A Systematic Approach for the Agricultural Sector

A rigorous description of the systematic approach to the most developed ergatic systems and a unified procedure for the study and construction of systems based on general systemic principles and postulates are presented. The adaptation of the general procedure for the systemic approach for the agricultural sector and its application to the analysis of the implemented programs of digitalization of agriculture are provided.

Center Bifurcation in the Lozi Map

We consider the well-known Lozi map, which is a 2D piecewise linear map depending on two parameters. This map can be considered as a piecewise linear analog of the Hénon map, allowing to simplify the rigorous proof of the existence of a chaotic attractor. The related parameter values belong to a part of the parameter plane where the map has two saddle fixed points. In the present paper, we investigate a different part of the parameter plane, namely, the vicinity of the curve related to a center bifurcation of the fixed point. A distinguishing property of the Lozi map is that it is conservative at the parameter value corresponding to this bifurcation. As a result, the bifurcation structure close to the center bifurcation curve is quite complicated. In particular, an attracting fixed point (focus) can coexist with various attracting cycles, as well as with chaotic attractors, and the number of coexisting attractors increases as the parameter point approaches the center bifurcation curve. The main result of the present paper is related to the rigorous description of this bifurcation structure. Specifically, we obtain, in explicit form, the boundaries of the main periodicity regions associated with the pairs of complementary cycles with rotation number [Formula: see text]. Similar approach can be applied to other periodicity regions. Our study contributes also to the border collision bifurcation theory since the Lozi map is a particular case of the 2D border collision normal form.

Modeling of the Effective Permittivity of Open-Cell Ceramic Foams Inspired by Platonic Solids

Open-cell solid foams are rigid skeletons that are permeable to fluids, and they are used as direct heaters or thermal dissipaters in many industrial applications. Using susceptors, such as dielectric materials, for the skeleton and exposing them to microwaves is an efficient way of heating them. The heating performance depends on the permittivity of the skeleton. However, generating a rigorous description of the effective permittivity is challenging and requires an appropriate consideration of the complex skeletal foam morphology. In this study, we propose that Platonic solids act as building elements of the open-cell skeletal structures, which explains their effective permittivity. The new, simplistic geometrical relation thus derived is used along with electromagnetic wave propagation calculations of models that represent real foams to obtain a geometrical, parameter-free relation, which is based only on foam porosity and the material’s permittivity. The derived relation facilitates an efficient and reliable estimation of the effective permittivity of open-cell foams over a large range of porosity.

Quantifying the Differences Between Lexical Categories

The Cambridge grammar of the English language (HUDDLESTON; PULLUM, 2002) attempts to present a comprehensive and rigorous description of Modern Standard English. Much of the book is taken up with describing the properties of the various lexical categories, including determinative and pronoun. The distinction between these categories has been questioned by various authors in English (ABNEY, 1987; CROFT, 2001; HUDSON, 2004; MATTHEWS, 2014; POSTAL, 2014/1966; SOMMERSTEIN, 1972) and other languages (e.g., NAU, 2016). Here, I employ energy distance, a novel family of non-parametric statistics, to adjudicate between these positions. Following Crystal (1967), I binarily encode the features (has/doesn’t have feature) of the determinatives and pronouns from CGEL in a 138 word-forms by 232 features matrix. The results provide support for CGEL’s analysis (k-groups produces a 93% correspondence with CGEL’s categorization) and show that energy distance statistics applied to such matrices can help us adjudicate between competing lexical category analyses without resorting to methodological opportunism (CROFT, 2001).

Modeling the mechanics of growing epithelia with a bilayer plate theory

Epithelia, which consists of cell sheets lying on a substrate, are prevalent structures of multi-cellular organisms. The physical basis of epithelial morphogenesis has been intensely investigated in recent years. However, as 2D mechanics focused most attention, we still lack a rigorous description of how the mechanical interactions between the cell layer and its substrate can lead to 3D distortions. This work provides a complete description of epithelial mechanics using the most straightforward model of an epithelium: a thin elastic bilayer. We first provide experimental evidence in Drosophila tissues that localized alterations of the cell-substrate (the extracellular matrix) can lead to profound 3D shape changes in epithelia. We then develop an analytical model modifying the Foppl-von Karman equation with growth for bilayers. We provide a complete description of all contributions from biophysical characteristics of epithelia. We show how any localized inhomogeneity of stiffness or thickness drastically changes the bending process when the two layers grow differently. Comparison with finite-element simulations and experiments performed on Drosophila wing imaginal discs validate this approach for thin epithelia.

On singularities of solution of the elasticity system in a bounded domain with angular corner points

This paper aims to give a mathematically rigorous description of the corner singularities of the weak solutions for the plane linearized elasticity system in a bounded planar domain with angular corner points on the boundary. The qualitative properties of the solution including its regularity depend crucially on these corner points or such types of boundary conditions. In particular, the resulting expansion of the solutions of the underlying problem involves singular vector functions, inlines, depending on a certain parameter ξ

Introduction

This chapter outlines the story of superconductivity, which started at the beginning of the twentieth century, and describes major breakthroughs, such as the discovery of the Meissner effect and the isotope effect. Several important developments preceded the microscopic theory formulated by Bardeen, Cooper, and Schrieffer: the two-fluid model, London equations, and the Ginzburg–Landau theory. Formulation of the theory brought further progress, such as quasiparticle tunnelling and the Josephson effect, and the search for new mechanisms of superconductivity and novel materials such as high-Tc oxides and hydrides. The main excitations in normal solids, including phonons, polaronic states, plasmons, and magnons, are described. A rigorous description of the adiabatic method, the foundation of the theory of solids, is provided, and the electron–phonon interaction, renormalisation phenomena, and the dynamic polaronic effect are introduced. The Heisenberg model, the key ingredient of the theory of magnetism, is also described.

Quantile Jensen’s inequalities

Quantiles of random variable are crucial quantities that give more delicate information about distribution than mean and median and so on. We establish Jensen’s inequality for q-quantile ($q\geq 0.5$ q ≥ 0.5 ) of a random variable, which includes as a special case Merkle (Stat. Probab. Lett. 71(3):277–281, 2005) where Jensen’s inequality about median (i.e. $q= 0.5$ q = 0.5 ) was given. We also refine this inequality in the case where $q<0.5$ q < 0.5 . An application to the confidence interval of parameters in pivotal quantity is also considered by virtue of the rigorous description on the relationship between quantiles and intervals that have required probability.

Human Eye Optics within a Non-Euclidian Geometrical Approach and Some Implications in Vision Prosthetics Design

An analogy with our previously published theory on the ionospheric auroral gyroscope provides a new perspective in human eye optics. Based on cone cells’ real distribution, we model the human eye macula as a pseudospherical surface. This allows the rigorous description of the photoreceptor cell densities in the parafoveal zones modeled further by an optimized paving method. The hexagonal photoreceptors’ distribution has been optimally projected on the elliptical pseudosphere, thus designing a prosthetic array counting almost 7000 pixel points. Thanks to the high morphological similarities to a normal human retina, the visual prosthesis performance in camera-free systems might be significantly improved.