The Ramsey theory based approach to the phase transitions of the second order is suggested. The phase transitions of the second order are seen as switching of physical interactions/chemical bonds between the entities forming the primitive cell of the material. Such a switching is typical for a phase change materials. If the energy of the primitive cell is kept constant under the change in the spatial order of the chemical bonds, the phase transition of the second order takes place. The switching of interactions between the entities forming the primitive cell is accompanied by the breaking of the initial symmetry of the cell. The order parameter/the degree of ordering characterizing the ordering within the primitive cell is re-defined. The introduced degree of ordering quantifies ordering of links/interactions/chemical bonds between entities constituting the 2D lattice; whereas, the classical “Landau degree of order” quantifies the symmetry breaking under variation in spatial locations of these entities. The suggested approach is generalized easily for 3D primitive cells. Thermal capacity of the non-symmetrical phase is larger than that of the symmetrical phase. For the primitive cells built of six interacting entities, the Ramsey Theory predicts inevitable appearance of the unstable monochromatic triangles, when the links correspond to attraction or repulsion interactions. The situation becomes different for the primitive cells built of five interacting entities.

This paper presents an approach to the Timoshenko beam theory (TBT) using the finite difference method (FDM). The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. The model developed in this paper consisted of formulating differential equations with finite differences and introducing additional points at the beam’s ends and at positions of discontinuity (concentrated loads or moments, supports, hinges, springs, brutal change of stiffness, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends. Moreover, grid points with variable spacing were considered, the grid being uniform within beam segments. First-order, second-order, and vibration analyses of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis, vibration analysis). Finally, a direct time integration method (DTIM) was presented; the FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid.

This paper presents an approach to the Euler-Bernoulli beam theory (EBBT) using the finite difference method (FDM). The EBBT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally, the finite difference approximations are derived based on fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection curve; the FOPH is made for the fourth and third derivative of the deflection curve while the SOPH is made for its second and first derivative. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, the FOPH was made for all of the derivatives of the deflection curve, and additional points were introduced at the beam’s ends and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. First-order analysis, second-order analysis, and vibration analysis of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis). Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid. Further research will be needed to investigate polynomial refinements (higher-order polynomials such as fifth-order, sixth-order…) of the deflection curve; the polynomial refinements aimed to increase the accuracy, whereby non-centered finite difference approximations at beam’s ends and positions of discontinuity would be used.

This paper presents an approach to the Kirchhoff-Love plate theory (KLPT) using the finite difference method (FDM). The KLPT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally in the case of KLPT, the finite difference approximations are derived based on the fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection surface. The FOPH is made for the fourth and third derivative of the deflection surface while the SOPH is made for its second and first derivative; this leads to a 13-point stencil for the governing equation. In addition, the boundary conditions and not the governing equations are applied at the plate edges. In this paper, the FOPH was made for all of the derivatives of the deflection surface; this led to a 25-point stencil for the governing equation. Furthermore, additional nodes were introduced at plate edges and at positions of discontinuity (continuous supports/hinges, incorporated beams, stiffeners, brutal change of stiffness, etc.), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at the plate edges and to satisfy the boundary and continuity conditions. First-order analysis, second-order analysis, buckling analysis, and vibration analysis of plates were conducted with this model. Moreover, plates of varying thickness and plates with stiffeners were analyzed. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. In first-order, second-order, buckling, and vibration analyses of rectangular plates, the results obtained in this paper were in good agreement with those of well-established methods, and the accuracy was increased through a grid refinement.

This paper presents an exact solution to the Timoshenko beam theory (TBT) for first-order analysis, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory (EBBT) neglects shear deformations. Thus, the Euler–Bernoulli beam is a special case of the Timoshenko beam. The moment-curvature relationship is one of the governing equations of the EBBT, and closed-form expressions of efforts and deformations are available in the literature. However, neither an equivalent to the moment-curvature relationship of EBBT nor closed-form expressions of efforts and deformations can be found in the TBT. In this paper, a moment-shear force-curvature relationship, the equivalent in TBT of the moment-curvature relationship of EBBT, was presented. Based on this relationship, first-order and second-order analyses were conducted, and closed-form expressions of efforts and deformations were derived for various load cases. Furthermore, beam stability was analyzed and buckling loads were calculated. Finally, first-order and second-order element stiffness matrices were determined.

The Work Ability Index (WAI) is the most widely used questionnaire for the self-assessment of working ability. Because of its different applications, shorter versions, and widespread use in healthcare activities, it is worthwhile assessing its characteristics. The WAI was distributed online among the workers of a healthcare company; the results were compared with data contained in the workers' personal health records and with absence registers. 340 out of 575 workers (59.1%) participated; 6.5% of them reported poor work ability. Exploratory factor analysis indicated that the one-factor version best described the characteristics of the WAI. The scores of the complete WAI, the shorter form without the list of diseases, and the minimal one-item version (WAS) had equal distribution and were significantly correlated. The WAI score was inversely related to age and significantly lower in women than in men, but it was higher in night workers than in colleagues due to the probable effect of selective factors. The WAI score was also correlated with absenteeism, but no differences were found between males and females in the average number of absences, suggesting that cultural or emotional factors influence the self-rating of the WAI. Workers tended to overreport illnesses in the online survey compared to data collected during occupational health checks. Musculoskeletal disorders were the most frequently reported illnesses (53%). Psychiatric illnesses affected 21% of workers and had the greatest impact on work ability. Multilevel ergonomic and human factor intervention seems to be needed to recover the working capacity of healthcare workers.

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described.

For many engineering applications it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches length scale parameter have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modelling as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

Abstract: Background/Objectives: There are indications that the microbial composition of the maternal mucosal surfaces is associated with adverse events during pregnancy. The aim of this review is to investigate the link between vaginal microbiome alterations and gestational com-plications risk. Methods: This comprehensive literature review was performed using Medline and Scopus databases. The following search algorithm was used "Pregnancy Complications"[Mesh] AND (Vagin*) and after literature screening 44 studies were included in the final review. Results: The studies that were included investigated the association between vaginal microbial composi-tion and preterm birth, miscarriage, preeclampsia, ectopic pregnancy, gestational diabetes mellitus, chorioamnionitis and preterm premature rupture of membranes. In most of the studies, it was well established that increased microbial diversity is associated with these conditions. Also, the depletion of Lactobacillus species is linked to most of the gestational complication, while the increased relative abundance and especially L. crispatus may exerts a protective effect in favor of the pregnant woman. Several pathogenic taxa including Gardnerella, Prevotella, Sneathia, Bac-terial Vaginosis-Associated Bacteria-2, Atopobium and Megasphera seem to be correlated to higher maternal morbidity. Conclusions: Vaginal microbiome aberrations seem to have an as-sociation with pregnancy related adverse events, but more high-quality homogenous studies are necessary to reliably verify this link.

Abstract. This paper proposes a Second Order Terminal Sliding Mode (2TSM) approach to the trajectory tracking of Differential Drive Mobile Robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the inner most loop, tracks the robot’s velocity quantities; while a kinematic controller, at the outer most loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated and finite time convergence is guaranteed by the second order TSM manifold which involves higher order derivatives of the state variables, resulting in inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods.

To extend the calculation power of tensor analysis, we introduce four new definition of tensor calculations. Some useful tensor identities have been proved. We demonstrate the application of the tensor identities in continuum mechanics: momentum conservation law and deformation superposition.

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of \textit{"Higgs Boson like"} potentials among others.

By making periodic thru-holes in a suspended film, the phonon system can be modified. Motivated by the BCS theory, the technique -- so-called phonon engineering -- was applied to a metallic niobium sheet. It was found that its electrical resistance dropped to zero at 175 K, and the zero-resistance state persisted up to 290 K in the subsequent warming process. Despite the initial motivation, neither these high transition temperatures nor the phase transition with thermal hysteresis can be accounted for by the BCS theory. Therefore, we abandon the BCS theory. Instead, it turns out that the metallic holey sheet is partly oxidized to form a niobium-oxygen square lattice, which has points of resemblance to a copper-oxygen plane, the fundamental component of cuprate high-T_c superconductors. Therefore, the pairing mechanism underlying this study should be related to that of cuprate high-T_c superconductors, which we may not yet understand. In addition to the electrical results of zero resistance, the holey sheet exhibited a decrease in magnetization upon cooling, i.e., the Meissner effect. Moreover, the remnant magnetization was clearly detected at 300 K, which can only be attributed to persistent currents flowing in a superconducting sample. Thus, this study meets the established criteria for a conclusive demonstration of true superconductivity. Finally, the superconducting transition with the unambiguous thermal hysteresis is discussed. According to Halperin, Lubensky, and Ma, or HLM for short, any superconducting transition must always be first order with thermal hysteresis because of the intrinsic fluctuating magnetic field. The HLM theory is very compatible with the highly oriented system harboring two-dimensional superconductivity.

In inflationary cosmology the form of the potential is still an open problem. In this work, second-order effects of the inflationary potential are evaluated and related to the known formula for the primordial perturbations in a wide range of scales. We found effects that may help to unravel the unknown inflationary potential form and impose new constraints on the parameters that define this potential. In particular, we demonstrate here that even slight deviations in the inflaton potential can lead to significant differences in the calculated spectra if inflation persists for sufficiently long and the normal modes of perturbations are affected by these variations.

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equations x_n+1 =x_n-1y_n - 1, y_n+1 = y_n-1x_n - 1 n = 0,1,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

Considering the fault "N-1" checksum and the power flow, the single-phase power flow model is further transformed into a three-phase power flow model, and the asymmetry of the three-phase power flow is measured by the three-phase unbalance factor. The calculation model is linearized by the second-order cone relaxation and the Big-M method. At the same time, the load response and distribution network reconstruction are used to improve the reliability of the power supply network to cope with the power failure. The relationship between power supply capability and power flow constraints, main transformer capacity and distributed power parameters is analyzed by IEEE 33-node three-phase power distribution system. The feasibility of the proposed model and the accuracy of the second-order cone relaxation are verified by numerical examples, which provides a technical reference for distribution network planning.

The semi-logarithmic plot of the cumulative number of cases of epidemics resembles the response of a first-order systems for a step load. This similarity was utilized to develop a first order model that can be used for extracting information about the dynamics of infectious disease epidemics. The developed model was validated using COVID-19 data of China. It was also heuristically fitted to other 13 countries. Obtained results indicated that the model can reliably forecasts the number of infected person, epidemic growth speed towards steady-state condition (process time constant, T), and time to reach steady-state condition (4T). The developed model will help public health authorities in developing more effective control strategies of epidemics.

We deal with Ulam stability of second order periodic linear differential equations with periodic damping. Necessary and sufficient condition for the Ulam stability of second order periodic linear differential equations is obtained by giving an Ulam stability theorem and an Ulam instability theorem. These results extend the conclusions in relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is given.

Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate local variances in generic regression problems by using of kernel smoothers. The proposed schemes can be applied in multidimesional scenarios (not just for time series analysis) and easily in a multi-output framework, as well. Moreover, they allow the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even comparing with benchmark techniques. One of these experiment involves a real dataset analysis.

The first hyperpolarizability of graphene quantum dots (GQDs) suspended in water was determined using the hyper-Rayleigh scattering (HRS) technique. To the best of our knowledge, this is the first application of the HRS technique to characterize GQDs. Two commercial GQDs (Acqua-Cyan and Acqua-Green) with different compositions were studied. The HRS experiments were performed with an excitation laser at 1064 nm. The measured hyperpolarizabilities were (1.0±0.1) × 10^(-27) esu and (0.9±0.1) × 10^(-27) esu for Acqua-Cyan and Acqua-Green, respectively. The results were used to estimate the hyperpolarizability per nanosheet obtained by assuming that each GQDs has five nanosheets with 0.3 nm thickness. The two-level model, used to calculate the static hyperpolarizability per nanosheet, provides the values of (2.4±0.1) × 10^(-28) esu (Acqua-Cyan) and (0.5±0.1) × 10^(-28) esu (Aqua-Green). The origin of the nonlinearity is discussed on the basis of polarized resolved HRS experiments, and an electric quadrupolar behavior with a strong dependence on surface effects is found. The nontoxic characteristics and order of magnitude indicate that these GQDs may be useful for biological microscopy imaging.

Friction has long been an important issue in multibody dynamics. Static friction models apply appropriate regularization techniques to convert the stick inequality and the non-smooth stick-slip transition of Coulomb’s approach into a continuous and smooth function of the sliding velocity. However, a regularized friction force is not able to maintain long-term stick. That is why, dynamic friction models were developed in the last decades. The friction force depends herein not only on the sliding velocity but also on internal states. The probably best known representative, the LuGre friction model, is based on a fictitious bristle but realizes a too simple approximation. The recently published second order dynamic friction model describes the dynamics of a fictitious bristle more accurately. Its performance is compared here to stick-slip friction models, developed and launched not long ago by commercial multibody software packages.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

In this paper, a horizontally moving suspended mass pendulum base is designed and controlled using robust control theory. H infinity optimal loop shaping with first and second order desired loop shaping function controllers are used to improve the performance of the system using Matlab/Simulink Toolbox. Comparison of the H infinity optimal loop shaping with first and second order desired loop shaping function controllers for the proposed system have been done to track the desired angular position of the pendulum using step and sine wave input signals and a promising result has been obtained succesfully.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

Long-term safety of a nutraceutical combination based on agnus castus and magnolia extracts combined with soy isoflavones (SI) and lactobacilli, and effectiveness on vasomotor symptoms and sleep disorders in postmenopausal women, were assessed. A controlled study was carried-out in menopausal women comparing this nutraceutical combination (ESP group) with formulation containing isoflavones alone (C group), at the dosage recommended. Kuppermann index, PSQI, and SF-36 were determined at baseline, 3, 6 and 12 months. Endometrial thickness, mammary density and liver function were evaluated at baseline and after 12 months. 180 women (100 in ESP group and 80 in C group, mean age 55.5 years, in menopause for about 36 months) were enrolled in the study. At the treatment end, mammary density, endometrial thickness, and hepatic function did not show substantial differences between groups. Kuppermann index, and particularly hot flushes, were progressively and significantly decreased in frequency and severity during ESP versus C treatment. No adverse events were observed. Agnus castus and magnolia, combined with SI + lactobacilli, can effectively and safely be used in symptomatic postmenopausal women, mainly when quality of sleep is the most disturbing complaint. Endometrium, mammary glands and liver function, were unaffected after 12 months treatment.

We evaluate the nested sum $\sum_{a_{n - 1} = c}^{a_n } {\sum_{a_{n - 2} = c}^{a_{n - 1} } { \cdots \sum_{a_0 = c}^{a_1 } {x^{a_0 } } } }$ where $a_n$ and $c$ are any integers and $x$ is a real or complex variable. Consequently, we evaluate multiple sums involving the terms of a general second order sequence, the Horadam sequence (W_j (a, b; p, q)), defined for all non-negative integers j by the recurrence relation W₀ = a, W₁ = b; W_j = pW_j−1 − qW_j−2 (j≥2); where a, b, p and q are arbitrary complex numbers, with p ≠ 0, q ≠ 0.

Frequency, amplitude and phase information of the grid voltage are of great importance in constructing a robust controller structure for grid connected inverter systems. This paper presents a simple and robust approach for the instantaneous estimation of positive and negative sequence voltage components under distorted voltage conditions. A second order generalized integrator (SOGI) is used to filter the distorted voltage and to generate orthogonal voltage components for each of the three phases. These filtered and orthogonal components are used for instantaneous calculation of symmetrical components. The implemented method is frequency adaptive; the method is demonstrated and compared to a conventional phase locked loop (PLL) technique with both MATLAB/Simulink simulations and experiments utilizing the dSPACE ds1103 digital controller.

In this paper we introduce the Adomian decomposition method for a class of first order fuzzy dynamic equations on arbitrary time scales for existence of solutions. The results are provided with suitable numerical examples.

We demonstrate a compact 4x4 wavelength selective switch with 50 % fewer electrical pads as compared with our previous generation. We report loss and crosstalk for different paths of the switch. We measure median loss of 5.32 dB and worst case crosstalk of -35 dB. The microring resonators tune by more than one free spectral range, which is an improvement over our previous generation of switches. This switch can support 8 channels at 400 GHz spacing. We conclude that it is not possible to drive both microring resonators with the same voltage and separate control is required because of fabrication variation of the current technology.

This paper presents an observer-based dynamic output feedback controller design procedure using Linear Matrix Inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state feedback gains, and observer gains are coupled into a dynamic output feedback optimal controller. The LMI set used in the two stages is matrix inversion-free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case.

Exercising surds to represent figures is a common practice in scientific and Engineering fields, especially in scripts where calculators are banned or unapproachable. Peter Chew Theorem make result becomes simple when dealing with converting Quadratic Surds. The substance of the Peter Chew Theorem lies in enabling the forthcoming generation to simple break problems related to Quadratic Surds more effectively, easing a direct comparison with contemporary results. By employing the Peter Chew Theorem, one can streamline the tutoring and literacy of math, particularly concerning second- order direct equations with constant portions. This theorem's objective aligns with Albert Einstein's famed quotation Everything should be made as simple as possible, but not simpler.

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

This study examines the bias in weighted least absolute deviation (WL1) estimation within the context of stationary first-order bifurcating autoregressive (BAR(1)) models, which are frequently employed to analyze binary tree-like data, including applications in cell lineage studies. Initial findings indicate that WL1 estimators can demonstrate substantial and problematic biases, especially when small to moderate sample sizes. The autoregressive parameter and the correlation between model errors influence the volume and direction of the bias. To address this issue, we propose two bootstrap-based bias-corrected estimators for the WL1 estimator. We conduct extensive simulations to assess the performance of these bias-corrected estimators. Our empirical findings demonstrate that these estimators effectively reduce the bias inherent in WL1 estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range.

A novel technique suitable for propulsion of small unmanned aerial vehicles (UAV) is discussed in this paper. This approach utilizes the rotational energy of airborne gyro rotors and converts it into translational propulsion for the vehicle. The energy conversion is achieved by generating precisely directed centrifugal force pulses through short-duration rotor unbalances. The accurate control of the timing and magnitude of these unbalances is crucial for successful propulsion generation. Our first-order theory of controlled unbalance propulsion (CUP) predicts the potential for achieving high translational accelerations and vehicle velocities up to orbital levels. Power saving levitation of UAVs can be attained. In this paper, we provide traceable evidence that pulsed centrifugal propulsion is based on well-established laws of physics and can be realized using state-of-the-art technologies.

Self-healing, stretchable and moldable hydrogels have a great potential application in tissue engineering and soft robotics. Despite great success in reported hydrogels, it is still a great challenge to construct the moldable hydrogels with an ultrafast self-healing performance. Herein, the dynamic double network (DN) composite hydrogels (PBLH) with ultrafast self-healing, stretchable and moldable were successfully constructed by poly (vinyl alcohol) (PVA), borate, ε-poly-L-lysine (EPL) and hyaluronic acid (HA) based on an efficient one-pot method. Fourier transform infrared spectroscopy, X-Ray diffraction and rheological measurements confirmed the formation of dynamic double networks among PVA, B, EPL and HA through the cross-linking of dynamic borate bonds, electrostatic interaction and hydrogen bonding. Having fabricated the dynamic double network structure, the damage gap of the composite hydrogels can heal within 1 min, presenting an excellent self-healing ability. Simultaneously, the DN hydrogels can be molded to various shapes and the length of the DN hydrogels can be stretched to 15 times than original length. In addition, the DN hydrogels exhibited an excellent antibacterial property against Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli). Our results illustrated that the DN composite hydrogels not only retain the advantages of traditional hydrogels, but also possess ultrafast self-healing, outstanding stretchable and antibacterial properties, presenting a prospective candidate for constructing biomedical materials.

Poplars (Populus spp.) are of significant ecological and economic importance. Long-term breeding efforts were aimed mainly at obtaining fast-growing and productive plants and less considered resistance to pests. This study aimed to identify the patterns of susceptibility to Saperda carcharias (Linnaeus, 1758) (Coleoptera: Cerambycidae) among Populus hybrids and pure species, considering crossing combinations and some other traits. In our research, 35 clones of poplar species and hybrids of the Ukrainian and foreign selection from the Aigeiros, Tacamahaca, and Leucoides sections were tested in 2021 and 2023 in the plantation created in 2014 in Eastern Ukraine. S. carcharias preferred infesting clones with earlier foliage development, larger diameters, and height increments. Specifically, hybrids with American maternal lineage showed the highest susceptibility, whereas those with European maternal lineage or Asian origin displayed lower infestation levels or resistance, respectively. This variability suggests a complex relationship between genetic background and pest resistance, underlining the need for a deeper understanding of the factors influencing susceptibility to S. carcharias. Selecting native species clones or creating mixed clone plantations could enhance the resilience of poplar plantations to pest threats.

Viruses have established symbiotic relationships with almost every other living organism on Earth and at all levels of biological organisation, from other viruses up to entire ecosystems. In most cases, peacefully coexisting with their hosts, but in most relevant cases, parasitising them and inducing diseases. Viruses are playing an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organisation, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as it occurs with temperatures separating phases in a liquid, define sharp qualitative types of behaviour. These {\em phase transitions} are very well known in Physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing to understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known examples of transition phenomena in virology and their simplest mathematical modelling approaches. We suggest that the advantages of abstract, simplified pictures used in Physics are also the key to properly understand the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across levels and their evolutionary and clinical implications are outlined.

High-performance motor drives that operate in harsh conditions require an accurate and robust angular position measurement to correctly estimate the speed and reduce the torque ripple produced by angular estimation error. For that reason, a resolver is used in motor drives as a position sensor due to its robustness. A resolver-to-digital converter (RDC) is an observer used to get the angular position from the resolver signals. Most RDCs are based on angle tracking observers (ATOs). On the other hand, generalized predictive control (GPC) has become a powerful tool in developing controllers and observers for industrial applications. However, no GPC-based RDC with zero steady-state error during constant speed operation was proposed. This paper proposes an RDC based on a second-order difference GPC (SOD-GPC). In SOD-GPC, the second-order difference operator is applied to design a GPC model with two embedded integrators. Thus, the SOD-GPC is used to design a type-II ATO whose steady-state angle estimation error tends to zero during constant speed operation. Simulation and experimental results prove that the proposed RDC system has better performance than other literature approaches.

In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.

Background/aims: Prior research identified a significant association between heart disease and metabolic dysfunction-associated liver steatohepatitis (MASLD), but the mechanisms are unclear. This study aims to search predictive biomarkers for grade I left ventricular diastolic dysfunction (LVDD), an early stage of heart failure (HF), in type 2 diabetes mellitus (T2DM) patients. Methods: This single-center, prospective observational study screened 73 T2DM patients for grade 1 LVDD and MASLD using 2D echocardiography, tissue analysis, spectral color Doppler, and Fibromax. Results: The study analyzed 50 patients (mean age 58±11.3 years) with a median diabetes duration of 7 years, abdominal obesity (mean BMI 34.4±5.9 kg/m2), and a mean HbA1c of 7.9±1.5%. The prevalence of grade I LVDD, fibrosis, mild steatosis, moderate to severe liver steatosis, mild MASLD, and moderate MASLD was 54%, 44%, 14%, 80%, 43%, and 34%, respectively. Regression analysis revealed that grade 1 LVDD was positively associated with age, Fibrotest, ɑ2-macroglobulin, epicardiac adipose tissue (EAT), and negatively associated with lateral s`, E wave, E/e`, E/A, medium E`, and septal e` (p&lt; 0.05 for all). ɑ2-macroglobulin &gt; 1.92 g/L (AUROC= 0.782, sensitivity 70.4%, specificity 81.2%) and fibrotest score &gt; 0.11 (AUROC 0.766, sensitivity 92.6%, specificity 56.2%) were significant predictors of grade I LVDD. Conclusion: HF is a multifaceted disorder associated with multisystem organ damage, including nonalcoholic MASLD. Although the underlying mechanisms remain unclear, innovative non-invasive biomarkers, such as ɑ2-macroglobulin or fibrotest, could concurrently indicate liver stiffness and the likelihood of grade I LVDD, an early, asymptomatic HF stage in T2DM patients.

In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.

In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

The Stirling engine is a simple type of external-combustion engine with an external combustion engine based on cyclic compression and expansion of gas at different temperature levels. It has high efficiency; low vibration levels, simple structure and can run on any combustible fuels. It has been the object of numerous studies. This paper presents an analysis of a Stirling engine model GENOA 03 for electric power generation, of 3 KW of nominal power with pressurized air as working fluid, currently under development. To improve its performance and ensure a good operational reliability, it is necessary to carry out a modelling of the engine in all its operating range. This requires complex numerical models that simulate the behaviour of any element of the engine in a cycle. Two typologies of thermodynamic models are developed in this work: isothermal and adiabatic. The main benefits and shortcomings of each model are mentioned. The geometry and conditions of the engine have been adapted through the Matlab ® tool, in order to obtain the operative conditions of the cooler that you want to replace, as well as an approximation to the expected behaviour.

The idealized rhombohedral unit cell of boron carbide is formed by a 12-atom icosahedron and a 3-atom linear chain. Phase transitions are second order and caused by the exchange of B and C sites or by vacancies in the structure. Nevertheless, the impact of such minimal structural changes on the properties can be significant. As the X-ray scattering cross sections of B and C atoms are very similar, the capability of X-ray fine structure investigation is restricted. Phonon spectroscopy helps closing this gap. Phase transitions known to date have been identified due to significant changes of properties: (1) The phase transition near the chemical composition B8C by clear change of the electronic structure; (2) The endothermic temperature-dependent phase transition at 712 K by the according change of specific heat; (3) The high-pressure phase transition at 33.2 GPa by the drastic change of optical appearance from opacity to transparency. These phase transitions affect IR- and Raman-active phonons and other solid-state properties. The phase transitions at B~8C and 712 K mean that a well-defined distorted structure is converted into another one each. In the high-pressure phase transition, an apparently well-defined distorted structure changes into a highly ordered one. In all these cases, the distribution of polar C atoms in the icosahedra plays a crucial role.

This article systematically studied the A-optimal designs of a high-order mixture central polynomial model, which is an advancement of the research results for the A-optimal design of the most recent third-order mixture central polynomial model and a more accurate response surface model. This article is based on the simplex center design, obtaining measurement values at various design points, and verifying them through the A-optimal equivalence theorem. We also compare the A-efficiency of designs through examples, which can be applied to the A-optimal precise design of the fourth-order mixture model.

Session-based recommendations which aim to predict subsequent user-item interaction based on historical user behavior during anonymous sessions can be challenging tasks. Two main challenges need to be addressed and improved: (1) How to analyze these sessions to accurately and completely capture users’ preferences, and (2) how to identify and eliminate any interference caused by noisy behavior. Existing methods have not adequately addressed these issues since they either neglected the valuable insight that can be gained from analyzing consecutive groups of items or failed to take these noisy data in sessions seriously and handled them properly, which can jointly impede recommendation systems from capturing users’ real intentions. To address these two problems, we designed a multi-order semantic denoising (MSD) model for session-based recommendations. Specifically, we grouped items of different lengths as varying multi-order semantic units to mine the user’s primary intention from multiple dimensions. Meanwhile, a novel denoising network was designed to alleviate the interference of noisy behavior and provide a more precise session representation. The result of extensive experiments on three real-world datasets demonstrated that the proposed MSD model exhibited improved performance compared with existing state-of-the-art methods in session-based recommendation.

We present a modified characteristic finite element method that exhibits second-order spatial accuracy for solving convection-reaction-diffusion equations on surfaces. The temporal direction adopted backward-Euler method, while the spatial direction employed surface finite element method. In contrast to regular domains, it is observed that the point in the characteristic direction traverses the surface only once within a brief time. Thus, the good approximation of the solution in the characteristic direction holds significant importance for the numerical scheme. In this regard, Taylor expansion is employed to reconstruct the solution beyond the surface in the characteristic direction. The stability of our scheme is then proved. A comparison is made with an existing characteristic finite element method based on face mesh. Numerical examples are provided to validate the effectiveness of our proposed method.

Integrating large-scale wind energy in modern power systems is demanding more efficient mathematical models to properly address classical assumptions in power system problems. In particular, there are two main assumptions in power system problems with wind integration that have not been adequately studied yet; First, non-linear AC power flow equations have been linearized in most of the literature. Such simplifications can lead to inaccurate power flow calculations that may result in other technical issues. Second, wind power uncertainties are inevitable and have been mostly modelled using the traditional uncertainty modelling approaches, that may not be suitable for large-scale wind power integration. In this paper, we address both challenges: we present a tight second-order conic relaxation (SOCR) for optimal power flow (OPF) problem, and simultaneously, implement the new effective budget of uncertainty approach for uncertainty modelling that determines the maximum wind power admissibility first and then addresses the uncertainty in the model. To the best of our knowledge, this is the first study that proposes an effective robust second-order conic programming (ERSOCP) model that simultaneously addresses the issues of power flow linearization and wind power uncertainty with the new paradigm on the budget of uncertainty approach. Our numerical results show the merit of the proposed model against traditional linearized power flow equations as well as traditional uncertainty modelling approaches.

Infection with human immunodeficiency virus (HIV) and induced acquired immune deficiency syndrome (AIDS) represent one of the greatest health burdens worldwide. The complex pathophysiological pathways that link highly active antiretroviral therapy (HAART) and HIV infection per se with dyslipidemia make the management of lipid disorders and the subsequent increase in cardiovascular risk essential for the treatment of people living with HIV (PLHIV). Amongst the HAART regimens, darunavir and atazanavir in terms of protease inhibitors, tenofovir disoproxil fumarate, nevirapine or rilpivirine in terms of nucleoside reverse transcriptase inhibitors and non-nucleoside reverse transcriptase inhibitors respectively, and especially integrase inhibitors, have demonstrated the most favorable lipid profile emerging as sustainable options in HAART substitution. To this day, statins remain the cornerstone pharmacotherapy for dyslipidemia in PLHIV, although important drug-drug interactions with different HAART agents should be taken into account upon treatment initiation. For those intolerant or not meeting therapeutic goals, the addition of ezetimibe, PCSK9, bempedoic acid, fibrates or fish oils should also be considered. This review summarizes the current literature on the multifactorial etiology and intricate pathophysiology of hyperlipidemia in PLHIV, with an emphasis on the role of different HAART agents, while also providing valuable insights into potential switching strategies and therapeutic options.

We study the deterministic dynamics of N point particles moving at constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback-control on the particles, inverting the horizontal component of their velocities, when their number in the channel exceeds a fixed threshold. Such a bounce--back mechanism is non-dissipative: it preserves volumes in phase space. An additional passive channel closes the billiard table forming a circuit in which a stationary current may flow. Under specific constraints on the geometry and on the initial conditions, the large N limit allows nonequilibrium phase transitions between homogeneous and inhomogeneous phases. The role of ergodicity in making a probabilistic theory applicable is discussed both for rational and irrational urns. The theoretical predictions are compared with the numerical simulation results. Connections with the dynamics of feedback-controlled biological systems are highlighted.

We show that the van der Waals gas does not exhibit just the celebrated liquid-gas 1 transition but also a quantum-classical one. We study the issue with reference to the LMC statistical 2 complexity and in relation to the order-disorder contrast.

Here, I present an alternate solution for the dark matter problem. I show that the stars of a galaxy’s arm attract each other with a force other than gravity, producing a chain of stars. We already have an abundance of data (ring and multiring galaxies) as proof for the existence of this strong stars’ chain. This attraction force does not end at the galaxy’s boundaries but gets deeper into the cosmos, and it may explain the dark-energy problem. This attraction force affects only stars and seems to have no effect on planets. I also offer a novel timeline order for the well-known galaxies using Hubble classification. I nominate entangled particles for the role that causes this phenomenon.

In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.

Background/Objectives: Chemerin, which is a multifunctional cytokine and adipokine, has been implicated in inflammatory and metabolic processes and might play a role in upper gastrointes-tinal (GI) malignancies, particularly gastric and esophageal cancer. The aim of this review is to explore the role of chemerin in the pathophysiology of upper GI cancers, as well as its potential as a biomarker for early detection and as a therapeutic target. Methods: A comprehensive review of recent studies about chemerin's biochemical properties and interaction with its receptors, as well as its effects on inflammatory responses, immune regulation and metabolic processes was con-ducted. Clinical implications of chemerin on gastric and esophageal cancer were analyzed, whereas the potential therapeutic strategies targeting chemerin were discussed. Results: Elevated chemerin levels are associated with poor prognosis in gastric cancer and promote invasiveness and metastasis in esophageal cancer. Chemerin receptor antagonists show promising results in inhibiting cancer cell migration, invasion and progression. Conclusions: Chemerin could repre-sent a valuable prognostic biomarker and therapeutic target for upper GI cancers. Future observa-tional studies should validate its clinical applications and investigate the efficacy of chemerin in-hibitors as potential therapeutic targets.

The climate change constitutes nowadays an enormous global threat for human health and environmental sustainability. The expanding world population and the increased global needs for food production have an important negative impact upon environment. Diet can link human health with environmental sustainability. Food production systems are closely related to anthropogenic greenhouse gas emissions and the aggravation of climate change, and current western type, animal-based, dietary patterns may lead to adverse environmental footprints. In the present narrative review, we address the interconnection of the Mediterranean diet (MD) with climate change and sustainability. MD is a highly recommended dietary intervention for the prevention and management of various endocrine and cardiometabolic diseases. Beyond its evidence-based, health-promoting effects, it also has beneficial environmental impact, reducing greenhouse gas emissions and enhancing biodiversity, food security and sustainability. Based on the evidence reviewed herein, MD should be incorporated within the framework of a “One Health” model, which involves the improvement not only of human health but also of planetary health and food system sustainability. Our review aims to provide a stimulus for health pro-fessionals to strongly recommend the implementation of MD under the current pressure of climate change, despite all barriers, targeting both human health preservation and the planetary well-being.

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

In this paper, we consider the problem that the maximal order consider the groups that consisting of transformations we called NG-Transformation on a nonempty set A has no bijection as its element. We find the order of these groups not greater that (n-1)!. In addition, we will prove our result by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A.

The relaxation process of lithium batteries caused by load variation is considered. It is shown that such processes have strong dependence on internal physical and chemical processes and battery technical conditions. Theoretical expressions of the relaxation process caused by a step-like load variation have been obtained for 1^st and 2^nd order equivalent electrical circuits. The experimental investigations show that the obtained models fit the real relaxation processes and the behavior of the identified parameters could be explained by specific features of physical and chemical processes within the lithium battery. It should be noted that the obtained results can be generalized for a different type of electrochemical power source. The proposed approach makes it possible to provide means for electrochemical power source characterization and diagnostic, the main advantages of which are good time localization of measurement procedures and inexpensive apparatus implementation.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

Background: Diagnostic accuracy of Parkinson’s disease (PD), a synucleinopathy, based on diagnostic criteria is suboptimal. A biomarker for synucleinopathies is pivotal both from a clinical and from a research aspect. CSF a-synuclein has been extensively studied over the past two decades as a candidate biomarker of synucleinopathies. Herein we present data on studies focusing on total, phosphorylated and oligomeric CSF a-synuclein in PD. Methods: Pubmed, Scopus and Web of Science were searched for studies with &gt;10 PD patients and control subjects, with data (mean, SD) on total, phosphorylated or oligomeric a-synuclein. Cohen’s d, as a measure of effect size, was calculated for all a-synuclein forms. Subgroup analysis and meta-regression were performed in an effort to explain between-study heterogeneity. Results: Thirty studies on total, six studies on oligomeric and one study on phosphorylated a-synuclein were included. Total a-synuclein was decreased and oligomeric a-synuclein increased in PD patients vs. controls. Effect size was medium for total and high for oligomeric a-synuclein. A-syn forms provided suboptimal combined sensitivity/specificity for the differentiation of PD from controls. There was significant between-study heterogeneity. PD cohort characteristics (sex, age, disease duration, UPDRS, H&amp;Y) and study characteristics (study design, healthy vs. neurological controls, control for CSF blood contamination, method of a-syn measurement) could not account for between-study heterogeneity. Publication bias was limited. Conclusions: CSF a-synuclein levels lack sufficient accuracy to be used as biomarkers for PD. Standardization of (pre)analytical variables may improve the discriminatory power of a-synuclein forms in the future.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

Transition metal dichalcogenides (TMDs) monolayers exhibit unique valleytronics properties due to the dependency of the coupled valley and spin state at the hexagonal corner of the first Brillouin zone. Precisely controlling valley spin-polarization via manipulating the electron population enables its application in valley-based memory or quantum technologies. This study uncovered the uncompensated spins of the antiferromagnetic oxide (NiO) serving as the ferromagnetic (FM) order to induce valley spin-polarization in molybdenum disulfide (MoS₂) monolayers via the magnetic proximity effect (MPE). A spin-resolved photoluminescence spectroscopy (SR-PL) was employed to observe MoS₂, where the spin-polarized trions appear to be responsible for the MPE, leading to a valley magnetism. Results indicate that local FM order from the uncompensated surface of NiO could successfully induce significant valley spin-polarization in MoS₂ with the depolarization temperature approximately at 100 K, which is relatively high compared to related literature. This study reveals new perspectives and potential of AFM materials in the field of exchange-coupled van der Waals heterostructures.

Existing scales assessing family relations are usually quite long. Our aim was to develop and validate the Family Functioning and Cohesion Scale (FFCS), a self-reported short instrument consisting of 14 items. The validation of the FFCS was based on its administration through an online platform to 481 subjects living in 46 different countries around the world. Cronbach's alpha was 0.85 (ranging from 0.83 to 0.86 if any one item was deleted), signifying high internal consistency. The scale can be considered as a sole factor based on its high consistency, while factor analysis produced three factors corresponding to “communication”, “anger/resentment/aggression” and “values and beliefs”. Test-retest reliability correlation coefficient was found to be 0.88 at a 2-week interval. As far as external validity is concerned, the correlation coefficient of the FFCS with the General Functioning subscale of the McMaster Family Assessment Device (FAD) was 0.83. The high measures of consistency, reliability, and validity of the FFCS, combined with its short length, make it an invaluable tool for use in research as well as in any professional dealing with families in the clinical fields of psychiatry, psychology, social work or any other relevant specialty.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

In a recent paper we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work we have kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that indeed a second order analysis will suffice, and higher order terms can be neglected.

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. In view of these empirical findings, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are explored.

Background: Contrast-induced acute kidney injury (CIAKI) is a common complication in hospital-acquired renal conditions, yet its pathogenesis remains unclear and effective treatments are limited. Intermedin (IMD), a peptide related to the calcitonin gene, exhibits vasodilatory and endothelial barrier-stabilizing effects via the calcitonin receptor-like receptor (CLR). However, the potential of IMD in mitigating CIAKI has not been thoroughly investigated. Aims: This study aimed to delineate the protective role of IMD in CIAKI through both in vitro and in vivo models, with a particular focus on elucidating the underlying mechanisms, specifically the cAMP/Rac1 signaling pathway. Methods: Human umbilical vein endothelial cells (HUVECs) were treated with iohexol to simulate kidney injury in vitro. The protective effects of IMD were evaluated using the CCK8 assay, flow cytometry, ELISA, and western blotting. A CIAKI rat model was developed to assess renal peritubular capillary endothelial cell injury and renal function using a range of techniques, including histopathology, immunohistochemistry, immunofluorescence, western blotting, and transmission electron microscopy. Results: In vitro, IMD significantly enhanced HUVEC viability and mitigated iohexol-induced toxicity by preserving intercellular adhesion junctions and activating the cAMP/Rac1 pathway. The protective effects of IMD were attenuated by Rac1 inhibition. In vivo, CIAKI caused considerable damage to peritubular capillary endothelial cell junctions, leading to impaired renal function. IMD treatment markedly improved renal function, an effect that was abolished by Rac1 inhibition. Conclusion: IMD protects against renal injury in CIAKI by activating the cAMP/Rac1 pathway, thereby preserving the integrity of peritubular capillary endothelial cells and mitigating acute renal injury induced by contrast media. These findings underscore the therapeutic potential of IMD in CIAKI and emphasize the critical role of the cAMP/Rac1 pathway in renal protection.

MicroRNAs (miRNAs), particularly miR-16 and miR-21, play a crucial role in mul-tiple myeloma (MM) pathogenesis by regulating gene expression. This study evalu-ated the prognostic significance of circulating miR-16 and miR-21 expression levels in 48 patients with MM at diagnosis treated with lenalidomide/dexamethasone (LD) compared with 15 healthy individuals (HI). All patients were treated with LD, 13 at first line and 35 at relapse, of whom 21 were tested twice at diagnosis and before LD initiation. The results revealed significantly lower levels of miR-16 and miR-21 in patients than in HIs, both at diagnosis and relapse, with decreased miR-16 levels at diagnosis, indicating improved overall survival (OS) (p value 0.024). Furthermore, miR-16 and miR-21 levels were associated with disease markers, while both corre-lated with the depth of response and mir-16 with sustained response to LD treatment. The ratios of both miR-16 and miR-21 expression levels (prior to LD treat-ment/diagnosis) below 2 predicted a shorter time to response (P = 0.027) and a longer time to next treatment (P = 0.042), respectively. These findings suggested a prognostic value for serum miR-16 and miR-21 levels in MM, as their expression levels corre-lated with disease variables and treatment outcomes.

Background/Objectives Gastroparesis, a chronic digestive disorder characterized by delayed gastric emptying, often results from diabetes, post-surgical complications, autoimmune diseases, and neurological disorders. In approximately 50% of cases, the cause is idiopathic gastroparesis (IGD). Recent studies suggest a link between chronic enteroviral infections and persistent gas-trointestinal symptoms, including delayed gastric emptying. This study investigates the effects of a silydianin-rich extract from Silybum marianum seeds on enteroviral infections in vitro and the mitigation of delayed gastric emptying in mice. Silydianin, a key bioactive compound known for its liver-protective and antioxidant properties, has not been extensively studied for its impact on enteroviral infections and gastroparesis; Methods NMR spectroscopy (¹H, ¹³C, and DEPT) identi-fied silydianin as the primary compound, with minor flavonolignans and trace amounts of an oxidation product. The study assessed the cytotoxicity and antiviral activity of the extract at various stages of the viral life cycle, including virucidal activity, cell protection, and post-infection effects, using neutral red assays in RD cells, with results confirmed by real-time PCR. The viruses studied included Coxsackievirus B2, Coxsackievirus A10, Poliovirus SL-1, and Enterovirus EV71. The impact on delayed gastric emptying was evaluated in a mouse model of gastroparesis using doses of 100 and 200 mg/kg compared to a control; Results: The silydianin-rich extract exhibited con-sistent antiviral activity, with the highest selectivity index (SI) for EV71 (4.08) during virucidal activity. It provided moderate cell protection, with EC50 values ranging from 120.88 to 186.10 µg/mL and SI values from 2.20 to 3.39. Post-infection treatment showed varying efficacy, with Coxsackie A10 demonstrating the highest SI (3.90). In vivo, the extract at 200 mg/kg significantly improved gastric emptying to 96.47% and slightly increased gastrointestinal transit from 50.33% to 61.46%; Conclusions These results suggest that silydianin may be effective in treating enteroviral infections and enhancing intestinal function, making it a promising candidate for gastroparesis treatment and warranting further research.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

The genetic code evolved by parallel tracks of chaotic and ordered processes. Liquid-liquid phase separation (hydrogels), a chaotic process, constructs diverse membraneless compartments within cells, resulting in regulated hydration and sequestration and concentration of reaction components. Hydrogels relate to chaotic amyloid fiber production. We propose that polyglycine and related hydrogels (i.e. GADV; G is glycine), phase separations, membraneless droplets and amyloid accretions organized protocell domains to drive the earliest evolution of the genetic code and the pre-life to cellular life transition. By contrast, evolution of tRNA, tRNAomes, aminoacyl-tRNA synthetases and translation systems followed highly ordered and systematic pathways, described by well-defined mechanisms and rules. The pathway of evolution of aminoacyl-tRNA synthetases, which tracked evolution of the genetic code, is clarified. Hydrogels and amyloids form a chaotic component, therefore, that complemented otherwise systematic processes. We describe with detail a pre-life world in which hydrogels and amyloids provided the selections of the first life.

Purpose: Perceptual learning and production practice are basic mechanisms that children depend on to acquire adult levels of speech accuracy. In this study, we examined perceptual learning and production practice as they contributed to changes in speech accuracy in three- and four-year-old children. Our primary focus was manipulating the order of perceptual learning and baseline production practice to better understand when and how these learning mechanisms interact. Method: Sixty-five typically-developing children between the ages of three and four were included in the study. Children were asked to produce CVCCVC nonwords like /bozjəm/ and /tʌvtʃəp/ that were described as the names of make-believe animals. All children completed two separate experimental blocks: a baseline block in which participants heard each nonword once and repeated it, and a test block in which the perceptual input frequency of each nonword varied between 1 and 10. Half of the participants completed a baseline-test order; half completed a test-baseline order. Results: Greater accuracy was observed for nonwords produced in the second experimental block, reflecting a production practice effect. Perceptual learning resulted in greater accuracy during the test for nonwords that participants heard 3 or more times. However, perceptual learning did not carry over to baseline productions in the test-baseline design, suggesting that it reflects a kind of temporary priming. Finally, a post hoc analysis suggested that the size of the production practice effect depended on the age of acquisition of the consonants that comprised the nonwords. Conclusions: The study provides new details about how perceptual learning and production practice interact with each other and with phonological aspects of the nonwords, resulting in complex effects on speech accuracy and learning of form-referent pairs. These findings may ultimately help speech-language pathologists maximize their clients’ improvement in therapy.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

This paperfocusesontheoscillatorypropertiesofthesemi-canonicalnonlineardelaydifferential equation ofthird-order (δ2(t)(δ1(t)ζ′(t))′)′ + η(t)ζα(τ(t))= 0, t ≥ t0, under theconditions ∞t01δ2(t)dt = ∞ andZ ∞t01δ1(t)dt < ∞. Using the new canonical transform method, we transformed the studied equation into a canonical type equation and then we find the conditions for the oscillation of the studied equation from the canonical equations. The obtained results are new and complement to the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

Initial periods of adsorption kinetics play an important role in estimating the initial adsorption rate and rate constant of adsorption process. Several adsorption processes rapidly occur, and the experimental data of adsorption kinetics under the initial periods can contain potential errors. The pseudo-second-order (PSO) kinetic model has been popularly applied in the field of adsorption. The use of the nonlinear optimization method to obtain the parameters of the PSO model can minimize error functions during modelling compared to the linear method. However, the nonlinear method has limitations in that it cannot directly recognize potential errors in the experimental points of time-dependent adsorption, especially under the initial periods. In this study, for the first time, the different linear types (Types 1–6) of the PSO model are applied to discover the error points under the initial periods. The result indicated that the fitting method using its linear equations (Types 2–5) is really helpful for identifying the error (doubtful) experimental points from the initial periods of adsorption kinetics. The imprecise points lead to low adjusted R2 (adj-R2), high reduced χ2 (red-χ2), and high Bayesian information criterion (BIC) values. After removing those points, the experimental data were adequately fitted with the PSO model. statistical analyses demonstrated that the nonlinear method must be used for modelling the PSO model because its red-χ2 and BIC were lower than the linear method. Type 1 has been extensively applied in the literature because of its very high adj-R2 (0.9999) and its excellent fitting to experimental points. However, its application should be limited because the potential errors from experimental points were not identified by this type. For comparison, the other kinetic models (i.e., pseudo-first-order, pseudo-nth-order, Avrami, and Elovich) are applied. The modelling result using the nonlinear forms of those models indicated that the fault experimental points from the initial periods were not detected.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

The higher-order interactions in complex systems are gaining attention. Extending the classic bounded confidence model where an agent’s opinion update is the average opinion of its peers, this paper proposes a higher-order version of the bounded confidence model. Each agent organizes a group opinion discussion among its peers. Then, the discussion’s result influences all participants’ opinions. Since an agent is also the peer of its peers, the agent actually participates in multiple group discussions. We assume the agent’s opinion update is the average over multiple group discussions. The opinion dynamics rules can be arbitrary in each discussion. In this work, we experiment with two discussion rules: centralized and decentralized. We show that the centralized rule is equivalent to the classic bounded confidence model. The decentralized rule, however, can promote opinion consensus. In need of modeling specific real-life scenarios, the higher-order bounded confidence is convenient to combine with other higher-order dynamics, from the contagion process to evolutionary dynamics.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Many real complex systems present multilayer structure where high-order metadata on one layer refers to dyadic data on a lower layer. Significant progresses to analyse high-order metadata under the assumption of community organization have been done. However, there are no planted communities in real-world networks, and the necessity of new frameworks to analyze high-order metadata regardless of community organization has been raised.Here, we propose to adopt hyperedge organization. Predicting ‘entanglements’ between a hyperedge and nodes scattered in the rest of the network might suggest structural or functional liaisons, without assumption of any community organization. We introduce a novel concept: hyperedge entanglement (HE), which associates to each hyperedge an entangled hyperedge, by means of a network operator that predicts significant ‘interactions at distance’ between network nodes and existing hyperedges. We also introduce a new challenge termed hyperedge entanglement prediction (HEP), and an algorithm to perform this task. We evaluated HEP performance on social, biological and synthetic data where, given only topology and hyperedges (such as communities or functional modules), the goal is to predict whether nodes not connected to a certain hyperedge might be candidates for a significant entanglement. Finally, as real application in diseasome systems biomedicine, we perform HEP on the human protein interactome to predict unknown gene entanglements with the COPD disease gene hyperedge. HEP predictions are validated by biological experiments, enlarging our understanding of molecular mechanisms behind COPD/aneurysm comorbidity.

This paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in W^m[0; 1] by multiscale orthonormal basis in W¹[0; 1]. We define approximate solution, and obtain the approximate solution of high-order BVPs by using the approximate theory. Moreover, the convergence and stability of the algorithm are improved. At last, several numerical experiments show the feasibility of the proposed method.

A premise of statistical learning research is that learners attend to and learn the frequencies of repeating or co-occurring elements in the input. When the input is a series of words, participants readily learn the frequencies of phoneme sequences, that is, to learn phonotactic frequencies. Inherent to the concepts of both frequency and phonotactics is order, or the temporal structure of the input. Order is similarly inherent to statistical learning, yet the effect of order on statistical learning is not well understood. In the present study, adult participants learned the relative frequencies of eight item-medial consonant sequences, for example, the /mk/ in /nʌmkət/. Across five ordering conditions, both familiarization and test stimuli were independently ordered and randomized, thus allowing for a relatively broad search for order effects in an established statistical learning paradigm. Participants learned the target frequencies equivalently across the five ordering conditions, indicating no modulating effect of order. Nevertheless, participants also approached the task by applying idiosyncratic, structured orders to their responses. The result is an unexpected but robust effect of order. Both the results and the design of the study also allow for increased integration of statistical learning with memory and other aspects of cognition.

Mass transfer restrictions of scaffolds are currently hindering the development of three-dimensional (3D), clinically viable, and tissue engineered constructs. For this situation, a 3D poly(lactide-co-glycolide)/hydroxyapatite porous scaffold, which was much favorable for transfer of nutrients to and waste products from the cells in the pores, was developed in this study. The 3D scaffold had an innovative structure, including macropores with diameters of 300−450 μm for cell ingrowth and microchannels with diameters of 2−4 μm for nutrition and waste exchange. The mechanical strength in wet state was strong enough to offer the structural support. The typical structure was more beneficial for the attachment, proliferation, and differentiation of rabbit bone marrow mesenchymal stem cells (rBMSCs). The alkaline phosphatase (ALP) activity and calcium (Ca) deposition were evaluated on the differentiation of rBMSCs, and the results indicated that the microchannel structure was very favorable for differentiating rBMSCs into maturing osteoblasts. For repairing rabbit radius defects in vivo, there was rapid healing in the defects treated with the 3D porous scaffold with microchannels, where the bridging by a large bony callus was observed at 12 weeks post-surgery. Based on the results, the 3D porous scaffold with microchannels was a promising candidate for bone defect repair.

Pulmonary arterial hypertension (PAH) is a chronic disease characterized by a progressive in-crease in mean pulmonary arterial pressure. Mutations in the BMPR2 and AQP1 genes have been described in familial PAH. The bone morphogenetic proteins BMP9 and BMP10 bind with high affinity to BMPR2. Administration of BMP9 has been proposed as a potential therapeutic strategy against PAH, although recent conflicting evidence dispute the effect of such practice. Considering the involvement of the above molecules in PAH onset, progression, and therapeutic value, we ex-amined the effects of modulation of BMP9, BMPR2, and AQP1 on BMP9, BMP10, BMPR2, AQP1, and TGFB1 expression in human pulmonary microvascular endothelial cells in vitro. Our results demonstrated that silencing the BMPR2 gene resulted in increased expression of its two main ligands, namely BMP9 and BMP10. Exogenous administration of BMP9 caused return of BMP10 to basal levels, while restored the decreased AQP1 protein levels and the decreased TGFB1 mRNA and protein expression levels caused by BMPR2 silencing. Moreover, AQP1 gene silencing also resulted in increased expression of BMP9 and BMP10. Our results might possibly imply that the effect of exogenously administered BMP9 on molecules participating in the BMP-signaling pathway could depend on the expression levels of BMPR2. Taken together, these results may pro-vide insight into the highly complex interactions of the BMP-signaling pathway.

Biological nanoparticles (NPs), such as extracellular vesicles (EVs), exosome-mimetic nanovesicles (EMNVs) and nanoghosts (NGs), are perspective non-viral delivery vehicles for all types of therapeutic cargo. Biological NPs are renowned for their exceptional biocompatibility and safety, alongside their ease of functionalization, but a significant challenge arises when attempting to load therapeutic payloads, such as nucleic acids (NAs). One effective strategy involves fusing biological NPs with liposomes loaded with NAs, resulting in hybrid carriers that offer the benefits of both biological NPs and the capacity for high cargo loads. Despite their unique parameters, one of the major issues of virtually any nanoformulation is the ability to escape degradation in the compartment of endosomes and lysosomes which determines the overall efficiency of nanotherapeutics. In this study, we fabricated all major types of biological and hybrid NPs and studied their response to acidic environment observed in endolysosomal compartment. In this study, we show that EMNVs display increased protonation and swelling relative to EVs and NGs in an acidic environment. Furthermore, the hybrid NPs exhibit an even greater response compared to EMNVs. Short-term incubation of EMNVs in acidic pH corresponding to late endosomes and lysosomes again induces protonation and swelling, whereas hybrid NPs are ruptured, resulting in the decline of their quantities. Our findings demonstrate that in an acidic environment, there is enhanced rupture and release of vesicular cargo observed in hybrid EMNVs that are fused with liposomes compared to EMNVs alone. This was confirmed through PAGE electrophoresis analysis of mCherry protein loaded into nanoparticles. In vitro analysis of NPs colocalization with lysosomes in HepG2 cells demonstrated that EMNVs mostly avoid endolysosomal compartment whereas hybrid NPs escape it over time. To conclude, (1) hybrid biological NPs fused with liposomes appear more efficient in the endolysosomal escape via the mechanism of proton sponge associated with scavenging of protons by NPs, influx of counterions and water, and rupture of endo/lysosomes, but (2) EMNVs are much more efficient than hybrid NPs in actually avoiding endolysosomal compartment in human cells. These results reveal biochemical differences across four major types of biological and hybrid NPs, and indicate that EMNVs are more efficient in escaping or avoiding endolysosomal compartment.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

The past few decades have brought tremendous insight into the molecular and pathophysiological mechanisms responsible for thrombus generation. For the clinician it is usually sufficient to explain the incident deep vein thrombosis (DVT) with provoking factors such as trauma with vascular injury, immobilization, hormonal factors, or inherited or acquired coagulation defects. About half of the DVTs are, however, lacking such triggers and are called unprovoked. Venous stasis and hypoxia at the valve sinus level may start a chain of reactions. In order to better understand the mechanisms behind DVT and reach beyond the above-mentioned simplifications animal models and clinical epidemiological studies have informed of the complex interplay between leukocytes, platelets, endothelium, cytokines, complements and coagulation factors and inhibitors. These pathways and the interplay will be reviewed here.

This work introduces the mathematical framework of the novel “First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (1st-CASAM-NODE)” which yields exact expressions for the first-order sensitivities of NODE decoder-responses to the NODE parameters, including encoder initial conditions, while enabling the most efficient computation of these sensitivities. The application of the 1st-CASAM-NODE is illustrated by using the Nordheim-Fuchs reactor dynamics/safety phenomenological model, which is representative of physical systems that would be modeled by NODE while admitting exact analytical solutions for all quantities of interest (hidden states, decoder outputs, sensitivities with respect to all parameters and initial conditions, etc.). This work also lays the foundation for the ongoing work on conceiving the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-CASAM-NODE)” which aims at yielding exact expressions for the second-order sensitivities of NODE decoder-responses to the NODE parameters and initial conditions while enabling the most efficient computation of these sensitivities.

Let $f:V\rightarrow V $ be a Cohomological Expanding Mapping¹ of a smooth complex compact homogeneous manifold with dim_C(V) = k ≥ 1 and Kodaira Dimension $\leq 0$. We study the dynamics of such mapping from a probabilistic point of view, that is, we describe the asymptotic behavior of the orbit $ O_{f} (x) = \{f^{n} (x), n \in \mathbb{N} \quad \mbox{or}\quad \mathbb{Z}\}$ of a generic point. Using pluripotential methods, we construct a natural invariant canonical probability measure of maximum Cohomological Entropy $ \mu_{f} $ such that ${\chi_{2l}^{-m}} (f^m)^\ast \Omega \to \mu_f \qquad \mbox{as} \quad m\to\infty$ for each smooth probability measure $\Omega $ on V . Then we study the main stochastic properties of $ \mu_{f}$ and show that $ \mu_{f}$ is a measure of equilibrium, smooth, ergodic, mixing, K-mixing, exponential-mixing and the unique measure with maximum Cohomological Entropy. We also conjectured that $\mu_f:=T_l^+ \wedge T_{k-l}^-$, $\dim_\H(\mu_f)= \Psi h_{\chi}(f) $ and $\dim_\H( \mbox{Supp} T_l^+) \geq 2(k-l) + \frac{\log \chi_{2l}}{\psi_l}.$

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

Based on molecular phylogenetic analyses, but also considering morphological characters, four new families are separated from the family Glomeraceae within the Glomerales and the class Glomeromycetes. The revised family Glomeraceae comprises only four genera: the type genus Glomus, Complexispora, Sclerocarpum and Simiglomus. Septoglomeraceae fam. nov. comprises, besides Septoglomus, also Funneliformis, Funneliglomus, Blaszkowskia and Viscospora. Sclerocystaceae fam. nov. is represented by the type genus Sclerocystis, but also by Halonatospora, Oehlia, Parvocarpum, Rhizoglomus and Silvaspora. Kamienskiaceae fam. nov. encompasses Kamienskia, Microkamienskia and Epigeocarpum. Finally, Dominikiaceae fam. nov. includes the genera Dominikia, Macrodominikia gen. nov. Microdominikia, Nanoglomus and Orientoglomus. The genera Oehlia and Halonatospora form two other clades well separated from Silvaspora, Sclerocystis and Rhizoglomus and might represent two further families within the Glomerales. Such deeper-going separation is to our opinion fully supported by molecular phylogeny, but in view of the low numbers of taxa, this separation is not yet needed at this stage of research progress.

This work presents the mathematical framework of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “2nd-CASAM-L”), which enables the most efficient computation of exactly obtained mathematical expressions of first- and second-order sensitivities of a generic system response with respect to functions (“features”) of model parameters. Subsequently, the first- and second-order sensitivities with respect to the model’s uncertain parameters, boundaries, and internal interfaces are obtained analytically and exactly, without needing large-scale computations. Within the 2nd-FASAM-L methodology, the number of large-scale computations is proportional to the number of model features (defined as functions of model parameters), as opposed to being proportional to the number of model parameters, which are considerably more than the number of features, being incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities (of any order) with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces. The application of the 2nd-CASAM-L methodology is illustrated using a simplified energy-dependent neutron transport model of fundamental significance in nuclear reactor physics.