On a class of linear functional equations without range condition

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The effect of a localized geothermal heat source on deep water formation.

In a simplified two-dimensional model of a buoyancy-driven overturning circulation, we numerically study the response of the flow to a small localized heat source at the bottom. The flow is driven by differential thermal forcing applied along the top surface boundary. We evaluate the steady state solutions versus the temperature difference between the two ends of the water surface in terms of different characteristic parameters that properly describe the transition from a weak upper-layer convection state to a robust full depth deep convection. We conclude that a small additional bottom heat flux underneath the “cold” end of the basin is able to initiate full-depth convection even when the surface heat forcing alone is not sufficient to maintain this state

Is the Definition of Roma an Important Matter? The Parallel Application of Self and External Classification of Ethnicity in a Population-Based Health Interview Survey

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An experimental study of the Atlantic variability on interdecadal timescales

A series of laboratory experiments has been carried out to model the basic dynamics of the multidecadal variability observed in North Atlantic sea surface temperature (SST) records. According to the minimal numerical sector model introduced by te Raa and Dijkstra (2002), the three key components to excite such a low-frequency variability are rotation, meridional temperature gradient and additive thermal noise in the surface heat forcing. If these components are present, periodic perturbations of the overturning background flow are excited, leading to thermal Rossby mode like propagation of anomalous patches in the SST field. Our tabletop scale setup was built to capture this phenomenon, and to test whether the aforementioned three components are indeed sufficient to generate a low-frequency variability in the system. The results are compared to those of the numerical models, as well as to oceanic SST reanalysis records. To the best of our knowledge, the experiment described here is the very first to investigate the dynamics of the North Atlantic multidecadal variability in a laboratory-scale setup

On a class of linear functional equations without range condition

The main purpose of this work is to provide the general solutions of a class of linear functional equations. Let n≥2 be an arbitrarily fixed integer, let further X and Y be linear spaces over the field K and let αi,βi∈K, i=1,…,n be arbitrarily fixed constants. We will describe all those functions f,fi,j:X×Y→K, i,j=1,…,n that fulfill functional equation f(∑i=1nαixi,∑i=1nβiyi)=∑i,j=1nfi,j(xi,yj)(xi∈X,yi∈Y,i=1,…,n). Additionally, necessary and sufficient conditions will also be given that guarantee the solutions to be non-trivial

On functional equations characterizing derivations: methods and examples

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and automorphisms are additive functions satisfying some further functional equations as well. It is an important question that how these morphisms can be characterized among additive mappings in general. The paper contains some multivariate characterizations of higher order derivations. The univariate characterizations are given as consequences by the diagonalization of the multivariate formulas. This method allows us to refine the process of computing the solutions of univariate functional equations of the form ∑k=1nxpkfk(xqk)=0, where pk and qk (k=1,…,n) are given nonnegative integers and the unknown functions f1,…,fn:R→R are supposed to be additive on the ring R. It is illustrated by some explicit examples too. As another application of the multivariate setting we use spectral analysis and spectral synthesis in the space of the additive solutions to prove that it is spanned by differential operators. The results are uniformly based on the investigation of the multivariate version of the functional equations