A Study on Cubic H-Relations in a Topological Universe Viewpoint

We introduce the concrete category CRel P ( H ) [resp. CRel R ( H ) ] of cubic H-relational spaces and P-preserving [resp. R-preserving] mappings between them and study it in a topological universe viewpoint. In addition, we prove that it is Cartesian closed over Set . Next, we introduce the subcategory CRel P , R ( H ) [resp. CRel R , R ( H ) ] of CRel P ( H ) [resp. CRel R ( H ) ] and investigate it in the sense of a topological universe. In particular, we obtain exponential objects in CRel P , R ( H ) [resp. CRel R , R ( H ) ] quite different from those in CRel P ( H ) [resp. CRel R ( H ) ].

Function spaces based on L-sets

For a commutative, integral, and divisible quantale L, a concept of top L-convergence spaces based on L-sets other than crisp sets is proposed by using a kind of L-filters, namely limited L-filters defined in the paper. Our main result is the existence of function spaces in the the concrete category of top L-convergence spaces over the slice category Set#L rather than the category Set of sets, such that the concrete category of top L-convergence spaces over the slice category Set#L is Cartesian closed. In order to support the existence of top L-convergence spaces, some nontrivial examples of limited L-filters and top L-convergence spaces are presented also.

TACTICAL TASKS AND MECHANISM OF THEIR SOLVING

Approaches ofscientists to the definition of the notion «tactical task» are considered. The attention is paid that among the tasks ofpre-judicial investigation being solved, it’s expedient to distinguish depending on the scope the basic (general, core) and the local (intermediate), and depending on realization sphere - strategic and tactical tasks. Along with, the basic tasks may be considered as strategic because they are preconditioned by circumstances which are subjects to clarification in the general course of investigation of a concrete category of crimes. They are directed on achievement of the legal purpose, are more stable by their nature and in a lesser degree they are subjected to the influence of situational factors. Local problems should be considered as tactical because they are caused by situations arising at a certain stage of investigation. Under tactical task it’s necessary to understand situationally caused complicated question (problem) which arises at a certain stage of investigation, has limited, local sphere of realization, has intermediate character, intended to establish unit facts about separate elements or circumstances of a crime event and is solved by applying exclusively available tactical means. In the mechanism of tactical task solving such elements are functioning: starting position; purpose; ways and means of its achievement which relate a starting position with purpose. The basic stages (phases) of adopting tactical decision are: a) informative preparation of the decision (the analysis of the initial information, that is the analysis of an investigative situation which has developed at the moment of tactical decision making); b) statement of a tactical task, construction of current images; c) near procedure of decision-making which is realized by means of formation and comparison of reference and current images, forecasting possible variants of coming result, correction of images, choice and construction of a reference hypothesis or the program of actions.

Durability Performance of Oil Palm Shell Lightweight Concrete as Insulation Concrete

This paper presents a solid agricultural solid waste, namely oil palm shell (OPS) as coarse aggregate to produce insulation concrete. This study will investigate the porosity, air permeability and thermal conductivity of OPS lightweight concrete (OPSLC). Nine mix designs were developed which comprised three OPS shapes and three volume fractions of OPS. The results indicated that increased volume fraction of OPS caused decreased durability performance and thermal conductivity. The shape of OPS is found to have significant effects to the porosity content and air permeability values. Thus, there is a strong relationship between porosity content and air permeability for all specimens. Based on the results, all specimens are found to be in the range of insulation concrete category except for specimen C-30, which has more than 0.75W/mK thermal conductivity according to RILEM requirement. The thermal conductivity of OPSLC is comparable with artificial lightweight aggregate.

A Category of Control Systems

We construct the concrete category LiCS of left-invariant control systems (on Lie groups) and point out some very basic properties. Morphisms in this category are examined briefly. Also, covering control systems are introduced and organized into a (comma) category associated with LiCS

New torsion theory in unital abelian ℓ-groups

This paper introduces the notion of a functorial torsion class (FTC): in a concrete category $\mathfrak{C}$ which has image factorization, one considers monocoreflective subcategories which are closed under formation of subobjects.Here the interest is in FTCs in the category of abelian lattice-ordered groups with designated strong order unit. The FTCs $\mathfrak{T}$ consisting of archimedean latticeordered groups are characterized: for each subgroup A of the rationals with the identity 1, either $\mathfrak{T} = \mathfrak{S}\left( A \right)$, the class of all lattice-ordered groups of functions on a set X which have finite range in A, or $$\mathfrak{T} = \mathbb{T}\left( A \right)$$, the class of all subgroups of A with 1.As for FTCs possessing non-archimedean groups, it is shown that if $\mathfrak{T}$ is an FTC containing a subgroup A of the reals with 1, of rank two or greater, then $\mathfrak{T}$ contains all ℓ-groups of the form $A\vec \times G$, for all abelian lattice-ordered groups G. Finally, the least FTC that contains a non-archimedean group is the class of all $\mathbb{Z}\vec \times G$, for all abelian lattice-ordered groups G.

Instantiation of semantic categories in sentence comprehension by Alzheimer patients

This study examined whether Alzheimer patients can make elaborative inferences based on the semantic context provided by a sentence. More specifically, if presented with the name of a category in a sentence do they, like normals, infer (instantiate) the particular member of that category most appropriate to the meaning of the sentence (e.g., if a sentence mentions a container of juice, do they infer it is a bottle). Patients were presented with a sentence containing the name of a concrete category. The sense of the sentence was consistent with a low-dominant member of that category. Patients were then shown drawings of four members of that category and asked to select the one appropriate to the sentence. They were later asked to name the drawings. If semantic information is degraded in Alzheimer patients for those objects Alzheimer patients cannot name (as has been claimed), then AD patients should be unable to carry out the type of elaborative semantic inference required to instantiate. Results showed that Alzheimer patients were highly accurate at instantiating even objects they could not name. This is consistent with a relative preservation of semantic knowledge about concrete objects in Alzheimer patients. (JINS, 1999, 5, 685–691.)

Towards Minimal Binding Varieties of Lattices

By classical results of Ambrust and Schmidt, every monoid is isomorphic to the endomorphism monoid of an algebra. Thus if we want to investigate in which varieties (or generally, in a concrete category) each monoid is isomorphic to the endomorphism monoid of an algebra in this variety (or an object of this category) then the important role is played by the concept of a binding category (see the definition below). Moreover, as shows the Hedrlín-Kučera Theorem [13] if the set-theoretical assumption (M) holds (i.e., there is an infinite cardinal α such that each ultrafilter closed under α intersections is trivial) every concrete category can be fully embedded into any binding category. Other properties of binding categories are in [7, 11, 13]. A list of the most important binding categories and the properties of binding categories can be found in an excellent monograph [13].