Crystal structures and proton dynamics in potassium and cesium hydrogen bistrifluoroacetate salts with strong symmetric hydrogen bonds

The crystal structures of potassium and cesium bistrifluoroacetates were determined at room temperature and at 20 K and 14 K, respectively, with the single crystal neutron diffraction technique. The crystals belong to the I2/a and A2/a monoclinic space groups, respectively, and there is no visible phase transition. For both crystals, the trifluoroacetate entities form dimers linked by very short hydrogen bonds lying across a centre of inversion. Any proton disorder or double minimum potential can be rejected. The inelastic neutron scattering spectral profiles in the OH stretching region between 500 and 1000 cm^{-1} previously published [Fillaux and Tomkinson, Chem. Phys. 158 (1991) 113] are reanalyzed. The best fitting potential has the major characteristics already reported for potassium hydrogen maleate [Fillaux et al. Chem. Phys. 244 (1999) 387]. It is composed of a narrow well containing the ground state and a shallow upper part corresponding to dissociation of the hydrogen bond.Comment: 31 pages, 7 figure

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

Orienting Role of Terminology in Context of Its Scientific-Popular Conceptualization

The article examines the structural and functional properties of terms in popular scientific discourse. The authors aim to characterize the orientation of a term as a combination of its linguistic and functional properties, which define the concept expressed by the term, its connections with other concepts, and its place within the terminological system. The object of the study is linguistic and speech units in popular scientific texts, while the subject is the means of expressing orienting properties of terms in popular scientific discourse. The novelty of the research lies in studying the orienting properties of terms in popular scientific style based on their linguistic and speech properties, and providing a classification of these properties according to the scope and content of the expressed concepts. The relevance of the study is determined by the important role of these properties in the process of forming specialized concepts, understanding scientific, popular scientific, and educational discourses, and solving practical problems related to terminology use. The authors focus on the orienting function of a term, which is carried out through linguistic and speech means, with logical definitions, textual explanations, intercategorical connections expressed by elements of word formation and morpho-syntactic systems being the most active ones. The authors conclude that orienting properties of terms play a significant role in terminological conceptualization (formation of specialized concepts)

Text-Speech Modeling of Addressee of Advertising Training Courses

The image of the target audience of training courses advertising is considered. The authors set a goal — to characterize the speech modeling of the addressee of advertisement on the basis of advertising discourse. The object of the study is the private discourse of Spanish courses advertising, the subject of the study is the language and speech units of the advertising text, which create a psychological and speech portrait of the addressee of the advertisement. The novelty of the study is seen in the fact that, on the basis of advertising texts, the communicative features of not their authors, but their addressees are analyzed. The relevance of the study is due to the importance of advertising discourse in modern mass culture, in particular, the interest in its influencing function. The authors dwell on the properties of the advertising text as one of the targeting tools, which is carried out due to the positive tone created by the system of language and speech units. The most active language and speech means of creating a positive tone in the text of advertising training courses are analyzed. Particular attention is paid to the vocabulary of different thematic groups. The authors conclude that the lexical composition of advertising training courses makes it possible to reconstruct fragments of the psychological and speech portrait of advertising recipients (students), to model their psychological characteristics, their range of interests and preferences

Potential Conservation Laws

We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.Comment: 36 pages, extended versio

Modelisation of transition and noble metal vicinal surfaces: energetics, vibrations and stability

The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces, i.e., surface energy, step energy, kink energy and electronic interactions between steps, is studied at 0K from electronic structure calculations in the tight-binding approximation using a {\it s, p} and {\it d} valence orbital basis set. Then, the surface phonon spectra of copper are investigated in the harmonic approximation with the help of a semi-empirical inter-atomic potential. This allows to derive the contribution of phonons at finite temperatures to the step free energy and to the interactions between steps. The last part is devoted to the stability of vicinal surfaces relative to faceting with special attention to the domain of orientations (100)-(111). Semi-empirical potentials are shown to be not realistic enough to give a reliable answer to this problem. The results derived from electronic structure calculations predict a variety of behaviors and, in particular, a possible faceting into two other vicinal orientations. Finally, temperature effects are discussed. Comparisons are made with other theoretical works and available experiments

Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte