Wood analyses helped to determine the location and approximate construction period of the Roman bridge over the Drava River in ancient Poetovio (Ptuj, Slovenia)

We present the results of a dendrochronological study and radiocarbon dating of the wooden piles of the bridge over the Drava River in Ptuj. The piles, together with stone elements (a fragment of an imperial building inscription and parts of the architectural decoration) were retrieved from the riverbed in 1913 and are now in the Regional Museum Ptuj - Ormož. Using dendrochronology, radiocarbon dating of carefully selected annual rings in the wood and calibration with the wiggle-matching method, the date of the last (outermost) annual ring on the pile was determined to be 161 ± 27 cal AD (1σ) or 160 ± 32 cal AD (2σ). Since the pile contained no sapwood, the dating approximately agrees with the date of the building inscription on the stone slab, which attributes the commission for the reconstruction or construction of the bridge to Emperor Hadrian in the last years of his reign (117-138 AD). The dating of the wood has thus confirmed that the remains examined do indeed belong to a Roman bridge, probably built or renovated during the reconstruction of the road network in the area of the colony of Poetovio under Hadrian or one of his successors.

Construindo o laço do planeta marte em relação às estrelas distantes no sistema copernicano

O presente trabalho visa apresentar uma proposta de construção aproximada do movimento de Marte, que gera para um observador na Terra um formato de laço em relação às estrelas distantes na perspectiva do sistema copernicano. Para tal, utilizaremos o conhecido software GeoGebra. Crescendo consideravelmente, o software está sempre sendo atualizado e chega a reunir fóruns e grupos, contando em sua plataforma com uma gigantesca variedade de atividades para a matemática e a ciência. Dentre as muitas possibilidades, o modelo que escolhemos nos gerará um cenário para se pensar sobre a história das ideias envolvidas. Acreditamos que por intermédio de trabalhos deste tipo é possível promover uma discussão mais ampla e interdisciplinar sobre os conceitos que utilizamos, indo além dos brevíssimos recortes apresentados em livros didáticos. The present work aims to present a proposal for an approximate construction of the Mars movement, which generates for an observer on Earth a loop shape in relation to distant stars in the perspective of the Copernican system. For this, we will use the well-known GeoGebra software. Growing considerably, the software is always being updated and comes to gather forums and groups, counting on its platform a huge variety of activities for mathematics and science. Among the many possibilities, the model we choose will provide us with a scenario to think about the history of the ideas involved. We believe that through works of this type it is possible to promote a broader and interdisciplinary discussion on the concepts we use, going beyond the very brief cutouts presented in textbooks.

ON A TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH MANY TRANSFORMED ARGUMENTS

A.M. Samoilenko’s numerical-analytic method is a well-known and effective research method of solvability and approximate construction of the solutions of various boundary value problems for systems of differential equations. The investigation of boundary value problems for new classes of systems of functional- differential equations by this method is still an actual problem. A boundary value problem for a system of differential equations with finite quantity of transformed arguments in the case of linear two-point boundary conditions is considered at this paper. In order to study the questions of the existence and approximate construction of a solution of this problem, we used a modification of A.M. Samoilenko’s numerical-analytic method without determining equation, i.e. the method has an analytical component only. Sufficient conditions for the existence of a unique solution of the considered boundary value problem and an error estimation of the constructed successive approximations are obtained. The use of the developed modification of the method is illustrated by concrete examples.

Approximate construction of new conservative physical magnitudes through the fractional derivative of polynomialtype functions: a particular case in semiconductors of type AlxGa1-xAs

The fractional calculus has a very large diversification as it relates to applications from physical interpretations to experimental facts to modeling of new problems in the natural sciences. Within the framework of a recently published article, we obtained the fractional derivative of the variable concentration x (z), the effective mass of the electron dependent on the position m (z) and the potential energy V (z), produced by the confinement of the electron in a semiconductor of type AlxGa1-xAs, with which we can intuit a possible geometric and physical interpretation. As a consequence, it is proposed the existence of three physical and geometric conservative quantities approximate character, associated with each of these parameters of the semiconductor, which add to the many physical magnitudes that already exist in the literature within the context of fractional variation rates. Likewise, we find that the fractional derivatives of these magnitudes, apart from having a common critical point, manifest self-similar behavior, which could characterize them as a type of fractal associated with the type of semiconductor structures under study.

On targeting an integral funnel of control system at a target set in the phase space

A control system in finite-dimensional Euclidean space is considered. On a given time interval, we investigate the problem of constructing an integral funnel for which a section corresponding to the last time moment of interval is equal to a target set in a phase space. Since the exact solution of such a funnel is possible only in rare cases, the question of the approximate construction of an integral funnel is being studied.

Nalanda

Nalanda, in eastern India's Bihar state, was once the most important Buddhist monastery in the world. The six excavated temples there are oriented approximately to the cardinal directions, but their east–west axes are tilted more than 4° south of east. Other key Buddhist temples within the same cultural milieu (Bodhgaya, Vikramasila, Somapura, and Samye) are similarly oriented a few degrees south of east. As M. B. Rajani and Viraj Kumar argue in Nalanda: A Tale in the Twist, this demands an explanation, because a method to orient structures to within 0.5° of the cardinal directions was known in the region for several centuries prior to the construction of these temples. Rajani and Kumar identify a temporal pattern in the orientation of Nalanda's temples; hypothesize that each temple was aligned with the rise of a specific star (Spica or Beta Librae), with the temporal pattern being a consequence of axial precession; propose a simple, unified explanation for the few exceptions to the pattern; and use this hypothesis to propose an approximate construction date for each temple based on its orientation.

DEVELOPMENT OF AN APPROXIMATE CONSTRUCTION DURATION PREDICTION MODEL DURING THE PROJECT PLANNING PHASE FOR GENERAL OFFICE BUILDINGS

Accurate prediction of the construction duration is imperative to the reliable cash flow analysis during the project planning phase when feasibility analysis is carried out. However, lack of information and frequent changes that occur as a result of a negotiation process between the owner and the designer in defining the project scope make it difficult to compute real-time construction duration. Domestic and foreign models for calculating the construction durations cannot be readily applied to computation of construction duration for general office buildings in Korea specifically during the project planning phase as there is a limit in its applicability due to numerous restrictions. Moreover, there are no preceding studies suggesting different computational approaches to predict the entire construction duration for office buildings with the approximate construction duration concept during planning phase. Therefore, based on the collected performance data, this study proposes a multiple linear regression model that facilitates reliable prediction of approximate construction duration for office buildings in the project planning phase. The model will allow the owner and other stakeholders to predict the real-time construction duration using the basic information on office buildings and to assess the construction durations incorporating frequent changes during the project planning phase.

Approximate DFT-based methods for generating diabatic states and calculating electronic couplings: models of two and more states

Four types of density functional theory (DFT)-based approaches are assessed in this work for the approximate construction of diabatic states and evaluation of the electronic couplings between these states.