Coalgebras for a functor T on a category X model many different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary strongly complete specification languages for Set-based coalgebras. We show how to associate a finitary logic to any finite-sets preserving functor T and prove the logic to be strongly complete under a mild condition on T . The proof i...

It has been pointed out that an n-variable Boolean function f has optimal resistance against fast algebraic attacks if and only if there does not exist a nonzero n-variable Boolean function g of degree lower than n 2 such that fg = h and deg(g) + deg(h) < n. In this corresponding, we show that there does not exist an n-variable Boolean function with optimal resistance against fast algebraic att...

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to e...

To simplify the sum in the above equation we separate it into two parts: k # j and k = j. We also note that (@-i ? j) k = N k k # j and (@-i ? j) k = N k-1 k = j. We then obtain Simple algebraic manipulation results in the following form of the above equation.

An extension of parts of the theory of partially ordered varieties and quasivarieties, as presented by Paaasińska and Pigozzi in the framework of abstract algebraic logic, is developed in the more abstract framework of categorical abstract algebraic logic. Algebraic systems, as introduced in previous work by the author, play in this more abstract framework the role that universal algebras play ...

We show that the only topological and algebraic copies of N∗ to be found in N∗ are the trivial ones, namely k · N∗ for k ∈ N. A similar statement holds for copies of Z∗ in Z∗. As a consequence, we obtain the corollary that N∗ contains no copies of Z∗ whatever.

We analyze the abstract structure of algebraic groups over an algebraically closed field K, using techniques from the theory of groups of

We prove the Kloosterman–Spectral sum formula for PSL2(Z[i])\PSL2(C), and apply it to derive an explicit spectral expansion for the fourth power moment of the Dedekind zeta function of the Gaussian number field. Our sum formula, Theorem 13.1, allows the extension of the spectral theory of Kloosterman sums to all algebraic number fields.

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature (p, q) where q ≥ 5. If π is a spacelike 2 plane, let R(π) be the associated skewsymmetric curvature operator. We classify the algebraic curvature tensors so R(·) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curva...

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result.