Metatext operator “to put it mildly”: the specificity of functionality

The object of this research is the introductory-modal phrase “to put it mildly”, viewed in pragmatic aspect. From the perspective of pragmatics, this phrase fulfills the function of metatext operator that forms the speaker's reflection towards their utterance. The unit “to put it mildly” is a typical meta-operator, as it includes a locutionary verb. The goal of this research is to determine the specificity of the phrase “to put it mildly” in carrying out the meta-operator function, as well as to establish its typical contexts and lexical compatibility. The research material was collected based on the Russian National Corpus using the method of continuous sampling. The author reveals that the phrase “to put it mildly” as a meta-operator combines two opposite functions: on the one hand, softens the extreme of the utterance, while on the other hand – enhances negative assessment of the fact of reality. Moreover, as the development of these functions, it acquires the ability to attribute the properties of contextual euphemism to the commented nomination. The indicated functional specificity is closely related to the lexical compatibility of meta-operator and the types of contexts. Most frequent contexts imply negation formed with the particle / prefix NOT. The lexical compatibility of meta-operator is predetermined by the aspects of speaker’s assessment of the facts of surrounding reality. The article describes most frequent aspects of such assessment. The acquired results may be applied in teaching Russian as a foreign language, as well as in lexicographic practice for creating metadata dictionary.

On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

On the rate of convergence for a class of Markovian queues with group services

There are many queuing systems that accept single arrivals, accumulate them and service only as a group. Examples of such systems exist in various areas of human life, from traffic of transport to processing requests on a computer network. Therefore, our study is actual. In this paper some class of finite Markovian queueing models with single arrivals and group services are studied. We considered the forward Kolmogorov system for corresponding class of Markov chains. The method of obtaining bounds of convergence on the rate via the notion of the logarithmic norm of a linear operator function is not applicable here. This approach gives sharp bounds for the situation of essentially non-negative matrix of the corresponding system, but in our case it does not hold. Here we use the method of differential inequalities to obtaining bounds on the rate of convergence to the limiting characteristics for the class of finite Markovian queueing models. We obtain bounds on the rate of convergence and compute the limiting characteristics for a specific non-stationary model too. Note the results can be successfully applied for modeling complex biological systems with possible single births and deaths of a group of particles.

Integrating Operator Function in Work Domain Analysis of Electric Grid Operations

The electric grid system is complex, and whether the failure of a subsystem can cascade through the whole system depends on the severity and the type of failures. Cascading failure analysis often uses Monte Carlo simulations to estimate the impacts to the system. Functional taxonomy can help researchers define the unexpected failures and events in the simulations systematically. Work domain analysis, a method in ecological interface design, describes a system at a functional level. Operators play an important role in electric grid operations, and understanding operators’ goals is crucial for modeling a cascading failure analysis. This paper describes an approach to integrate users’ goals (operator function) in the work domain analysis of electric grid operations. It can support not only the task analysis but also design affordances related to the goals, experience, and capabilities of users.

Electromagnetic Steklov eigenvalues: approximation analysis

We continue the work of [Camano, Lackner, Monk, SIAM J.\ Math.\ Anal., Vol.\ 49, No.\ 6, pp.\ 4376-4401 (2017)] on electromagnetic Steklov eigenvalues. The authors recognized that in general the eigenvalues due not correspond to the spectrum of a compact operator and hence proposed a modified eigenvalue problem with the desired properties. The present article considers the original and the modified electromagnetic Steklov eigenvalue problem. We cast the problems as eigenvalue problem for a holomorphic operator function $A(\cdot)$. We construct a ``test function operator function'' $T(\cdot)$ so that $A(\lambda)$ is weakly $T(\lambda)$-coercive for all suitable $\lambda$, i.e.\ $T(\lambda)^*A(\lambda)$ is a compact perturbation of a coercive operator. The construction of $T(\cdot)$ relies on a suitable decomposition of the function space into subspaces and an apt sign change on each subspace. For the approximation analysis, we apply the framework of T-compatible Galerkin approximations. For the modified problem, we prove that convenient commuting projection operators imply T-compatibility and hence convergence. For the original problem, we require the projection operators to satisfy an additional commutator property involving the tangential trace. The existence and construction of such projection operators remain open questions.

Inverse source problem for the abstract fractional differential equation

In a Banach space, the inverse source problem for a fractional differential equation with Caputo–Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements from D(A), and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator 𝐴 is a generator of positive and compact semigroup the uniqueness, existence and stability of the solution are proved.

MATHEMATICAL THEORY OF NORMAL WAVES IN AN OPEN METAL-DIELECTRIC REGULAR WAVEGUIDE OF ARBITRARY CROSS SECTION

The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found.