference materials, the analytical procedure was transferred and applied to commercial meals sampled on market for sale. A critical comparison with spectroscopic measurements is also discussed. [source] The implementation of international nature conservation agreements in Europe: the case of the NetherlandsENVIRONMENTAL POLICY AND GOVERNANCE, Issue 3 2001Graham Bennett Nature conservation policy in European countries is increasingly determined by the requirements of a wide range of international agreements. The most important are two EU directives (the Birds Directive and the Habitats Directive) and four conventions (the Ramsar Convention, the Bern Convention, the Bonn Convention and the UN Convention on Biological Diversity). The main foci of these instruments are habitats and species that are of international importance or require international cooperation to secure their effective conservation. Despite the importance of these habitats and species, implementation of the instruments has been uneven. The Netherlands provides a interesting example of implementation issues. The legislation necessary to enable the government to legally designate areas that have to be protected under the Birds Directive was only adopted in 1998, 17 years after the deadline fixed by the directive. This legislation has enabled the government to nominate areas for designation under the Birds and Habitats Directive. However, not all the sites that fall under the criteria of the Directives have been included in the list, and the legislation does not include the required provision concerning compensation for areas that are protected under the Habitats Directive and then damaged by activities that are authorized in the public interest. In the case of the Ramsar Convention, the government is planning to increase the number of designated sites, but the total number of sites will still represent inadequately the types of wetland of international importance that are found in the Netherlands. Despite this uneven implementation, the instruments , particularly the EU Directives , are having far-reaching effects on nature conservation in Europe. The most important consequences are that ecological considerations are the sole and absolute criteria for determining whether a site should be protected under the EU Directives and that many areas that until now only enjoyed limited protection under the spatial planning system now have to be legally protected from virtually all forms of damage. However, in practice many development plans take only limited account of the biodiversity conservation requirements implied by international conventions. Copyright © 2001 John Wiley & Sons, Ltd. and ERP Environment [source] Pursuing paradoxical proconvulsant prophylaxis for epileptogenesisEPILEPSIA, Issue 7 2009Caren Armstrong Summary There are essentially two potential treatment options for any acquired disorder: symptomatic or prophylactic. For acquired epilepsies that follow a variety of different brain insults, there remains a complete lack of prophylactic treatment options, whereas at the same time these epilepsies are notoriously resistant, once they have emerged, to symptomatic treatments with antiepileptic drugs. The development of prophylactic strategies is logistically challenging, both for basic researchers and clinicians. Nevertheless, cannabinoid-targeting drugs provide a very interesting example of a system within the central nervous system (CNS) that can have very different acute and long-term effects on hyperexcitability and seizures. In this review, we outline research on cannabinoids suggesting that although cannabinoid antagonists are acutely proconvulsant, they may have beneficial effects on long-term hyperexcitability following brain insults of multiple etiologies, making them promising candidates for further investigation as prophylactics against acquired epilepsy. We then discuss some of the implications of this finding on future attempts at prophylactic treatments, specifically, the very short window within which prevention may be possible, the possibility that traditional anticonvulsants may interfere with prophylactic strategies, and the importance of moving beyond anticonvulsants,even to proconvulsants,to find the ideal preventative strategy for acquired epilepsy. [source] Great Framework Variation of Polymers in the Manganese(II) Maleate/,,,,-Diimine System: Syntheses, Structures, and Magneto-Structural CorrelationEUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 15 2003Chengbing Ma Abstract Three novel manganese(II) coordination polymers, [Mn (maleate)(phen)]n (1; phen = 1,10-phenanthroline), [Mn(maleate)(phen)]n·nH2O (2), and [Mn(maleate)(bpy)]n (3; bpy = 2,2,-bipyridine), have been synthesized by treatment of Mn2+ with maleic acid with participation of chelate diimine ligands, and have been identified by single-crystal X-ray diffraction to have either one-dimensional (1D) zigzag chain structures (1 and 2) or a two-dimensional (2D) sinuous layer structure (3). Each maleate dianion coordinates to three Mn centers, in different bridging modes (syn - anti in 1 and 2, syn - syn and anti - anti in 3). These compounds represent an interesting example of structural topology variation from 1D to 2D mediated by chemically similar auxiliary chelate ligands. Variable-temperature magnetic susceptibility measurements show weak anti-ferromagnetic exchange interactions between the adjacent MnII ions, with J = ,0.06 cm,1 (2) and J = ,1.3 cm,1, zJ, = ,0.27 cm,1 (3). The differences in the magnitudes of these coupling interactions agree well with the nature of the carboxylate-bridging coordination of maleate. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003) [source] Mixing processes in the Amazon River at the confluences of the Negro and Solimões Rivers, Encontro das Águas, Manaus, BrazilHYDROLOGICAL PROCESSES, Issue 22 2009Alain Laraque Abstract The confluence of the rivers Negro and Solimões gives birth to the Amazon River near Manaus (Brazil). At their confluence, these two rivers with their very different physical and geochemical characteristics provide an interesting example of the mixing of waters along a reach of approximately one-hundred kilometres. The purpose of this article is to describe and explain the spatial configuration of the Solimões,Negro Rivers mixing zone, based on a systematic sampling survey carried out in September 1997, using a special sampler and an acoustic Doppler current profiler (Acoustic Doppler Current Profiler). The waters of the Negro River differ from those of the Solimões River in their lower velocity (0·3 vs 1 m s,1), conductivity (8 vs 80 µS cm,1 at 25 °C), turbidity (5 vs 80 NTU), pH (5·5 vs 7·0) and higher temperatures (by 1 °C). Due to their higher density, the waters of the Solimões River slide under those of the Negro River, and consequently, Negro River waters are located at the surface, close to the left bank, and Solimões River waters are located at the bottom, close to the right bank. The contact between the waters of the two rivers changes from a clearly defined vertical boundary to a diffuse horizontal boundary, as they move downstream. The complete mixing process takes more than 30 h and 100 km. Copyright © 2009 John Wiley & Sons, Ltd. [source] Phylogeny and biogeography of Yellow-headed and Blue-fronted Parrots (Amazona ochrocephala and Amazona aestiva) with special reference to the South American taxaIBIS, Issue 3 2007CAMILA C. RIBAS The Yellow-headed Parrot (Amazona ochrocephala) has a broad Neotropical distribution, ranging from Mexico to the Amazon Basin, and a history of complex taxonomy and controversial species limits. Recent molecular analyses have started to clarify the taxonomic arrangement of the complex, but have not included a representative geographical sampling from South America. These studies have shown that the Yellow-headed complex can be divided into three main lineages, and seems to be paraphyletic, due to the inclusion of the Blue-fronted Parrot (Amazona aestiva) that occurs in central South America. Here we present a phylogenetic analysis based on mitochondrial DNA sequences of 45 representatives of the Yellow-headed complex from South and Central America, plus 13 Blue-fronted individuals from different localities in South America. Our analyses recover the three primary lineages found previously in the Yellow-headed complex, show that there is genetic structure in the South American lineage, which can be divided into two well-supported, closely related clades, and demonstrate that Blue-fronted samples are distributed in both clades. Differentiation of South American Blue-fronted and Yellow-headed Parrot populations does not correspond to the plumage differences used to distinguish the Blue-fronted Parrot from the Yellow-headed Parrot, nor to plumage differences used to distinguish among South American Yellow-headed subspecies. This suggests that traditional taxonomy based on plumage characters needs revision, and that this may be an interesting example of ongoing divergence-with-gene-flow related to the forest/open area ecotone in southern Amazonia. [source] Residual rickets or osteomalacia: a case dating from the 16,18th centuries from Krosno Odrza,skie, PolandINTERNATIONAL JOURNAL OF OSTEOARCHAEOLOGY, Issue 5 2009E. Haduch Abstract A skeleton from a 16,18th century burial site in Krosno Odrza,skie, Poland, was examined using classical morphological, metric and macroscopic palaeopathological observations, as well as radiography and tomography of the skull and long bones. A wide variety of the observed bone deformations probably occurred as a consequence of past rickets and/or osteomalacia, whose primary cause may also have been chronic renal failure. Preservation of the bones enables a discussion of the cause of such pathological changes. The subject under study appears to be a very interesting example of an individual whose skeleton shows advanced pathological alterations associated with the subject's vitamin D deficiency, overall health conditions and relatively long lifespan. Copyright © 2008 John Wiley & Sons, Ltd. [source] Correlating the positional reactivity of a masked electrophilic center to the topology of the electron densityINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2005Harry L. Price Abstract Masking of electrophilic centers in biological molecules via structural modifications serves to control chemical reactivity and in some cases may affect the regioselectivity of a reaction. In the work presented the regioselective reactivity of the electrophilic cyclopropylpyrrololindole (CPI) center in the DNA alkylator CC-1065, a highly toxic antibiotic that has served as a structural template for the development of a series of novel anticancer drugs containing the CPI reactive center has been examined. The CPI reactive center is an interesting example of chemical masking as it relates to acid-dependent electrophilicity, and regioselective addition of a nucleophile to an electrophilic center. In an effort to better understand the reactivity of the CPI center, calculations using the B3LYP density functional theory (DFT) method, the 6-31G(d) basis set, and the atoms in molecules (AIM) theory were performed on unprotonated and protonated forms of the CPI reactive center. The results of these calculations demonstrate that activation of the CPI group via protonation induces significant changes in the electron density (,), the Laplacian of the density (,2,), and the bond ellipticity (,), and that these changes are linked to the observed reactivity of the CPI reaction center. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Stat1-mediated cytoplasmic attenuation in osteoimmunologyJOURNAL OF CELLULAR BIOCHEMISTRY, Issue 2 2005Hiroshi Takayanagi Abstract Signal transducer and activator of transcription 1 (Stat1) is a critical mediator of gene transcription in type I interferon (IFN-,/,) signaling that is essential for host defense against viruses. In the skeletal system, type I IFNs (IFN-,/,) also play an important physiological role in the inhibition of receptor activator of NF-,B ligand (RANKL)-induced osteoclast differentiation and bone resorption: mice deficient in IFN signaling exhibit decreased bone mass accompanied by the activation of osteoclastogenesis. On the other hand, an unexpected increase in bone mass was observed in Stat1-deficient mice, indicating that Stat1 has a hitherto unknown function in the regulation of bone formation. Indeed, Stat1 was found to have a unique, non-canonical function as a cytoplasmic attenuator of Runx2, a key transcription factor for osteoblast differentiation. Thus, the loss of Stat1 results in excessive activation of Runx2 and osteoblast differentiation, thereby tipping the balance in favor of bone formation over bone resorption. This is an interesting example in which a latent transcription factor attenuates the activity of another transcription factor in the cytoplasm, and reveals a novel regulatory mechanism of bone remodeling by immunomodulatory molecules. Here, we summarize recent advances in the study of Stat1 and IFNs in the context of osteoimmunology, including latest reports that question whether the inhibitory function of Stat1 in chondrocytes is responsible for dwarfism in achondroplasia. © 2004 Wiley-Liss, Inc. [source] Costs and benefits of genetic heterogeneity within organismsJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 6 2004M. Pineda-Krch Abstract An increasing number of studies have recently detected within-organism genetic heterogeneity suggesting that genetically homogeneous organisms may be rare. In this review, we examine the potential costs and benefits of such intraorganismal genetic heterogeneity (IGH) on the fitness of the individual. The costs of IGH include cancerous growth, parasitism, competitive interactions and developmental instability, all of which threaten the integrity of the individual while the potential benefits are increased genetic variability, size-specific processes, and synergistic interactions between genetic variants. The particular cost or benefit of IGH in a specific case depends on the organism type and the origin of the IGH. While mosaicism easily arise by genetic changes in an individual, and will be the more common type of IGH, chimerism originates by the fusion of genetically distinct entities, and is expected to be substantially rare in most organisms. Potential conflicts and synergistic effects between different genetic lineages within an individual provide an interesting example for theoretical and empirical studies of multilevel selection. [source] On the importance of controls in enzyme assays , an odd exampleBIOCHEMISTRY AND MOLECULAR BIOLOGY EDUCATION, Issue 2 2001Subita Sudarshana An interesting example of interference in the arginase assay is presented. This can be exploited to convey the importance of taking precautions and appropriate controls to the students of enzymology. © 2001 IUBMB. Published by Elsevier Science Ltd. All rights reserved. [source] Worldwide mitochondrial DNA diversity and phylogeography of pilot whales (Globicephala spp.)BIOLOGICAL JOURNAL OF THE LINNEAN SOCIETY, Issue 4 2009MARC OREMUS Pilot whales (Globicephala spp.) provide an interesting example of recently diverged oceanic species with a complex evolutionary history. The two species have wide but largely non-overlapping ranges. Globicephala melas (long-finned pilot whale; LFPW) has an antitropical distribution and is found in the cold-temperate waters of the North Atlantic and Southern Hemisphere, whereas Globicephala macrorhynchus (short-finned pilot whale; SFPW) has a circumglobal distribution and is found mainly in the tropics and subtropics. To investigate pilot whale evolution and biogeography, we analysed worldwide population structure using mitochondrial DNA (mtDNA) control region sequences (up to 620 bp) from a variety of sources (LFPW = 643; SFPW = 150), including strandings in New Zealand and Tasmania, and whale-meat products purchased on the markets of Japan and Korea. Phylogenetic reconstructions failed to support a reciprocal monophyly of the two species, despite six diagnostic substitutions, possibly because of incomplete lineage sorting or inadequate phylogenetic information. Both species had low haplotype and nucleotide diversity compared to other abundant widespread cetaceans (LFPW, , = 0.35%; SFPW, , = 0.87%) but showed strong mtDNA differentiation between oceanic basins. Strong levels of structuring were also found at the regional level. In LFPW, phylogeographic patterns were suggestive either of a recent demographic expansion or selective sweep acting on the mtDNA. For SFPW, the waters around Japan appear to represent a centre of diversity, with two genetically-distinct forms, as well as a third population of unknown origin. The presence of multiple unique haplotypes among SFPW from South Japan, together with previously documented morphological and ecological differences, suggests that the southern form represents a distinct subspecies and/or evolutionary significant unit. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 98, 729,744. [source] Redox proteins in mammalian cell death: an evolutionarily conserved function in mitochondria and prokaryotesCELLULAR MICROBIOLOGY, Issue 4 2003Vasu Punj Summary Mammalian cell mitochondria are believed to have prokaryotic ancestry. Mitochondria are not only the powerhouse of energy generation within the eukaryotic cell but they also play a major role in inducing apoptotic cell death through release of redox proteins such as cytochrome c and the apoptosis-inducing factor (AIF), a flavoprotein with NADH oxidase activity. Recent evidence indicates that some present day prokaryotes release redox proteins that induce apoptosis in mammalian cells through stabilization of the tumour suppressor protein p53. p53 interacts with mitochondria either directly or through activation of the genes for pro-apoptotic proteins such as Bax or NOXA or genes that encode redox enzymes responsible for the production of reactive oxygen species (ROS). The analogy between the ancient ancestors of present day bacteria, the mitochondria, and the present day bacteria with regard to their ability to release redox proteins for triggering mammalian cell death is an interesting example of functional conservation during the hundreds of millions of years of evolution. It is possible that the ancestors of the present day prokaryotes released redox proteins to kill the ancestors of the eukaryotes. During evolution of the mitochondria from prokaryotes as obligate endosymbionts, the mitochondria maintained the same functions to programme their own host cell death. [source] Site-Specific Investigation of the Steady-State Kinetics and Dynamics of the Multistep Binding of Bile Acid Molecules to a Lipid Carrier ProteinCHEMISTRY - A EUROPEAN JOURNAL, Issue 37 2010Dr. Clelia Cogliati Abstract The investigation of multi-site ligand,protein binding and multi-step mechanisms is highly demanding. In this work, advanced NMR methodologies such as 2D 1H,15N line-shape analysis, which allows a reliable investigation of ligand binding occurring on micro- to millisecond timescales, have been extended to model a two-step binding mechanism. The molecular recognition and complex uptake mechanism of two bile salt molecules by lipid carriers is an interesting example that shows that protein dynamics has the potential to modulate the macromolecule,ligand encounter. Kinetic analysis supports a conformational selection model as the initial recognition process in which the dynamics observed in the apo form is essential for ligand uptake, leading to conformations with improved access to the binding cavity. Subsequent multi-step events could be modelled, for several residues, with a two-step binding mechanism. The protein in the ligand-bound state still exhibits a conformational rearrangement that occurs on a very slow timescale, as observed for other proteins of the family. A global mechanism suggesting how bile acids access the macromolecular cavity is thus proposed. [source] A Concerted Approach for the Determination of Molecular Conformation in Ordered and Disordered MaterialsCHEMISTRY - A EUROPEAN JOURNAL, Issue 22 2007Jan Sehnert Abstract We present the successful application of a concerted approach for the investigation of the local environment in ordered and disordered phases in the solid state. In this approach we combined isotope labeling with computational methods and different solid-state NMR techniques. We chose triphenylphosphite (TPP) as an interesting example of our investigations because TPP exhibits two crystalline modifications and two different amorphous phases one of which is highly correlated. In particular we analyzed the conformational distribution in three of these phases. A sample of triply labeled 1-[13C]TPP was prepared and 1D MAS as well as wide-line 13C NMR spectra were measured. Furthermore we acquired 2D 13C wide-line exchange spectra and used this method to derive highly detailed information about the phenyl orientation in the investigated TPP phases. For linkage with a structure model a DFT analysis of the TPP molecule and its immediate environment was carried out. The ab initio calculations of the 13C chemical shift tensor in three- and six-spin systems served as a base for the calculation of 1D and 2D spectra. By comparing these simulations to the experiment an explicit picture of all phases could be drawn on a molecular level. Our results therefore reveal the high potential of the presented approach for detailed studies of the mesoscopic environment even in the challenging case of amorphous materials. [source] A Measure of Representativeness of a Sample for Inferential PurposesINTERNATIONAL STATISTICAL REVIEW, Issue 2 2006Salvatore Bertino Summary After defining the concept of representativeness of a random sample, the author proposes a measure of how much the observed sample represents its parent distribution. This measure is called Representativeness Index. The same measure, seen as a function of a sample and of a distribution, will be called Representativeness Function. For a given sample it provides the value of the index for the different distributions under examination, and for a given distribution it provides a measure of the representativeness of its possible samples. Such Representativeness Function can be used in an inferential framework just as the likelihood function, since it gives to any distribution the "experimental support" provided by the observed sample. This measure is distribution-free and it is shown to be a transformation of the wellknown Cramér,von Mises statistic. By using the properties of that statistic, criteria for providing set estimators and tests of hypotheses are introduced. The utilization of the representativeness function in many standard statistical problems is outlined through examples. The quality of the inferential decisions can be assessed with the usual techniques (MSE, power function, coverage probabilities). The most interesting examples turn out to be those of situations that are "non-regular", as for instance the estimation of parameters involved in the support of the parent distribution, or less explored (model choice). Résumé Après avoir défini le concept de répresentativité d'un échantillon aléatoire, l'auteur propose une mesure de combien l'échantillon observé réprésente la distribution parente. Cette mesure est dite Fonction de Répresentativité. Pour un échantillon donné la fonction donne les valeurs de l'indice pour toutes le distributions de la famille consideée, tandis que, pour une distribution donnée, elle donne la mesure de la répresentativité de chaque possible échantillon. La Fonction de Répresentativité peut être employée dans les problèmes d'inference statistique justement comme la fonction de vraisemblance, puisque elle donne à chaque distribution le "support expérimental" produit par l'échantillon observé. La measure est à distribution libre et on demontre que elle est une tranformation de la bien connue statistique de Cramér,von Mises. En utilisant le propriétés de la dite statistique, on introduit des crières pour obtenir estimateur ensemblistes et test d'hypothèse. L'utilization de la fonction de répresentativité dans plusieurs problèmes statistique est montrée par des examples. La qualité des decisions inférentielles peut être evaluée par les techniques usuelles (MSE, fonction de puissance, probabiliés de couverture). Les examples les plus interessant sont ceux qui concerne les situations "non regulères", par exemple l'estimation de paramètres qui figurent dans le support de la population parente, ou situations moins exploées (choix du modèle). [source] Atypical polysaccharide physical gels: structure/property relationshipsMACROMOLECULAR SYMPOSIA, Issue 1 2003Alexandra Clayer Abstract Chitin and chitosan are polysaccharides produced by the biomass. They have the same general chemical structure and constitute the series of linear copolymers of linked ,, (1->4) glucosamine and N-actylglucosamine. We studied the possibility of forming physical gels with all the terms of this series, whatever the proportion of the two kinds of residues included in the polymer chains. We show that physical gelation is still possible through a percolating process when certain important conditions are met. Initially the concentration in polymer must be above C*; a critical value of the balance between hydrophobic and hydrophilic interactions must be achieved and gelation must occur simultaneously everywhere in the medium. These conditions were observed in several situations allowing the formation of different kinds of gels at all values of DA. In view of the rare bio-active properties of chitin and chitosan, these gels were tested for living tissue regeneration and constitute very interesting examples in illustration of our concept of decoys for biological media. [source] RISK MEASURES ON ORLICZ HEARTSMATHEMATICAL FINANCE, Issue 2 2009Patrick Cheridito Coherent, convex, and monetary risk measures were introduced in a setup where uncertain outcomes are modeled by bounded random variables. In this paper, we study such risk measures on Orlicz hearts. This includes coherent, convex, and monetary risk measures on Lp -spaces for 1 ,p < , and covers a wide range of interesting examples. Moreover, it allows for an elegant duality theory. We prove that every coherent or convex monetary risk measure on an Orlicz heart which is real-valued on a set with non-empty algebraic interior is real-valued on the whole space and admits a robust representation as maximal penalized expectation with respect to different probability measures. We also show that penalty functions of such risk measures have to satisfy a certain growth condition and that our risk measures are Luxemburg-norm Lipschitz-continuous in the coherent case and locally Luxemburg-norm Lipschitz-continuous in the convex monetary case. In the second part of the paper we investigate cash-additive hulls of transformed Luxemburg-norms and expected transformed losses. They provide two general classes of coherent and convex monetary risk measures that include many of the currently known examples as special cases. Explicit formulas for their robust representations and the maximizing probability measures are given. [source] Dirichlet duality and the nonlinear Dirichlet problemCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2009F. Reese Harvey We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F(Hess u) = 0 on a smoothly bounded domain , , ,n. In our approach the equation is replaced by a subset F , Sym2(,n) of the symmetric n × n matrices with ,F , {F = 0}. We establish the existence and uniqueness of continuous solutions under an explicit geometric "F -convexity" assumption on the boundary ,,. We also study the topological structure of F -convex domains and prove a theorem of Andreotti-Frankel type. Two key ingredients in the analysis are the use of "subaffine functions" and "Dirichlet duality." Associated to F is a Dirichlet dual set F, that gives a dual Dirichlet problem. This pairing is a true duality in that the dual of F, is F, and in the analysis the roles of F and F, are interchangeable. The duality also clarifies many features of the problem including the appropriate conditions on the boundary. Many interesting examples are covered by these results including: all branches of the homogeneous Monge-Ampère equation over ,, ,, and ,; equations appearing naturally in calibrated geometry, Lagrangian geometry, and p -convex Riemannian geometry; and all branches of the special Lagrangian potential equation. © 2008 Wiley Periodicals, Inc. [source] | |||||||||||||||||||