Functionalism about truth is the view that truth is an explanatorily significant but multiply-realizable property. According to this view the properties that realize truth vary from domain to domain, but the property of truth is a single, higher-order, domain insensitive property. We argue that this view faces a challenge similar to the one that Jaegwon Kim laid out for the multiple realization...

For a field F and an integer d ≥ 1, we consider the universal associative F-algebra A generated by two sets of d+1 mutually orthogonal idempotents. We display four bases for the F-vector space A that we find attractive. We determine how these bases are related to each other. We describe how the multiplication in A looks with respect to our bases. Using our bases we obtain an infinite nested seq...

In [CK] and [SZ], the authors constructed the bases of cluster algebras of finite types and of type e A1,1, respectively. In this paper, we will deduce Z-bases for cluster algebras of affine types and compare Z-bases with generic variables in [Du2]. Moreover, we give inductive formulas for computing the multiplication between two generalized cluster variables associated to objects in a tube.

Unlike those used in the West, a typical Chinese multiplication table includes only smaller-operand-first entries (e.g., 3 x 7=21, but not 7 x 3=21). Due to this unique feature, multiplication for Chinese subjects has been found to show an operand-order effect. The present study aims to investigate the neural bases of the operand-order effect. Subjects were 20 Mainland Chinese subjects who lear...

Based on a recently proposed Toeplitz matrix-vector product approach, a subquadratic computational complexity scheme is presented for multiplications in binary extended finite fields using Type I and II optimal normal bases.

A wavelet-like transform is introduced to represent discretizations of the single layer operator from potential theory by a nearly sparse matrix. Unlike the wavelet-based approaches that have appeared in the past, our construction of the basis is independent of a surface parameterization and therefore suitable for complex, multiply connected domains. Furthermore, the diagonal blocks of the tran...

We report a new transformation, the LogDet, that is consistent for sequences with differing nucleotide composition and that have arisen under simple but asymmetric stochastic models of evolution. This transformation is required because existing methods tend to group sequences on the basis of their nucleotide composition, irrespective of their evolutionary history. This effect of differing nucle...

Contemporary debates on the rural sector in Latin America have led many to question the future viability of peasant livelihoods in the Andes. The paper first discusses certain limitations in these discussions of peasant viability. Firstly, they conflate agrarian with rural livelihoods, thus deflecting attention from the myriad transitions that have occurred in the ways through which people make...

We present efficient computational solutions to the problems of checking equality, performing multiplication, and computing minimal representatives elements free bands. A band is any semigroup satisfying identity x2≈x FB(k) object in variety k-generated Radoszewski Rytter developed a linear time algorithm for whether two words represent same element band. In this paper we describe an alternate ...

In this paper we compute moments of a Wishart matrix variate U of the form E(Q(U)) where Q(u) is a polynomial with respect to the entries of the symmetric matrix u, invariant in the sense that it depends only on the eigenvalues of the matrix u. This gives us in particular the expected value of any power of the Wishart matrix U or its inverse U−1. For our proofs, we do not rely on traditional co...