Muslim Coins as a Commodity and Means of Payment in International and Internal Trade In Volga-Ural Region In 8th- Beginning of 11th cc

The article examines the spread of Muslim Kufic coins in Eastern, Western and Northern Europe, on the territory of Volga Bulgaria, Ancient Rus, the neighbours of Bulgars – ancestors of the Mari, Udmurt, Mordva and other Finno-Ugric ethnicities during the early Middle Ages in the 8th – beginning of the 11th centuries. The research of these coins shows the list of countries and Muslim dynasties the above-mentioned countries had trade relations with and their chronological framework. Coins of Umayyads, Abbasids, Samanids, Buwayhids, Ziyarids, Qarakhanids and other Muslim dynasties were discovered. Ways of Kufic dirhems expansion and their chronological framework are shown. The main role of Khazar Khanate is marked for the time span of 8th – 9th centuries whereas since X century the principal part was played by Volga Bulgaria. American numismatist T. Noonan designated them as Khazar and Bulgar phases of trade of Kufic coins. Bulgar coins, minted in 902–990-s, participated actively in this process. Together they acted as a commodity and medium of exchange, which reflected the scale of trade operations of the early Middle Ages. The study of Muslim Kufic dirhems allowed the author to clear up the role of Khazar Khanate and Volga Bulgaria in the functioning of Great Silk and Volga routes in the 8th – beginning of the 11th centuries.

Bringing the German Pavilion Back Home

<p>This research investigates a correspondence between the architectural representational tool of drawing, and the translations of these into something recognised as ‘built’. It is fundamentally concerned around representation in architecture driven by the principles that our entire engagement with architecture is via representation. Architects do not produce buildings but produce images of buildings, and the role of two-dimensional representation plays a principal part in architecture. Architecture is always representational, and the more we engage with representation the more we might push the envelope with what we understand architecture to be. This thesis aims to establish within the contemporary discipline, what we understand about the responsibility of linear perspective as a representational tool. By understanding what lies behind the canon of perspective in architecture, this thesis questions whether the representation of conventional architecture could benefit from a new way of drawing linear perspective? The discovery of perspective during the Renaissance has influenced not only our way of representing architecture but also how we view, and therefore design it. It has become integrated with our understanding of architecture at an unconscious level. Architects no longer need control of projective geometry, and due to this cannot be critical of the system of representation or control its limits. This leads to mediate a shift in perspective, with the intention to generate a representation of new form. The motivation for this thesis was that from linear perspective, as it has done so for centuries, we can produce evocative and meaningful vocabularies that attempt to enrich architecture.</p>

Bringing the German Pavilion Back Home

<p>This research investigates a correspondence between the architectural representational tool of drawing, and the translations of these into something recognised as ‘built’. It is fundamentally concerned around representation in architecture driven by the principles that our entire engagement with architecture is via representation. Architects do not produce buildings but produce images of buildings, and the role of two-dimensional representation plays a principal part in architecture. Architecture is always representational, and the more we engage with representation the more we might push the envelope with what we understand architecture to be. This thesis aims to establish within the contemporary discipline, what we understand about the responsibility of linear perspective as a representational tool. By understanding what lies behind the canon of perspective in architecture, this thesis questions whether the representation of conventional architecture could benefit from a new way of drawing linear perspective? The discovery of perspective during the Renaissance has influenced not only our way of representing architecture but also how we view, and therefore design it. It has become integrated with our understanding of architecture at an unconscious level. Architects no longer need control of projective geometry, and due to this cannot be critical of the system of representation or control its limits. This leads to mediate a shift in perspective, with the intention to generate a representation of new form. The motivation for this thesis was that from linear perspective, as it has done so for centuries, we can produce evocative and meaningful vocabularies that attempt to enrich architecture.</p>

Multiple Critical Points for Symmetric Functionals without Upper Growth Condition on the Principal Part

This paper is concerned with variational methods applied to functionals of the calculus of variations in a multi-dimensional case. We prove the existence of multiple critical points for a symmetric functional whose principal part is not subjected to any upper growth condition. For this purpose, nonsmooth variational methods are applied.

Optimal estimates from below for Green functions of higher order elliptic operators with variable leading coefficients

Estimates from above and below by the same positive prototype function for suitably modified Green functions in bounded smooth domains under Dirichlet boundary conditions for elliptic operators L of higher order $$2m\ge 4$$ 2 m ≥ 4 have been shown so far only when the principal part of L is the polyharmonic operator $$(-\Delta )^m$$ ( - Δ ) m . In the present note, it is shown that such kind of result still holds when the Laplacian is replaced by any second order uniformly elliptic operator in divergence form with smooth variable coefficients. For general higher order elliptic operators, whose principal part cannot be written as a power of second order operators, it was recently proved that such kind of result becomes false in general.

The Model of Degressive Taxation of Trucks: Case of the Czech Republic

The article examines issues related to the design of road tax as an instrument supporting the operation of trucks that are more environment-friendly to the transport infrastructure. The Introduction presents analyses of road taxation in the European Union Member States, whose aim was to identify features supporting trucks that are eco-friendly with regard to the infrastructure. The principal part of the contribution is the formulation of a regression model of road tax rates, which is subjected to statistical, econometric and economic verification in order to confirm or disprove degressivity of road tax rates for trucks. The economic verification is based on typical examples of vehicles defined in Annex 2 to the text. The Conclusion presents the results achieved, which verify the degressive nature of road tax in the Czech Republic. The tax rates are degressive in relation to the number of truck axles; therefore, a proposal for the elimination of degressivity in the system of tax rates for trucks was designed based on the principle of fair taxation, which is also discussed in the contribution.

Patterns of interpredictability and principal parts in Latin verb paradigms: an entropy-based approach

This paper provides a fully word-based, abstractive analysis of predictability in Latin verb paradigms. After reviewing previous traditional and theoretically grounded accounts of Latin verb inflection, a procedure is outlined where the uncertainty in guessing the content of paradigm cells given knowledge of one or more inflected wordforms is measured by means of the information-theoretic notions of unary and n-ary implicative entropy, respectively, in a quantitative approach that uses the type frequency of alternation patterns between wordforms as an estimate of their probability of application. Entropy computations are performed by using the Qumin toolkit on data taken from the inflected lexicon LatInfLexi. Unary entropy values are used to draw a mapping of the verbal paradigm in zones of full interpredictability, composed of cells that can be inferred from one another with no uncertainty. N-ary entropy values are used to extract categorical and near principal part sets, that allow to fill the rest of the paradigm with little or no uncertainty. Lastly, the issue of the impact of information on the derivational relatedness of lexemes on uncertainty in inflectional predictions is tackled, showing that adding a classification of verbs in derivational families allows for a relevant reduction of entropy, not only for derived verbs, but also for simple ones.

Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth

<p style='text-indent:20px;'>It is established existence of solutions for subcritical and critical nonlinearities considering a fourth-order elliptic problem defined in the whole space <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>. The work is devoted to study a class of potentials and nonlinearities which can be periodic or asymptotically periodic. Here we consider a general fourth-order elliptic problem where the principal part is given by <inline-formula><tex-math id="M2">\begin{document}$ \alpha \Delta^2 u + \beta \Delta u + V(x)u $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M3">\begin{document}$ \alpha &gt; 0, \beta \in \mathbb{R} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ V: \mathbb{R}^N \rightarrow \mathbb{R} $\end{document}</tex-math></inline-formula> is a continuous potential. Hence our main contribution is to consider general fourth-order elliptic problems taking into account the cases where <inline-formula><tex-math id="M5">\begin{document}$ \beta $\end{document}</tex-math></inline-formula> is negative, zero or positive. In order to do that we employ some fine estimates proving the compactness for the associated energy functional.</p>

A converse of Sturm's separation theorem

We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a turning point in the principal part of the equation. Related results are discussed.

Refining the Galerkin method error estimation for parabolic type problem with a boundary condition

The article considers a parabolic-type boundary value problem with a divergent principal part, when the boundary condition contains the time derivative of the required function: { ut−d/dxiai(x,t,u,∇u)+a(x,t,u,∇u)=0,a0ut+ai(x,t,u,∇u)cos(v,xi)=g(x,t,u,),(x,t)∈St, u(x,0)= u0(x), x∈Ω Such nonclassical problems with boundary conditions containing the time derivative of the desired function arise in the study of a number of applied problems, for example, when the surface of a body, whose temperature is the same at all its points, is washed off by a well-mixed liquid, or when a homogeneous isotropic body is placed in the inductor of an induction furnace and an electro-magnetic wave falls on its surface. Such problems have been little studied, therefore, the study of problems of parabolic type, when the boundary condition contains the time derivative of the desired function, is relevant. In this paper, the definition of a generalized solution of the considered problem in the space H˜1,1(QT) is given. This problem is solved by the approximate Bubnov-Galerkin method. The coordinate system is chosen from the space H1(Ω). To determine the coefficients of the approximate solution, the parabolic problem is reduced to a system of ordinary differential equations. The aim of the study is to obtain conditions under which the estimate of the error of the approximate solution in the norm H1(Ω) has order O(hk−1) The paper first explores the auxiliary elliptic problem. When the condition of the ellipticity of the problem is satisfied, inequalities are proposed for the difference of the generalized solution of the considered parabolic problem with a divergent principal part, when the boundary condition contains the time derivative of the desired function and the solution of the auxiliary elliptic problem. Using these estimates, as well as under additional conditions for the coefficients and the function included in the problem under consideration, estimates of the error of the approximate solution of the Bubnov-Galerkin method in the norm H1(Ω) of order O(hk−1) for the considered nonclassical parabolic problem with divergent principal part, when the boundary condition contains the time derivative of the desired function.