344,853 research outputs found

### Cartesian Minds

According to a basic dualistic conception that
originated in Descartes, minds are immaterial, non-spatial
and simple thinking particulars that are independent of
anything material. Call this view the Cartesian conception,
and minds thus conceived, Cartesian minds. In what
follows I propose a new version of an argument against the
Cartesian conception that can be traced back to
Descartes" days (Garber and Ayers 1998, 232). The
inspiration behind my version is an argument suggested by
Strawson"s seminal discussion of the concept of a person
(1959, Chaps. 3-4). However, in both form and substance
my argument takes its own course

### Two dimensional vernier

A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction

### On products in the coarse shape categories

The paper is devoted to the study of coarse shape of Cartesian products of
topological spaces. If the Cartesian product of two spaces $X$ and $Y$ admits
an HPol-expansion, which is the Cartesian product of HPol-expansions of these
spaces, then $X\times Y$ is a product in the coarse shape category. As a
consequence, the Cartesian product of two compact Hausdorff spaces is a product
in the coarse shape category. Finally, we show that the shape groups and the
coarse shape groups commute with products under some conditions.Comment: 11 page

### Partial Horn logic and cartesian categories

A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modified. It is developed here in its minimal form, with equality and conjunction, as “partial Horn logic”.
Various kinds of logical theory are equivalent: partial Horn theories, “quasi-equational” theories (partial Horn theories without predicate symbols), cartesian theories and essentially algebraic theories.
The logic is sound and complete with respect to models in , and sound with respect to models in any cartesian (finite limit) category.
The simplicity of the quasi-equational form allows an easy predicative constructive proof of the free partial model theorem for cartesian theories: that if a theory morphism is given from one cartesian theory to another, then the forgetful (reduct) functor from one model category to the other has a left adjoint.
Various examples of quasi-equational theory are studied, including those of cartesian categories and of other classes of categories. For each quasi-equational theory another, , is constructed, whose models are cartesian categories equipped with models of . Its initial model, the “classifying category” for , has properties similar to those of the syntactic category, but more precise with respect to strict cartesian functors

### Fast Recognition of Partial Star Products and Quasi Cartesian Products

This paper is concerned with the fast computation of a relation $\R$ on the
edge set of connected graphs that plays a decisive role in the recognition of
approximate Cartesian products, the weak reconstruction of Cartesian products,
and the recognition of Cartesian graph bundles with a triangle free basis.
A special case of $\R$ is the relation $\delta^\ast$, whose convex closure
yields the product relation $\sigma$ that induces the prime factor
decomposition of connected graphs with respect to the Cartesian product. For
the construction of $\R$ so-called Partial Star Products are of particular
interest. Several special data structures are used that allow to compute
Partial Star Products in constant time. These computations are tuned to the
recognition of approximate graph products, but also lead to a linear time
algorithm for the computation of $\delta^\ast$ for graphs with maximum bounded
degree.
Furthermore, we define \emph{quasi Cartesian products} as graphs with
non-trivial $\delta^\ast$. We provide several examples, and show that quasi
Cartesian products can be recognized in linear time for graphs with bounded
maximum degree. Finally, we note that quasi products can be recognized in
sublinear time with a parallelized algorithm

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