English grammatical collocations of the verb and the preposition for and their collocational equivalents in the Slovak language

This paper focuses on empirical research of grammatical collocations of the type: verb and preposition FOR. Subject to analysis were the verbal prepostional structures of the pattern 1: V+prepositional phrase in the function of the object and the pattern 2: V+ preposition+fixed element. The study is based on comparisons of the English and Slovak sentences containing this specific verbal-prepositional structure. Data for contrastive study of English and Slovak languages are taken from the electronic corpus Slovak National Corpus, ie. English- Slovak Parallel Corpus. The aim of the study is to analyse, describe and classify only prepositional counterparts.

Poncelet property and quasi-periodicity of the integrable Boltzmann system

We study the motion of a particle in a plane subject to an attractive central force with inverse-square law on one side of a wall at which it is reflected elastically. This model is a special case of a class of systems considered by Boltzmann which was recently shown by Gallavotti and Jauslin to admit a second integral of motion additionally to the energy. By recording the subsequent positions and momenta of the particle as it hits the wall, we obtain a three-dimensional discrete-time dynamical system. We show that this system has the Poncelet property: If for given generic values of the integrals one orbit is periodic, then all orbits for these values are periodic and have the same period. The reason for this is the same as in the case of the Poncelet theorem: The generic level set of the integrals of motion is an elliptic curve, and the Poincaré map is the composition of two involutions with fixed points and is thus the translation by a fixed element. Another consequence of our result is the proof of a conjecture of Gallavotti and Jauslin on the quasi-periodicity of the integrable Boltzmann system, implying the applicability of KAM perturbation theory to the Boltzmann system with weak centrifugal force.

On S-2-absorbing primary submodules

This article introduces the concept of S-2-absorbing primary submodule as a generalization of 2-absorbing primary submodule. Let S be a multiplicatively closed subset of a ring R and M an R-module. A proper submodule N of M is said to be an S-2-absorbing primary submodule of M if (N :R M) ? S = ? and there exists a fixed element s ? S such that whenever abm ? N for some a,b ? R and m ? M, then either sam ? N or sbm ? N or sab ? ?(N :R M). We give several examples, properties and characterizations related to the concept. Moreover, we investigate the conditions that force a submodule to be S-2-absorbing primary.

Phineas Gage's great legacy

ABSTRACT. The case of Phineas Gage is an integral part of medical folklore. His accident still causes astonishment and curiosity and can be considered as the case that most influenced and contributed to the nineteenth century's neuropsychiatric discussion on the mind-brain relationship and brain topography. It was perhaps the first case to suggest the role of brain areas in determining personality and which specific parts of the brain, when affected, can induce specific mental changes. In addition, his case contributed to the emergence of the scientific approaches that would later culminate in psychosurgery. Gage is a fixed element in the studies of neurology, psychology, and neuroscience, having been solidified as one of the greatest medical curiosities of all time, deserving its prominence.

Post-quantum digital signature schemes: setting a hidden group with two-dimensional cyclicity

For the construction of post-quantum digital signature schemes that satisfy the strengthened criterion of resistance to quantum attacks, an algebraic carrier is proposed that allows one to define a hidden commutative group with two-dimensional cyclicity. Formulas are obtained that describe the set of elements that are permutable with a given fixed element. A post-quantum signature scheme based on the considered finite non-commutative associative algebra is described.

Generalised Inner Derivations in Semi Prime Rings

Let A be any ring and f(xy) = f(x)y+xha(y), where f be any generalised inner derivation(G.I.D ) a be the fixed element of A. In this paper, it is shown that (i) ha must necessarily be a derivation for semi prime ring A. (ii) ∃ no generalized inner derivations f : A → A such that f(x ◦ y) = x ◦ y or f(x ◦ y) + x ◦ y = 0 ∀ x,y ∈ A, We have proved Havala [2] def. p.1147, Herstein [3] Lemma 3.1 p. 1106 as corollaries, along with other results.

Geopolitical Location of the Republic of Azerbaijan: temporal and Spatial Changes

For instance, the evolution of the Republic of Azerbaijan was examined in three different periods. The first one is the republican period (1918–1920); the second one is the sovereign state period (1920–1991); and the third one is the period since 1991. Each period was compared with the others and the similarities and differences experienced in the geopolitics of the country were evaluated. Three main lines are clearly seen in the geopolitics conducted approximately throughout the last century by different Azerbaijans. Firstly, the main geopolitical competitor is the Republic of Armenia; secondly, the competition taking place in the region between Russia and the West creates the atmosphere which influences the geopolitical behaviors; and thirdly, the fixed element which determines the status of the country is the energy resources.

Italian ma ‘but’ in deverbal pragmatic markers: Forms, functions, and productivity of a pragma-dyad

This paper focuses on the development, paradigmaticization, and productivity of a set of complex pragmatic markers in Italian, which are constituted by two distinct elements, namely the adversative conjunction ma ‘but’ and a deverbal pragmatic marker (e.g., ma dai ‘come on! really!’, literally: ‘but give’, or ma piantala ‘just stop! give it a rest!’, literally ‘but dump it’). The main idea we will develop is that such a complex pattern can be better described in terms of a pragma-dyad, i.e., a dyadic construction with a pragmatic meaning, featuring a fixed element which systematically combines with a set of preferential fillers. In our case, the fixed element is ma, which generally signals a contrast with the interlocutors’ point of view, thus shaping the pragmatic meaning of the resulting complex in terms of interactional contrast. Such a meaning is then functionally enriched through a variety of fillers compatible with the schema, which actualize it in conveying mock politeness, disagreement, counter-expectation, and pragmatically neighbouring values. By providing a corpus-based study of the development and productivity of these complex markers, we illustrate the empirical and theoretical advantages which a pragma-dyadic approach can offer in exploring processes of functional enrichment involving complex markers.

ON DISCRETENESS OF SUBGROUPS OF QUATERNIONIC HYPERBOLIC ISOMETRIES

Let $\mathbf{H}_{\mathbb{H}}^{n}$ denote the $n$-dimensional quaternionic hyperbolic space. The linear group $\text{Sp}(n,1)$ acts on $\mathbf{H}_{\mathbb{H}}^{n}$ by isometries. A subgroup $G$ of $\text{Sp}(n,1)$ is called Zariski dense if it neither fixes a point on $\mathbf{H}_{\mathbb{H}}^{n}\cup \unicode[STIX]{x2202}\mathbf{H}_{\mathbb{H}}^{n}$ nor preserves a totally geodesic subspace of $\mathbf{H}_{\mathbb{H}}^{n}$. We prove that a Zariski dense subgroup $G$ of $\text{Sp}(n,1)$ is discrete if for every loxodromic element $g\in G$ the two-generator subgroup $\langle f,gfg^{-1}\rangle$ is discrete, where the generator $f\in \text{Sp}(n,1)$ is a certain fixed element not necessarily from $G$.