Geometric description of C-vectors and real L\"osungen

We introduce real Loesungen as an analogue of real roots. For each mutation sequence of an arbitrary skew-symmetrizable matrix, we define a family of reflections along with associated vectors which are real Loesungen and a set of curves on a Riemann surface. The matrix consisting of these vectors is called L-matrix. We explain how the L-matrix naturally arises in connection with the C-matrix. Then we conjecture that the L-matrix depends (up to signs of row vectors) only on the seed, and that the curves can be drawn without self-intersections, providing a new combinatorial/geometric description of c-vectors

Lattice gas models derived from effective field theory

We start from a low-energy effective field theory for interacting fermions on the lattice and expand in the hopping parameter to derive the nearest-neighbor interactions for a lattice gas model. In this model the renormalization of couplings for different lattice spacings is inherited from the effective field theory, systematic errors can be estimated a priori, and the breakdown of the lattice gas model description at low temperatures can be understood quantitatively. We apply the lattice gas method to neutron matter and compare with results from a recent quantum simulation.Comment: 13 pages, 4 figure

Toward a Lockean Unification of Formal and Traditional Epistemology

Can there be knowledge and rational belief in the absence of a rational degree of confidence? Yes, and cases of "mistuned knowledge" demonstrate this. In this paper we leverage this normative possibility in support of advancing our understanding of the metaphysical relation between belief and credence. It is generally assumed that a Lockean metaphysics of belief that reduces outright belief to degrees of confidence would immediately effect a unification of coarse-grained epistemology of belief with fine-grained epistemology of confidence. Scott Sturgeon has suggested that the unification is effected by understanding the relation between outright belief and confidence as an instance of the determinable-determinate relation. But determination of belief by confidence would not by itself yield the result that norms for confidence carry over to norms for outright belief unless belief and high confidence are token identical. We argue that this token-identity thesis is incompatible with the neglected phenomenon of “mistuned knowledge”—knowledge and rational belief in the absence of rational confidence. We contend that there are genuine cases of mistuned knowledge and that, therefore, epistemological unification must forego token identity of belief and high confidence. We show how partial epistemological unification can be secured given determination of outright belief by degrees of confidence even without token-identity. Finally, we suggest a direction for the pursuit of thoroughgoing epistemological unification

Post Borders: Informal Bilingual Blogging and Iintercultural Ccommunication Competence

This paper describes an informal bilingual blogging environment that was created to develop intercultural communicative competence. After a consideration of ICC, the paper explores the opportunities for development of ICC that were created by three features of this blogging activity. A descriptive analysis shows that the design features of informality of topic, and intentional lack of strict language protocol, as well as attention to cultures of use of blogging\ud were associated with users’ display of ICC

A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra

Quasilocal Smarr relation for an asymptotically flat spacetime

A quasilocal Smarr relation is obtained from Euler's theorem for Einstein-Maxwell(-Dilaton) theory for an asymptotically flat spacetime, and its associated first law is studied. To check both, we calculate quasilocal variables by employing Brown-York quasilocal method along with Mann-Marolf counterterms, which are consistent with Tolman temperature. We also derive entropy by constructing a quasilocal thermodynamic potential via Euclidean method. Here we found that the Euclidean action value in a quasilocal frame just yields a usual thermodynamic potential form, which do not include a $PA$ term, and entropy just becomes the Bekenstein-Hawking one. Through the examples, we confirmed that our quasilocal Smarr relation is satisfied with all cases, and its first law is also exactly satisfied except the dyonic black hole with the dilaton coupling constant $a=\sqrt{3}$. In that case when making a large $R$ expansion, the first law is satisfied up to $1/R$ order but it does not hold for higher sub-leading order of $R$. This issue should be resolved in future.Comment: 24 page