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SARS-CoV-2 is a worldwide serious health problem. The aim of this study was to demonstrate the number of potentially infectious particles present during endoscopic procedures and find effective tools to eliminate the risks of SARS-CoV-2 infection while performing them. An experimental model which focused on aerosol problematics was made in a specialized laboratory. This model simulated conditions present during endoscopic procedures and monitored the formation of potentially infectious fluid particles from the patient's body, which pass through the endoscope and are then released into the environment. For this reason, we designed and tested a prototype of a protective cover for the endoscope's control body to prevent the release and spread of these fluid particles from its working channel. We performed measurements with and without the protective cover of the endoscope's control body. It was found that liquid coming through the working channel of the endoscope with forceps or other instruments inside generates droplets with a diameter in the range of 0.1-1.1 mm and an initial velocity of up to 0.9 m/s. The average number of particles per measurement per whole measured area without a protective cover on the endoscope control body was 51.1; with this protective cover on, the measurement was 0.0, p<0.0001. Our measurements proved that fluid particles are released from the working channel of an endoscope when forceps are inserted. A special protective cover for the endoscope control body, made out of breathable material (surgical cap) and designed by our team, was found to eliminate this release of potentially infectious fluid particles.

The cleaning of particles from smooth and rough paper surfaces using a high-speed CO2 snow jet was investigated. The measurements included characterization of the jet properties, determination of the cleaning efficiency, and evaluation of any possible adverse effects. The method was compared with nitrogen jet cleaning and dry cleaning by commercial materials. The results showed that the CO2 snow jet is able to effectively remove particles from the paper surface and did not cause any observable degradation. The CO2 snow jet cleaning compared with the mechanical dry cleaning showed similar effectiveness without any adverse effects on the paper surface. It was proved that the CO2 snow technique is a suitable method for cleaning common types of paper materials.

Neonatal vitamin B12 (B12) deficiency can cause neurodevelopmental harm, and newborn screening (NBS) may enable early detection and treatment. We conducted a multicenter pilot project in four Prague university hospitals between 1 June 2022 and 30 June 2025. Algorithms included the determination of propionylcarnitine-derived primary markers using flow-injection tandem mass spectrometry and second-tier methylmalonic acid (MMA), with total homocysteine measured only when MMA was increased. Of 34,302 screened newborns with consent, 1365 (3.98%) triggered second-tier testing; 9 had MMA > 2.5 µmol/L, of which 8 met the case definition after confirmatory testing, giving a birth frequency of 1:4228 (95% CI 1:2176–1:9931). Positive predictive value was 0.59% (95% CI 0.25–1.15%) and 88.89% (95% CI 51.75–99.72%) for the primary test and second-tier MMA, respectively, with a false positive rate of 0.00292% (95% CI 0.000074–0.01625%). All affected infants were treated orally with cyanocobalamin. Maternal work-up identified confirmed B12 deficiency in four of eight mothers and premalignant gastric changes in two of four positive women. These data support the feasibility, low cost, and clinical utility of incorporating B12 deficiency into Czech NBS, with benefits extending beyond newborn health.

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated abelian extension of commutative groups) if and only if it is not Boolean complete, reaffirming the connection between computational complexity and solvability. Finally, we briefly discuss relations between nilpotence and solvability for loops and the associated multiplication groups and inner mapping groups.

We find a short equational basis for the variety of \\(3\\)-supernilpotent loops. We also present a conceptually simple proof that \\(k\\)-nilpotence and \\(k\\)-supernilpotence are equivalent for groups. Connections between \\(3\\)-supernilpotent loops, Moufang loops, code loops, automorphic loops and AIM loops are explored.

Idempotent left nondegenerate solutions of the Yang-Baxter equation are in one-to-one correspondence with twisted Ward left quasigroups, which are left quasigroups satisfying the identity \\((x*y)*(x*z)=(y*y)*(y*z)\\). Using combinatorial properties of the Cayley kernel and the squaring mapping, we prove that a twisted Ward left quasigroup of prime order is either permutational or a quasigroup. Up to isomorphism, all twisted Ward quasigroups \\((X,*)\\) are obtained by twisting the left division operation in groups (that is, they are of the form \\(x*y=(x^-1y)\\) for a group \\((X,)\\) and its automorphism \\(\\)), and they correspond to idempotent latin solutions. We solve the isomorphism problem for idempotent latin solutions.

Wolfgang Rump showed that there is a one-to-one correspondence between nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation and binary algebras in which all left translations \\(L_x\\) are bijections, the squaring map is a bijection, and the identity \\((xy)(xz) = (yx)(yz)\\) holds. We call these algebras rumples in analogy with quandles, another class of binary algebras giving solutions of the Yang-Baxter equation. We focus on latin rumples, that is, on rumples in which all right translations are bijections as well. We prove that an affine latin rumple of order \\(n\\) exists if and only if \\(n=p_1^p_1 k_1 p_m^p_m k_m\\) for some distinct primes \\(p_i\\) and positive integers \\(k_i\\). A large class of affine solutions is obtained from nonsingular near-circulant matrices \\(A\\), \\(B\\) satisfying \\([A,B]=A^2\\). We characterize affine latin rumples as those latin rumples for which the displacement group generated by \\(L_x L_yınv\\) is abelian and normal in the group generated by all translations. We develop the extension theory of rumples sufficiently to obtain examples of latin rumples that are not affine, not even isotopic to a group. Finally, we investigate latin rumples in which the dual identity \\((zx)(yx) = (zy)(xy)\\) holds as well, and we show, among other results, that the generators \\(L_x L_yınv\\) of their displacement group have order dividing four.

We enumerate central and medial quasigroups of order less than \\(128\\) up to isomorphism, with the exception of those quasigroups that are isotopic to \\(C_4 C_2^4\\), \\(C_2^6\\), \\(C_3^4\\) or \\(C_5^3\\). We give an explicit formula for the number of quasigroups that are affine over a finite cyclic group.

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated abelian extension of commutative groups) if and only if it is not Boolean complete, reaffirming the connection between computational complexity and solvability. Finally, we briefly discuss relations between nilpotence and solvability for loops and the associated multiplication groups and inner mapping groups.

Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group. We specialize the fundamental theorem into several varieties of loops, and also discuss the commutator of two normal subloops. Consequently, we argue that some standard definitions of loop theory, such as elementwise commutators and associators, should be revised and linked more closely to inner mappings. Using the new definitions, we prove several natural properties of loops that could not be so elegantly stated with the standard definitions of loop theory. For instance, we show that the subloop generated by the new associators defined here is automatically normal. We conclude with a preliminary discussion of abelianess and solvability in loops.