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*BASIC* *NOTIONS*

"... Transition metal oxides (TMOs) are an ideal arena for the study of electronic correlations because the s-electrons of the transition metal ions are removed and transferred to oxygen ions, and hence the strongly correlated d-electrons determine their physical properties such as electrical transport, ..."

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Transition metal oxides (TMOs) are an ideal arena for the study of electronic correlations because the s-electrons of the transition metal ions are removed and transferred to oxygen ions, and hence the strongly correlated d-electrons determine their physical properties such as electrical transport, magnetism, optical response, thermal conductivity, and superconductivity. These electron correlations prohibit the double occupancy of metal sites and induce a local entanglement of charge, spin, and orbital degrees of freedom. This gives rise to a variety of phenomena, e.g., Mott insulators, various charge/spin/orbital orderings, metal-insulator transitions, multiferroics, and superconductivity. 1 In recent years, there has been a burst of activity to manipulate these phenomena, as well as create new ones, using oxide heterostructures. 2 Most fundamental to understanding the physical properties of TMOs is the concept of symmetry of the order parameter. As Landau recognized, the essence of phase transitions is the change of the symmetry. For example, ferromagnetic ordering breaks the rotational symmetry in spin space, i.e., the ordered phase has lower symmetry than the Hamiltonian of the system. There are three most important symmetries to be considered here. (i) Spatial inversion (I), defined as r

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*Basic* *Notions*

, 2010

"... Facts about bounded distributive quasi lattices Facts about Priestley’s duality PP-Spaces pp-spaces → bdq-lattices bdq-lattices → pp-spaces pp-spaces and bdq-lattices in partnership ..."

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Facts about bounded distributive quasi lattices Facts about Priestley’s duality PP-Spaces pp-spaces → bdq-lattices bdq-lattices → pp-spaces pp-spaces and bdq-lattices in partnership

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*BASIC* *NOTIONS*

, 2006

"... ❑ proper T-invariants-> Pascoletti 1986 ❑ minimal T-invariants-> Lautenbach 1973 ..."

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❑ proper T-invariants-> Pascoletti 1986 ❑ minimal T-invariants-> Lautenbach 1973

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*Basic* *Notions* of Information Structure

"... This article takes stock of the basic notions of Information Structure (IS). It first provides a general characterization of IS — following Chafe (1976) — within a communicative model of Common Ground (CG), which distinguishes between CG content and CG management. IS is concerned with those feature ..."

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This article takes stock of the

*basic**notions*of Information Structure (IS). It first provides a general characterization of IS — following Chafe (1976) — within a communicative model of Common Ground (CG), which distinguishes between CG content and CG management. IS is concerned with those###
I. *BASIC* *NOTIONS*

, 2005

"... Abstract — In this paper a model for the concept of bornology from the point of view of an observer is presented. By the use of relative bornological spaces, the notion of attractor for relative semi-dynamical systems is considered. Copyright c ○ 2007 Yang’s ..."

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Abstract — In this paper a model for the concept of bornology from the point of view of an observer is presented. By the use of relative bornological spaces, the

*notion*of attractor for relative semi-dynamical systems is considered. Copyright c ○ 2007 Yang’s###
Graphs, *Basic* *Notions*

"... Graphs are mathematical structures that have many applications to computer science, electrical engineering and more widely to engineering as a whole, but also to sciences such as biology, linguistics, and sociology, among others. For example, relations among objects can usually be encoded by graphs. ..."

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. Whenever a system has a

*notion*of state and state transition function, graph methods may be applicable. Certain problems are naturally modeled by undirected graphs whereas others require directed graphs. Let us give a concrete example. Suppose a city decides to create a public-transportation system###
1. *Basic* *notions*.

, 2010

"... All the theorems are to be intended with their proof, except if explicitly written wp (that is without proof). ..."

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All the theorems are to be intended with their proof, except if explicitly written wp (that is without proof).