Diverse Multiple Lump Analytical Solutions for Ion Sound and Langmuir Waves

In this work, we study a time-fractional ion sound and Langmuir waves system (FISLWS) with Atangana–Baleanu derivative (ABD). We use a fractional ABD operator to transform our system into an ODE. We investigate multiwaves, periodic cross-kink, rational, and interaction solutions by the combination of rational, trigonometric, and various bilinear functions. Furthermore, 3D, 2D, and relevant contour plots are presented for the natural evolution of the gained solutions under the selection of proper parameters.

Set characterizations and convex extensions for geometric convex-hull proofs

In the present work, we consider Zuckerberg’s method for geometric convex-hull proofs introduced in Zuckerberg (Oper Res Lett 44(5):625–629, 2016). It has only been scarcely adopted in the literature so far, despite the great flexibility in designing algorithmic proofs for the completeness of polyhedral descriptions that it offers. We suspect that this is partly due to the rather heavy algebraic framework its original statement entails. This is why we present a much more lightweight and accessible approach to Zuckerberg’s proof technique, building on ideas from Gupte et al. (Discrete Optim 36:100569, 2020). We introduce the concept of set characterizations to replace the set-theoretic expressions needed in the original version and to facilitate the construction of algorithmic proof schemes. Along with this, we develop several different strategies to conduct Zuckerberg-type convex-hull proofs. Very importantly, we also show that our concept allows for a significant extension of Zuckerberg’s proof technique. While the original method was only applicable to 0/1-polytopes, our extended framework allows to treat arbitrary polyhedra and even general convex sets. We demonstrate this increase in expressive power by characterizing the convex hull of Boolean and bilinear functions over polytopal domains. All results are illustrated with indicative examples to underline the practical usefulness and wide applicability of our framework.

Cell Length Growth in the Fission Yeast Cell Cycle: Is It (Bi)linear or (Bi)exponential?

Fission yeast is commonly used as a model organism in eukaryotic cell growth studies. To describe the cells’ length growth patterns during the mitotic cycle, different models have been proposed previously as linear, exponential, bilinear and biexponential ones. The task of discriminating among these patterns is still challenging. Here, we have analyzed 298 individual cells altogether, namely from three different steady-state cultures (wild-type, wee1-50 mutant and pom1Δ mutant). We have concluded that in 190 cases (63.8%) the bilinear model was more adequate than either the linear or the exponential ones. These 190 cells were further examined by separately analyzing the linear segments of the best fitted bilinear models. Linear and exponential functions have been fitted to these growth segments to determine whether the previously fitted bilinear functions were really correct. The majority of these growth segments were found to be linear; nonetheless, a significant number of exponential ones were also detected. However, exponential ones occurred mainly in cases of rather short segments (<40 min), where there were not enough data for an accurate model fitting. By contrast, in long enough growth segments (≥40 min), linear patterns highly dominated over exponential ones, verifying that overall growth is probably bilinear.

DIFFERENTIAL EQUATIONS OF EQUILIBRIUM OF ELASTIC PERFECTLY PLASTIC CONTINUOUS MEDIUM FOR PLANE DEFORMATION IN CYLINDRICAL COORDINATES AT BILINEAR APPROXIMATION OF THE CLOSING EQUATIONS

The article considers the construction of differential equations of equilibrium in displacements for plane deformation of elastic perfectly plastic regarding shear deformations continuous medium and nonlinearly elastic continuous medium with respect to volumetric deformations with bilinear approximation of the closing equations, both regarding and regardless geometrical nonlinearity in a cylindrical coordinate system. Nonlinear diagrams of volumetric and shear deformation are approximated by bilinear functions. Proceeding from the assumption of independence, generally speaking, of volume and shear deformation from each other, five main cases of physical dependencies are considered, depending on the relative position of the break points of bilinear diagrams of volume and shear deformation. The construction of bilinear physical dependencies is based on the calculation of the secant moduli of volumetric and shear deformation. In this case, in the first section of the diagrams, the secant modulus of both volumetric and shear deformation is constant, while in the second section of the diagrams, the secant modulus of volumetric deformation is a function of volumetric deformation, and the secant shear modulus is a function of the intensity of shear deformations. Substituting the corresponding bilinear physical relations into the differential equations of equilibrium of a continuous medium, written both regardless and regarding geometrical nonlinearity, the resolving differential equations of equilibrium in displacements for plane deformation in a cylindrical coordinate system are received. The received differential equations of equilibrium in displacements in cylindrical coordinates can be applied in determining the stress-strain state of elastic perfectly plastic with respect to shear deformations continuous medium and nonlinearly elastic with respect to volumetric deformations continuous medium under conditions of plane deformation, both regarding and regardless geometrical nonlinearity, physical relations for which are approximated by bilinear functions.

Is mainstream LCA linear?

Purpose It is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity. Here we study the meaning of the term linear, and in relation to that, the question if LCA is indeed linear. Methods We explore the different meanings of the term linearity in the context of mathematical models. This leads to a distinction between linear functions, homogeneous functions, homogenous linear functions, bilinear functions, and multilinear functions. Each of them is defined in accessible terms and illustrated with examples. Results We analyze traditional, matrix-based, LCA, and conclude that LCA is not linear in any of the senses defined. Discussion and conclusions Despite the negative answer to the research question, there are many respects in which LCA can be regarded to be, at least to some extent, linear. We discuss a few of such cases. We also discuss a few practical implications for practitioners of LCA and for developers of new methods for LCI and LCIA.

MODEL OF INVESTMENT STRATEGIES IN CYBER SECURITY SYSTEMS OF TRANSPORT SITUATIONAL CENTERS

The actual task of finding the optimal strategy for control the procedure of mutual financial investments to the situation center for cyber security on transport. The aim of the work – the development of a model for a decision support system on the continuous mutual investment in a cyber security situational center, which differs from the existing ones by solving a bilinear differential quality game with several terminal surfaces. In order to achieve the goal there was used a discrete-approximation method for solving a bilinear differential quality game with dependent motions. Application of this method in the developed decision support system, unlike existing ones, gives concrete recommendations ft choosing control decisions in the investment process. The proposed model gives concrete recommendations at choosing strategies in the investment process at the creation of a protected situational center. In the course of the computational experiment, there was considered a new class of bilinear differential games that allowed adequately to describe the process of investing in cyber security means of situational transport centers in Kazakhstan and Ukraine. For the first time, there was proposed a model describing the process of mutual investment based on the solution of bilinear equations and a differential quality game with several terminal surfaces. Considered the peculiarity of the differential game on the example of mutual investment in the means of cyber security of the situational transport center. In this case, the right-hand side of the system of differential equations is represented in the form of bilinear functions with arbitrary coefficients. The model allows to predict the results of investment and to find strategies for managing the investment process in the protection and cyber security systems of the situational transport center.

A Discontinuous Finite Volume Element Method Based on Bilinear Trial Functions

We propose a discontinuous finite volume element (DFVE) method for second order elliptic and parabolic problems. Discontinuous bilinear functions are used as the trial functions. We give the stability analysis of this DFVE method and derive the optimal error estimates in the broken [Formula: see text]-norm. Specifically, the optimal [Formula: see text]-error is obtained for the first time for the bilinear DFVE methods solving elliptic and parabolic problems.