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Alexander Levin – One of the best experts on this subject based on the ideXlab platform.

  • bivariate kolchin type dimension polynomials of non reflexive prime Difference differential ideals the case of one translation
    Journal of Symbolic Computation, 2021
    Co-Authors: Alexander Levin

    Abstract:

    Abstract We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate Kolchin-type dimension polynomial associated with a non-reflexive Difference-differential ideal in the algebra of Difference-differential polynomials with several basic derivations and one translation. In particular, we obtain a new proof and a method of computation of the dimension polynomial of a non-reflexive prime Difference ideal in the algebra of Difference polynomials over an ordinary Difference field. As a consequence, it is shown that the reflexive closure of a prime Difference polynomial ideal is the inverse image of this ideal under a power of the basic translation. We also discuss applications of our results to the analysis of systems of Algebraic Difference-differential equations.

  • Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations
    Mathematics in Computer Science, 2020
    Co-Authors: Alexander Evgrafov, Alexander Levin

    Abstract:

    In this paper we present a method of characteristic sets for inversive Difference polynomials and apply it to the analysis of systems of quasi-linear Algebraic Difference equations. We describe characteristic sets and compute Difference dimension polynomials associated with some such systems. Then we apply our results to the comparative analysis of Difference schemes for some PDEs from the point of view of their Einstein’s strength. In particular, we determine the Einstein’s strength of standard finite-Difference schemes for the Murray, Burgers and some other reaction–diffusion equations.

  • Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations
    arXiv: Commutative Algebra, 2019
    Co-Authors: Alexander Evgrafov, Alexander Levin

    Abstract:

    In this paper we present a method of characteristic sets for inversive Difference polynomials and apply it to the analysis of systems of quasi-linear Algebraic Difference equations. We describe characteristic sets and compute Difference dimension polynomials associated with some such systems. Then we apply our results to the comparative analysis of Difference schemes for some PDEs from the point of view of their Einstein’s strength. In particular, we determine the Einstein’s strength of standard finite-Difference schemes for the Murray, Burgers and some other reaction-diffusion equations.

Klaus Von Gadow – One of the best experts on this subject based on the ideXlab platform.

  • Dynamic base-age invariant site index models for Tectona grandis in peninsular India
    Southern Forests: a Journal of Forest Science, 2014
    Co-Authors: Vindhya Prasad Tewari, Juan Gabriel Álvarez-gonzález, Klaus Von Gadow

    Abstract:

    Data from 27 remeasured sample plots were used to evaluate dynamic base-age invariant site index models for teak (Tectona grandis) forests in Karnataka, India. The data were obtained in observational field studies covering a wide range of sites in Karnataka and provided up to three interval measurements per plot. All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The model evaluation criteria were bias, root mean square error and the adjusted coefficient of determination. The best results were obtained with the generalised Algebraic Difference equations derived from the Korf base model. The selected model accounted for 99.8% of the total variance in height–age relationships in dominant trees. The dynamic base-age invariant site index model proved to be effective and accurate in presenting polymorphic site index curves with multiple asymptotes. The new dynamic base-age invariant site index models based on generalised Algebraic Difference approach (GADA) methodology can be recommended for dominant height prediction and forest site quality evaluations in the teak forests in Karnataka, India.

  • Estimating growth in beech forests: a study based on long term experiments in Switzerland
    Annals of Forest Science, 2010
    Co-Authors: Juan Gabriel Álvarez-gonzález, Andreas Zingg, Klaus Von Gadow

    Abstract:

    • This contribution presents a dynamic stand growth model for Beech (Fagus sylvatica L.) forests, based on a dataset provided by the Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf. The dataset includes 143 research plots, covering a wide range of growing sites and providing up to 16 interval measurements per research plot. • The objective of this research is to complement the range of existing beech growth models by bridging the gap between the historical yield tables and the single tree growth models. The specific aim is to develop transition functions which will project three state variables (dominant height, basal area and number of trees per hectare) at any particular time, in response to any arbitrary silvicultural treatment. • Two of the transition functions were derived using the generalized Algebraic Difference approach (GADA), the third one was derived with the Algebraic Difference approach (ADA). All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The influence of thinnings on basal area growth was included by fitting different transition functions for thinned and unthinned stands. • The overall model provides satisfactory predictions for time intervals up to 20 years. The new model is robust and its relatively simple structure makes it suitable for economic analysis and decision support.

  • Comparative modeling of stand development in Scots pine dominated forests in Estonia
    Forest Ecology and Management, 2007
    Co-Authors: Ahto Kangur, Andres Kiviste, Allan Sims, Kalev Jõgiste, Henn Korjus, Klaus Von Gadow

    Abstract:

    Abstract In general, forests in Estonia are characterized by great variability, not only in protected areas but in commercial forests as well. The data needed for the derivation and calibration of growth models can be obtained by continuous observation of permanent growth plots (also known as longitudinal studies) or by establishing chronosequences with temporary plots distributed over a wide range of growing sites, densities and ages (also known as cross-sectional studies). A compromise may be achieved by a system of “interval plots” (also known as a short-time series: series which covers a short time). Since the measurement interval is a period of undisturbed growth, it is possible to measure change rates as in a longitudinal study and at the same time cover a wide range of initial conditions as in a cross-sectional study. Numerous models of stand growth have been derived from re-measured sample plots. This study, which uses the data of 142 five-year intervals from 134 unmanaged Scots pine stands, compares six different model combinations involving Algebraic Difference equations and fixed time-step increment equations. New stand-level diameter and basal area increment equations and a tree survival model which showed close correspondence with the existing stand-level model for Estonia were developed. The main advantage of the use of Algebraic Difference equations over the fixed-step increment equations is the ability to use flexible time steps. However, the projection intervals should not deviate too much from the time steps of the measurement data. An important constraint when using the Algebraic Difference equations is to avoid long-term predictions in one projection sequence.

Miren Del Río – One of the best experts on this subject based on the ideXlab platform.

  • dominant height growth equations including site attributes in the generalized Algebraic Difference approach
    Canadian Journal of Forest Research, 2008
    Co-Authors: Miren Del Río, Margarida Tomé, Felipe Bravo, Gregorio Montero, Andres Bravooviedo

    Abstract:

    We present a new dynamic dominant height growth model based on Cieszewski’s generalized Algebraic Difference approach (GADA) advanced dynamic site equation strengthened by the use of explicit climate and soil variables (i.e., H = f(H0,T0, T, site conditions)). The results suggest that the inclusion of climatic variables would improve the applicability of the inter-regional model in regions in which climate and soil type lead to intra-regional variability. The new model reduces the bias present in a previous dynamic model that did not include climatic at- tributes and improves the model efficiency across the different age classes. Climate has a multiplicative effect on dominant tree growth in the early development stages (<20 years) and an additive effect in older stands. Resume ´ : Nous presentons ici un nouveau modele dynamique de croissance en hauteur dominante fondesur l'equation de la methode de la Difference algebrique generalisee (GADA) de l’indice de qualitede station de Cieszewski renforcee par l’utilisation des variables explicites du climat et du sol, c.-a `-d. H = f(H0, T0, T ,etat du site). Les resultats indiquent que l’inclusion des variables climatiques permettrait d’ameliorer l’applicabilitedu modele interregional dans les regions oule climat et le type de sol sont al’origine de la variabiliteintraregionale. Le nouveau modele permet de reduire le biais present dans un modele dynamique precedent qui n’incluait pas les caracteristiques climatiques et ameliore l’efficacitede ce modele pour l’ensemble des classes d’age. Le climat exerce un effet multiplicateur sur la croissance des arbres domi- nants durant les premiers stades de developpement (<20 ans) et un effet additif dans les vieux peuplements. (Traduit par la Redaction)

  • Dominant height growth equations including site attributes in the generalized Algebraic Difference approach
    Canadian Journal of Forest Research, 2008
    Co-Authors: Andrés Bravo-oviedo, Margarida Tomé, Felipe Bravo, Gregorio Montero, Miren Del Río

    Abstract:

    We present a new dynamic dominant height growth model based on Cieszewski’s generalized Algebraic Difference approach (GADA) advanced dynamic site equation strengthened by the use of explicit climate and soil variables (i.e., H = f(H0,T0, T, site conditions)). The results suggest that the inclusion of climatic variables would improve the applicability of the inter-regional model in regions in which climate and soil type lead to intra-regional variability. The new model reduces the bias present in a previous dynamic model that did not include climatic at- tributes and improves the model efficiency across the different age classes. Climate has a multiplicative effect on dominant tree growth in the early development stages (

  • Long-term trends in dominant-height growth of black pine using dynamic models
    Forest Ecology and Management, 2008
    Co-Authors: Dario Martin-benito, Miren Del Río, Guillermo Gea-izquierdo, Isabel Cañellas

    Abstract:

    Abstract Black pine (Pinus nigra Arn.) is a pan-Mediterranean species of high ecological importance and one of the most important timber species in the area. We compare several site dependent height–age models for the species in three regions along its natural distribution area in Spain. The best model was a generalized Algebraic Difference approach (GADA) polymorphic model with variable asymptotes (Cieszewski, C.J., Bailey, R.L., 2000. Generalized Algebraic Difference approach: theory based derivation of dynamic site equations with polymorphism and variable asymptotes. For. Sci. 46, 116–126). There was no significant increase in error when a reduced model common to the three regions was tested instead of a full model with region-specific parameters. To study possible biases of the proposed model along the trees’ lifespan we carried out a LOWESS analysis of residuals in time. We detected deviations in the model residuals, and a patent growth reduction in the 1960s and 1970s, which might be related to climate and/or changing stand characteristics. Departures from estimated mean past growth should be monitored in the future to adapt models to a changing environment.