SITE INDEX IN EUCALYPTUS STANDS APPLYING ORDINARY KRIGING: AN APPROACH WITH DIFFERENT MODELS AND METHODS OF CLASSIFICATION

The objective of this work was to evaluate the efficiency of models and methods to obtain the site index, associated with ordinary kriging, to classify productive capacity in eucalyptus stands. Thus, the site quality was performed considering the traditional modeling in clonal stands (2,119 hectares) located in Minas Gerais state, Brazil. 170 plots of 400m2 were randomly allocated, representing a sampling intensity of 0.32%. The dominant height of trees (Assmann) was measured at 24, 36, 48, 60, 72, and 84 months. The site index (S) was estimated by the guide curve and algebraic difference methods, using the models of Schumacher, Chapman and Richards, and Bailey and Clutter. 136 plots were used in the fit and 34 plots in the predictive validation. The spatial dependence of site index was evaluated by experimental semivariogram and adjustment of exponential, spherical, and gaussian models. After confirming the spatial dependence, ordinary kriging was performed to spatialize the site index. For the predictive validation, the dominant height values at 72 months were used. The algebraic difference method provided excellent estimates of site index, which showed spatial dependence in all adjustments, from moderate to strong. In most cases, the gaussian model was the most accurate. It is concluded that the algebraic difference method was more efficient and the site index showed strong spatial dependence at all ages, regardless of the model used. Thus, regression models for site index estimation can be used in combination with ordinary kriging techniques.

Torsors for difference algebraic groups

We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also present an application to the Galois theory of differential equations depending on a discrete parameter.

Modeling dominant height growth using permanent plot data for Pinus brutia stands in the Eastern Mediterranean region

Aim of the study: At current, forest management in the Eastern Mediterranean region is largely based on experience rather than on management plans. To support the development of such plans, this study develops and compares site index equations for pure even-aged Pinus brutia stands in Syria using base-age invariant techniques that realistically describe dominant height growth.Materials and methods: Data on top height and stand age were obtained in 2008 and 2016 from 80 permanent plots capturing the whole range of variation in site conditions, stand age and stand density. Both the Algebraic Difference Approach (ADA) and the Generalized Algebraic Difference Approach (GADA) were used to fit eight generalized algebraic difference equations in order to identify the one which describes the data best. For this, 61 permanent plots were used for model calibration and 19 plots for validation.Main results: According to both biological plausibility and model accuracy, the so-called Sloboda equation based on the GADA approach showed the best performance.Research highlights: The study provides a solid classification and comparison of Pinus brutia stands growing in the Eastern Mediterranean region and can thus be used to support sustainable forest management planning.Keywords: site index; Generalized Algebraic Difference Approach (GADA); Sloboda equation.

Dynamic top height models for several major forest tree species in Great Britain

In this paper, we present new dynamic top height models for 10 major species in Great Britain. These models for pure, even-aged stands replace the current, static top height-age curves published in the 1980s, which are no longer reliable in the light of the new data that have been added over the past decades. We followed the generalized algebraic difference approach (GADA) to build the new models and specifically focused on models derived from the Hessfeld IV and Chapman–Richards height-age base equations. We selected a multi-asymptote and polymorphic GADA version of the Chapman–Richards equation for all the species, with the anamorphic functional form as a special case derived from the non-significance of one of the global parameters. The new models are dynamic, accurate and robust, which will permit unbiased yield predictions from current top height-dependent yield simulators in Great Britain.

Finiteness Properties of Affine Difference Algebraic Groups

We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the matrix entries can indeed be defined by finitely many such equations. As an application, we show that the difference ideal of all difference algebraic relations among the solutions of a linear differential equation is finitely generated.

INTEGRATED APPROACH TO THE GEODESIC CONTROL OF THE INSTALLATION OF ASPHALT-CONCRETE COATING ON THE EXAMPLE OF THE CONSTRUCTION OF THE ROAD BRIDGE TRANSITION ACROSS THE KERCH SHEET

During the construction of bridges, special attention is paid to geometric parameters, one of the most important parameters of the rideable bed is the evenness of the bases and coatings. Geodetic works provide an integrated approach to solving the problem of controlling the flatness of the base layers, which includes: geodetic survey of the rideable canvas, verification of working documentation, control of the copying string, geometric control of the evenness of the laid asphalt concrete floor slab for the steel concrete span and bridge deck for a metal span structure. Various options for controlling the height position of a copier string and a laid asphalt concrete pavement (using trigonometric and geometric leveling) were reviewed and tested. A priori assessment of the accuracy of the measurement results for each of the methods for monitoring algebraic difference of elevations (amplitudes) was previously performed. The article proposes a combined approach to geodetic control at all stages of work on checking the evenness of the asphalt concrete pavement.

Influence study of parameters of the railway track in plan and profile on the indicators of the railway track and rolling stock interaction

Modern level of development of automated systems opens up great opportunities for designers, making it possible to find optimal solutions for the construction of the railway track using digital modeling methods and automated programs. Moreover, the expansion of technical capabilities should be based on a responsible approach to choosing configuration of the railway track, its parameters in plan and profile. The article is devoted to the study of the influence of the parameters of the railway track in plan and profile on the interaction indicators of the track and rolling stock. Author presented a retrospective analysis of the norms for choosing the largest difference in the slopes of adjacent profile elements and the smallest length of separating pads and transition steepness elements. Also shown is the dependence of the length of separating pads and elements of transition steepness and the dependence of the algebraic difference of the slopes of adjacent elements of the profile of railway lines on the weight of the train with different linear loads. The results of modeling the freight cars running in sections with different combination of the plan and profile of the railway track in the software package “Universal Mechanism” are presented. During the modeling, the dependence of the frame forces on the algebraic difference of the matching slopes was obtained, and a comparative analysis of other indicators of the interaction of the track and rolling stock (lateral forces, vertical forces, longitudinal forces, stability margin) was carried out. The article conclusions summarize the results of the calculations and give recommendations for calculations and modeling the effect of a combination of vertical curves and curves in plan on the indicators of the dynamic interaction of the track and rolling stock.