Alkali-activated metallurgical slag as a sustainable adsorbent

This paper is devoted to obtaining a zeolite-containing sorbent based on metallurgical waste — slag. The synthesis of zeolite adsorbent from ash and slag was carried out by hydrochemical and thermal treatment. The initial object and the obtained material were characterized using following methods: Fourier-transform infrared spectroscopy, scanning electron microscopy, energy dispersive analysis, X-ray phase analysis, titrimetry. The way of converting solid-phase waste into a beneficial product has been demonstrated. The study results showed that the surface of the obtained material is saturated with functional groups (hydroxy-, carboxy-, lactone), which predetermine the ability to bind metal ions during adsorption. The adsorption capacity of the product has been estimated for iodine and methylene blue. A thermodynamic analysis of the process of sorption of copper (II) ions from an aqueous solution has been conducted. It has identified that the sorbent can also be used for the adsorptive concentration of ions of rare-earth elements by the example of lanthanum and erbium. Laboratory testing of the possible use of the sorbent to purify industrial water was carried out using the example of wastewater from a chromium plating shop

Functoriality of the Schmidt Construction

After proving, in a purely categorial way, that the inclusion functor InAlg(Σ) from Alg(Σ), the category of many-sorted Σ-algebras, to PAlg(Σ), the category of many-sorted partial Σ-algebras, has a left adjoint FΣ, the (absolutely) free completion functor, we recall, in connection with the functor FΣ, the generalized recursion theorem of Schmidt, which we will also call the Schmidt construction. Next we define a category Cmpl(Σ), of Σ-completions, and prove that FΣ, labeled with its domain category and the unit of the adjunction of which it is a part, is a weakly initial object in it. Following this we associate to an ordered pair (α,f), where α=(K,γ,α) is a morphism of Σ-completions from F=(C,F,η) to G=(D,G,ρ) and f a homomorphism in D from the partial Σ-algebra A to the partial Σ-algebra B, a homomorphism ΥαG,0(f):Schα(f)B. We then prove that there exists an endofunctor, ΥαG,0, of Mortw(D), the twisted morphism category of D, thus showing the naturalness of the previous construction. Afterwards we prove that, for every Σ-completion G=(D,G,ρ), there exists a functor ΥG from the comma category (Cmpl(Σ)↓G) to End(Mortw(D)), the category of endofunctors of Mortw(D), such that ΥG,0, the object mapping of ΥG, sends a morphism of Σ-completion in Cmpl(Σ) with codomain G, to the endofunctor ΥαG,0.

THE PROBABILITY OF FAILURE OF THE HEATING CONTROL UNIT DURING THE FLIGHT AND ITS CONSEQUENCES

The article presents the results of predicting the probability of failure of the heating control unit during flight on the basis of mathematical modeling of multistage processes of performing operations in stochastic productive systems. The problem statement is formed as follows: to determine the probability of failure of the heating control unit during the flight and its possible consequences. The structural and functional diagram of the heating control unit using a strict formal mathematical description based on equations describing the Ornstein-Uhlenbeck process was considered as an initial object for determining the probability of failure.

OPTIMIZATION ALGORITHM OF TILTED IMAGE MATCHING BASED ON ADAPTIVE INITIAL OBJECT ASPECT

When adopting the matching method of the least squares image based on object-patch to match tilted images, problems like the low degree of connection points for images with the discontinuity of depth or the discrepancy in elevation or low availability of aerotriangulation points would frequently appear. To address such problems, a tilted-image-matching algorithm based on an adaptive initial object-patch is proposed by this paper. By means of the existing initial values of the interior and exterior orientation elements of the tilted image and the information of object points generated in the matching process, the algorithm takes advantage of the method of multi-patch forward intersection and object variance partition so as to adaptively calculate the elevation of the object-patch and the initial value of the normal vector direction angle. Furthermore, this algorithm aims to solve the problem of difficulties in matching the tilted image with its corresponding points brought about by the low accuracy of the initial value of the tilted image when adopting the matching method of the least squares image based on object-patch to match the tilted image with high discrepancy in elevation. We adopt the algorithm as proposed in this paper and the least squares image matching method in which the initial state of the object-patch is horizontal to the object-patch respectively to conduct the verification process of comparing and matching two groups of tilted images. Finally, the effectiveness of the algorithm as proposed in this paper is verified by the testing results.

The new Directive on Contracts for the Supply of Digital Content and Digital Services – Scope of Application and Trader’s Obligation to Supply – Part 1

After more than 3 years of discussions and negotiations the new contract law package consisting of the directive on the contracts for the supply of digital content and digital services and the new consumer sales directive have been finally adopted. The initial object-based regulatory approach has been kept, whereas the object of the contract now also encompasses digital services. The contract typology is still left within the discretion of the Member States and also the innovative concept of data as counter-performance is kept in the final version. The article discusses the scope of the digital content directive, including the complicated regulation on ancillary digital services (‘goods with digital elements’) as well as the trader’s main obligation – the obligation to supply. Conformity criteria, including the updating obligation, consumer’s remedies, trader’s liability as well as his right to make modifications will be dealt with in the follow-up article to be published in the next issue.

Set-theoretic solutions to the Yang–Baxter equation, skew-braces, and related near-rings

Skew-braces have been introduced recently by Guarnieri and Vendramin. The structure group of a non-degenerate solution to the Yang–Baxter equation is a skew-brace, and every skew-brace gives a set-theoretic solution to the Yang–Baxter equation. It is proved that skew-braces arise from near-rings with a distinguished exponential map. For a fixed skew-brace, the corresponding near-rings with exponential form a category. The terminal object is a near-ring of self-maps, while the initial object is a near-ring which gives a complete invariant of the skew-brace. The radicals of split local near-rings with a central residue field [Formula: see text] are characterized as [Formula: see text]-braces with a compatible near-ring structure. Under this correspondence, [Formula: see text]-braces are radicals of local near-rings with radical square zero.

Concatenation of Finite Sequences

Summary The coexistence of “classical” finite sequences [1] and their zero-based equivalents finite 0-sequences [6] in Mizar has been regarded as a disadvantage. However the suggested replacement of the former type with the latter [5] has not yet been implemented, despite of several advantages of this form, such as the identity of length and domain operators [4]. On the other hand the number of theorems formalized using finite sequence notation is much larger then of those based on finite 0-sequences, so such translation would require quite an effort. The paper addresses this problem with another solution, using the Mizar system [3], [2]. Instead of removing one notation it is possible to introduce operators which would concatenate sequences of various types, and in this way allow utilization of the whole range of formalized theorems. While the operation could replace existing FS2XFS, XFS2FS commands (by using empty sequences as initial elements) its universal notation (independent on sequences that are concatenated to the initial object) allows to “forget” about the type of sequences that are concatenated on further positions, and thus simplify the proofs.