Pirmais teikums: zinātniskā raksta pieteikums

Tips for writers found in books, articles, blogs, and website forums often focus on the first sentence, engaging the reader to read the entire text. Tips for writing the first sentence are mostly applied to essays, including academic essays. On the other hand, good examples of the first sentence are usually chosen from classical literary works, making it possible to assume that the first sentence has meaning in every text, including a scientific article. The aim is to study and describe the first sentence in articles in various disciplines in the Latvian language to establish the connections between the recommendations on how to start the text and the actual language material. For the aim’s implementation, sentences from 848 scientific articles in Latvian (a total of 9700-word usage) are analyzed. The articles chosen for the study have been published between 2008 and 2018 in three branches and sub-branches of science: medical and health sciences, social sciences, humanities and arts. The main conclusions are as follows: the authors of Latvian scientific articles most often choose in the first sentence 1) to make a statement, 2) indicate the historical or geographical context, 3) define the main term used in the article. This is partly consistent with the suggestions given by writing instructors on the possible attractive content of the first sentence.

Asymptotics of the Sum of a Sine Series with a Convex Slowly Varying Sequence of Coefficients

We study the asymptotic behavior in a neighborhood of zero of the sum of a sine series g(b,x)=∑k=1∞bksinkx whose coefficients constitute a convex slowly varying sequence b. The main term of the asymptotics of the sum of such a series was obtained by Aljančić, Bojanić, and Tomić. To estimate the deviation of g(b,x) from the main term of its asymptotics bm(x)/x, m(x)=[π/x], Telyakovskiĭ used the piecewise-continuous function σ(b,x)=x∑k=1m(x)−1k2(bk−bk+1). He showed that the difference g(b,x)−bm(x)/x in some neighborhood of zero admits a two-sided estimate in terms of the function σ(b,x) with absolute constants independent of b. Earlier, the author found the sharp values of these constants. In the present paper, the asymptotics of the function g(b,x) on the class of convex slowly varying sequences in the regular case is obtained.

Asymptotic soliton-like solutions to the Benjamin–Bona–Mahony equation with variable coefficients and a strong singularity

The paper deals with constructing an asymptotic one-phase soliton-like solution to the Benjamin--Bona--Mahony equation with variable coefficients and a strong singularity making use of the non-linear WKB technique. The influence of the small-parameter value on the structure and the qualitative properties of the asymptotic solution, as well as the accuracy with which the solution satisfies the considerable equation, have been analyzed. It was demonstrated that due to the strong singularity, it is possible to write explicitly not only the main term of the asymptotics but at least its first-order term.

The fourth moment of derivatives of Dirichlet L-functions in function fields

We obtain the asymptotic main term of moments of arbitrary derivatives of L-functions in the function field setting. Specifically, we obtain the first, second, and mixed fourth moments. The average is taken over all non-trivial characters of a prime modulus $$Q \in {\mathbb {F}}_q [T]$$ Q ∈ F q [ T ] , and the asymptotic limit is as $${{\,\mathrm{deg}\,}}Q \longrightarrow \infty $$ deg Q ⟶ ∞ . This extends the work of Tamam who obtained the asymptotic main term of low moments of L-functions, without derivatives, in the function field setting. It is also the function field q-analogue of the work of Conrey, who obtained the fourth moment of derivatives of the Riemann zeta-function.

Asymptotic stepwise solutions of the Korteweg--de Vries equation with a singular perturbation and their accuracy

The paper deals with the Korteweg-de Vries equation with variable coefficients and a small parameter at the highest derivative. The asymptotic step-like solution to the equation is obtained by the non-linear WKB technique. An algorithm of constructing the higher terms of the asymptotic step-like solutions is presented. The theorem on the accuracy of the higher asymptotic approximations is proven. The proposed technique is demonstrated by example of the equation with given variable coefficients. The main term and the first asymptotic approximation of the given example are found, their analysis is done and statement of the approximate solutions accuracy is presented.

Asymptotic analysis of the Korteweg-de Vries equation by the nonlinear WKB technique

The paper deals with the Korteweg-de Vries equation with variable coefficients and a small parameter at the highest derivative. The non-linear WKB technique has been used to construct the asymptotic step-like solution to the equation. Such a solution contains regular and singular parts of the asymptotics. The regular part of the solution describes the background of the wave process, while its singular part reflects specific features associated with soliton properties. The singular part of the searched asymp\-totic solution has the main term that, like the soliton solution, is the quickly decreasing function of the phase variable $\tau$. In contrast, other terms do not possess this property. An algorithm of constructing asymptotic step-like solutions to the singularly perturbed Korteweg--de Vries equation with variable coefficients is presented. In some sense, the constructed asymptotic solution is similar to the soliton solution to the Korteweg-de Vries equation $u_t+uu_x+u_{xxx}=0$. Statement on the accuracy of the main term of the asymptotic solution is proven.

Synonyms in the texts of laws (based on Russian laws)

The paper considers the issues of the use of synonyms in the texts of Russian laws. The re-search materials are the texts of federal and regional laws, expert practice. It is noted that syn-onymy, despite the requirement for the unification of legal terminology, is also characteristic of legislative texts. At the same time, synonyms are used not to exclude repetitions of the same words but for the sake of completeness, accuracy, clarity of the transfer of legal mean-ing. Legal synonyms are an integral genre and stylistic feature of the legislative text. Synonyms perform informative, pragmatic, text-forming, and other functions. There are some trends in the use of synonyms in the laws. Preference is given to one or another word from the synonymous series. The choice depends on the subject of the law, aspects of legal regulation, with the chosen synonym not always being stylistically neutral, devoid of evaluative seman-tics. Some terms are used not as synonyms but exclusively in terms of generic relationship. Paronyms may be used as synonyms. Frequent joint (contact) use of synonyms occurs when an additional (qualifying) term is given in brackets after the main term. Such synonyms are characterized by semantic and stylistic differences, the ratio of meanings, and integrated con-tent. A special clause on the equivalence of terms may be made in the law. However, the context always reveals the semantic difference of “equivalent” terms, their semantic shades. The methods and principles of analysis are traditional for Russian studies and legal linguis-tics: discursive, genre-stylistic, lexical-semantic, comparative, statistical, etc.

On the error term of a lattice counting problem, II

Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl’s bound for exponential sums of polynomials and a device due to Popov allowing us to get an improved main term in the sums of certain fractional parts of polynomials.

Potential of the Idea of Collegiality in Intercultural Interaction

The article’s goal is to study the idea of collegiality in order to find out whether or not it can be used as a possible cultural principle for the dialogue of cultures. The culture of the dialogue of cultures as the main term of possible dialogue has many options. One of them can be the idea of collegiality, which was developed by Russian religious philosophers since the value of a theory does not depend on the time of its creation. This implies the possibility of reconstructing previous concepts in theory and actualizing them creatively in the modern social context.