Abstract: In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory. (C) 2021 Elsevier Inc. All rights reserved.

Abstract: Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geo-statistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the multivariate case has been elusive so far. The new challenges provided by modern spatial datasets, being typ-ically multivariate, call for a deeper study of cokriging. In particular, we deal with the problem of misspecified cokriging prediction within the framework of fixed domain asymptotics. Specifically, we provide conditions for equivalence of measures associated with multivariate Gaussian random fields, with index set in a compact set of a d-dimensional Euclidean space. Such conditions have been elusive for over about 50 years of spatial statistics. We then focus on the multivariate Matern and Generalized Wendland classes of matrix valued covariance functions, that have been very popular for having parameters that are crucial to spatial interpolation, and that control the mean square differentiability of the associated Gaussian process. We provide sufficient conditions, for equivalence of Gaussian measures, relying on the covariance parameters of these two classes. This enables to identify the parameters that are crucial to asymptotically equivalent interpolation in multivariate geostatistics. Our findings are then illustrated through simulation studies.

Abstract: Irrigation scheduling based on soil water content (Ow) sensors requires that Ow be maintained within a range (management lines) that is optimal for plant growth. The lower limit or “breaking point ” is determined following the soil water content dynamics on the transition of a rapid rate of depletion to a slower, under similar reference evapotranspiration. Although this criterion is practical, its implementation should be validated with plant water status measurement that contemplate weather condition, such as stem water potential “non-stressed ” baseline (Tx as a function of vapor-pressure deficit (VPD) in Ow conditions that do not limit yield). A study was con-ducted on a mature cv. 'Hass' avocado orchard in Central Chile during two seasons. There were 5 irrigation treatments: T1, Control; T2 and T3 with 29% less and 25% more of what was applied in T1, respectively; T4 and T5 same as Control until first and second fruit drop abscission, respectively, and then with 29% less. T1 trees were irrigated using a continuous frequency domain reflectometry (FDR) probe to maintain the root zone be-tween field capacity and the breaking point. There was biweekly monitoring of the Ow prior to irrigation, Tx and VPD. The Tx decline proportional to the intensity and the timing of water restriction; however, no treatment affected the crop load in either season. T2 did not show significant detrimental in fruit size, production and maturation, despite that frequently reached water content levels at the limit of the breaking point, and showed lower levels of stem water potential than Control, being the treatment with the highest water productivity. The results confirm that breaking point is an effective criterion to establish irrigation management. Additionally, when comparing the baseline for our non-stressed trees with a baseline from full irrigation treatments obtained from the literature, 30% water savings were achieved.

Abstract: The self-sufficient cytochrome P450 RhF and its homologues belonging to the CYP116B subfamily have attracted considerable attention due to the potential for biotechnological applications based in their ability to catalyse an array of challenging oxidative reactions without requiring additional protein partners. In this work, we showed for the first time that a CYP116B self-sufficient cytochrome P450 encoded by the ohpA gene harboured by Cupriavidus pinatubonensis JMP134, a beta-proteobacterium model for biodegradative pathways, catalyses the conversion of 2-hydroxyphenylacetic acid (2-HPA) into homogentisate. Mutational analysis and HPLC metabolite detection in strain JMP134 showed that 2-HPA is degraded through the well-known homogentisate pathway requiring a 2-HPA 5-hydroxylase activity provided by OhpA, which was additionally supported by heterologous expression and enzyme assays. The ohpA gene belongs to an operon including also ohpT, coding for a substrate-binding subunit of a putative transporter, whose expression is driven by an inducible promoter responsive to 2-HPA in presence of a predicted OhpR transcriptional regulator. OhpA homologues can be found in several genera belonging to Actinobacteria and alpha-, beta- and gamma-proteobacteria lineages indicating a widespread distribution of 2-HPA catabolism via homogentisate route. These results provide first time evidence for the natural function of members of the CYP116B self-sufficient oxygenases and represent a significant input to support novel kinetic and structural studies to develop cytochrome P450-based biocatalytic processes.

Abstract: We show that the time-dependent harmonic oscillator has a repulsive or inverted oscillator as a time domain SUSY-like partner. Examples of several kinds of super-symmetrical time dependent frequency systems are presented.

Abstract: We solve first-kind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three dimensions with either Dirichlet or Neumann conditions. The proposed Galerkin-Bubnov methods take as discretization elements pushed-forward weighted azimuthal projections of standard spherical harmonics onto the unit disk. By exactly depicting edge singular behaviors we show that these spectral or high-order bases yield super-algebraic error convergence in the corresponding energy norms whenever the screen is an analytic deformation of the unit disk. Moreover, we provide a fully discrete analysis of the method, including quadrature rules, based on analytic extensions of the spectral basis to complex neighborhoods. Finally, we include numerical experiments to support our claims as well as appendices with computational details for treating the associated singular integrals.

Abstract: This contribution proposes an approach for the assessment of the failure probability associated with a particular class of series systems. The type of systems considered involves components whose response is linear with respect to a number of Gaussian random variables. Component failure occurs whenever this response exceeds prescribed deterministic thresholds. We propose multidomain Line Sampling as an extension of the classical Line Sampling to work with a large number of components at once. By taking advantage of the linearity of the performance functions involved, multidomain Line Sampling explores the interactions that occur between failure domains associated with individual components in order to produce an estimate of the failure probability. The performance and effectiveness of multidomain Line Sampling is illustrated by means of two test problems and an application example, indicating that this technique is amenable for treating problems comprising both a large number of random variables and a large number of components.