Obstructions to fibering a manifold

Given a map f : M → N of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S ¹, these torsion obstructions are identified with the ones due to Farrell (Indiana Univ Math J 21:315–346, 1971/1972).     

Nuclear Fukui functions from nonintegral electron number calculations

Numerical results for the nuclear Fukui function (NFF) based on a nonintegral number of electrons methodology (NIEM) are reported for a series of simple diatomic molecules. A comparison with those obtained from other methodologies is focused on the estimation of the error associated with a finite difference approximation for the evaluation of the NFF. The dependence of NFFs on the type and size of the basis set is also discussed. The NIEM values are in close agreement with those obtained from a finite difference approximation using ΔN = ±1 with large basis sets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Repeat‐pulse 13CO2 labeling of canola and field pea: implications for soil organic matter studies

Both the quantity and quality of plant residues can impact soil properties and processes. Isotopic tracers can be used to trace plant residue decomposition if the tracer is homogeneously distributed throughout the plant. Continuous labeling will homogeneously label plants but is not widely accessible because elaborate equipment is needed. In order to determine if the more accessible repeat‐pulse labeling method could be used to trace plant residue decomposition, this labeling procedure was employed using ¹³CO₂ to enrich field pea and canola plants in a controlled environment. Plants were exposed weekly to pulses of 33 atom% ¹³CO₂ and grown to maturity. The distribution of the label throughout the plant parts (roots, stem, leaves, and pod) and biochemical fractions (ADF and ADL) was determined. The label was not homogeneously distributed throughout the plant; in particular, the pod fractions were less enriched than other fractions indicating the importance of continuing labeling well into plant maturity for pod‐producing plants. The ADL fraction was also less enriched than the ADF fraction. Because of the heterogeneity of the label throughout the plant, caution should be applied when using the repeat‐pulse method to trace the fate of ¹³C‐labeled residues in the soil. However, root contributions to below‐ground C were successfully determined from the repeat‐pulse labeled root material, as was ¹³C enrichment of soil within the top 15 cm. Canola contributed more above‐ and below‐ground residue C than field pea; however, canola was also higher in ADF and ADL fractions indicating a more recalcitrant residue. Copyright © 2010 John Wiley & Sons, Ltd.     

Phragmén-Lindelöf theorems for nonlinear elliptic equations

We obtain theorems of Phragmén-Lindelöf type for the following classes of elliptic partial differential inequalities in an arbitrary unbounded domain \(\Omega \subseteq \mathbb{R}^n ,{\text{ }}n \geqq 2\) (A.1) $$\sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial x_i }}\left( {a_{ij} 9(x)\frac{{\partial u}}{{\partial xj}}} \right)} + \sum\limits_{i = 1}^n {b_i (x,{\text{ }}u,{\text{ }}\nabla u)\frac{\partial }{{\partial x_i }}} \geqq f(x,{\text{ }}u)$$ where a _ij are elliptic in Ω and b _i ε L^∞(Ω) and where also a _ij are uniformly elliptic and Holder continuous at infinity and b _i = O(|x|⁺¹) as x → ∞; (A.2) $${\text{(A}}{\text{.2) }}\sum\limits_{i,j = 1}^n {a_{ij} (x,{\text{ }}u,{\text{ }}\nabla u)\frac{{\partial ^2 u}}{{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^n {b_i (x,{\text{ }}u,{\text{ }}\nabla u)\frac{\partial }{{\partial x_i }}} \geqq f(x,{\text{ }}u)$$ where a_ijare uniformly elliptic in Ω and b _iε L^∞(Ω); and finally (A.3) $${\text{div(}}\nabla u^p \nabla u {\text{)}} \geqq f{\text{(}}u{\text{), }}p > - 1,$$ where the operator on the left is the so-called P-Laplacian. The function f is always supposed positive and continuous. Moreover u is assumed throughout to be in the natural weak Sobolev space corresponding to the particular inequality under consideration, namely u ε. W _loc ^1,2 (Ω) ∩L _loc ^t8 (Ω) for (A.I), W _loc ^2,n(Ω) for (A.2), and W _loc ^1,p+2 (Ω) ∩ L _loc ^t8 (Ω) for (A.3). As a consequence of our results we obtain both non-existence and Liouville theorems, as well as existence theorems for (A.1).     

Convergence of a level‐set algorithm in scalar conservation laws

This article is concerned with the convergence of the level‐set algorithm introduced by Aslam (J Comput Phys 167 (2001), 413–438) for tracking the discontinuities in scalar conservation laws in the case of linear or strictly convex flux function. The numerical method is deduced by the level‐set representation of the entropy solution: the zero of a level‐set function is used as an indicator of the discontinuity curves and two auxiliary states, which are assumed continuous through the discontinuities, are introduced. We rewrite the numerical level‐set algorithm as a procedure consisting of three big steps: (a) initialization, (b) evolution, and (c) reconstruction. In (a), we choose an entropy admissible level‐set representation of the initial condition. In (b), for each iteration step, we solve an uncoupled system of three equations and select the entropy admissible level‐set representation of the solution profile at the end of the time iteration. In (c), we reconstruct the entropy solution using the level‐set representation. We prove the convergence of the numerical solution to the entropy solution in for every , using ‐weak bounded variation (BV) estimates and a cell entropy inequality. In addition, some numerical examples focused on the elementary wave interaction are presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1310–1343, 2015     

A note on the strong maximum principle and the compact support principle

In this note we are concerned with the strong maximum principle (SMP) and the compact support principle (CSP) for non-negative solutions to quasilinear elliptic inequalities of the form

     

Conditions for Permutability of Congruences in Implication Algebras

In this paper we give conditions on an implication algebra A so that two congruences θ ₁, θ ₂ on A permute, i.e. θ ₁ ∘ θ ₂ = θ ₂ ∘ θ ₁. We also provide simpler conditions for permutability in finite implication algebras. Finally we present some applications of these characterizations. The support of Universidad Nacional del Sur and CONICET is gratefully acknowledged.