Conditional Density Matrix in the Context of Noncontextuality

Conditional density matrix represents a quantum state of subsystem in different schemes of quantum communication. Here we discuss some properties of conditional density matrix and its place in general scheme of quantum mechanics.Comment: 10 pages, LaTe

On some categorical properties of the functor UR

AbstractWe deal with the unit ball UR(X) of non-negative Radon measures on a Tychonoff space X. UR is a functor in the category Tych. It is proved that UR has all properties of a normal functor, with the exception of point preservation

On some categorical properties of uniform spaces of probability measures

AbstractWe deal with the functor Pβu:Unif → Unif of uniform spaces of probability measures, defined by Sadovnichy (1994). We show that there is a unique natural transformation T: S ∘ Pgbu → P ∘ S, where S: Unif → cUnif is the functor of Samuel compactification. In our first main result (Theorem 4.3) it is established that for a uniform space (X,u) the component Tu of this natural transformation T is a homeomorphism iff u is a precompact uniformity. The second main result (Theorem 4.6) shows that there is no embedding U: Tych → Unif such that Pβu ∘ U = U ∘ Pβ

On sheaves of Abelian groups and universality

[EN] Universal elements are one of the most essential parts in research fields, investigating if there exist (or not) universal elements in different classes of objects. For example, classes of spaces and frames have been studied under the prism of this universality property. In this paper, studying classes of sheaves of Abelian groups, we construct proper universal elements for these classes, giving a positive answer to the existence of such elements in these classes. Moscow Center of Fundamental and Applied MathematicsIliadis, S.; Sadovnichy, YV. (2021). On sheaves of Abelian groups and universality. Applied General Topology. 22(1):149-167. https://doi.org/10.4995/agt.2021.14422OJS149167221G. E. Bredon, Sheaf Theory, McGraw-Hill, New York, 1967T. Dube, S. Iliadis, J. van Mill and I. Naidoo, Universal frames, Topology and its Applications 160, no. 18 (2013), 2454-2464. https://doi.org/10.1016/j.topol.2013.07.039D. N. Georgiou, S. D. Iliadis and A. C. Megaritis, On base dimension-like functions of the type Ind, Topology and its Applications 160, no. 18 (2013), 2482-2494. https://doi.org/10.1016/j.topol.2013.07.042D. N. Georgiou, S. D. Iliadis, A. C. Megaritis and F. Sereti, Universality property and dimension for frames, Order 37, no. 3 (2019), 427-444. https://doi.org/10.1007/s11083-019-09513-3D. N. Georgiou, S. D. Iliadis, A. C. Megaritis and F. Sereti, Small inductive dimension and universality on frames, Algebra Universalis 80, no. 2 (2019), 21-51. https://doi.org/10.1007/s00012-019-0593-5P. S. Gevorgyan, S. D. Iliadis and Yu V. Sadovnichy, Universality on frames, Topology and its Applications 220 (2017), 173-188. https://doi.org/10.1016/j.topol.2017.02.010S. D. Iliadis, A construction of containing spaces, Topology and its Applications 107 (2000), 97-116. https://doi.org/10.1016/S0166-8641(00)90095-6S. D. Iliadis, Mappings and universality, Topology and its Applications 137, no. 1-3 (2004), 175-186. https://doi.org/10.1016/S0166-8641(03)00207-4S. D. Iliadis, Universal Spaces and Mappings, North-Holland Mathematics Studies 198, Elsevier, 2005.S. D. Iliadis, On isometrically universal spaces, mappings, and actions of groups, Topology and its Applications 155, no. 14 (2008), 1502-1515. https://doi.org/10.1016/j.topol.2008.03.006S. D. Iliadis, Universal elements in some classes of mappings and classes of G-spaces, Topology and its Applications 156, no. 1 (2008), 76-82. https://doi.org/10.1016/j.topol.2008.04.010S. D. Iliadis, A separable complete metric space of dimension n containing isometrically all compact metric spaces of dimension n, Topology and its Applications 160, no. 11 (2013), 1271-1283. https://doi.org/10.1016/j.topol.2013.04.020S. D. Iliadis and I. Naidoo, On isometric embeddings of compact metric spaces of a countable dimension, Topology and its Applications 160, no. 11 (2013), 1284-1291. https://doi.org/10.1016/j.topol.2013.04.021S. D. Iliadis, On embeddings of topological groups, Fundamental and Applied Mathematics 20, no. 2 (2015), 105-112 (Russian). Journal of Mathematical Sciences 223, no. 6 (2017), 720-724 (English). https://doi.org/10.1007/s10958-017-3381-9S. D. Iliadis, On isometric embeddings of separable metric spaces, Topology and its Applications 179 (2015), 91-98. https://doi.org/10.1016/j.topol.2014.08.019S. D. Iliadis, Dimension and universality on frames, Topology and its Applications 201 (2016), 92-109. https://doi.org/10.1016/j.topol.2015.12.029S. D. Iliadis, On spaces continuously containing topological groups, Topology and its Applications 272 (2020),107072. https://doi.org/10.1016/j.topol.2020.107072S. D. Iliadis, On actions of spaces continuously containing topological groups, Topology and its Applications 275 (2020), 107035. https://doi.org/10.1016/j.topol.2019.10703

Selling Money on Ebay: A Field Study of Surplus Division

We study the division of trade surplus in a competitive market environment by conducting a natural field experiment on German eBay. Acting as a seller, we offer Amazon gift cards with face values of up to 500 Euro. Randomly arriving buyers, the subjects of our experiment, make price offers according to eBay rules. Using a novel decomposition method, we infer offered shares of trade surplus and find that the average share proposed to the seller amounts to 29%. Additionally, we document: (i) insignificant effects of stake size; (ii) poor use of strategically relevant public information; and (iii) behavioural differences between East and West German subjects