Periodic Points Research Articles

Highly parallelizable electronic transport calculations in periodic rhodium and copper nanostructures

We extend the highly-parallelizable open-source electronic transport code TRANSEC (Feldman et al 2014 Phys. Rev. B 90 035445; https://gitlab.com/computational-physics2/transec/) to perform real-space atomic-scale electronic transport calculations with periodic boundary conditions in the lateral dimensions. We demonstrate the use of TRANSEC in periodic Cu and Rh bulk structures and in large periodic Rh point contacts, in preparation to perform calculations of reflection probability across Rh grain boundaries.

Fixed point theorems for modified F-weak contractions via α-admissible mapping with application to periodic points

In (Fixed Point Theory Appl. 94:6, 2012), Wardowski introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalizes the Banach contraction principle. The aim of this paper is to introduce a modified -F-weak contractions with respect to a self-mapping on a metric space and to obtain fixed point results. Examples are provided to support results and concepts presented herein. As an application of our results, periodic point results for the F-contractions in metric spaces are proved.

Topology of attractors and periodic points

Topology of attractors and periodic points

СИНХРОНИЗАЦИЯ 2-ЦИКЛОВ ДЛЯ ТРЕХ МИГРАЦИОННО СВЯЗАННЫХ ПОПУЛЯЦИЙ

The work deals with investigation of the oscillation synchronization in a system of three populations, migration – related in a ring. The dynamics model represents a system of three identical logistic dissipatively interconnected mappings. The author has constructed a complete phase portrait of the model using qualitative methods of dynamic systems study. It is shown that there are several periodic points in the phase space, corresponding to synchronous and asynchronous cycles.

ОСОБЕННОСТИ СИНХРОНИЗАЦИИ ДИНАМИКИ ЧИСЛЕННОСТИ В СИСТЕМЕ ТРЕХ МИГРАЦИОННО СВЯЗАННЫХ ПОПУЛЯЦИЙ

The article is devoted to the study of oscillations (cycles) synchronization in a system of three populations coupled by migration in a circle. We consider a discrete time model of population dynamics, which is a system of three identical dissipatively connected logistic maps. One-dimensional bifurcation diagrams (trees) were constructed, supplemented with the capture index of the population numbers cycles phases at adjacent sites. We conducted numerical experiments that show phase multistability – the cycles coexistence with different phases. Using qualitative methods for studying dynamic systems, a complete phase portrait of the model is constructed, showing that in the phase space there are several periodic points corresponding to elements of synchronous (in-phase) and asynchronous (out-of-phase) cycles. The 2- and 3-cycle stability conditions are investigated. It is shown that these two cycles are represented by three options: 1) a fully synchronous regime, when the abundances in the three populations coincide at any point in time; 2) a partially synchronous regime, when abundances coincide only for two populations, 3) a non-synchronous (out-of-phase) regime, when all three numbers have different values. For a 2-cycle, the third regime is unstable, possible as part of a long transition process. We found that for the 3-cycle, besides to the synchronous and partially synchronous regime, it is possible a stable out-of-phase behavior of three populations. It is shown that stable and unstable periodic points lie on certain surfaces (invariant manifolds), which separate the areas of attraction for regimes with different degrees of phase synchronization.

Periodic Points, Stability, Bifurcations, and Transition to Chaos in Generalized Fractional Maps

This paper is a review of the recent advances in the investigation of the properties of generalized fractional maps. These maps are Volterra difference equations of the convolution type with power-law-like kernels. They include fractional and fractional difference maps of a constant or variable order. The main objective of this article is to describe the criteria of stability, equations defining periodic points and bifurcations, and transition to chaos that are common for all generalized fractional maps.

Dynamic Cluster Zoning of Arch Dam Deformation Considering Changing Working Conditions

Arch dam deformation has regional characteristics, and clustering is a common method of regional classification for arch dams. Traditional methods ignore the impact of dynamic changes in temperature and water level. Besides, the noise of deformation data is detrimental to mining potential information. The objective is to devise a dynamic cluster zoning method for arch dams, which considers the changing working conditions under the coupling of water level and temperature in this study. First, the deformation periods are classified by K‐means clustering, and the arch dam deformation series are denoised using a sparrow search algorithm‐optimized variational mode decomposition combined with wavelet threshold (SSA–VMD–WT) denoising method. The arch dam measuring points for different periods are then clustered. The engineering case study demonstrates that the SSA–VMD–WT denoising method improves the reliability of deformation data. The dynamic cluster zoning method reasonably describes the deformation regularity of the arch dam under different working conditions.

The incidence and risk factors of depression across six time points in the perinatal period: a prospective study in China.

Perinatal depression (PND) affects approximately 15%-20% of women. This study aimed to determine the incidence of PND and identify risk factors. A prospective study was conducted at the Affiliated People's Hospital of Ningbo University. The Edinburgh Postnatal Depression Scale (EPDS) was used to screen for PND. Classification models were constructed using Extreme Gradient Boosting (XGBoost), Logistic Regression (LR), Random Forest (RF), and Support Vector Machine (SVM), and the optimal model was selected. Between March 2019 and August 2021, a total of 485 participants completed all valid questionnaires. Depression was observed in 75 (15.5%), 47 (9.7%), 25 (5.2%), 94 (19.4%), 85 (17.5%), and 43 (8.9%) cases during the first trimester, the second trimester, the third trimester, 1 week postpartum, 6 months postpartum, and 12 months postpartum, respectively. During the prenatal period, factors such as monthly income, employment status, marital status, and thyroid function significantly impacted depression. Additionally, factors including monthly income, employment status, marital status, parity, and unintended pregnancy were found to affect the likelihood of developing postpartum depression. XGBoost was chosen for its accuracy (0.9097) and precision (0.9005) in predicting prenatal depression, as well as for its accuracy (0.9253) and precision (0.9523) in predicting postpartum depression. In conclusion, the incidence of depression varies throughout the perinatal period, with different factors influencing prenatal and postpartum depression.

Review of the research on the qualitative theory of differential equations at St. Petersburg University. II. Locally qualitative analysis of essentially nonlinear systems

This article is the second one in a series of articles devoted to a review of the results of scientific research that have been carried out at the Department of Differential Equations of St.Petersburg University over the past three decades and continue to be carried out at the present time. The first article talked about studies of stable periodic points of diffeomorphisms with homoclinic points and systems of differential equations with weakly hyperbolic invariant sets. This paper presents the results of locally qualitative analysis of essentially nonlinear systems in the neighbourhood of the zero solution, obtained by employees and graduates of the department. A system is said to be essentially nonlinear if the Taylor series expansion of its right-hand sides does not contain linear terms. The study of such systems, firstly, is complicated by a more complex picture of the behavior of solutions compared to quasilinear systems. Secondly, there are not even theoretical formulas for the general solution of a nonlinear first-approximation system, the presence of which is so helpful in the quasi-linear case. All this complicates analysis and significantly limits technical capabilities. Therefore, almost any new results and any new methods of working with such systems are of great interest. One of the most effective tools for working with essentially nonlinear systems turned out to be the logarithmic Lozinsky norms. In a sense, they are an analogue of the characteristic exponents (eigenvalues) used in the theory of quasilinear systems. Research conducted at the department has demonstrated the wide possibilities of using logarithmic norms in a wide variety of problems.

A new class of hybrid contractions with higher-order iterative Kirk's method for reckoning fixed points

<p>The concept of contraction mappings plays a significant role in mathematics, particularly in the study of fixed points and the existence of solutions for various equations. In this study, we described two types of enriched contractions: enriched $ F $-contraction and enriched $ F^{\prime } $-contraction associated with $ u $-fold averaged mapping, which are involved with Kirk's iterative technique with order $ u $. The contractions extracted from this paper generalized and unified many previously common super contractions. Furthermore, $ u $-fold averaged mappings can be seen as a more general form of both averaged mappings and double averaged mappings. Moreover, we demonstrated that the $ u $-fold averaged mapping with enriched contractions has a unique fixed point. Our work examined the necessary conditions for the $ u $-fold averaged mapping and weak enriched contractions to have equal sets of fixed points. Additionally, we illustrated that an appropriate Kirk's iterative algorithm can effectively approximate a fixed point of a $ u $-fold averaged mapping as well as the two enriched contractions. Also, we delved into the well-posedness, limit shadowing property, and Ulam-Hyers stability of the $ u $-fold averaged mapping. Furthermore, we established necessary conditions that guaranteed the periodic point property for each of the illustrated strengthened contractions. To underscore the generality of our findings, we presented several examples that aligned with comparable results found in the existing literature.</p>

ФУНКЦИОНАЛЬНЫЕ УРАВНЕНИЯ КАК МАТЕМАТИЧЕСКИЕ МОДЕЛИ ЗАДАЧ СОПРЯЖЕНИЯ С ЦИКЛИЧЕСКИМ СДВИГОМ НА СЛОЖНЫХ КРИВЫХ

The paper considers linear functional equations with a shift function having a nonzero derivative satisfying the Helder condition on an arbitrary piecewise smooth curve. Such equations are studied in connection with the theory of boundary value problems for analytical functions, which are a mathematical tool in the study of mathematical models of elasticity theory in which the conjugation conditions contain a boundary shift. The shift function acts cyclically on a set of simple curves forming a given curve, and except the ends of simple curves, there are no periodic points relative to the shift function. The purpose of the study is to find conditions for the existence and uniqueness of a solution (and in the case of non–uniqueness of the cardinality of the set of solutions) of such equations in the classes of Helder and primitive Lebesgue functions with a coefficient and the right part of the same classes.

Permutation of periodic points of Veech surfaces in $ \mathscr{H}(2) $

Permutation of periodic points of Veech surfaces in $ \mathscr{H}(2) $

On limit sets of simplest skew products defined on multidimensional cells

The purpose of this work is to describe two important types of limit sets of the most simple skew products of interval maps, the phase space of each of which is a compact n-dimensional cell (n ≥ 2): firstly, a non-wandering set and, secondly, ω-limit sets of trajectories. Methods. A method for investigating of a nonwandering set (new even for the two-dimensional case) is proposed, based on the use of the concept of C0-Ω-blow up in continuous closed interval maps, and the concept of C0-Ω-blow up introduced in the work in the family of continuous fibers maps. To describe the ω-limit sets, the technique of special series constructed for the trajectory and containing an information about its asymptotic behavior is used. Results. A complete description is given of the nonwandering set of the continuous simplest skew product of the interval maps, that is, a continuous skew product on a compact n-dimensional cell, the set of (least) periods of periodic points of which is bounded. The results obtained in the description of a nonwandering set are used in the study of ω-limit sets. The paper describes a topological structure of ω-limit sets of the maps under consideration. Sufficient conditions have been found under which the ω-limit set of the trajectory is a periodic orbit, as well as the necessary conditions for the existence of one-dimensional ω-limit sets. Conclusion. Further development of the C0-Ω-blow up technique in the family of maps in fibers will allow us to describe the structure of a nonwandering set of skew products of one-dimensional maps, in particular, with a closed set of periodic points defined on the simplest manifolds of arbitrary finite dimension. Further development of the theory of special divergent series constructed in the work will allow us to proceed to the description of ω-limit sets of arbitrary dimension d, where 2 ≤ d ≤ n - 1, n ≥ 3, in the simplest skew products.

Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model

This study investigates a structurally unstable synchronization phenomenon observed in the two-coupled Izhikevich neuron model. As the result of varying the system parameter in the region of parameter space close to where the unstable synchronization is observed, we find significant changes in the stability of its periodic motion. We derive a discrete-time dynamical system that is equivalent to the original model and reveal that the unstable synchronization in the continuous-time dynamical system is equivalent to border-collision bifurcations in the corresponding discrete-time system. Furthermore, we propose an objective function that can be used to obtain the parameter set at which the border-collision bifurcation occurs. The proposed objective function is numerically differentiable and can be solved using Newton’s method. We numerically generate a bifurcation diagram in the parameter plane, including the border-collision bifurcation sets. In the diagram, the border-collision bifurcation sets show a novel bifurcation structure that resembles the “strike-slip fault” observed in geology. This structure implies that, before and after the border-collision bifurcation occurs, the stability of the periodic point discontinuously changes in some cases but maintains in other cases. In addition, we demonstrate that a border-collision bifurcation set successively branches at distinct points. This behavior results in a tree-like structure being observed in the border-collision bifurcation diagram; we refer to this structure as a border-collision bifurcation tree. We observe that a periodic point disappears at the border-collision bifurcation in the discrete-time dynamical system and is simultaneously replaced by another periodic point; this phenomenon corresponds to a change in the firing order in the continuous-time dynamical system.

Superstructures over Cartesian products of orientation-preserving rough circle transformations

One of the constructions for obtaining flows on a manifold is building a superstructure over a cascade. In this case, the flow is non-singular, that is, it has no fixed points. C. Smale showed that superstructures over conjugate diffeomorphisms are topologically equivalent. The converse statement is not generally true, but under certain assumptions the conjugacy of diffeomorphisms is tantamount to equivalence of superstructures. Thus, J. Ikegami showed that the criterion works in the case when a diffeomorphism is given on a manifold whose fundamental group does not admit an epimorphism into the group Z . He also constructed examples of non-conjugate diffeomorphisms of a circle whose superstructures are equivalent. In the work of I. V. Golikova and O. V. Pochinka superstructures over diffeomorphisms of circles are examined. It is also proven in this paper that the complete invariant of the equivalence of superstructures over orientation-preserving diffeomorphisms is the equality of periods for periodic points generating their diffeomorphisms. For the other side, it is known from the result of A.G. Mayer that the coincidence of rotation numbers is also necessary for conjugacy of orientation-preserving diffeomorphisms. At the same time, superstructures over orientation-changing diffeomorphisms of circles are equivalent if and only if the corresponding diffeomorphisms of circles are topologically conjugate. Work of S. Kh. Zinina and P. I. Pochinka proved that superstructures over orientation-changing Cartesian products of diffeomorphisms of circles are equivalent if and only if the corresponding diffeomorphisms of tori are topologically conjugate. In this paper a classification result is obtained for superstructures over Cartesian products of orientation-preserving diffeomorphisms of circles.

Homoclinic points of symplectic partially hyperbolic systems with 2D centre

We consider a generic symplectic partially hyperbolic diffeomorphism close to direct/skew products of symplectic Anosov diffeomorphisms with area-preserving diffeomorphisms and prove that every hyperbolic periodic point has transverse homoclinic points.

Pain reduction as the main parameter for monitoring improvement in Health-Related Quality of Life (HRQoL) following endovascular treatment of Pelvic Congestion Syndrome (PCS)

The purpose of this study was to evaluate pain reduction as the main parameter for monitoring improvements in Health-Related Quality of Life (HRQoL) in a female patient following endovascular treatment of Pelvic Congestion Syndrome (PCS).A 38-year-old female patient with chronic intermittent, “dragging” abdominal pain, lasting more than two years, mainly in the lower abdomen, radiating to the sacral region, underwent SARS CoV-2 infection in October 2021, and COVID-19, which lasted 10 days. Eight months later, complaints of pain in the lower abdominal area, during the mentrual cycle, during prolonged standing, after sports activities and during and after intercourse, increased. The patient was compelled to begin diagnosis of these complaints due to the severe pain and concerns about whether she had contracted cancer of the cervix uteri. She was diagnosed on transvaginal ultrasound-Doppler and Angio-MR of the pelvic vessels with PCS. Treatment was undertaken at the Department of Vascular Surgery and Endovascular Interventions, St. John Paul II Hospital, Krakow, Poland. Intraoperatively, after confirmation through selective angiography, of previously diagnosed insufficiency of the left ovarian vein (LOV) and of the parametrial veins (PMV), the selective obliteration was performed with an adhesive dedicated to endovascular closure of veins and vascular malformations (Glubran2). The range of pain intensity, according to theVisual Analogue Scale (VAS), in Exam. 1 (before surgery), was in the premenstrual period (BM) 7.0 points, which increased during menstruation (DM) or after intense activity (AIA) to 8.0 points, and occasionally during and after intercourse even to 9.0 points. These values were very high, indicating that pain significantly affected the patient's quality of life. The extent of pain severity decreased significantly in Study 2 (two months after surgery) and Study 3 (four months after surgery) and was 2.0 points in the premenstrual period (BM), which increased only slightly during menstruation (DM) or after intense activity (AIA) to 3.0 points, and decreased again to 2.0 points during and after intercourse. The patient reported that the procedure significantly and positively affected her functioning in daily life, especially in caring for a young child, which is evidence of the achievement of HRQoL improvement.Endovascular treatment for Pelvic Congestion Syndrome (PCS) was effective in reducing pain and improving the Health-Related Quality of Life (HRQoL) of a patient with PCS.

DIA-based quantitative proteomic analysis of porcine endometrium in the peri-implantation phase

The 12th day of gestation is a critical period for embryo loss and the beginning of imminent implantation in sows. Data independent acquisition (DIA) technology is one of the high-throughput, high-resolution and reproducible proteomics technologies for large-scale digital qualitative and quantitative research. The aim of this study was to identify and characterize the protein abundance landscape of Yorkshire pig endometrium on the 12th day of pregnancy (P12) and estrous cycle (C12) using DIA proteomics. A total of 1251 differentially abundant proteins (DAPs) were identified, of which 882 were up-regulated and 369 were down-regulated at P12. Functional enrichment analysis showed that the identified proteins were related to metabolism, biosynthesis and signaling pathways. Three proteins were selected for Western blot (WB) validation and the results were consistent with the DIA data. Further combined with transcriptome data, fibrinogen like 2 (FGL2) and S100 calcium binding protein A8 (S100A8) were verified to be highly abundant in the P12 endometrial epithelium. In summary, there were significantly different abundance of proteome profiles in C12 and P12 endometrium, suggesting that DAPs are associated with changes in endometrial receptivity, which laid the foundation for further research on related regulatory mechanisms. SignificanceThe 12th day of gestation is an important point in the peri-implantation period of pigs, when the endometrium presents a receptive state under the stimulation of estrogen. DIA proteomics technology is an emerging protein identification technology in recent years, which can obtain protein information through comprehensive and unbiased scanning. In this study, DIA technology was used to characterize endometrial proteins in pigs during the peri-implantation period. The results showed that higher protein abundance was detected using the DIA technique, and some of these DAPs may be involved in regulating embryo implantation. This study will help to better reveal the related proteins involved in embryo implantation, and lay a foundation for further research on the mechanism of endometrial regulation of embryo implantation. Significance of the studyThe 12th day of gestation is an important point in the peri-implantation period of pigs, when the endometrium presents a receptive state under the stimulation of estrogen. DIA proteomics technology is an emerging protein identification technology in recent years, which can obtain protein information through comprehensive and unbiased scanning. In this study, DIA technology was used to characterize endometrial proteins in pigs during the peri-implantation period. The results showed that higher protein abundance was detected using the DIA technique, and some of these DAPs may be involved in regulating embryo implantation. This study will help to better reveal the related proteins involved in embryo implantation, and lay a foundation for further research on the mechanism of endometrial regulation of embryo implantation.

Algebraic properties of periodic points to the additive cellular automata

This paper characterizes the periodic points of additive cellular automata such as, arbitrary union and arbitrary intersection, relationship between periodic sets and existence of additive cellular automata with cardinality of periodic points one and two and existence for higher cardinality more than two

Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations

We introduce the concept of controlled extended Branciari quasi-b-metric spaces, as well as a Gq-implicit type mapping. Under this new space setting, we derive some new fixed points, periodic points, right and left Ulam–Hyers stability, right and left weak well-posed properties, and right and left weak limit shadowing results. Additionally, we use these findings to solve the fractional differential equations of a Riesz–Caputo type with integral anti-periodic boundary values, as well of nonlinear matrix equations. All ideas, results, and applications are properly illustrated with examples.