WORD-FORMATION MEANS OF VERBALIZITION OF CONCEPTS "PERSISTENCE" AND "STUBBORNNESS" IN THE RUSSIAN LANGUAGE

This article is devoted to the analysis of word-formation means of objectification of spiritual concepts “persistence” and “stubbornness” in the Russian language. The study of semantic features, derivational relations between lexical units in word-formation nests allows us to identify several cognitive features of the studied concepts. Comparative analysis shows similarities and differences between concepts “persistence” and “stubbornness” in terms of the word-formation means of their representation. The similarities lie in the fact that units in both word-formation nests are expressing “action, behavior” and “sign, property”. The differences are manifested in the fact that the word-formation field of the concept of "persistence" is characterized by metaphorical motivating connections in terms of describing the object, and the features of the representation of the concept of "stubbornness" in the word-formation aspect are mainly manifested in productivity in terms of the formation of verbs, in indicating the carrier of the property, and also in the high degree of its representation.

Alternating sign and sign-restricted matrices: representations and partial orders

Sign-restricted matrices (SRMs) are $(0, \pm 1)$-matrices where, ignoring 0's, the signs in each column alternate beginning with a $+1$ and all partial row sums are nonnegative. The most investigated of these matrices are the alternating sign matrices (ASMs), where the rows also have the alternating sign property, and all row and column sums equal 1. We introduce monotone triangles to represent SRMs and investigate some of their properties and connections to certain polytopes. We also investigate two partial orders for ASMs related to their patterns alternating cycles and show a number of combinatorial properties of these orders.

From graph topology to ODE models for gene regulatory networks

A gene regulatory network can be described at a high level by a directed graph with signed edges, and at a more detailed level by a system of ordinary differential equations (ODEs). The former qualitatively models the causal regulatory interactions between ordered pairs of genes, while the latter quantitatively models the time-varying concentrations of mRNA and proteins. This paper clarifies the connection between the two types of models.We propose a property, called the constant sign property, for a general class of ODE models. The constant sign property characterizes the set of conditions (system parameters, external signals, or internal states) under which an ODE model is consistent with a signed, directed graph. If the constant sign property for an ODE model holds globally for all conditions, then the ODE model has a single signed, directed graph. If the constant sign property for an ODE model only holds locally, which may be more typical, then the ODE model corresponds to different graphs under different sets of conditions. In addition, two versions of constant sign property are given and a relationship between them is proved.As an example, the ODE models that capture the effect of cis-regulatory elements involving protein complex binding, based on the model in the GeneNetWeaver source code, are described in detail and shown to satisfy the global constant sign property with a unique consistent gene regulatory graph. Even a single gene regulatory graph is shown to have many ODE models of GeneNetWeaver type consistent with it due to combinatorial complexity and continuous parameters.Finally the question of how closely data generated by one ODE model can be fit by another ODE model is explored. It is observed that the fit is better if the two models come from the same graph.

A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws

This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with a suitable numerical diffusion operator that based on a fourth order non-oscillatory reconstruction which satisfies the sign property. The constructed scheme possesses two features: (1) it achieves fourth order accuracy in the smooth area while keeping high resolution with sharp discontinuity transitions in the nonsmooth area; (2) it is entropy stable. Some typical numerical experiments are performed to illustrate the capability of the new entropy stable scheme.

Entropy stable essentially nonoscillatory methods based on RBF reconstruction

To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second order finite volume method (RBF-EFV2) for one-dimensional problems. Thus, we show that methods based on radial basis functions are as powerful as methods based on polynomial reconstruction. The main contribution is the construction of an algorithm and a smoothness indicator that ensures an interpolation function which fulfills the sign-property on general one dimensional grids.

Onη-Upper Sign Property and Upper Sign Continuity and Their Applications in Equilibrium-Like Problems

We first introduce the notion ofη-upper sign property which is an extension of the upper sign property introduced in Castellani and Giuli, 2013, by relaxing convexity on the set. Afterwards, we establish a link between the solution sets of local dual equilibrium problem (Minty local equilibrium problem) and equilibrium problem for mappings whose domains are not necessarily convex by relaxing the upper sign continuity on the map, as it is assumed in the literature (Bianchi and Pini, 2005; Castellani and Giuli, 2013; Farajzadeh and Zafarani, 2010). Accordingly, it allows us to extend and obtain some existence results for equilibrium-like problems.