Regional Patterns of Late Medieval and Early Modern European Building Activity Revealed by Felling Dates

Although variations in building activity are a useful indicator of societal well-being and demographic development, historical datasets for larger regions and longer periods are still rare. Here, we present 54,045 annually precise dendrochronological felling dates from historical construction timber from across most of Europe between 1250 and 1699 CE to infer variations in building activity. We use geostatistical techniques to compare spatiotemporal dynamics in past European building activity against independent demographic, economic, social and climatic data. We show that the felling dates capture major geographical patterns of demographic trends, especially in regions with dense data coverage. A particularly strong negative association is found between grain prices and the number of felling dates. In addition, a significant positive association is found between the number of felling dates and mining activity. These strong associations, with well-known macro-economic indicators from pre-industrial Europe, corroborate the use of felling dates as an independent source for exploring large-scale fluctuations of societal well-being and demographic development. Three prominent examples are the building boom in the Hanseatic League region of northeastern Germany during the 13th century, the onset of the Late Medieval Crisis in much of Europec. 1300, and the cessation of building activity in large parts of central Europe during armed conflicts such as the Thirty Years’ War (1618–1648 CE). Despite new insights gained from our European-wide felling date inventory, further studies are needed to investigate changes in construction activity of high versus low status buildings, and of urban versus rural buildings, and to compare those results with a variety of historical documentary sources and natural proxy archives.</jats:p

An Impedance Effect of a Thin Adhesive Layer in Some Boundary Value and Transmission Problems Governed by Elliptic Differential Equations

В данной работе рассматривается задача о двух телах, скрепленных тонким клеевым слоем (третий материал) толщины delta. При delta, стремящемся к нулю, получается краевая задача переноса на фиксированной области. Получены новые результаты по исследованию данной задачи в пространствах Гельдера, а именно, явное представление решения. С помощью теории полугрупп и вещественных интерполяционных пространств получены необходимые и достаточные условия на границе раздела при которых существует единственное решение задачи

Elliptic Problems with Robin Boundary Coefficient-Operator Conditions in General L_p Sobolev Spaces and Applications

В статье доказаны некоторые новые результаты о полных операторно-дифференциальных уравнениях эллиптического типа второго порядка с граничными операторно-коэффициентными условиями Робина в пространстве L^{p}(0,1;X) в случае, когда p in1,+infty), а X - банахово UMD-пространство. Доказано существование, единственность и оптимальная регулярность классического решения. Статья дополняет и завершает предыдущие исследования авторов по данной проблематике

An Impedance Effect of a Thin Adhesive Layer in Some Boundary Value and Transmission Problems Governed by Elliptic Differential Equations

In this paper we consider a problem of two bodies bonded through a thin adhesive layer (a third material) of thickness \delta. Leeting \delta go to zero, one obtain a boundary value transmission problem set on a fixed domain. We then give new results for the study of this problem set on a fixed domain, We then give new results for the study of this problem in the framework of Hoelder spaces: an explicit representation of the solution. Necessary and sufficient conditions at the interface for its optimal regularity are obtained using the semigroups theory and the real interpolation spaces

On the solvability of complete abstract differential equations of elliptic type

In this work we give some new results on complete abstract second order differential equations of elliptic type in a Banach space. The existence and the uniqueness of the strict solution are proved under some natural assumptions generalising previous theorems on the subjec

Boundary value problem for elliptic differential equations in non-commutative cases

We consider a boundary value problem for elliptic differential equations in non-commutative case

NEW results on complete elliptic equations With robin boundary coefficient-operator conditions in non commutative case

In this paper, we prove some new results on operational second order differential equations of elliptic type with general Robin boundary conditions in a non-commutative framework. The study is performed when the second member belongs to a Sobolev space. Existence, uniqueness and optimal regularity of the classical solution are proved using interpolation theory and results on the class of operators with bounded imaginary powers. We also give an example to which our theory applies. This paper improves naturally the ones studied in the commutative case by M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri: in fact, introducing some operational commutator, we generalize the representation formula of the solution given in the commutative case and prove that this representation has the desired regularity

Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces

In this paper we prove some new results concerning a complete abstract second-order differential equation with general Robin boundary conditions. The study is developped in UMD spaces and uses the celebrated Dore-Venni Theorem. We prove existence, uniqueness and maximal regularity of the strict solution. This work completes previous one [3] by authors; see also [11]