This article gives a complex analysis lighting on the problem which consists in restoring a bordered connected riemaniann surface from its boundary and its Dirichlet-Neumann operator. The three aspects of this problem, unicity, reconstruction and characterization are approached. Statements of the Main ResultsLet X be an open-bordered riemannian real surface (i.e. the interior of an oriented riemannian two-dimensional real manifold all of whose components have non-trivial one-dimensional smooth boundary) and g its metric. Using the boundary-control method, Belishev and Kurylev ([B1], [BK]) began the study of the inverse problem consisting in recovering (X , g) from the operators N λ : C ∞ (bX ) u → (∂ u λ /∂ν) bX where bX is the boundary of X , ν is the normal exterior unit to bX and u λ is the unique solution of ∆ g U = λU such that U | bX = u. The principal result of [BK] implies that the knowledge of λ → N λ on an non-empty open set of R + determines (X , g) up to isometry. The important question whether (X , g) is uniquely determined by only one operator N λ * with λ * = 0, remains open. This article mainly deals with the case of the Dirichlet-Neumann operator N X := N 0 . Section 2 gives an intrinsic interpretation electrical impedance tomography on manifolds, EIT for short, in terms of the inverse Dirichlet-Neumann problem for twisted Laplacian. In dimension two, this clearly underlines how the complex structure of Riemannian surfaces is involved.Two surfaces in the same conformal class which have the same oriented boundary and whose metrics coincide there, need to have the same Dirichlet-Neumann operator. Conversely, Lassas and Uhlmann [LU] have
The effect of a soil amendment (SA) composed of urea (200 kg of N per ha) and CaO (5,000 kg/ha) on the survival of Ralstonia solanacearum in four Philippine soils was investigated in a series of laboratory experiments. Within 3 weeks after application, the SA either caused an initial decrease, a final decline, or no change in the pathogen population, depending on the particular soil type. An initial decrease occurred in a soil with a basic pH and resulted in a significantly (P < 0.001) lower pathogen population immediately and at 1 week after amending the soil. This decrease was probably due to the high pH in the soil during urea hydrolysis. A final decline in the R. solanacearum population after 3 weeks occurred in two soils in which nitrite accumulated after 1 week. In these soils, no decline in bacterial levels occurred when nitrite formation was inhibited by 2-chloro-6-trichloromethylpyridine. In the soil with low pH, no nitrite accumulated and the R. solanacearum population did not decline. The suppressive effects of pH and nitrite on R. solanacearum growth were confirmed by in vitro experiments. Ammonium reduced the growth of R. solanacearum, but was not suppressive. Interactions of pH with ammonium and nitrite also occurred, whereby ammonium reduced growth of R. solanacearum only at pH 9 and nitrite was suppressive only at pH 5. Nitrate had no effect on R. solanacearum growth in vitro.
Potato virus Y (PVY) is one of the most damaging viruses of tobacco. In particular, aggressive necrotic strains (PVY ) lead to considerable losses in yield. The main source of resistance against PVY is linked to the va locus. However, va-overcoming PVY isolates inducing necrotic symptoms were observed in several countries. In this context, it is important to find va-independent protection strategies. In a previous study, the phenotyping of 162 tobacco varieties revealed 10 accessions that do not carry the va allele and do not exhibit typical PVY -induced veinal necrosis. Despite the absence of necrotic symptoms, normal viral accumulation in these plants suggests a va-independent mechanism of tolerance to PVY -induced systemic veinal necrosis. Fine mapping of the genetic determinant(s) was performed in a segregating F2 population. The tolerance trait is inherited as a single recessive gene, and allelism tests demonstrated that eight of the 10 tolerant varieties carry the same determinant. Anchoring the linkage map to the tobacco genome physical map allowed the identification of a RPP8-like R gene, called NtTPN1 (for Nicotiana tabacum Tolerance to PVY-induced Necrosis1), with the same single-nucleotide polymorphism in the eight tolerant accessions. Functional assays using homozygous NtTPN1 EMS mutants confirmed the role of NtTPN1 in the tolerance phenotype. PVY -induced systemic veinal necrosis in tobacco likely represents an inefficient defense response with hypersensitive response-like characteristics. The identification of NtTPN1 opens breeding options to minimize the impact of emerging and so far uncontrolled va-breaking necrotic PVY isolates.
An electrical potential U on a bordered Riemann surface X with conductivity function σ > 0 satisfies equation d(σd c U ) = 0. The problem of effective reconstruction of σ from electrical currents measurements (Dirichlet-to-Neumann mapping) on the boundary: U bX → σd c U bX is studied. We extend to the case of Riemann surfaces the reconstruction scheme given, firstly, by R.Novikov [N1] for simply connected X. We apply for this new kernels for∂ on the affine algebraic Riemann surfaces constructed in [H2].0. Introduction 0.1. Inverse conductivity problem. Let X be bordered oriented real two-dimensional manifold in R 3 equiped with a smooth symmetric and positive tensorσ : T * X → T * X on cotangent bundle T * X, called anisotropic conductivity tensor on X,σ is called symmetric and positive ifσa ∧ b =σb ∧ a andσa ∧ a > 0 for any a, b ∈ T * X. Let u (correspondingly U ) be a smooth function on bX (correspondingly on X) such that U bX = u, called electric potential on bX and correspondingly on X. 1-formσdU on X is called electrical current on X. By Maxwell equation Under conditions above ∀ couple (X,σ) there exist a unique complex structure c on X and smooth scalar valued, positive conductivity function σ such that the equationThis statement permits to reduce the inverse conductivity problem to the questions about reconstruction from Dirichlet-to-Neumann mapping of the genus of X, of the complex structure of X and of the scalar conductivity function σ on X.These questions are well answered for the important case when X is a domain in R 2 , due to the sequence of works:The exact reconstruction scheme for this case was discovered by R.Novikov [N1]. Formulated questions are well answered also for the case when conductivity function σ is known to be constant on X, i.e. when only Riemann surface X must be reconstructed from Dirichlet-to-Neumann data [LU], [Be], [HM].
Intercropping and soil amendment experiments were conducted to determine if they reduced populations of Pseudomonas solanacearum and bacterial wilt of tomato at the Asian Vegetable Research and Development Center (AVRDC) and at three other locations in Taiwan. At AVRDC, intercropping tomato with cowpea planted within the row significantly reduced bacterial wilt (P < 0.05) compared to when tomato was cropped alone. The P. solanacearum population in soil was not affected by intercropping with cowpea, soybean, or Welsh onion.At the same site, however, a preplanting soil amendment consisting of urea (200 kg ha−1 N) and CaO (5000 kg ha−1) significantly reduced the pathogen population and tomato bacterial wilt (P < 0.001). The effect of the soil amendment was not consistent when applied to soil from three other sites in Taiwan; in soil from two sites no reduction of the pathogen population occurred. At these sites, tomato bacterial wilt in the field was not reduced significantly after amending. In comparison with a non‐amended control, the addition of only CaO reduced the P. solanacearum population in AVRDC soil significantly (P < 0.05), but the reduction was significantly greater when the complete soil amendment was added. In contrast, urea alone did not affect the survival of P. solanacearum in the soil. In a greenhouse experiment with AVRDC soil, P. solanacearum was undetectable 2 weeks after soil amendment, but in the same treatment tomato yield was significantly reduced by 48% (P < 0.05) compared with non‐amended treatments. The suppressive effect of the soil amendment on the P. solanacearum population was probably due to the generation of one or several toxic substances during the transformation of urea in the presence of CaO.
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