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All 2-Solid Varieties of Semigroups
Semigroup Forum, 2000For a given type \(\tau\), a mapping from a set of operation symbols into the set of all terms of type \(\tau\) is called a hypersubstitution. The set \(\text{Hyp}(\tau)\) of all hypersubstitutions is a monoid with respect to composition and the identity map.
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Hyperidentities and solid varieties
Algebra universalis, 2006Let V be a variety of type τ. A type τ hyperidentity of V is an identity of V which also holds in an additional stronger sense: for every substitution of terms of the variety (of appropriate arity) for the operation symbols in the identity, the resulting equation holds as an identity of the variety.
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Toward a Paradigm Shift in Electrocatalysis Using Complex Solid Solution Nanoparticles
ACS Energy Letters, 2019Complex solid solution (CSS) nanoparticles were recently discovered as efficient electrocatalysts for a variety of reactions. As one of many advantages, they exhibit the potential to replace noble-metal catalysts with multinary combinations of transition
T. Löffler +6 more
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All Reg-solid varieties of commutative semigroups
Semigroup Forum, 2008The author denotes by \(W(X)\) the set of all terms formed from a binary operation symbol \(f\) and the set \(X\) of variables. A hypersubstitution \(\sigma\) of type (2) is defined by specifying a term \(\sigma(f)\in W(\{x_1,x_2\})\); it is called regular if both variables \(x_1\) and \(x_2\) occur in the term \(\sigma(f)\). Every hypersubstitution \(\
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P-Compatible Hypersubstitution and MP-Solid Varieties
Studia Logica, 2000The authors consider hypersubstitutions which are compatible with a partition \(P\) of the set of operations, and a corresponding generalized equational theory for \(P\)-compatible hyperidentities is developed.
Hałkowska, K., Denecke, K.
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\(M\)-solid varieties of semigroups
1995Fix a type \(\tau = (n_i)_{i \in I}\), \(n_i > 0\) for all \(i \in I\), and operation symbols \((f_i)_{i \in I}\), where \(f_i\) is \(n_i\)-ary. Let \(W_\tau(X)\) be the set of all terms of type \(\tau\) over some fixed alphabet \(X\). A mapping \(\sigma: \{f_i \mid i\in I\} \to W_\tau(X)\) is called a hypersubstitution of type \(\tau\) if it assigns ...
Denecke, Klaus-Dieter, Koppitz, Jörg
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Progress and prospect on failure mechanisms of solid-state lithium batteries
Journal of Power Sources, 2018By replacing traditional liquid organic electrolyte with solid-state electrolyte, the solid-state lithium batteries powerfully come back to the energy storage field due to their eminent safety and energy density. In recent years, a variety of solid-state
Jun Ma +3 more
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G. Birkhoff's theorems for M -solid varieties
Algebra Universalis, 1998Let \(M\) be a submonoid of hypersubstitutions of type \(\tau \). For an algebra \(A=(A,(f_i\); \(i\in I))\) of type \(\tau \) and for \(\delta \in M\), an algebra \((A,(\delta (f_i)\); \(i\in I))\) is called an \(M\)-derived algebra of \(A\). Further, \(D_M\) denotes the operator of taking \(M\)-derived algebras. An \(M\)-hypervariety of type \(\tau \)
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Revealing the role of the cathode–electrolyte interface on solid-state batteries
Nature Materials, 2021B. Zahiri +6 more
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\(M\)-solid polynomial varieties of semigroups
2001In a previous article by the same authors [Contributions to general algebra 12, 155-163 (2000; Zbl 0970.20032)] it was proved that there exist exactly 2 non-trivial solid polynomial varieties of semigroups which are definable by identities, namely the polynomial varieties given by the identities \(\{xyz=xy\}\) and \(\{xy=x^2y=xy^2\), \(xyzt=xzyt ...
Denecke, Klaus-Dieter +1 more
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