Lipoic Acid Combined with Melatonin Mitigates Oxidative Stress and Promotes Root Formation and Growth in Salt-Stressed Canola Seedlings (Brassica napus L.)

Lipoic acid (LA) and melatonin (MT) are pleiotropic molecules participating in plant stress resistance by modulating cellular biochemical changes, ion homeostasis, and antioxidant enzyme activities. However, the combined role of these two molecules in counteracting the detrimental impacts of salinity stress is still unknown. In the present study, we determined the effects of exogenous LA (0.5 µM), MT (1 µM) and their combination (LA + MT) on growth performance and biomass accumulation, photosynthetic pigments, enzymatic and non-enzymatic antioxidant activities, and ions homeostatic in canola (Brassica napus L.) seedlings under salinity stress (0, 100 mM) for 40 days. The results indicate that exogenous application of LA + MT improved the phenotypic growth (by 25 to 45%), root thickness (by 68%), number of later lateral roots (by 52%), root viability (by 44%), and root length (by 50%) under salinity stress. Moreover, total soluble protein, chlorophyll pigments, the concentration of superoxide dismutase (SOD), catalase peroxidase (CAT), and ascorbic peroxidase (ASA) increased with the presence of salt concentration into the growth media and then decreased with the addition of LA + MT to saline solution. Leaf protein contents and the degradation of photosynthetic pigments were lower when LA + MT treatments were added into NaCl media. The proline and phenol contents decreased in the exogenous application of LA + MT treatments more than individual LA or MT treatments under the salinity stress. The incorporation of LA or MT or a combination of LA + MT to saline solution decreased salinity-induced malondialdehyde and electrolyte leakage. In conclusion, the alteration of metabolic pathways, redox modulation, and ions homeostasis in plant tissues by the combined LA and MT application are helpful towards the adaptation of Brassica napus L. seedlings in a saline environment. The results of this study provide, for the first time, conclusive evidence about the protective role of exogenous LA + MT in canola seedlings under salinity stress.     

The Rain on Underground Porous Media Part I: Analysis of a Richards Model

The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem.     

Existence and Global Asymptotic Behavior of Positive Solutions for Sublinear and Superlinear Fractional Boundary Value Problems

In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form(P_(a,b)){D~αu(x) + f(x, u(x)) = 0, x ∈(0, 1),u(0) = u(1) = 0, D~(α-3)u(0) = a, u(1) =-b,where 3 α≤ 4, Dαis the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f(x, t) =-p(x)t~σ, with σ∈(-1, 1)and p being a nonnegative continuous function that may be singular at x = 0 or x = 1and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch¨auder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem(P_(0,0)).Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a + b 0 and f(x, t) = tφ(x, t), with φ(x, t) being a nonnegative continuous function in(0, 1)×[0, ∞) that is required to satisfy some suitable integrability condition. Using estimates on the Green's function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem(P_(a,b)), which behaves like the unique solution of the homogeneous problem corresponding to(P_(a,b)). Some examples are given to illustrate the existence results.     

Pseudomonotone Variational Inequalities: Convergence of Proximal Methods

In this paper, we study the convergence of proximal methods for solving pseudomonotone (in the sense of Karamardian) variational inequalities. The main result is given in the finite-dimensional case, but we show that we still obtain convergence in an infinite-dimensional Hilbert space under a strong pseudomonotonicity or a pseudo-Dunn assumption on the operator involved in the variational inequality problem.     

A New Hybridized Mixed Weak Galerkin Method for Second-Order Elliptic Problems

In this paper, a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic problem. This method is designed by approximate some operators with discontinuous piecewise polynomials in a shape regular finite element partition. Some discrete inequalities are presented on discontinuous spaces and optimal order error estimations are established. Some numerical results are reported to show super convergence and confirm the theory of the mixed weak Galerkin method.     

ChemInform Abstract: β-Dicobalt Pyrophosphate.

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