Quality improvement of monolithic steel fiber concrete floor slabs with void formers

The features of the technology for the monolithic floors construction using void formers have been studied, its disadvantages have been identified and the ways to eliminate them have been proposed. At the first stage of this work, the reasons for the low quality of monolithic floors with void formers were studied by the method of visual and measuring control, and by comparing with known scientific and industrial data. At the second stage, by the method of systematization the main defects and damages arising in the construction, repair and usage of these floor slabs were classified and ways to eliminate them were proposed. At the third stage, the features of the quality control system, carried out directly during the construction of monolithic floor slabs using void formers, were studied, the composition of operations and control tools were proposed. According to the research results, it was found that the use of steel-fiber concrete in floors with non-removable void formers allows to reduce the percentage of reinforcement by 9.82%, compared to other known options, and also to reduce the consumption of concrete in comparison with a solid monolithic slab almost by half. The proposed quality control system will improve the efficiency of monolithic floor slabs using void formers.

Partial clones

A set [Formula: see text] of operations defined on a nonempty set [Formula: see text] is said to be a clone if [Formula: see text] is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the [Formula: see text]-ary operations defined on set [Formula: see text] for all natural numbers [Formula: see text] and the operations are the so-called superposition operations [Formula: see text] for natural numbers [Formula: see text] and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set [Formula: see text] and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.

Elementary transformations of systems of equations over quasigroups and generalized identities

The paper is devoted to the study of equations with the left-hand side having the form of a composition of operations which belong to given sets S1, …, Sn, … of quasigroup operations. Elementary transformations are described which allow reducing systems of this kind to the form where all equations except one do not depend essentially on the variable xn. A class of systems is said to be Gaussian if every system obtained via such transformations also belongs to this class. It is evident that for Gaussian classes of systems of equations there is an efficient solving algorithm. This motivates the problem of finding conditions under which the class is Gaussian. In this work it is shown that for a class of systems to be Gaussian the operations in the sets Si should satisfy the generalized distributivity law. Sets of operations obeying this condition are to be investigated in the future.

A new description of orthogonal bases

We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative †-Frobenius monoid in the category FdHilb, which has finite-dimensional Hilbert spaces as objects and continuous linear maps as morphisms, and tensor product for the monoidal structure. The basis is normalised exactly when the corresponding commutative †-Frobenius monoid is special. Hence, both orthogonal and orthonormal bases are characterised without mentioning vectors, but just in terms of the categorical structure: composition of operations, tensor product and the †-functor. Moreover, this characterisation can be interpreted operationally, since the †-Frobenius structure allows the cloning and deletion of basis vectors. That is, we capture the basis vectors by relying on their ability to be cloned and deleted. Since this ability distinguishes classical data from quantum data, our result has important implications for categorical quantum mechanics.