Conjugate Functions Research Articles

General theory of orthotropic shells. Part II

Modern mechanical engineering sets the tasks of calculating thin-walled structures that simultaneously combine sometimes mutually exclusive properties: lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of orthotropic materials and plastics seems quite justified.
 The article demonstrates the complex representation method of the equations of orthotropic shells general theory, which allowed in a complex form to significantly reduce the number of unknowns and the order of the system of diferential equations. A feature of the proposed technique for orthotropic shells is the appearance of complex conjugate unknown functions. Despite this, the proposed technique allows for a more compact representation of the equations, and in some cases it is even possible to calculate a complex conjugate function. In the case of axisymmetric deformation, this function vanishes, and in other cases the influence of the complex conjugate function can be neglected.
 Verification of the correctness of the proposed technique was demonstrated on a shallow orthotropic spherical shell of rotation under the action of a distributed load. In the limiting case, results were obtained for an isotropic shell as well.

Delineation of a lactococcal conjugation system reveals a restriction-modification evasion system.

Plasmid pUC11B is a 49.3-kb plasmid harboured by the fermented meat isolate Lactococcus lactis subsp. lactis UC11. Among other features, pUC11B encodes a pMRC01-like conjugation system and tetracycline-resistance. In this study, we demonstrate that this plasmid can be conjugated at high frequencies to recipient strains. Mutational analysis of the 22 genes encompassing the presumed pUC11B conjugation cluster revealed the presence of several genes with essential conjugation functions, as well as a gene, trsR, encoding a putative transcriptional repressor of this conjugation cluster. Furthermore, plasmid pUC11B encodes an anti-restriction protein, TrsAR, which facilitates higher conjugation frequencies when pUC11B is transferred into recipient strains containing Type II or Type III RM systems. These findings demonstrate how RM mechanisms can be circumvented when they act as a biological barrier for conjugation events.

Probabilistic assessment of drought stress vulnerability in grasslands of Xinjiang, China.

In the process of climate warming, drought has increased the vulnerability of ecosystems. Due to the extreme sensitivity of grasslands to drought, grassland drought stress vulnerability assessment has become a current issue to be addressed. First, correlation analysis was used to determine the characteristics of the normalized precipitation evapotranspiration index (SPEI) response of the grassland normalized difference vegetation index (NDVI) to multiscale drought stress (SPEI-1 ~ SPEI-24) in the study area. Then, the response of grassland vegetation to drought stress at different growth periods was modeled using conjugate function analysis. Conditional probabilities were used to explore the probability of NDVI decline to the lower percentile in grasslands under different levels of drought stress (moderate, severe and extreme drought) and to further analyze the differences in drought vulnerability across climate zones and grassland types. Finally, the main influencing factors of drought stress in grassland at different periods were identified. The results of the study showed that the spatial pattern of drought response time of grassland in Xinjiang had obvious seasonality, with an increasing trend from January to March and November to December in the nongrowing season and a decreasing trend from June to October in the growing season. August was the most vulnerable period for grassland drought stress, with the highest probability of grassland loss. When the grasslands experience a certain degree of loss, they develop strategies to mitigate the effects of drought stress, thereby decreasing the probability of falling into the lower percentile. Among them, the highest probability of drought vulnerability was found in semiarid grasslands, as well as in plains grasslands and alpine subalpine grasslands. In addition, the primary drivers of April and August were temperature, whereas for September, the most significant influencing factor was evapotranspiration. The results of the study will not only deepen our understanding of the dynamics of drought stress in grasslands under climate change but also provide a scientific basis for the management of grassland ecosystems in response to drought and the allocation of water in the future.

Fractals: The Secret Code of Creation

Fractals: The Secret Code of Creation

Preface

The 2022 International Conference on Mechanics and Applied Mathematics (MAM 2022) was successfully held in Guangzhou, China from November 18th-20th, 2022 (virtual conference). The conference is a leading international academic meeting and has the potential to bring new horizons and insights to the researchers and practitioners in the fields of mechanics and applied mathematics.The close relationship and interaction between mechanics and mathematics and the research activities on them has promoted the stable development of society and economy. MAM 2022 created an academic platform for scientific innovation, brought together experts, scholars, and scientists from all over the world to present their work and exchange information, promoted the industrial cooperation of academic achievements, and facilitated future business contacts among all the participants.The scope of the conference covered all areas of research in mechanics and applied mathematics, including Newtonian Mechanics, Explosion Mechanics, Elementary Algebraic Topology, Discrete Mathematics, Coupled Numerical Simulation, Mathematical Methods in Mechanics, etc. The conference brought together about 100 participants, primarily from China and India, but also from Malaysia, French, and other countries.A three-day program of the conference was divided into three sessions, including keynote speeches, oral presentations, and poster presentations. Each keynote speaker was given 30-40 minutes for keynote speeches and every presenter was given 10-15 minutes. Among them, Prof. Dr. Antti Rasila from Guangdong Technion-Israel Institute of Technology, China performed a keynote speech on the title: Conjugate Function Method and Numerical Conformal Mappings. He discussed the so-called conjugate function method, an algorithm based on properties of so-called conformal invariants, to obtain numerical representations of conformal mappings and its applications. Besides, he presented the basics of the algorithm, and discussed its potential applications related to various engineering problems, for example, stress analysis, crack propagation, inverse problems, and mesh generation. The insightful speeches of each keynote speakers triggered interesting discussions and a number of informal talks between all the participants.List of Committee member are available in this pdf.

Conjugation's Toolkit: the Roles of Nonstructural Proteins in Bacterial Sex.

Bacterial conjugation, a form of horizontal gene transfer, relies on a type 4 secretion system (T4SS) and a set of nonstructural genes that are closely linked. These nonstructural genes aid in the mobile lifestyle of conjugative elements but are not part of the T4SS apparatus for conjugative transfer, such as the membrane pore and relaxosome, or the plasmid maintenance and replication machineries. While these nonstructural genes are not essential for conjugation, they assist in core conjugative functions and mitigate the cellular burden on the host. This review compiles and categorizes known functions of nonstructural genes by the stage of conjugation they modulate: dormancy, transfer, and new host establishment. Themes include establishing a commensalistic relationship with the host, manipulating the host for efficient T4SS assembly and function and assisting in conjugative evasion of recipient cell immune functions. These genes, taken in a broad ecological context, play important roles in ensuring proper propagation of the conjugation system in a natural environment.

Symmetric matrix representations of truncated Toeplitz operators on finite dimensional spaces

In this paper, we answer an open conjecture concerning complex symmetric matrices and truncated Toeplitz operators. We study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particular, we determine necessary and sufficient conditions for when a symmetric matrix is the matrix representation of a truncated Toeplitz operator with respect to a given conjugation invariant orthonormal basis. We specialise our result to the case when the conjugation invariant orthonormal basis is a modified Clark basis. With this specialisation, we answer an open conjecture in the negative, and show not every unitary equivalence between a complex symmetric matrix and a truncated Toeplitz operator arises from modified Clark basis representations. We pose a new refined conjecture for how to realise a model theory for symmetric matrices through the use of truncated Toeplitz operators, and we show this conjecture is equivalent to a specified system of polynomial equations being satisfied.

Convex Optimization Problems on Differentiable Sets

Given a closed convex set in a Banach space , motivated by the continuity and Fréchet differentiability of introduced, respectively, in [D. Gale and V. Klee, Math. Scand., 7 (1959), pp. 379–391] and [X. Y. Zheng, SIAM J. Optim., 30 (2020), pp. 490–512], this paper considers the -differentiability, subdifferentiability, and Gâteaux differentiability of . Using the technique of variational analysis, it is proved that is -differentiable (resp., subdifferentiable or Gâteaux differentiable) if and only if for every continuous convex function with the corresponding constrained optimization problem is 2/ -order-well-posed solvable (resp., generalized well-posed solvable or weak well-posed solvable). It is also proved that if the conjugate function of a continuous convex function on is -differentiable on , then for every closed convex set in with the corresponding optimization problem is -order-well-posed solvable. As a byproduct, every constrained convex optimization problem with a strongly convex quadratic objective function is proved to be globally second-order-well-posed solvable. Our main results are new even in the case of finite dimensional spaces.

ГРАМАТИЧНІ ОСОБЛИВОСТІ ДІЄСЛІВ КЛАСИЧНОЇ ЯПОНСЬКОЇ МОВИ БУНҐО

Background. Classical bungo Japanese and modern Japanese languages have a number of differences that make it difficult, and in some cases impossible, for an untrained reader to understand a text written in the bungo style, even if the reader has a high level of modern Japanese. This makes it necessary to first familiarize yourself with the grammatical features of the classical Japanese language. Verbs in bungo texts are the most difficult element due to their grammatical differences with modern Japanese, which makes them the object of this study. Methods. The following methods were used: comparative – for comparing verbs in modern Japanese and classical; descriptive – for the description of conjugation rules and functions of auxiliary verbs. Results. The rules of conjugation of verbs in the classical Japanese language were formulated according to the bases of the verbs, examples are given in the form of tables. Examples of verbs in modern and classical Japanese are given, which refer to different conjugations, which complicates the perception of classical texts. After the analysis of literary works written in bungo style, the most common auxiliary verbs (suffixes) are singled out and the features of their use are outlined. The following suffixes have been highlighted: ～ず、～き、～けり、～ぬ、 ～つ、～たり、～り、～む、～けむ、～らむ、～らし、～まし、～べし、～めり、～なり. Such auxiliary verbs as ～ず、～たり、～べし, etc. exist in the modern Japanese language as well, but perform a narrower range of functions. Conclusions. Given the leading role of the verb in the system of the classical Japanese language bungo, the article only provides the list of the main verb suffixes and their functions, therefore, in further research, it is necessary to carry out a detailed analysis of less common verb suffixes, as well as grammatical features of other parts of the language. This will contribute to a deeper and more systematic understanding of bungo texts.

Cauchy Integral and Pluriharmonic Conjugate Functions on Banach Function Spaces

This paper establishes the boundedness of the Cauchy integral and the pluriharmonic conjugate functions on Banach function spaces. As a special case of our main result, we have the boundedness of the Cauchy integral and pluriharmonic conjugate functions on Morrey spaces.

Jackson-type theorem in the weak $L_{1}$-space

The weak $L_{1}$-space meets in many areas of mathematics. For example, the conjugate functions of Lebesgue integrable functions belong to the weak $L_{1}$-space. The difficulty of working with the weak $L_{1}$-space is that the weak $L_{1}$-space is not a normed space. Moreover, infinitely differentiable (even continuous) functions are not dense in this space. Due to this, the theory of approximation was not produced in this space. In the present paper, we introduced the concept of the modulus of continuity of the functions from the weak $L_{1}$-space, studied its properties, found a criterion for convergence to zero of the modulus of continuity of the function from the weak $L_{1}$-space, and proved in this space an analogue of the Jackson-type theorem.

Optimal control of higher-order retarded differential inclusions

The article investigates an optimal control problem described by retarded differential inclusions (DFIs) of higher order with endpoint constraints. In terms of the Euler-Lagrange type adjoint inclusions and the Hamiltonian, a sufficient optimality condition is derived for higher-order DFIs that have different forms in different time intervals depending on the delay parameter, which in the problem without delay, these two adjoint inclusions coincide. It is shown that the adjoint inclusion for the DFIs of the first order, defined in terms of locally conjugate mappings, coincides with the classical Euler-Lagrange inclusion. Thus, the obtained results are universal in the sense that sufficient optimality conditions can be formulated for a DFI of any order. At the end of the paper, problems with a high-order polyhedral DFIs and higher-order linear optimal control problems are considered, the optimality conditions of which are transformed into the Pontryagin maximum principle. Also, for high-order polyhedral optimization with delay, from the point of view of abstract economics, non-negative adjoint variables can be interpreted as the price of a resource.

Representation of exact trajectory solutions for chaotic one-dimensional maps in Schroder form

Purpose of the article is to illustrate the genesis, meaning and significance of the functional Schroder equation, introduced in the theory of iterations of rational functions, for the theory of deterministic chaos by analytical calculations of exact trajectory solutions, invariant densities and Lyapunov exponents of one-dimensional chaotic maps. We demonstrate the method for solving the functional Schroder equation for various chaotic maps by passing to a topologically conjugate mappings, for which finding the exact trajectory solution is a simpler mathematical procedure. Results of the analytical solution of the Schroder equation for 12 chaotic mappings of various types and the calculation of the corresponding expressions for exact trajectory solutions, invariant densities and Lyapunov exponents are presented. Conclusion is made about the methodological expediency of formulating and solving the Schroder equations by the study of the dynamics of one-dimensional chaotic mappings.

Stable strong duality for cone-constrained set-valued optimization problems: A perturbation approach

In this paper we consider a general set-valued otimimization problem of the model Winf F(x), s.t. x in X where $F\colon X\rightrightarrows Y\cup\{+\infty_{Y}\}$ is a proper mapping. The problem is then embed into a parametric problem and can be express as (P) $\mathop{\winf}\bigcup\limits_{x\in X}\Phi(x,0_Z)$ where $\Phi\colon X\times Z\rightrightarrows Y^\bullet$ is a proper set-valued {\it perturbation mapping} such that $ \Phi(x,0_Z) = F(x) $. A representation of the epigraph of the conjugate mapping $\Phi^\ast$ is established (Theorem 1) and it is used as the basic tool for establishing a general stable strong duality for the problem (P) (Theorem 3). As applications, the mentioned general strong duality result is then applied to a cone-constrained set-valued optimization problem (CSP) to derive three dual problems for (CSP): The Lagrange dual problem and two forms of Fenchel-Lagrange dual problems for (CSP). Consequently, three stable strong duality results for the three primal-dual pairs of problems are derived (Theorems 4 and 5), among them, one is entirely new while the others extend some known ones in the literature.

GENERAL THEORY OF ORTHOTROPIC SHELLS. PART I

Modern mechanical engineering sets the tasks of calculating thin-walled structures that simultaneously combine sometimes mutually exclusive properties: lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of orthotropic materials and plastics seems quite justified.The article demonstrates the complex representation method of the equations of the orthotropic shells general theory, which allowed in a complex form to significantly reduce the number of unknowns and the order of the system of differential equations. A feature of the proposed technique for orthotropic shells is the appearance of complex conjugate unknown functions. Despite this, the proposed technique allows for a more compact representation of the equations, and in some cases it is even possible to calculate a complex conjugate function. In the case of axisymmetric deformation, this function vanishes, and in other cases the influence of the complex conjugate function can be neglected.
 Verification of the correctness of the proposed technique was demonstrated on a shallow orthotropic spherical shell of rotation under the action of a distributed load. In the limiting case, results were obtained for an isotropic shell as well.

Influence of Part Size Error on the Characteristics of a Feeding Transmission Mechanisms based on a Conjugate Cam-Spatial Linkage

Reasonable size accuracy of the mechanical part may be a key for the design of the complex transmission mechanism; thus, it is very important to evaluate the size errors of each part. Taking the conjugate cam-spatial rank feeding transmission mechanism as an example, the functions, such as the near-dwelling, fast-forwarding, working feeding, slow-forwarding, far-dwelling, fast-returning, quick-feeding-back, and slow-returning, are realized with the appropriate conjugate cam governing equations. The analytical expressions of the conjugate cams and functions of the angular motion and angular velocity between the conjugate cam and crank are derived. Considering the real machining errors of part, a concept of parameter sensitivity is proposed, and the magnitude and direction of the influence of typical parameter errors on the mechanism motion transfer characteristics are evaluated by this concept. This method provides a reliable reference for the precision design of mechanical structure parameters.

Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior

In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter r and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes.

Robust TDOA localization based on maximum correntropy criterion with variable center

In this paper, we propose a new robust method for the time-difference-of-arrival (TDOA) localization of a source under non-line-of-sight (NLOS) conditions. According to the maximum correntropy criterion with variable center (MCC-VC), the method jointly estimates the source position together with the kernel center and bandwidth using the TDOA measurements. In particular, we formulate two optimization problems based on MCC-VC, one estimating the kernel center and bandwidth, and the other the source position. The first problem is solved by dividing it into two subproblems, which are further approximated by convex problems that can be easily solved by a convex optimization package. The second problem is also divided into two subproblems by invoking the property of the convex conjugate function, which is then solved iteratively by solving the two subproblems in an alternating manner for each iteration. The proposed method does not require any prior information on the NLOS errors, making it easy to apply. Both simulation and real experimental results show that the proposed method performs well in both sparse and dense NLOS environments.

Climatology of Nighttime Medium‐Scale Traveling Ionospheric Disturbances at Mid and Low Latitudes Observed by the DEMETER Satellite in the Topside Ionosphere During the Period 2005–2010

AbstractThermal ion measurements from the French Detection of Electro‐Magnetic Emissions Transmitted from Earthquake Regions micro‐satellite have been used to study the climatology of nighttime Medium‐scale traveling ionospheric disturbances (MSTIDs) in the topside ionosphere at 650 km altitude during the 6 years of the satellite operation, from 2005 to 2010. This period encompasses the declining phase of solar cycle 23, the deep solar minimum of 2008–2009 and the early rise of solar cycle 24. MSTIDs were detected from the quasi‐periodic variations of the density of the dominant ionospheric O+ ions. Mostly present between ∼15° and ∼40° invariant latitudes with a small number of events in equatorial regions, the MSTIDs exhibit, on the average, larger occurrence rates in the Southern hemisphere with a peak in the Eastern Pacific‐South America longitude sector. The dependence of MSTID activity on solar activity appears more complex than the previously reported simple anti‐correlation. In addition to year‐to‐year variations, our study has, in particular, put in evidence a noticeable hemispheric asymmetry in the seasonal variations during the deep solar minimum of 2008–2009. These statistical observations provide a remarkable observational support to the key role of sporadic Es layers and the conjugate mapping of the associated electric fields. Yet, improved theoretical and numerical models, taking into account the actual inter‐hemispheric differences of the seasonal and solar activity variations of thermospheric and ionospheric processes, are needed for a better understanding of the highly complex MSTID phenomena.

On Fiber Bundles and Quaternionic Slice Regular Functions

The papers (González-Cervantes in Adv Appl Clifford Algebras 31:55, 2021; González-Cervantes Complex Variables and Elliptic Equations 2021) are the first works to apply the theory of fiber bundles in the study of the quaternionic slice regular functions. The main goal of the present work is to extend the results given in González-Cervantes (2021), where the quaternionic right linear space of quaternionic slice regular functions was presented as the base space of a fiber bundle. When the quaternionic right linear space of quaternionic slice regular functions is associated to certain domains then this paper shows that the elements of total space, given in González-Cervantes (2021), are defined from a pair of harmonic functions and a pair of orthogonal vectors. Simplifying the computations presented in González-Cervantes (2021), where each element of the total space is formed by two pair of conjugate harmonic functions and a pair of orthogonal unit vectors. This work also gives some interpretations of the behavior of the zero sets of some quaternionic slice regular polynomials in terms of the theory of fiber bundles.