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.

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.

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.

We make use of generalized iterations of the Sacks forcing to define cardinal-preserving generic extensions of the constructible universe L in which the axioms of ZF hold and in addition either 1) the parameter-free countable axiom of choice AC* fails, or 2) AC* holds but the full countable axiom of choice AC fails in the domain of reals. In another generic extension of L, we define a set X⊆P(ω), which is a model of the parameter-free part PA2* of the 2nd order Peano arithmetic PA2, in which CA(Σ21) (Comprehension for Σ21 formulas with parameters) holds, yet an instance of Comprehension CA for a more complex formula fails. Treating the iterated Sacks forcing as a class forcing over $L_{\omega_1}$, we infer the following consistency results as corollaries. If the 2nd order Peano arithmetic PA2 is formally consistent then so are the theories: 1) PA2 + negation of AC*, 2) PA2 + AC* + negation of AC, 3) PA2* + CA(Σ21) + negation of CA.

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.

The efficiency of a new composite material of the layered double hydroxide (LDH) of ZnMgAl and rice husk biochar (RHB) for the removal of Cu(II) and Pb(II) ions from synthetic wastewater was investigated in this study. The images of scanning electron microscope showed extremely fine crystalline LDH particles decorated on the rough surface of the RHB while the succesful formation of the composite adsorbent (LDH/RHB) was confirmed by the corresponding energy dispersive X-ray and the Fourier-transform infrared spectroscopy. An equilibrium contact time of 30 and 15 min for Cu2+ and Pb2+, respectively, was proposed for the optimum performance of the batch adsorption process. The dose of the LDH/RHB adsorbent was optimized at 0.4 g yielding maximum adsorption capacities of 117 and 124 mg g-1 for Cu2+ and Pb2+, respectively, with corresponding maximum removal efficiencies of nearly 94% and 99%. The initial meta concentrations was optimized at 50 or 60 mg L-1 corresponding to maximum removal efficiencies or adsorption capacities. For the changing initial metal’s concentration, the removal efficiencies remained unchanged for up to 50 mg L-1 and decreased by about 50% by increasing the initial concentrations from 50 to 100 mg L-1. The adsorption capacities observed a linear increasing trend by increasing the initial concentrations from 5 to 60 mg L-1 and remained unchanged afterward up to 100 mg L-1. A solution pH of 6.0 yielded optimum results with an increasing trend in adsorption capacities and percentage removal by changing the solution pH from 2.0 to 7.0. Based on the best-fit of the pseudo second-order kinetic model to the experimental data, the chemisorption was suggested to be the controlling mechanism of adsorption. The fitting of the Langmuir model suggested a monolayer sorption of Cu2+ and Pb2+ in addition to a heterogeneous adsorption as supported by the fitting of the Temkin isotherm. The application of the Dubinin–Radushkevich isotherm proposed a physical adsorption (mean free energy of adsorption less than 8 kJ mol−1) of both heavy metal ions on the surface of the LDH/RHB adsorbent.

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is “broken” by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses; but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created.

In this paper, we investigate the new degenerate Daehee polynomials and numbers which are called the degenerate Daehee polynomials of the second kind, and derive some new and interesting identities and properties of those polynomials.

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.

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.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

Direct femtosecond laser writing or inscription is a useful technique, and it has been 1 employed to engineer various materials in many applications including nonlinear photonic crystals, 2 which are of periodically patterned second-order nonlinearity to get and control the coherent light at 3 new frequencies. By manipulation of second-order nonlinearity, either erased or poled, quasi-phase 4 matching has been achieved in several crystals, especially three-dimensional nonlinear photonic 5 crystals have been originally proposed and proved to be truly three-dimensional. Here we shortly 6 review on the recent advances in the research field of nonlinear photonic crystals inscribed by 7 femtosecond laser. We also discuss some phenomena that not understood yet and the future possible research topics in this field.

This work introduces the mathematical framework of the novel “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations” (1st-FASAM-NODE). The 1st-FASAM-NODE methodology produces and computes most efficiently the exact expressions of all of the first-order sensitivities of NODE-decoder responses with respect to the parameters underlying the NODE’s decoder, hidden layers, and encoder, after having optimized the NODE-net to represent the physical system under consideration. Building on the 1st-FASAM-NODE, this work subsequently introduces the mathematical framework of the novel “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-FASAM-NODE).” The 2nd-FASAM-NODE methodology yields and computes most efficiently the exact expressions of the second-order sensitivities of NODE decoder-responses with respect to the NODE parameters. Since the physical system modeled by the NODE-net necessarily comprises imprecisely known parameters that stem from measurements and/or computations subject to uncertainties, the availability of the first-and second-order sensitivities of decoder responses to the parameters underlying the NODE-net are essential for performing sensitivity analysis and quantifying the uncertainties induced in the NODE-decoder responses by uncertainties in the underlying uncertain NODE-parameters.

An in-depth study of the failure of granular materials, which is known as a mechanism to generate defects, can reveal the facts about the origin of the imperfections such as cracks in the carbon anodes. The initiation and propagation of the cracks in the carbon anode, especially the horizontal cracks below the stub-holes, reduce the anode efficiency during the electrolysis process. In order to avoid the formation of cracks in the carbon anodes, the failure analysis of coke aggregates can be employed to determine the appropriate recipe and operating conditions. In this paper, it will be shown that a particular failure mode can be responsible for the crack generation in the carbon anodes. The second-order work criterion is employed to analyze the failure of the coke aggregate specimens and the relationships between the second-order work, the kinetic energy, and the instability of the granular material are investigated. In addition, the coke aggregates are modeled by exploiting the discrete element method (DEM) to reveal the micro-mechanical behavior of the dry coke aggregates during the compaction process. The optimal number of particles required for the failure analysis in the DEM simulations is determined. The effects of the confining pressure and the strain rate as two important compaction process parameters on the failure are studied. The results reveal that increasing the confining pressure enhances the probability of the diffusing mode of the failure in the specimen. On the other hand, the increase of strain rate augments the chance of the strain localization mode of the failure in the specimen.

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.

Estimation of core and surface temperature is one of the crucial functionalities of the lithium-ion Battery Management System (BMS) towards providing effective thermal management, fault detection and operational safety. While, it is impractical to measure core temperature using physical sensors, implementing a complex estimation strategy in on-board low-cost BMS is challenging due to high computational cost and the cost of implementation. Typically, a temperature estimation scheme consists of a heat generation model and a heat transfer model. Several researchers have already proposed ranges of thermal models having different levels of accuracy and complexity. Broadly, there are first-order and second-order heat capacitor-resistor-based thermal models of lithium-ion batteries (LIBs) for core and surface temperature estimation. This paper deals with a detailed comparative study between these two models using extensive laboratory test data and simulation study to access suitability in online prediction and onboard BMS. The aim is to guide whether it’s worth investing towards developing a second-order model instead of a first-order model with respect to prediction accuracy considering modelling complexity, experiments required and the computational cost. Both the thermal models along with the parameter estimation scheme are modelled and simulated using MATLAB/Simulink environment. Models are validated using laboratory test data of a cylindrical 18650 LIB cell. Further, a Kalman Filter with appropriate process and measurement noise levels are used to estimate the core temperature in terms of measured surface and ambient temperatures. Results from the first-order model and second-order models are analyzed for comparison purposes.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

This paper presents the analysis of four error models that can appear in the field of adaptive systems, where adaptive laws for parameter estimation are represented as fractional order differential equations whose order can switch between an order within the range (0,1) and 1. These switched adaptive laws have been proposed in the past few years to improve the balance between control energy and system performance, which is often a challenge when using traditional integer-order or fractional-order adaptive laws in adaptive identification and control. Boundedness of the solutions is proved for all cases, together with the convergence to zero of the estimation/tracking error. Additionally, sufficient conditions for parameter convergence are presented, showing that the excitation condition required for parameter convergence in the vector case is also sufficient for parameter estimation in the matrix case.

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.

This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam, with a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems and spring-mass systems was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, a second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.

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 bioactive marine sulfated polysaccharides ulvan and carrageenan, formulated in gels at 1.5, 5.0 and 10% w/w concentrations, were evaluated for their wound healing potential on second-degree burn wounds. The polysaccharide-based gels were administered on the burn-inflamed skin of hairless female SKH-hr2 mice, and the therapeutic effect of the various treatments was assessed based on histopathological analysis, the clinical condition of mice, photo-documentation, evaluation of biophysical skin parameters, and FT-IR spectroscopy.Clinical and histopathological assessment, as well as the reduction rate of the burn wound area, indicated that the 10% w/w carrageenan gel significantly enhanced wound healing, especially at the early stages of the healing process, recovering both the α-helix of collagen and the glycosaminoglycans configuration as evidenced by the FT-IR absorption bandsof skin in vivo and ex vivo. At later stages, the healing effect of the 5% w/w ulvan gel was also notably significant, indicating that carrageenan and ulvan wound dressing gels could potentially contribute to the efficient wound healing of burn wounds.

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.

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.

In the ongoing shift towards electric vehicles (EVs) primarily utilizing lithium-ion battery technology, a significant population of hybrid electric vehicles (HEVs) remains operational, reliant on established NiMH battery systems. Over the last twenty years, these HEVs have generated a substantial quantity of NiMH batteries that are either inoperable, experiencing performance degradation, or approaching the end of their service life. This results in a twofold challenge: a growing volume of environmentally hazardous waste due to the difficulty of NiMH battery reclamation, and escalating maintenance costs for HEV owners necessitated by replacement battery purchases. Patent WO2015092107A1, published in 2015, proposed a "Method for regenerating NiMh batteries." This method claims the ability to restore NiMH batteries to their original functionality. However, a comprehensive review of relevant scientific literature fails to identify any empirical evidence supporting the efficacy of the regeneration technique detailed in the patent. Within this context, this paper presents a detailed analysis and evaluation of the feasibility of the aforementioned patented method. To achieve this objective, the authors propose a prototype constructed utilizing NiMH battery cells sourced from a Toyota Prius. The experimental results obtained from this prototype demonstrate the potential for battery regeneration using the proposed method. These findings offer a promising solution for mitigating the challenges associated with NiMH battery disposal and maintenance within the HEV domain.

In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo's law instead of the usual Fourier's law. The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effects of heat conduction induced by Cattaneo's law. By considering related penalized problems, proving some a priori estimates and passing to the limit, we prove the global existence of the solutions. By considering the approximate framework, constructing some new functionals and applying the perturbed energy method, we obtain the exponential decay result for the approximate solution, and then prove the exponential decay rate to the original problem by utilizing the weak lower semicontinuity arguments.

Pedagogical translanguaging (PTL) refers to the use of educational techniques which incorporate learners’ entire linguistic repertoire. Recent studies indicate that PTL is efficient in the teaching of morphological awareness to bilingual children. The question remains whether it can successfully be applied in the highly specific context of adult forced migrants' classrooms. This study describes a new protocol developed within the framework of PTL to teach derivational morphology to L2 French and Greek adults. We used questionnaires to assess quantitatively and qualitatively the feasibility of the protocol, teachers' and learners' attitudes, and learners' emotions in the PTL lesson. A total of 141 migrant learners (79 forced migrants) and 13 teachers were involved in 23 2-hour lessons. Teachers and learners gave overall high evaluations of the feasibility of the PTL protocol and of their pleasure to teach and learn using PTL tools. Learners’ ease to learn and learning benefits were positively influenced by their perception of the proximity between their L1 and L2. Learners reported higher positive emotions and lower negative emotions during the PTL lesson, while forced migrants showed globally higher hope and shame than voluntary migrants, as well as higher benefits from PTL on enjoyment. These findings suggest that the use of pedagogical translanguaging in migrants’ classrooms is feasible and develops positive attitudes and emotions, which are more pronounced in forced migrants.

In order to achieve its carbon peak and neutrality targets, a high proportion of distributed power sources are connected to the distribution network in China, which greatly increases the risk of distribution network operation. Aiming at the above problems, this paper proposes an active distribution network risk planning model based on multi-source data from carbon capture and power internet of things, and conducts exceeding testing of distribution network based on the stochastic load flow algorithm with semi-invariant and level expansion, calculates the semi-invariant of each order of node state vectors and branch current vectors, and then utilizes the Gram-Charlier level expansion to obtain the exceeding probability density function and probability distribution function of the node voltages and line powers of the distribution network. The probability density function and probability distribution function of the exceeding are obtained using the Gram-Charlier series expansion. Combined with multi-source data, the active distribution network with integrated energy system considering carbon capture is modeled. According to the risk scenario of the distribution network, the nonconvex constraints in the model are simplified by the second-order cone relaxation, and the optimal planning scheme of the distribution network is solved by combining the gurobi solver with the risk index as the first-level objective and the economic benefit as the second-level objective. The simulation results of a coupled network consisting of a 39-node distribution network and an 11-node transportation network verify the effectiveness of the proposed model.

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.

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.

We offered the circuit of a discrete analog filter (DAF) low frequencies of second-order on switchable capacitors, which differs from the known ones in that three capacitors with one terminal are connected to a common bus, and the frequency of the DAF pole depends not only on the ratio of the capacitances of the frequency-setting capacitors, but also on the ratio of resistances two additional resistors in the feedback. This allows at constant values ​​of the capacitances and a fixed switching frequency of electronic switches, control the pole frequency by changing the resistance ratio of additional resistors. Computer simulation of the developed circuit was performed in the Micro-Cap environment. It has been established that the DAF has a transmission coefficient close to minus one at very low frequencies and a transmission coefficient close to zero at higher frequencies.

In pediatric burn care, achieving swift healing with minimal complications remains paramount. This investigation assesses polyhexamethylene biguanide (PHMB)'s role in managing superficial partial-thickness burns in children, focusing on the effects of various patient-specific factors on recovery. Through a retrospective analysis of 27 pediatric cases treated with PHMB, we explored the impact of age, burn size, dressing frequency, treatment delay, cold therapy application, and analgesic usage on the duration until reepithelialization. Notably, the majority of patients benefited from early cold therapy, yet only 1 in 3 patients received analgesics. The study reveals a mean healing time of 8.78 days, with the extent of the burn showing a strong correlation to recovery speed. Most treatments were managed outpatient, evidenced by a negligible average hospital stay. Impressively, the intervention recorded no complications. Our findings endorse PHMB as a promising treatment for second-degree burns in young patients, offering healing efficiency on par with or surpassing traditional methods, without increasing complication risks. This investigation underscores the necessity for continued exploration into the optimal application of prehospital interventions and the comprehensive benefits of PHMB in pediatric burn management, advocating for future research aimed at assessing long-term outcomes, including scar quality and patient satisfaction.

The differential-equation of second order for space-time oscillation in flat tangential-spacetime of Minkowski-type can be written as an energy-equation. For this energy-equation the analogon of damping energy in two coupled Minkoswki-spacetimes with ftl can be calculated and formulated over Lamberts W-function or via Euler-equation.

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.

The bulk LiNa5Mo9O30 (LNM) crystals were successfully grown in the [010] and [001] directions without internal inclusions and cracks by the Czochralskii method with low temperature gradient. The crystal grown in the [010] direction showed a tendency to twinning. The crystal grown in the [001] direction demonstrated high structural perfection (FWHM=13'') for the (001) plane and high optical quality Δn≈210-5. The laser induced damage threshold was measured along a, b and c axes and was 15.7, 27.0 and 27.5 J/cm2 respectively. The thermo-optical coefficient dn/dT was measured for the main crystallographic axes, which was -5.7510-6, -2.0210-5 and 3.6510-6 K-1 along the a, b and c axes, respectively. The second harmonic generation (SHG) is conducted in crystalline LNM sample. The maximum efficiency value of 3.5% at pump power of 12 W had been achieved.

The purpose of this systematic review is to provide second language acquisition (SLA) researchers with an overview of research trends in this field in the last ten years (2009-2019). In doing so, three international peer-reviewed journals, Studies in Second Language Acquisition, Language Teaching Research, and The Modern Language Journal, were selected. 150 articles were systematically selected and analyzed. The analysis of data resulted in identifying six descriptive themes. Results showed that some areas of second language acquisition still need further exploration while some areas are of great interest for researchers. Some suggestions for future research as well as implications of the study were discussed in detail.

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 the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

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 the preservation property of the average intensity order and the preservation property of the monotonic average intensity classes under distorted distributions. Several sufficient conditions are given to get the preservation properties. It is shown that the imposed conditions are achievable as we examine in some examples. The preservation of the average intensity order and the preservation of the decreasing average intensity class under the structure of a parallel system with independent and identically distributed components' lifetime are made. A lower bound for the average intensity function of a random lifetime with an increasing failure rate in average distribution is derived. The results are applied to some semiparametric models as a particular standard family of distorted distribution.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

This study aimed to evaluate the impact of different closures used in second fermentation on the aromatic fraction of sparkling wine. Six types of closures (cork stoppers and screw cap) and 94 months of aging in bottle were investigated. Head-space-solid phase microextraction (HS-SPME) and thermal desorption (TD) procedures coupled to gas chromatography-mass spectrometry (GCMSMS) analysis was applied. The vectors containing the relative abundance of the volatile compounds are compositional vectors. The statistical analysis of compositional data requires specific techniques that differ from standard techniques.101 volatile compounds were identified. HS-SPME extracted highest percentage of ester, ketones and other compounds while TD was a useful tool for the obtention of alcohol, acid, ether and alkanes compounds. Esters was the most abundant family of compounds. Compositional data analysis applied to study the impact of different closures used in bottle-aging after second fermentation on the volatile composition of sparkling wine concluded that there are differences in the relative abundance of certain volatile compounds between cork stoppers and screw cap closures group. Overall, the most abundant part in screw cap closures was Ethyl hexanoate and, Ethyl octanoate in cork stoppers. Also, the proportion amount of Dimethylamine was higher in screw cap closures than cork stoppers group relative to the entire of the sample.

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.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.

In the periodic table of the elements, ruthenium is ideally placed, right in the middle, just above iron. And like iron, it possesses several oxidation states, with +2 and +3 being the most common. Accordingly, ruthenium chemistry is extremely rich and well developed, ruthenium complexes show excellent catalytic aptitude, tremendous redox capacity, and intriguing biological activity. However, in the design of sensors, the use of ruthenium complexes remains scarce, despite valuable electro- and photochemical properties. Therefore, there is an opportunity here, and ruthenium-based complexes might become one day, key players in sensing technology. Starting ourselves a new research project with ruthenium-based sensors, writing this review was essential to see the current state of research in the field, to identify opportunities, and to have an overview of state-of-the-art examples.

In the paper the new, fractional order, state space model of a heat transfer in a one- 1 dimensional metallic rod is addressed. The fractional orders of derivative along space and time 2 are not exactly known and they are described by intervals. The proposed model is the interval 3 expanding of the state space fractional model of the one dimensional heat transfer. It is expected to 4 better describe the reality because interval order of each real process is hard to estimate. Elementary 5 properties of the proposed model are analysed. Theoretical results are experimentally validated using 6 data from real experimental laboratory system.

A topological representation theory of chiral spin liquid is proposed to unify the integral and fractional quantum Hall fluid based on hyperbolic geometry, knot lattice and Thurston's train track theory. The integral and fractional Hall resistivity obeys an exact unified equation, $R_{xy} = (h/e^2)B_{e}$, $B_{e} = (n+\nu)^{-1}$, with respect to the bulk energy gap ${\Delta}E = {\hbar{e}B_{e}}/{Mc}$. The Wen-Zee matrix formulation of topological fluid for quantum Hall effect is constructed by topological surgery and train track. The chirality of spin liquid is spontaneously distinguished by Jones polynomial. The integral Chern number for Hall conductance is fractionalized by generalizing Thurston's train track to folding laminations in three dimensions, which spontaneously bring fractional quantum Hall fluid and anyons into three dimensions and provided an theoretical explanation on the competing fractional quantum Hall states. The many body system of interacting fermions or bosons are mapped into many interacting liquid droplets that interwind into knot lattice, which provide an effective topological representation for superfluid and superconductor, the strange metal state in superconductor is explained by topological dislocation and topological surgery. The Kauffman decomposition rule in knot theory is extended to describe the topological relations between different two dimensional manifolds, which further reveals the non-trivial relationship between the partition functions of pairing fermions and free electrons. The minimal energy state is the most stable topological state, even thought it maybe shares the same topological number with the excited states. The topological representation theory predicts a circular motion of electrons in hyperbolic space, that is implementable and testable by inhomogeneous magnetic field in three dimensions. The folding lamination representation of topological quantum fluid provides an promising implementation of string theory in high energy physics.

To date, theoretical analyses have provided several useful methods/algorithms for studying transition states and non-covalent interactions. Potential Energy Scan (PES) is one such method that has found wide application in the physicochemical community. Analyzing the PES profiles of the catalytic system of FeBr3 in Electrophilic Aromatic Substitution (EAS) with molecular halogens, one can notice an obvious difference from the modern textbook mechanisms proposed in this area of study. Moreover, the newly presented Graphic Methodology (GM) allows a simple and reliable transition state determination even for very weakly bound charge transfer complexes using second-order derivatives as an efficient tool in the graphical analysis. Relative errors that can be reduced to a few parts per thousand in transition state estimation make this method a potentially very useful tool in further graphical studies of non-covalent interactions. Studies performed using high-precision semiempirical methods suggest that the process of halonium ion quenching proceeds along a completely different pathway, suggesting a possible novel transition metal-nonmetal catalytic system involved in the EAS electrophilic quenching step. The results presented here strongly suggest a future GM application that is widely used and the introduction of pseudo and pre-transition states as new terms in the description of non-covalent interactions.

In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the idle time of such systems. It is assumed that, at a time t the failure of a cold standby system is observed, but the actual time of the failure is a time before t. The idle time of the inactive cold standby system is measured as the time between the exact time of failure, which is a random variable, and time t. We use the idle times of the components of the system to obtain lower and upper bounds on the lifetime of the standby system to which they are assembled. We bring some examples to show that the results and the conditions imposed to get them are achievable.

This research investigates the impact of Al and Ti elements on the formation of self-generated ordered phase in high-entropy alloys (HEA), which have been receiving widespread concentration in present times thanks to their remarkable multifunctional properties and wide range of component selection. By adjusting the dual elements of Al and Ti, the study explores the regulation of quantity and distribution of the in-situ self-generated ordered phases in the alloy. The results of the annealing heat treatment process demonstrated that, through accession Al and Ti elements, the Cr-Fe-Ni medium-entropy alloy transfer from BCC phase to BCC+FCC phase and the precipitation of new phases such as B2, L21, and σ. This led to a synergistic impact of second phase strengthening, and also of solid solution strengthening, resulting in improved compressive properties of HEA.

Aiming at the development of the application of massive and heterogeneous LEO constellations, the influence of typical perturbation forces on the orbit prediction of LEO satellites at different altitudes is analyzed. Firstly, the main perturbation force model of LEO satellites is introduced. Then experiments for analyzing the influence of orbit prediction on LEO satellites at different altitudes are designed. Finally, the influence of typical perturbation forces on the orbit prediction under different prediction durations by numerical analysis is assessed systematically, and the orbit prediction of LEO satellites with different non-spherical gravitational field orders, ocean tide orders and atmospheric density models were compared and calculated. The research results show that different orders of non-spherical gravitational fields should be considered when the altitude of satellites is different, the reasonable gravitational field orders for LEO satellites at 500km, 1000km, 1500km and 2000km under 1-hour forecast time are 140x140, 80x80, 60x60 and 40x40 orders, the reasonable orders of ocean tide perturbation for 1500km and 2000km satellites are 20x20 orders. Under the 24-hour forecast time, atmospheric resistance has a great influence on the precision of LEO satellites at orbit altitude below 1,000km. The forecast deviation of the LEO satellites orbit at 500km reaches 8751.576m. The difference of orbit precision between different atmospheric density models is in the meter level. The orbit deviation by the Standard Atmosphere 1976 and NRLMSISE 2000 atmospheric models respectively reaches 25.494m. Relevant conclusions provide support for the optimization and selection of dynamical models in high precision orbit determination and fast orbit prediction of LEO satellites.

The aim of the paper is to provide an overview of the monastic houses operated on the northernmost periphery of Roman Catholic Europe during the Middle Ages. The intention is to debunk the long-held theory of Iceland and Norse Greenland’s supposed isolation from the rest of the world, as it is clear that medieval monasticism reached both of these societies, just as it reached their counterparts elsewhere in the North Atlantic. During the Middle Ages, fourteen monastic houses were opened in Iceland and two in Norse Greenland, all following the Benedictine or Augustinian Order.

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.

Despite being stored at 113 K and atmospheric pressure, LNG cold potential is not exploited to reduce green ships’ energy needs. An innovative system based on three Organic Ranking Cycles integrated into the regasification equipment is proposed to produce additional power and recover cooling energy from condensers. A first-law analysis identified ethylene and ethane as suitable working fluids for the first and the second ORC making available freshwater and ice. Propane, ammonia and propylene could be arbitrarily employed in the third ORC for air-conditioning. An environmental analysis that combines exergy efficiency, ecological indices and hazard aspects for marine environment and ship’s passengers, indicated propylene as safer and more environmentally friendly. The exergy analysis confirms more than 20% of the LNG potential can be recovered from every cycle to produce a net clean power of 76 kW, whereas 270 kW can be saved by recovering condensers' cooling power to satisfy some ship needs. Assuming the sailing mode, a limitation of 162 kg in LNG consumptions was determined, avoiding the emission of 1584 kg of CO2 per day. Marine thermal pollution is reduced by 3.5 times by recovering the working fluids' condensation heat for the LNG pre-heating.

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.

The atomic structures of Zn and Na borophosphate glasses were studied by X-ray and neutron diffraction. Peaks assigned to the B−O, P−O, and O−O distances confirm that only BO4 units co-exist with the PO4 tetrahedra. The Zn−O and Na−O coordination numbers are found to be a little larger than four. The narrowest peaks of the Zn−O first-neighbor distances exist for the glasses along a line connecting the Zn(PO3)2 and BPO4 compositions (50 mol% P2O5) which is explained by networks of ZnO4, BO4, and PO4 tetrahedra with twofold coordinated oxygens. Calculated amounts of the available oxygen support this interpretation. Broadened peaks occur for glasses with lower P2O5 contents, consistent with the presence of threefold coordinated oxygens. The two distinct P−O peak components of the Zn and Na borophosphate glasses differ in their relative abundances which is interpreted by Na+ cations that coordinate oxygens in some P−O−B bridges, something not seen for the Zn2+ ions.

Ambiguity exists over treatment and surveillance strategies after endoscopic submucosal dissec-tion (ESD) for esophageal squamous cell neoplasia (ESCN) with unfavorable histologic features. This study investigated the long-term outcomes of ESD in high-risk ESCN patients. We retro-spectively included early ESCN patients treated with ESD at two medical centers in Taiwan be-tween August 2010 and December 2023. Demographic, endoscopic, and pathological data were collected. Among 146 patients (mean age 59.17 years) with 183 lesions, 73 (50%) had a history of head and neck cancer (HNC). En bloc and R0 resection were achieved in 100% and 95.6% of the lesions, respectively. The 5-year overall survival (OS), disease-specific survival (DSS) and local recurrence rates were 42.7%, 94.7% and 11%. R0 resection was significantly associated with re-currence in univariate analysis (adjusted OR: 0.23, 95% CI: 0.05-0.99, P=0.05). Alcohol abstinence was independently associated with lower recurrence (adjusted OR: 0.20, 95% CI: 0.08-0.48, P

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the ‘probability assumption’ needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann’s Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.

(1) Background: Second Victims are health care workers negatively affected by adverse events and are prone to developing dysfunctional coping strategies compromising not only their own, but also patient safety. An effective way to address this issue is the implementation of peer support programs. This paper reports on the effectiveness of a peer support program at the Austrian Hietzing Clinic (KHI). (2) Methods: Telephone interviews were carried out after peer support sessions using a questionnaire. Descriptive analysis was carried out reporting frequencies and proportions for nominal variables, means with standard deviations for ordinal and interval-scaled variables. (3) Results: So far, 45 peer supporters have completed telephone interviews after a peer support session. The main reasons for the session were bad news from the private sphere and death of a patient. The peer supporters rated the helpfulness of the sessions for their colleagues as very high while not feeling very burdened themselves afterwards. (4) Conclusions: Underutilization of the program is probable. However, the high rating of helpfulness of the carried-out sessions by the peer supporters in combination with them not feeling very burdened, shows that the program is safe for the peer supporters and an upscaling is warranted.

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

This study investigates the impact of narrow-band terahertz pulses on the ferroelectric order parameter in Ba0.8Sr0.2TiO3 films on various substrates. The 375 nm thick BST film on an MgO (001) substrate exhibits enhanced THz-induced second harmonic generation when excited by THz pulses with a central frequency of 1.6 THz, due to the resonant excitation of the soft phonon mode. Conversely, the BST film on a Si (001) substrate shows no enhancement, due to its polycrystalline state. The 800 nm thick BST film on an MgO (111) substrate demonstrates maximum of second harmonic generation signal when excited by THz pulses at 1.8 THz, that is also very close to it`s soft mode frequency (1.9 THz). Notably, the frequency spectrum of the BST/MgO (111) film reveals peaks at both the fundamental and doubled frequencies, highlighting the quadratic dependence of SHG intensity on the THz pulse's electric field strength.

The primary purpose of this article is to study the asymptotic and numerical estimates in detail for higher degree polynomials in $\pi(x)$ having a general expression of the form, \begin{align*} P(\pi(x)) - \frac{e x}{\log x} Q(\pi(x/e)) + R(x) \end{align*} $P$, $Q$ and $R$ are arbitrarily chosen polynomials and $\pi(x)$ denotes the \textit{Prime Counting Function}. The proofs require specific order estimates involving $\pi(x)$ and the \textit{Second Chebyshev Function} $\psi(x)$, as well as the famous \textit{Prime Number Theorem} in addition to certain meromorphic properties of the \textit{Riemann Zeta Function} $\zeta(s)$ and results regarding its non-trivial zeros. A few generalizations of these concepts have also been discussed in detail towards the later stages of the paper, along with citing some important applications.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained.

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.

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

This paper explores the effectiveness of the Non-dominated Sorting Genetic Algorithm III (NSGA-III) and traditional Mean-Variance optimization in financial portfolio management. Using a dataset comprising global financial assets, we applied both methodologies to optimize portfolios based on multiple objectives, including risk, return, skewness, and kurtosis. The findings reveal that NSGA-III outperforms the Mean-Variance method in achieving a more diverse set of Pareto-optimal portfolios. NSGA-III portfolios exhibited superior performance in balancing risk and return, demonstrated by higher Sharpe ratios, more favorable skewness, and lower kurtosis. Additionally, NSGA-III's ability to simultaneously optimize across multiple conflicting objectives highlights its robustness in navigating complex financial landscapes, offering enhanced portfolio resilience. In contrast, the Mean-Variance approach, while effective in achieving balanced risk and return, was limited in addressing higher-order moments of the return distribution. These results underscore NSGA-III's potential as a powerful tool for portfolio optimization, providing a comprehensive alternative to traditional methods in modern financial markets where multiple objectives must be considered.

Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.

In an era where digital technologies are integral to daily life, developing higher-order thinking skills with appropriate information and communication technology (ICT) support is crucial. The purpose of this study was to examine synergies of systems thinking and technology-enhanced learning from the perspective of flow theory. For that purpose, we surveyed more than 65 pre-service preschool teachers engaged in a design, technology, and engineering (DTE) course at the University of Ljubljana. Mapping of systems thinking revealed that pre-service preschool teachers needed support with regard to feedback and understanding the interrelationship dimen-sion of systems thinking. Predictive and mediation analyses yielded some interesting results. Those who participated in the ICT-enhanced DTE course showed higher cognitive and social engage-ment, which is correlated with better systems thinking, while their aesthetic engagement was lower. Experiencing a flow state during ICT activities positively influenced systems thinking, par-ticularly in terms of clear goals and autotelic experiences. Flow theory seems to be a solid and ap-propriate framework to use for studying synergies in technology-enhanced systems thinking for sustainable education. These findings underscore the importance of integrating systems thinking into curricula to enhance learning outcomes and prepare students for future challenges toward the achievement of Sustainable Development Goals.

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.

The search for new food products that promote consumers health has always been of great interest. The dairy industry is perhaps the best example regarding the emergence of new products with claimed health benefits. Cheese whey (CW), the by-product resulting from cheese production, and second cheese whey (SCW), which is the by-product of whey cheese manufacture, have proven to be potential ingredients for the development of food products with improved nutritional characteristics and other functionalities. Nowadays, due to their nutritional quality, whey products have gained a prominent position among healthy food products. However, for long, CW and SCW were usually treated as waste or as animal feed. Due to their high organic content, these by-products can cause serious environmental problems if discarded without appropriate treatment. Small and medium size dairy companies do not have equipment and structure to process whey and second cheese whey. In these cases, generally, they are used for animal feed or discarded without an appropriate treatment, being the cause of several constraints. There are several studies regarding CW valorization and there is a wide range of whey products in the market. However, in the case of SCW remains a lack of studies regarding its nutritional and functional properties, as well as ways to reuse this by-product in order to create economic value and reduce environmental impacts associated to its disposal.

In this work, we demonstrate that cutting diamond crystals with a laser (532 nm wavelength, 0.5 mJ energy, 200 ns pulse duration at 15 kHz) produces a ≲20nm thick surface layer with magnetic order at room temperature. We have measured the magnetic moment with a SQUID magnetometer of six natural and six CVD diamond crystals of different size, nitrogen content and surface orientations. A robust ferromagnetic response at 300 K is observed only for crystals that were cut with the laser along the (100) surface orientation. The magnetic signals are much weaker for the (110) and negligible for the (111) orientations. We attribute the magnetic order to the disordered graphite layer produced by the laser at the diamond surface. The ferromagnetic signal vanished after chemical etching or after moderate temperature annealing. The obtained results indicate that laser treatment of diamond may pave the way to create ferromagnetic spots at its surface.

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion formula for the Bell polynomials in terms of the Stirling numbers of the first and second kinds, with the aid of the above explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials; (3) constructs some determinantal and product inequalities and deduces the logarithmic convexity of the Bell polynomials, with the assistance of the complete monotonicity of generating functions of the Bell polynomials. These inequalities are main results of the paper.

Background: The front-line treatment of advanced NeuroEndocrine Neoplasms (NENs) depends on clinical and pathological factors but there are no standard second-line therapies. Methods: Metastatic NENs patients were treated at the ENETS (European NeuroEndocrine Tumor Society) center of excellence of Naples (Italy), from 2014 to 2017 with second-line metronomic temozolomide, 75 mg/m2 per os “one week on/one week off”. Toxicity was graded with NCI-CTC criteria v4.0; objective responses with RECIST v1.1 and performance status (PS) according to ECOG. Results: Twenty-six consecutive patients were treated. Median age was 65.5 years. The predominant primary organs were pancreas and lung. Grading was G2 in 11 patients, G3 in 15. Eleven patients presented with PS 1 and 15 with PS 2. The median time-on-temozolomide therapy was 12.2 months (95% CI: 11.4-19.6). No G3/G4 toxicities were registered. Complete response was obtained in 1 patient, partial response in 4, stable disease in 19 (disease control rate: 92.3%), and progressive disease in 2. The median overall survival from temozolomide start was 28.3 months. PS improved in 73% of patients. Conclusions: Metronomic temozolomide is a safe and active treatment for G2 and G3 NENs. Prospective and larger trials are needed to confirm these results.

In this paper, the transmutation operator method is used to construct an exact solution to the initial boundary value problem for the equation of multidimensional free transverse vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If formulas for solutions are known for a simple equation, then we also obtain representations for solutions to the first complex partial differential equation with singular coefficients. In particular, it is successfully applied to the singular differential equations, especially with Bessel-type operators. Using this operator, the considered problem is reduced to a similar problem without the Bessel operator. Based on the solution to the auxiliary problem, an exact solution to the original problem is constructed and analyzed.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

The transportation sector significantly contributes to greenhouse gas emissions, thus imposing sig-nificant environmental hazards. In response, many nations have begun promoting Electric Vehicles (EVs) as an ecologically sustainable substitute for traditional combustion vehicles. Lithium-Ion Batteries (LIBs), characterized by their high energy density, extended lifespan, and relatively low self-discharge rate, have become the suitable energy storage system for EVs, advancing the field of sustainable transportation. The decreasing cost of LIB production has primarily driven this progression, realized through a combination of economies of scale, advancements in electrode materials and cell design, and re-finements in manufacturing processes. All these elements collectively contribute to the cost reduc-tion of LIBs. A foreseeable implication of this trend is an expected surge in LIBs that will exhaust their operational lifespan and, consequently, be cast away into the environment. One mitigating strategy for this impending environmental issue involves collecting these spent EV batteries, re-configuring them, and repurposing them for applications with less rigorous weight, performance, and size prerequisites. This approach would not only prolong the utility life of the batteries but also ameliorate their environmental impacts. Nevertheless, second-life batteries are anticipated to exhibit a higher rate of gas evolution, necessitating comprehensive testing and readjustments to ensure safe operation in secondary ap-plications. The regulatory framework encompassing the second-life battery sector still needs to be defined regarding norms, technical standards, and legislation. This paper aims to elucidate the primary regulations and technical standards proposed thus far in the second-life battery marketplace. The results underscore the exigency for neutral evaluative entities, such as universities, research centers, and governmental institutions, to perform an unbi-ased assessment of the second-life battery market. This would pave the way for novel technical standards and legislative measures specifically tailored to this emerging sector.

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order two, GQ(2,2), whose representation has been dubbed “the doily” by Stan Payne in 1973. In this paper we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order two.

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}.

Motivated by important applications to the analysis of complex noise-induced phenomena, a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise is considered. Using apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noise. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with the example of the van der Pol oscillator with hard excitement.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

When a grid-forming (GFM) inverter is connected to a low or medium voltage weak power grid, the line impedance with resistive-inductive characteristics will cause power coupling. Typical GFM decoupling control strategies are designed under nominal line impedance parameters. However, there are deviations between the nominal line impedance and actual parameters, resulting in poor decoupling effects. Aiming at this problem, this paper proposes a power decoupling strategy based on a reduced-order extended state observer (ESO). Firstly, the power dynamic model of GFM is established based on the dynamic phasor method. Then, the model deviation and power coupling due to line impedance parameter perturbation are estimated as internal disturbances of the system, and the disturbances are compensated on the basis of typical power control strategy and virtual impedance decoupling. Good decoupling performance is obtained under different impedance parameters, improving the control strategy's robustness. Finally, the effectiveness of the proposed method is verified by the results of RT Box hardware-in-the-loop experiments.

Background: The Second Victim Phenomenon (SVP) significantly impacts the well-being of healthcare professionals and patient safety. While SVP has been explored in various healthcare settings, there is limited data on its prevalence and associated factors among nurses in Austria. This study investigates the prevalence, symptomatology, and preferred support measures for SVP among Austrian nurses. Methods: A nationwide, cross-sectional, anonymous online survey was conducted using the SeViD questionnaire (Second Victims in German-speaking Countries), which includes the Big Five Inventory-10 (BFI-10). Statistical analyses included binary logistic regression and multiple linear regression using the bootstrapping, bias-corrected and accelerated (BCa) method based on 5000 bootstrap samples. Results: 928 participants responded to the questionnaire. Among the respondents, 81.58% (744/912) identified as Second Victims (SVs). The primary cause of becoming a SV was aggressive behavior from patients or relatives. Females reported a higher symptom load than males, and higher agreeableness was linked to increased symptom severity. Notably, 92.47% of SVs who sought help preferred support from colleagues, and the most pronounced desire among participants was to process the event for better understanding. Conclusions: The prevalence of SVP among Austrian nurses is alarmingly high, with aggressive behavior identified as a significant trigger. The findings emphasize the necessity for tailored support strategies, including peer support and systematic organizational interventions to mitigate the impact of SVP on nurses and to improve overall patient care. Further research should focus on developing and implementing effective prevention and intervention programs for healthcare professionals in similar settings.

By this contribution we would like to briefly highlight the problems in conceiving the “Hydrogen Bond” (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-years’ old theoretical background, which depicts water as a two-fluid system (where one of the two phases is coherent). The HB emerge to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than the non-coherent (gas-like) fraction. Thus, the HB can be properly looked at, i.e. no more as a “dipolar force” among molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground-state, compatibly with temperature and pressure. This perspective allows to account for many “anomalous” behaviours of water and to understand why the calculated energy associated to HB should change when considering two molecules (water-dimer), or the liquid state, or the several kinds of ice. The emergence of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the framework of spontaneous symmetry breakings (SSB). The switch from a still semi-classical Quantum Mechanical (QM) in the 1st quantization to a Quantum Field Theory (QFT) view embedded in the 2nd quantization is advocated for a more realistic and authentic description of water, condensed matter and living systems.

A classical model is presented for persistent currents in superconductors. Their existence is argued to be warranted because their decay would violate the second law of thermodynamics. This conclusion is achieved by analyzing comparatively Ohm's law and the Joule effect in normal metals and superconducting materials. Whereas Ohm's law applies in identical terms in both cases, the Joule effect is shown to cause the temperature of a superconducting sample to \textit{decrease}. An experiment is proposed to check the validity of this work in superconductors of both types I and II.

The Convective Rainfall Rate from Cloud Physical Properties (CRPh) for Meteosat Second Generation Satellites is a day-only precipitation algorithm developed at the Spanish Meteorological Agency (AEMET) for EUMETSAT’ Satellite Application Facility in support to Nowcasting and Very Short Range Forecasting (NWC SAF). It is therefore mainly intended to provide input for monitoring and near-real-time forecasts for the next few hours. This paper critically discusses the theoretical basis of the algorithm with special emphasis in the empirical values and assumptions in the microphysics of precipitation and compares the performances of the CRPh with its antecessor, the Convective Rainfall Rate algorithm (CRR), using an object-based method. The analyses show that AEMET’s CRPh is physically consistent and that outperforms the CRR. The applicability of the algorithm for nowcasting and the challenges to evolve the product to an all-day algorithm are also presented.

High frequency knowledge of the spatio-temporal distribution of the Downwelling Surface Shortwave Flux (DSSF) and its diffuse fraction (fd) at the surface is nowadays essential for understanding climate processes at the surface-atmosphere interface, plant photosynthesis and carbon cycle, and for the solar energy sector. The EUMETSAT Satellite Application Facility for Land Surface Analysis operationally delivers estimation of the MDSSFTD (Downwelling Surface Short-wave radiation Fluxes – Total and Diffuse fraction) product with an operational status since the year 2019. The method for the retrieval was presented in the companion paper [40]. The part 2 now focuses on the evaluation of the MDSSFTD algorithm and presents the comparison of the corresponding outputs, i.e. total DSSF and diffuse fraction (fd) components, against in-situ measurements acquired at four BSRN stations over a seven-month period. The validation is performed on an instantaneous basis. We show that the satellite estimates of DSSF and fd meet the target requirements defined by the user community for all-sky (clear and cloudy) conditions. For DSSF, the requirements are 20Wm^-2 for DSSF<200Wm^-2, and 10% for DSSF>=200Wm^-2. The MBE and rMBE compared to the ground measurements are 3.618Wm^-2 and 0.252%, respectively. For fd, the requirements are 0.1 for fd<0.5, and 20% for fd>=0.5. The MBE and rMBE compared to the ground measurements are -0.044 and -17.699%, respectively. The study also provides a separate analysis of the product performances for clear sky and cloudy sky conditions. The importance of representing the cloud-aerosol radiative coupling in the MDSSFTD method is discussed. Finally, it is concluded that the quality of the Aerosol Optical Depth (AOD) forecasts currently available is enough accurate to obtain reliable diffuse solar flux estimates. This quality of AOD forecasts was still a limitation a few years ago.

Self-sustained learning (SSL) is considered a crucial factor in promoting students’ long-term learning and development in a sustainable society. To deepen the understanding of SSL, especially in the context of learning English as a second language, the current study examined the influence of intercultural communicative skills, language mindset, and positive L2 self on SSL in English learning among 1,238 college students in China. The results showed that students not only had a strong language mindset, positive L2 self, and intercultural communicative skills but also scored higher in long-term self-sustained English learning. Findings from the Structural Equation Modeling indicated that both language mindset and intercultural communicative skills positively predicted positive L2 self and self-sustained English learning. Furthermore, language mindset and intercultural communicative skills had an indirect impact on self-sustained English learning through positive L2 self. These findings suggest that to promote English learners’ SSL, instructors should help facilitate students’ intercultural communicative skills and foster a growth language mindset, as well as positive language learning beliefs.

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.

I deal with perception and action (e.g. movements) using results from Synergetics, a comprehensive mathematical theory of the selforganized formation ("emergence“) of spatial, temporal, or functional structures in complex systems. I illustrate basic concepts such as order parameters (ops), enslavement, complexity reduction, circular causality first by examples of well known collective, spontaneous modes of human behavior such as rhythmic clapping of hands etc., and then by face recognition. The role played by ops depends on context. In the case of face (or pattern) recognition an op represents the concept of an individual face (action of mind) and it enslaves the action (firing rates) of neurons (body). This insight allows me to interpret syndroms as order parameters playing their mind/body double role. I present criteria for the identification of ops and discuss their general properties including error correction and "remedy“ of deficiencies. Contact is made with a recent paper by Sabine Koch on embodied aesthetics. My approach includes the saturation of attention at various time scales (ambiguous figures/fashion). Adopting a psychological perspective, I discuss some ingredients of beauty such as proportionality and symmetry, but also the importance of irregularities.

Small-cell lung cancer (SCLC) is a cancer with poor prognosis. For relapsed extensive-stage (ES) SCLC, second-line treatment options are scarce. Topotecan was the only approved treatment in this setting until 2020. Since topotecan induces significant toxicities, alternative off-label regimens are being used. This study evaluated real-world efficacy and safety of Paclitaxel Gemcitabine chemotherapy in patients with relapsed ES-SCLC. We retrospectively reviewed data from all consecutive patients with relapsed ES-SCLC who received Paclitaxel Gemcitabine chemotherapy from september 2008 to january 2022 in two centers. Patient characteristics (n=188) were: PS≥2: 24.5%; brain metastasis: 42%; platinum-sensitive disease: 41%. Patients received Paclitaxel Gemcitabine as second- (77%) third (18%) or fourth (6%) line of therapy. Median progression-free and overall survival were 2.1 (95CI 1.8–2.4) and 3.8 (95CI 3.3–4.8) months in the overall population, respectively, with 17% response rate (RR) and 28% disease-control rate. PS, history of brain radiation, platinum-sensitive disease, liver, and adrenal gland metastasis were associated with longer survival in univariate analysis. PS was the only prognostic factor in multivariate analysis, with 21% RR and 4.1 months median DOR in PS 0-1 patients. Paclitaxel Gemcitabine chemotherapy may represent a treatment option in PS0-1 relapsed SCLC.

Due to the high effectiveness of cancer screening and therapies, the diagnosis of second primary cancers (SPCs) has increased in women with endometrial cancer (EC). However, there’s no previous literature mentioned about adequate evidence to support screening for SPCs in endometrial cancer. This study was aimed to develop effective risk prediction models of second primary endometrial cancer in women with obesity (Body-mass index; BMI > 25) and this study includes datasets of the incidence of SPCs and the other risks of SPCs in 4480 primary cancer survivors by a hospital-based cancer registry database. In our study, we found the obesity played a key role in SPCs. There’re 10 independent variables used as predicting variables, which corelated to obesity should be monitored for the early detection of SPCs in endometrial cancer. In conclusion, it is a promising SPCs prediction. The proposed scheme can support the important influence of obesity and clinical data representations in all cases after primary treatments. Our results suggested that obesity is still a crucial risk factor to SPCs in endometrial cancer.

: This paper presents a comparison between direct integer orders or classical model reference adaptive control (IO-DMRAC) versus its fractional orders counterpart (FO-DMRAC) applied to the F-16 aircraft longitudinal model pitch rate control. A substantial improvement is achieved when using fractional order adaptive control, since, in addition to performance indices, such as Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) being lower, the oscillations of the system output (pitch rate) in the transient period, are eliminated. Moreover, it is the first attempt in literature of adaptive control that a FO-DMRAC is applied to the pitch rate control of an aircraft. A F-16 short-period model, whose relative degree is equal to 1 (n^*=1) is analyzed by mean of simulations with good results. A FO-DMRAC is designed, for a specific operating flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the boundedness of all signals, including the internal ones ω(t) are assured.