Despite the successes earned in cataloguing and finding the role of the most of molecular components in living matter, the “biochemical and molecular” perspective, popular in biology, medicine and genetics, is unable to give account for crucial topics as the faculty of living systems to “feel”, to “perceive” what a given stimulus implies (means, indeed) for their survival. Condensed matter physics too, if bounded to a local, short-range, and perturbative approach, fails dramatically. This is also due to the role commonly assigned to water – actually the main constituent of living matter – deemed for long time to be merely chemical (as “solvent” or a reactant/product). Nonetheless, today many evidences show how living matter can be right conceived as a super-structured coherent water-based matrix, suggesting that the characterization of bio(electro)chemical and physical processes undertaken at molecular level in living matter, would let us unable to answer a question like this: what allows an amoeba, moreover without any neurons, to “know” to get closer to a nutrient or escape away from a toxin? I propose that to pursue such a fundamental inquiry it’s necessary an essentially relational approach, that is: to consider the living being at its grounding as the outcome of a physical history of relationships where symmetry-breakings, dissipation and coherence yield the emergence of the living state of matter, conceivable only as a time-dependent open process, and not as a portraited “body”. The effective tools to build up such an approach may be retrieved in far-from-equilibrium thermodynamics (TD), symmetry-breakings and gauge-fields theory, science of complexity, within the framework of a Quantum Field Theory. Indeed, within a field-view of matter, and of water especially, as it has been developed by a Quantum Electrodynamic (QED) description of condensed matter, it’s possible to give account for a physical basis too such an epistemologically elusive, though crucial, feature of living systems (i.e.: perception and meaning). The emerging landscape allows some important meditations about adaptation, evolution, ecodynamics, and about different conceptions of complexity and “information” in living realm. Furthermore, some neuroscientific themes like consciousness, qualia and their links to artificial intelligence could be supplied with due insights.

We search for limit cycles in the dynamical model of two-species chemical reactions that contain seven reaction rate coefficients as parameters and at least one third-order reaction step, that is, the induced kinetic differential equation of the reaction is a planar cubic differential system. Symbolic calculations were carried out using the Mathematica (or, Wolfram language) mathematical program package, and it was also used for the numerical verifications to show the following facts: the kinetic differential equations of these reactions each has two limit cycles surrounding the stationary point of focus type in the positive quadrant. In the case of Model 1, the outer limit cycle is stable and the inner one is unstable that appears in a supercritical Hopf bifurcation. Moreover, the oscillations in a neighborhood of the outer limit cycle are slow-fast oscillations. In the case of Model 2, the outer limit cycle is unstable and the inner one is stable. With another set of parameters, the outer limit cycle can be made stable and the inner one unstable.

Change orders have received considerable attention from researchers thus far, but none have considered pricing strategies of change orders through the interaction between general contractors and subcontractors. Previous studies found that contractors’ opportunistic bidding considering beyond-contractual reward (BCR) in the execution stage can be reduced by improving the construction management system and strengthening the supervision of contractors’ performance. However, the BCR remains in ecology of construction engineering. This study proposes an integrated evolutionary game theory-system dynamics model (ET-SD model) and simulates the pricing strategy of change orders between general contractors and subcontractors to explore the root cause of BCR phenomenon. Sensitivity analysis on the evolutionary dynamics of payoff is explored. Results reveal that change orders with BCR maintain Nash equilibrium and evolutionary stable strategy (ESS) unless changing the payoff structure between general and subcontractors’ pricing strategies. This study presents important managerial insights from the evolutionary game perspectives, nature of change orders, and payoff of the alternative.

Permanent magnet synchronous motor (PMSM) AC servo system shows the characteristics of uncertainty, time-varying and non-linearity, which makes it difficult for traditional PID control to achieve ideal control effect. Fuzzy control has strong adaptability to the problems of parameter variation, non-linearity and model inaccuracy of the controlled object. Vector control strategy is used to study its control principle and the realization of SVPWM. Because the motor object has certain fractional order characteristics, the fuzzy parameter self-tuning PIλ control is chosen as the position regulator of servo motor. It combines the accuracy of fractional order PI control and the adaptability of fuzzy control. A simulation model of PMSM three-closed-loop system is built in MATLAB/Simulink environment. The results show that the control method is effective and can satisfy the trajectory tracking of servo control.

A new approach is presented to defining the amount of information, in which information is understood as the data about a finite set as a whole, whereas the average length of an integrative code of elements serves as a measure of information. We obtain a formula for the syntropy of reflection, that is, the information that two intersecting finite sets reflect about each other. The specificities of reflection of discrete systems through the combination of their parts are considered, and it is shown that the additive syntropy and entropy of reflection are measures of structural order and chaos. Three information laws have been established: the law of conservation of the sum of chaos and order; information law of reflection; the law of conservation and transformation of information. An assessment of the structural organization and the level of development of discrete systems is presented. It is shown that various measures of information are structural characteristics of integrative codes of elements of discrete systems. The conclusion is made that, from the informational-genetic positions, the synergetic theory of information is primary in relation to the Hartley-Shannon information theory. In the appendix we consider the asymmetry of the mutual reflection of finite sets and the proportionality of arbitrary quantities.

The origination of most free-living animal species is predictable. ‘Light’ order production in the trophic levels below is the key. Absent from the abiotic environment (pre-primary level) and prokaryotes, ‘light’ order consists of differences in species composition between highly-developed, species-packed communities in which extinction may be the precursor to speciation, particularly ecologically comparable tropical continental lowland ones of Africa, Australia, India, and South America. Based on but not itself of matter and non-burnable, its nil waste heat content ‘compensates’ for burned-up food energy. Where the amounts of it on infra-apical trophic levels form an inverted pyramid like waste heat’s, occupancy of trophic levels from primary to apical is predictable (variation and selection assumed). Terminal non-inversion predicts post-apical vacancy. Examined communities were from grasslands (grasses, large grazing mammals, large carnivores), and woodlands (woody plants, butterflies, insect-eating birds, raptorial birds). Linnaeus’s binomial classificational system turned out to be unexpectedly rich in new content. A new object of study, the neoLinnaean, is recognised and a new process, the neoLyellian, advanced to explain it. Relations to Darwin’s and Lyell’s non-predictive theories of change, to ecology and evolution, to thermodynamics, statistical mechanics and quantum mechanics, and to neurology are discussed.

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.

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.

: 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.

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.

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.

In this paper, we present a three-step sixth-order iterative schemes to estimate the solutions of a nonlinear systems of equations, for predicting the shear strength of a reinforced concrete beam. This procedure is designed by means of a weight function technique. The values for the parameters of this system were randomly selected inside the prescribed ranges by technical standards for structural concrete; moreover, some of this parameters were fixed taking into consideration the solvability region of the adopted steel constitutive model. The efficiency of the new class is compared with other current schemes, with very good results.

Cavitation resulting from underwater explosions in compressible multiphase or multicomp-onent flows presents significant challenges due to the dynamic nature of shock-cavitation-structure interactions, as well as the complex and discontinuous nature of the involved interfaces. Achieving accurate resolution of interfaces between different phases or components, in the presence of shocks, cavitating regions, and structural interactions, is crucial for modeling such problems. Furthermore, pressure convergence in simulations involving shock-cavitation-structure interactions requires accurate algorithms. In this research paper, we employ the diffuse interface method, also known as the interface capturing scheme, to investigate cavitation in various underwater explosion test cases near different surfaces; free surface and a rigid surface. The simulations are conducted using the Unstructured Compressible Navier-Stokes (UCNS3D) finite volume framework employing central-weighted essentially non-oscillatory (CWENO) reconstruction schemes, utilising the five-equation diffuse interface family of methods. Quantitative comparisons are made between the performance of both models. Additionally, we examine the effects of cavitation as a secondary loading source on structures, and evaluate the ability of the CWENO schemes to accurately capture and resolve material interfaces between fluids with minimal numerical dissipation or smearing. The results are compared with existing high-order methods and experimental data, where possible, to demonstrate the robustness of the CWENO schemes in simulating cavitation bubble dynamics, as well as their limitations within the current implementation of interface capturing.

The magnetic properties of RCo3B2 compounds, with heavy rare earths, are investigated by using magnetic measurements and electronic structure calculations. The cobalt sublattice magnetizations are very small and antiparallel oriented to rare earths moments. Contributions of cobalt moments to the Curie constants were also shown. The cobalt magnetic behavior has been analyzed in spin fluctuations model. The presence of short-range order above the Curie temperatures in RCo3B2 compounds with R=Tb, Dy, and Ho has been attributed to reminiscent R5d-Co3d interactions.

Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.

It is a classic topic in algebras to construct and verify equalities that are composed of various algebraic operations of elements and their inverses or generalized inverses. In this note, the author constructs a matrix equality $(AB)^{\dag} = B^{\ast}(A^{\ast}ABB^{\ast})^{\#}A^{\ast}$ (called a mixed reverse-order law), where $A$ and $B$ are two matrices of appropriate sizes, $(\cdot)^{\ast}$, $(\cdot)^{\dag}$, and $(\cdot)^{\#}$ denote the conjugate transpose, the Moore--Penrose inverse, and the group inverse of a matrix, respectively, and shows that the mixed reverse-order law always holds. A list of variation forms of this matrix equality are also given, and necessary and sufficient conditions are obtained for them to hold. Especially, we show a remarkable fact that the two reverse-order laws $(AB)^{\dag} = B^{\dag}A^{\dag}$ and $(A^{\ast}ABB^{\ast})^{\#} = (BB^{\ast})^{\#}(A^{\ast}A)^{\#}$ are equivalent.

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

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

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

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

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

The optical conductivity in the charge order phase is calculated in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)₂I₃ using the mean field theory and the Nakano-Kubo formula. A peak structure due to interband excitation being characteristic in two-dimensional Dirac electron system is found above the charge order gap. It is shown that the peak structure originates from the Van Hove singularities of the conduction and valence bands, where those singularities are located at a saddle point between two Dirac cones in momentum space. The frequency of the peak structure exhibits drastic change in the vicinity of the charge order transition.

Abstract: Discussed is an expansion of SRT to fourth-order of space-time including any velocities and possible negative kinetic energies by real rest mass in analogy of the model amplitude of enforced damped oscillation. This paper serves an introduction to developed SRT including superluminar translating velocities without tachyons or imaginary restmass. Focused is on those parts, which develop the elaborated lorentz-transformations. Discussed are the problems of this theory.

The licensing of new reactors implies the use of verified and validated neutronics codes. Numerical validation can rely on sensitivity and uncertainty studies but they require repeated execution of time-consuming neutron flux and depletion calculations. The computational costs can be shortened by using perturbation theories. However, Depletion Perturbation Theory is restricted to single integral values such as a nuclide density. Relying on reduced basis approaches, which reconstruct the whole nuclide densities at once, is one way to get around this restriction. Furthermore, the adjoint-based reduced-order model uses the direct and adjoint equations for the projection. For diffusion or transport calculations, Exact-to-Precision Generalized Perturbation Theory has been developed. Still, no models for depletion calculations are readily available. Therefore, this paper describes a novel adjoint-based reduced order model for the Bateman equation. It uses a range-finding algorithm to create the basis and the Depletion Perturbation Theory for the reconstruction of the nuclide densities at first order. Our paper shows that for several perturbed cases, the depletion reduced-order model successfully reconstructs the nuclide densities. As a result, this serves as a proof of concept for our adjoint-based reduced order model which can perform sensitivity and uncertainty burn-up analysis in a shorter time.

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.

Data obtained by Direct Numerical Simulations (DNS) of pressure-driven turbulent channel flow are studied in the range 180 ≤ Reτ≤ 10,000. Reynolds number effects on the Mean Velocity Profile (MVP) and second order statistics are analyzed with a view of finding logarithmic behavior in the overlap region or even further from the wall, well in the boundary layer’s outer region. Values of Kármán constant for the MVPs and the Townsend-Perry constants for the streamwise and spanwise fluctuation variances are determined for the Reynolds numbers considered. A data-driven model of the MVP, proposed and validated for zero pressure gradient flow over a flat plate, is employed for pressure-driven channel flow by appropriately adjusting Coles’ strength of the wake function parameter, Π. There is excellent agreement between the analytic model predictions of MVP and the DNS-computed MVP as well as of the Reynolds shear stress profile. The skin friction coefficient Cf is calculated analytically. The agreement between the analytical model predictions and the DNS-based computed discrete values of Cf is excellent.

This study was aimed to assess visual performance and overall satisfaction of extended depth of focus (EDOF) contact lenses (CLs) in a presbyopic population. We prospectively investigated visual acuity at all distances (0.3, 0.4, 0.5, 0.7, 1, and 5 m), higher-order aberrations (HOAs), contrast sensitivity function, and, overall satisfaction score, before and during EDOF CL wear. Binocular visual acuity at 0.3, 0.5, 0.7, 1, 2, 3, and 5 m when wearing EDOF CLs was 0.01 ± 0.14, -0.08 ± 0.02, -0.08 ± 0.02, -0.08 ± 0.00, -0.08 ± 0.00, -0.08 ± 0.02, and -0.07 ± 0.02, respectively. We found a significant improvement at near to intermediate distances (0.3, and 0.5 m), but no significant change at intermediate to far distances (0.7, 1, 2, 3, and 5 m) between before and during CL wear. The area under the log contrast sensitivity function was not significantly changed neither under photopic nor mesopic conditions (p=0.099, and p=0.689). Ocular third-order aberrations, fourth-order aberrations or total HOAs for a 4-mm pupil significantly increased. The overall satisfaction score significantly improved by wearing EDOF CLs. EDOF CLs significantly improved visual acuity at near to intermediate dis-tances, while maintaining far vision, and the effect of contrast sensitivity was minimal, suggesting its viability of presbyopic correction in such candidates.

Environmental responsibility and economic benefits have promoted the development of closed-loop supply chain (CLSC), and shortages and channels are considered to be two important issues in CLSC. This paper explores ordering and channel decisions in CLSC with new and differentiated remanufactured products, and considers the price and sales effort-dependent demands, as well as the proportion of emergency orders determined by emergency order costs and backorder losses, and establishes an integrated and decentralized CLSC game models. We introduce a stochastic sales effort, which affects two types of products. Numerical results show that sales effort and the order quantity of new and remanufactured products exhibit concave and convex functions, respectively. Wherein, the upper limit of sales effort has a greater impact on supply chain decisions. High sales efforts can serve as a means of coordinating dispersed supply chains. Moreover, in different cases, decisions of integrated channel are better than those of decentralized channel. Finally, whether the supply chain adopts an emergency order strategy depends on the relative cost of emergency orders and out of stock costs. According to the research in this article, some management insights are also provided.

In this paper, we present a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations. After the convergence analysis, we study the stability of this class by using the tools of complex discrete dynamics. This allows us to select those elements of the class with lower dependence on initial estimations. We verify by means of numerical tests that the stable members on quadratic polynomials perform better than the unstable ones, when applied to other non-polynomial functions. We also compare the performance of the best elements of the family with known methods, such as the schemes by Newton or Chun, among others, showing robust and stable behaviour.

We introduce and discuss a generalization of the classical multi-objective optimization to pairs of functions. This procedure is referred to as bi-multi-objective optimization. A justification of this general optimization procedure is presented, related both to multi-objective optimization under ambiguity concerning individual preferences and to Pareto optimality for a family of preferences with nontransitive indifference. Incidentally, the binary relation naturally associated to a bi-multi-objective optimization problem is represented by a finite bi-multi-utility, which generalizes to the nontransitive case the classical finite multi-utility representation. An important application is presented to Markowitz portfolio selection under ambiguity concerning both the vector of returns and the covariance matrix.

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.

We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1-control problem for quasi-linear parabolic equation with non-local p[u]-Laplacian and with a cost functional of a tracking type. The main characteristic feature of the considered class of parabolic problems is the fact that the variable exponent p(t,x) and the anisotropic diffusion tensor D(t,x) are not well predefined a priori, but instead these characteristic non-locally depend on a solution of this problem, i.e., pu=p(t,x,u) and Du=D(t,x,u). We prove the existence of optimal pairs with sparse L1-controls using for that the indirect approach and a special family of approximation problems.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

We study the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The initial SoP of a twisted vector optical field (TVOF) modulated by the high-order twisting phase possesses various symmetric distributions. The propagating properties of a high-order TVOF with locally linear polarization and hybrid SoP are explored, including the intensity compression, expansion, and conversion between the linear and circular polarization components. In particular, orbital angular momentum (OAM) appears in a high-order TVOF during propagation where no OAM exists in the initial field. The variation of OAM distribution in cross-section becomes more frequent with the increase of the twisting phase order. In addition, a non-symmetric OAM distribution appears in an anisotropic TVOF, leading to the rotation of the beam around the propagation axis during propagation. These results provide a new approach for optical field manipulation in a high-order TVOF.

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice-gas model, each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

In this paper, an iterative procedure to find the solution of a nonlinear structural model is introduced. The model presents different multiplicities where parameters are randomly selected within a solvability region. To achieve this aim, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, reaching the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The structural problem, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness and applicability of the proposed scheme.

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step – generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

The global Covid-19 crisis has seen the push for many education institutions substituting traditional classroom learning to online platforms. This change in the learning experience has been expected to cause major and likely unequal interruption not only in students’ learning, but their well-being overall. Given this, the present study aims to investigate how online or open distance learning, implemented during times of a health crisis, impacted the mental well-being of UiTM students. The study was conducted via an online survey and an online group discussion during the last week of online classes between 29th June to 1st July 2020. Following research on negative emotional states, the short form of the Depression Anxiety Stress Scales (DASS-21) was included in the survey. Results indicate that students experienced varying levels of negative emotions, specifically feeling anxious over situations that might cause panic, feeling emotionally sensitive as well as feeling less motivated to do things. Discussions include how the government of Malaysia needs to ensure for students to be equipped with the right amenities that will offer a smoother ODL experience and that educational institutions provide their stakeholders with clear information so that students can make a more informed choice about their education.

The concepts of fractional calculus and the related techniques have been gaining momentum in circuit system fields, and an increasing body of evidence suggests that fractional-order characteristics are widely distributed in electronic components. In this paper, we consider the fractional characteristics of non-solid aluminum electrolytic capacitors and focus on the nonlinear dynamic characteristics of peak-current-mode controlled (PCMC) dc-dc boost converters with such components. In the work, we establish a piecewise smooth non-commensurate fractional-order model to describe the converter, in which the fractional-order equivalent impedance model of capacitors is adopted and the detailed control loop is considered. In order to analyze the converter, we use the fractional Adams-Bashforth-Moulton typed method (F-ABM) and stroboscopic map technique to obtain the time-domain solutions and the bifurcation diagram. The results of bifurcation diagrams indicate that, with the change of different parameters, the converter enters chaotic state through period doubling bifurcation. In order to provide empirical evidence for the nonlinear dynamic analysis, we consider both circuit-level simulation and experiments in the work, the results of which further confirm the results of theoretical analysis.

In European thought, the relationship among the fields of psychology, education, and health is both complex and obscured. Foucault’s acclaimed work, The Order of Things, offers a framework to evaluate their interconnection by identifying three distinct periods of European thought since the 16th century with respect to the ordering of phenomena—Renaissance, Classical and Modern. Theoretically dense and often difficult to decipher, the book’s categorization of language, value and being has been understandably underused, yet it provides deep insights into what have come to be known as psychology, education and health and remains invaluable in understanding the origin, limits and consequences of these fields. How Foucault’s analysis can be interpreted concerning the development of these areas as to each of the three periods of European thought is investigated. An approach based on narrative research appraises the analysis offered in the book. The results, presented for the first time in table form, compare these three periods, demonstrating a continuing practical value to Foucault’s insights. With the aid of the framework revealed by these tables, the boundaries and relationship of psychology, education and health become clear and their limitations—plus potential solutions to them—can be identified to mitigate anticipated negative consequences.

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

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

Ofloxacin is a highly efficient and widely used antibiotic drug. It is classified as a refractory pollutant due to its poor biodegradability. Consequently, it is commonly found in water sources, requiring efficient methods for its removal. Advanced Oxidation Processes (AOPs) offer efficient alternatives since those yield complete degradation not achieved in adsorption or membrane processes. Previous studies suggest ofloxacin degradation follows a pseudo-first or -second order processes, whereas for full removal of refractory pollutants – lower pseudo-orders are required. Monitoring the actual “pseudo-order” degradation kinetics of ofloxacin is needed to evaluate any proposed AOP process. This study presents a simple procedure to evaluate pseudo-orders of AOPs. Photolysis of 20 mM ofloxacin solutions follow pseudo-zero order kinetics, with half-life times (t_1/2) of approx. 60 min. TiO₂ heterogenous catalyst show to have no influence at low concentration (0.2 mg L^-1) but a significant reduction of half-life time (t_1/2 = 20 min) and increase in pseudo-order (0.8) is measured at 2.0 mg L^-1. Similar results are obtained with homogenous catalysis by 2.0 mg L^-1 H₂O₂. The combination of H₂O₂ and TiO₂ catalysts shows additional reduction in half-time life with increase in the pseudo-order to 1.2. The conclusions are (1) heterogenous and homogenous photocatalysis can effectively degrade ofloxacin, (2) combined photocatalysis yields higher pseudo-order, being less prone to achieve full removal, (3) analysis of specific pseudo-orders in AOPs of refractory pollutants helps to further elucidate the efficiency of the processes.

Chivalry is a concept that is both familiar and distant to many Japanese. There is no other social class in the world that resembles knights as much as the samurai in Japan. However, why is it that there is such a gap between knights and warriors, even though they are both warriors with the same social status and honor? This paper reviews the legal debates on the deposed sovereigns’ rights have emerged since 20th century. Among them, the right to appoint knights by heads of deposed royal families is one of the focal points. The author begins with a comprehensive review of legal debates on the subject. Six principles on the appointment are extracted from the review. Then, a comparison between chivalry and Bushido, the Japanese Samurai code, was carried out.

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

This paper is our attempt on the basis of physical theory to bring more clarification on the question ``What is life?'' formulated in the well-known book of Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the ``global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

District heating networks have become widespread due to their ability to distribute thermal energy efficiently, which leads to reduced carbon emissions and improved air quality. The characteristics of these networks vary remarkably depending on the urban layout and system amplitude. Moreover, extensive data about the energy distribution and thermal capacity of different areas are seldom available. Design, optimization and control of these systems are enabled by the availability of fast and scalable models of district heating networks. This work addresses this issue by proposing a novel method to develop a scale-free model of large-scale district heating networks. Starting from coarse data available at the main substations, a physics-based model of the system aggregated regions is developed by identifying the heat capacity and heat loss coefficients. The model validation on the network of Västerås, Sweden, shows compatibility with literature data and can therefore be exploited for system design, optimization and control-oriented applications. In particular, the possibility to estimate the heat storage potential of network regions allows new smart management strategies to be investigated.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

In this work we present the results obtained with an artificial neural network (ANN) which we trained to predict the expected output of high-order harmonic generation (HHG) process, while exploring a multi-dimensional parameter space. We argue on the utility and efficiency of the ANN model and demonstrate its ability to predict the outcome of HHG simulations. In this case study we present the results for a loose focusing HHG beamline, where the changing parameters are: the laser pulse energy, gas pressure, gas cell position relative to focus and gas cell length. The physical quantity which we predict here using ANN is directly related to the total harmonic yield in a specified spectral domain (20-40 eV). We discuss the versatility and adaptability of the presented method.

In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.

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.

Stochastic modelling of geometrically imperfect steel frame structures requires inputs of statistical values of the imperfection parameters, in some cases also with suitably selected mutual correlations between these input parameters. The paper presents a verification study of two stochastic methods to directly model the initial global geometrical imperfections of the steel frame structures. The stochastic input values of geometrical imperfections are derived from the tolerance criteria of the corresponding European Standard. Two advanced stochastic methods have been developed, referred as #RSS (random story sway) and #RSP (random story position). These methods are verified using random sampling simulations. This study provides useful provisions for the advanced numerical analyses of multi-story steel frames of various geometries. The proposed methods are verified for equidistant story heights and for structures of up to 24 stories, hence might be used for the most types of the standard steel frame structures.

In this paper we compare the effects of forecasting demand using individual (disaggregated) components versus first aggregating the components either fully or into several clusters. Demand streams are assumed to follow autoregressive moving average (ARMA) processes. Using individual demand streams will always lead to a superior forecast compared to any aggregates, however we show that if several aggregated clusters are formed in a structured manner then these subaggregated clusters will lead to a forecast with minimal increase in mean-squared forecast error. We show this result based on theoretical MSFE obtained directly from the models generating the clusters as well as estimated MSFE obtained directly from simulated demand observations. We suggest a pivot-algorithm, that we call Pivot Clustering, to create these clusters. We also provide theoretical results to investigate sub-aggregation, including for special cases such as, aggregating MA(1) streams and ARMA streams with similar or same parameters.

In a previous paper, we solved the partial differential equation of Mullins problem in the case of the evaporation-condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed 〖y'〗^2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation-condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions.

For effective warehouse management, various criteria should be taken into consideration in terms of inventory management, demand, transportation distance, usage area, delivery-waiting times, and minimizing the costs that may arise from them. Because, the purpose of the product assignment problem is to minimize the total transport distance during storage and to reduce the space required for product assignment. However, the storage location assignment problem (SLAP) occurs simultaneously with production planning activities in real life. In this study, an integrated mixed-integer nonlinear (MINLP) mathematical model is proposed, which includes the assignment of products to storage areas and production planning, using the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) class based policy for storage systems where multiple criteria are important. In the TOPSIS class-based policy, weight and waiting time criteria are taken into account, as well as the COI (Cube-per-order index index), which is widely used in the literature. In addition, a decision support system flow has been proposed that takes into account the single criterion, multiple criteria and COI index criteria of the developed model and provides its integration with different product assignment policies. Detailed literature research; It has been revealed that the proposed mathematical model and decision support system flow have the feature of applying an existing field of science to a new problem.

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.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

Optical parametric amplification (OPA) represents a powerful solution to achieve broadband amplification in wavelength ranges beyond the scope of conventional gain media, for generating high-power optical pulses, optical microcombs, entangled photon pairs and a wide range of other applications. Here, we demonstrate optical parametric amplifiers based on silicon nitride (Si₃N₄) waveguides integrated with two-dimensional (2D) layered graphene oxide (GO) films. We achieve precise control over the thickness, length, and position of the GO films using a transfer-free, layer-by-layer coating method combined with accurate window opening in the chip cladding using photolithography. Detailed OPA measurements with a pulsed pump for the fabricated devices with different GO film thicknesses and lengths show a maximum parametric gain of ~24.0 dB, representing a ~12.2 dB improvement relative to the device without GO. We perform a theoretical analysis of the device performance, achieving good agreement with experiment and showing that there is substantial room for further improvement. This work demonstrates a new way of achieving high photonic integrated OPA performance by incorporating 2D materials.

Lithium batteries are widely used due to their advantages such as high energy density, stable performance, low pollution, and long recyclable life. Accurate SOC estimation is important for the use of lithium batteries. To address the problem of low accuracy of SOC estimation by traditional methods, this paper proposes a joint method of fractional order robust unscented Kalman filter (FORUKF) and robust unscented Kalman filter (RUKF) to estimate SOC. The method is based on a fractional order model (FOM) that combines the unscented transformation (UT) technique, the H∞ observer and the joint estimator. Specifically, an adaptive genetic algorithm (AGA) was first used to identify the parameters of the FOM for lithium batteries and to verify the accuracy of the model. Estimation and updating of the ohmic resistance R0 and the capacity QN in the model in real-time by RUKF and then estimation of the SOC by FORUKF. Finally, the accuracy of FORUKF-RUKF was verified under the Federal Urban Driving Schedule (FUDS), US06 Highway Driving Schedule and Beijing Dynamic Stress Test (BJDST). According to the results, the FORUKF-RUKF estimated SOC was found to have better accuracy and robustness than the RUKF, FOUKF and EKF.

Centromeres, the chromosomal loci where spindle fibers attach during cell division to segregate chromosomes, are typically found within satellite arrays in plants and animals. Satellite arrays have been difficult to analyze because they comprise megabases of tandem head-to-tail highly repeated DNA sequences. Much evidence suggests that centromeres are epigenetically defined by the location of nucleosomes containing the centromere-specific histone H3 variant cenH3, independently of the DNA sequences where they are located; however, the reason that cenH3 nucleosomes are generally found on rapidly evolving satellite arrays has remained unclear. Recently, long read sequencing technology has clarified the structures of satellite arrays and sparked rethinking of how they evolve, while new experiments and analyses have helped bring both understanding and further speculation about the role these highly repeated sequences play in centromere identification.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which are also BICs in a laser-written second-order topological lattice, and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such an HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

Damage in concrete structures initiates as the growth of diffuse microcracks that is followed by damage localisation and eventually leads to structural failure. Weak changes such as diffuse microcracking processes are failure precursors. Identification and characterisation of these failure precursors at an early stage of concrete degradation and application of suitable precautionary measures will considerably reduce the costs of repair and maintenance. To this end, a reduced order multiscale model for simulating microcracking-induced damage in concrete at the mesoscale levelis proposed. The model simulates the propagation of microcracks in concrete using a two-scale computational methodology. First, a realistic concrete specimen that explicitly resolves the coarse aggregates in a mortar matrix was generated at the mesoscale. Microcrack growth in the mortar matrix is modelled using a synthesis of continuum micromechanics and fracture mechanics. Model order reduction of the two-scale model is achieved using clustering technique. Model predictions are calibrated and validated using uniaxial compression tests performed in the laboratory.

We report on the application of femtosecond laser micromachining to the fabrication of complex glass microdevices, for high-order harmonic generation in gas. The three-dimensional capabilities and extreme flexibility of femtosecond laser micromachining allow us to achieve accurate control of gas density inside the micrometer interaction channel. This device gives a considerable increase in harmonics generation efficiency if compared with traditional harmonic generation in gas jets. We propose different chip geometries that allow to control the gas density and driving field intensity inside the interaction channel to achieve quasi-phase matching conditions in the harmonic generation process. We believe that these glass micro-devices will pave the way to future downscaling of High-order Harmonic Generation beamlines.

In addition to the canonical loss-of-function mutations, mutations in proteins may additionally result in gain-of-function through the binary activation of cryptic ‘structural capacitance elements’. Our previous bioinformatic analysis allowed us to propose a new mechanism of protein evolution - structural capacitance – that arises via the generation of new elements of microstructure upon mutations that cause a disorder-to-order (DO) transition in previously disordered regions of proteins. Here we propose that the DO transition is a necessary follow-on from expected early codon-anticodon and tRNA acceptor stem-amino acid usage, via the accumulation of structural capacitance elements - reservoirs of disorder in proteins. We develop this argument further to posit that structural capacitance is an inherent consequence of the evolution of the genetic code.

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

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Humans are incapable of judging the temporal order of visual events at brief temporal separations with perfect accuracy. Their performance---which is of much interest in visual cognition and attention research---can be measured with the temporal-order judgment task, which typically produces S-shaped psychometric functions. Occasionally, researchers reported plateaus within these functions, and some theories predict such deviation from the basic S shape. However, the centers of the psychometric functions result from the weakest performance at the most difficult presentations and therefore fluctuate strongly, leaving existence and exact shapes of plateaus unclear. This study set out to investigate whether plateaus disappear if the data accuracy is enhanced, or if we are ``stuck on a plateau'', or rather with it. For this purpose, highly accurate data were assessed by model-based analysis. The existence of plateaus is confidently confirmed and two plausible mechanisms derived from very different models are presented. Neither model, however, performs well in the presence of a strong attention manipulation, and model comparison remains unclear on the question which of the models describes the data best. Nevertheless, the present study includes the highest accuracy in visual TOJ data and the most explicit models of plateaus in TOJ studied so far.

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

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 this study, we evaluated the antibacterial effect against Staphylococcus aureus and Salmonella Typhimurium in fried fish paste using floating electrode-dielectric barrier discharge (FE-DBD) plasma (1.1 kV, 43 kHz, N2 1.5 m/s, 1-60 min). In addition, quality evaluation (pH, VBN) of fried fish paste was conducted after FE-DBD plasma treatment. When FE-DBD plasma was treated for 1, 5, 10, 20, 30 and 60 min, S. aureus decreased by 0.16-1.13 log10 CFU/g, and S. Typhimurium decreased 0.25-1.13 log10 CFU/g. Both decreased > log10 CFU/g at 60 min. The D-value was 58.92 and R2 was 0.97 for S. aureus using first-order kinetics, and the D-value was 43.60 and R2 was 0.97 for S. Typhimurium using the Weibull model. There was no significant difference in pH after FE-DBD plasma treatment (p > 0.05). However, volatile basic nitrogen (VBN) significantly decreased as the treatment time increased (p < 0.05), and it was the lowest at 60 min to 3.46. Therefore, FE-DBD plasma treatment could be considered as a technology for preserving the quality of processed foods.

The performance of laser beams in tracking Lissajous scan trajectories is severely limited by beam jitter. To enhance the performance of fast steering mirror (FSM) control in tracking Lissajous scan trajectories, this paper proposed a fractional order active disturbance rejection controller (FOADRC) and verified its effectiveness in improving system scanning tracking accuracy. A dynamic mathematical model of fast steering mirror was studied and the design of parameters for the control mode of the closed-loop system was determined. A reduced order linear active disturbance rejection controller suitable for FSM systems was designed and the corresponding fractional order proportional differentiation (FOPD) controller were determined according to the mathematical model. The use of the designed controller enabled high-performance tracking of high-frequency Lissajous scanning curves (X-axis 500 Hz, Y-axis 350 Hz) and met the need for high-frequency repetitive scanning. The controller has the characteristics of simple implementation and low computational complexity and is suitable for closed-loop control applications in engineering.

Modern power systems are confronted with a spread concern on the frequency stability issue due to the widespread integration of randomly fluctuating renewable resources. To address the above concern, this work introduces a load frequency control (LFC) scheme based on a hydrogen based energy-storage unit and a parameter tuning strategy for fractional-order proportional-integral-derivative (FOPID) controller. Firstly, a two-area interconnected power system (IPS) model, including thermal, hydro, solar, wind, gas power generator, and hydrogen based energy-storage unit, is established. Then, a FOPID controller is designed for this IPS model, and an improved gradient-based optimizer (IGBO) is developed to adaptively regulate the parameters of the FOPID controllers. Finally, the effectiveness of the offered LFC scheme are tested through load disturbance and renewable energy fluctuations test scenarios, and provides comparison and robustness analysis among different schemes. The test results validated that the offered LFC scheme can effectively suppress the frequency fluctuations of IPS and has excellent robustness.

In the field of computational fluid dynamics (CFD) for rotorcraft, two significant challenges are resolving the complex vortex structures in rotor wakes, and representing the moving rotor blades in the ambient airflow. This study addresses the first challenge by using a third-order unstructured finite volume solver, which, compared to its second-order counterpart, has substantially lower dissipation. Consequently, even relatively coarse meshes are capable of resolving small vortices. With this background flow field solver, the second challenge is addressed by modeling each rotor as an Actuator Disk Model (ADM), or describing individual rotor blades as actuator lines, designated as the Actuator Line Model (ALM). Both of these models are equipped with an improved correction for aerodynamic losses at blade tips, which is thoroughly presented in the methodology section. The numerical experiments section centers on analyzing errors linked to various sampling approaches. Additionally, the article discusses comparisons between vortex theory and ALM, specifically regarding calculations for fixed-wing aircraft. Furthermore, high-order precision and parallel efficiency are exemplified in scenarios encompassing rotors engaged in both hovering and forward flight rotors. The results in this paper demonstrate that the combination of the ALM/ADM with the improved tip loss correction and the third-order finite volume solver presents a new way of developing efficient tools for the aerodynamic analysis of helicopter rotors.

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

For order-of-addition experiments, the response is affected by the addition order of the experimental materials. Consequently, the main interest focuses on creating a predictive model and an optimal design for optimizing the response. Van Nostrand (1995) proposed the pairwise-order (PWO) model for detecting PWO effects. Under the PWO model, the full PWO design is optimal under various criteria but is often unaffordable because of the large run size. In this paper, we consider the D-, A- and M.S.-optimal fractional PWO designs. We first present some results on information matrices. Then, a flexible and efficient algorithm is given for generating these optimal PWO designs. Numerical simulation shows that the generated design has an appealing efficiency in comparison with the full PWO design, though with only a small fraction of runs. Several comparisons with existing designs illustrate that the generated designs achieve better efficiencies, and the best PWO designs and some selected 100% efficient PWO designs generated by the new algorithm are reported.

The paper draws attention and opens the debate on major societal issues that concern not only Muslims but human societies, at large, because of their profound implications, afflictions, and their present and future transitive dimensions. The paper discusses two major issues that have attracted a great deal of attention in the recent past: wealth and income disparities, and global indebtedness. Four remedies have stressed upon and/or proposed to eradicate and/or lessen some of the burdens of these problems have been thoroughly examined. These are: - Stripping commercial banks of their power to create money out of thin air (i.e., Ex Nihilo). Thus, reviving financial reform in line with the spirit of the call for the “Establishment of a National Bank [in England]” in the 1820s by the renowned British economist David Ricardo (1772-1823). The Bank of England was a private commercial entity at that time. - Prohibiting of ‘harmful’ speculation activities in financial and economic transactions and/or imposing hefty taxes on transactions relating to such activities. The implementation of such a policy requires and clear-cut distinction between the ‘harmful’ and ‘non-harmful’ speculative activities in financial and non-financial markets. - Levying adequate and fair taxes on the wealthiest upper class at the global scene. Calls for such a policy is on rise in the past few years. For instance, “Speakers at the European Development Days summit in Brussels, [in 2017], said that a just tax system should be “at the heart” of the development debate, and that more transparency is needed to ensure that companies pay their fair share. Tax avoidance schemes used by multinational companies, such as moving profits to tax havens, result in global losses of around $650 billion a year in tax receipts — with developing countries losing $200 billion, according to a study from the International Monetary Fund”, (Edwards, 2017; Crivello et al., 2015, p. 21) - Establishing a neutral legislative and tax regimes for different modes of financing. Thus, providing ‘a level playing field’ for equity and debt modes of financing due to the current biasness of the tax regimes to debt-based financing instruments as it has been documented in various studies carried out by the IMF, the European Commission, and other international prominent bodies.

Proteomic analysis revealed the preservation of many proteins in the “Heslington brain” (which is at least 2,600-year-old brain tissue uncovered within the skull excavated in 2008 from a pit in Heslington, Yorkshire, England). Five of these proteins (“main proteins”), heavy, medium, and light neurofilament proteins (NFH, NFM, and NFL), glial fibrillary acidic protein (GFAP), and myelin basic (MBP) protein are engaged in the formation non-amyloid protein aggregates, such as intermediate filaments and myelin sheath. We used a wide spectrum of bioinformatics tools to evaluate the prevalence of functional disorder in several related sets of proteins, such as “main proteins” and their 44 interactors, as well as all other protein identified in the Heslington brain. These analyses revealed that all five “main proteins”, half of their interactors and almost one third of the Heslington brain proteins are expected to be mostly disordered. Furthermore, most of the remaining proteins are expected to contain sizable disordered regions. This is in contrary the expected substantial (if not complete) elimination of the disordered proteins from the Heslington brain. Therefore, it seems that the intrinsic disorder of NFH, NFM, NFL, GFAP, and MBP, their interactors and many other proteins might play a crucial role in preserving the Heslington brain by forming tightly folded brain protein aggregates, in which different parts are glued together via the disorder-to-order transitions.

Since 1974, when Heinz von Foerster made the distinction between “the cybernetics of observed systems” as first-order cybernetics (1oC) and “the cybernetics of observing systems” as second-order cybernetics (2oC), cybernetics has been dominated by this observer-centric paradigm that he claimed cannot be extended meaningfully to a third-order. Rather than attempting to extend his paradigm, we derive an alternative, model-centric paradigm from first principles of regulation that naturally extends to three orders, where the third order is ethical regulation. We thus consider a type of regulator that requires a third model and a third observer: If the third model is a model of acceptable (ethical) situations, then a third observer is a necessary element of the system’s “conscience” that prevents or detects any violations of the model of ethical situations. In this paradigm, the cybernetics of systems that are designed to exhibit ethical behaviour can be characterized as third-order cybernetics (3oC). By being able to extend the paradigm to include ethical systems, the model-centric paradigm brings clarity and utility that is not possible using the philosopher-friendly observer-centric paradigm and its under-specified (abstract) observers. Finally new definitions for cybernetics are proposed that clearly differentiate between the science and the philosophy, of cybernetics.

The high dimensions and governing non linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non linearities. The work here presented applies the ideas motivated by non linear dynamical systems theory - the Koopman Operator - to an innovative algorithm in the context of wind farm systems - Input Output Dynamic Mode Decomposition - to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

The search for new materials that could improve the energy density of Li-ion batteries (LIB) is one of today’s most challenging issues. Recently, cation-disordered lithium-excess metal oxides have emerged as a promising new class of cathode materials for LIB, due to their high reversible capacities and nice structural stability. However, a full structural model of the Li-transition metal (TM) sharing sublattice and the origin of short range ordering (SRO) of cation ions requires further investigation. In this work, we put forward a Monte Carlo strategy of building a cation-disordered rocksalt material supercell model. The cation ions of Li_1.0Ti_0.5Ni_0.5O₂ (LTNO) are placed at the FCC sublattice sites with the constraint of Pauling’s electroneutrality rule, instead of a random way. This constraint causes the Li-Ti and Ni-Ni clustering (the cation short range ordering). Based on this model, we discussed the relationship between the short range ordering, the local distorting, the theoretic capacity and the order-disorder strengths. A unified understanding of these factors in cation-disordered materials may enable a better design of disordered-electrode materials with high capacity and high energy density.

Materials design for processing and application requires fundamental understanding of their properties based interatomic interaction. The use of the novel concept of total bond order density (TBOD) as a single quantum mechanical metric to characterize the internal cohesion of a crystal and correlate with the calculated physical properties is particularly appealing. This requires detailed first-principles calculation of the electronic structure, interatomic bonding and related properties. In this article, we use this new concept and apply it to chalcogenide crystals based on data obtained from 25 crystals: Ag₂S, Ag₂Se, Ag₂Te, As₂S₃, As₂Se₃, As₂Te₃, As₄Se₄, Cu₂S, Cu₂Se, Cu₂Te, Cu₄GeS₄, Cu₂SnS₃, Cu₂SnSe₃, GeS₂, GeSe₂, Ge₄Se₉, Sb₂S₃, Sb₂Se₃, Sb₂Te₃, SnS, SnSe, CdSe, CdTe, ZnSe, and ZnTe. Together with the calculated optical and mechanical properties, we demonstrate the efficacy of using this novel approach for materials design that could facilitate the exploration and development of new chalcogenide crystals and glasses. Moreover, the TBOD and its partial components (PBOD) could be the key descriptors in machine learning protocol for broader scale design when a large database is available.

Mixing is considered as a critical process parameter (CPP) during process development due to its significant influence on reaction selectivity and process safety. Nevertheless, mixing issues are difficult to identify and solve owing to their complexity and dependence on knowledge of kinetics and hydrodynamics. In this paper, we proposed an optimization methodology using Computational Fluid Dynamics (CFD) based compartmental modelling to improve mixing and reaction selectivity. More importantly, we have demonstrated that through the implementation of surrogate-based optimization, the proposed methodology can be used as a computationally non-intensive way for rapid process development of reaction unit operations. For illustration purpose, reaction selectivity of a process with Bourne competitive reaction network is discussed. Results demonstrate that we can improve reaction selectivity by dynamically controlling rates and locations of feeding in the reactor. The proposed methodology incorporates mechanistic understanding of the reaction kinetics together with an efficient optimization algorithm to determine the optimal process operation and thus can serve as a tool for quality-by-design (QbD) during product development stage.

Sustainability in material purchasing is a growing area of research. Goods purchasing decisions strongly affect transportation path flows, vehicle consolidation, inventory levels and related obsolescence costs. Within a global sourcing context, companies experience the need of new decision making approaches capable to consider a large variety of factors, also linked with society and environment. Environmental impact assessment has become a key requirement for materials purchasing and transportation decisions since global warming is a rising concern both in academic and industrial researches. In fact, it is well known that the freight transport industry is responsible for large amounts of carbon emissions contributing to global warming. In this paper, we initially analyse and compare the environmental economic policies established by the International Governments in relation to the carbon trading systems adopted. Then, we develop a multi-objective lot sizing approach useful in practice to define the sustainable quantity to purchase when a Cap and Trade mitigation policy is present. We further analyse the model behaviour according to different carbon price values by demonstrating that carbon prices are still far too low to motivate managers towards sustainable purchasing choices.

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.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

In this paper, we concentrate on the study of the properties of residual Tsallis entropy for order statistics. Order statistics have an important role in reliability structural engineering for example for modelling lifetimes of series and parallel systems. The residual Tsallis entropy of ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of ith order statistics from a uniform distribution is investigated. In a mathematical framework, a method to express the residual Tsallis entropy of the ith order statistic from a continuous distribution in terms of the residual Tsallis entropy of the ith order statistic from a uniform distribution is provided. This approach may provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. Further, we study the monotonicity properties of the residual Tsallis entropy of order statistics under dierent conditions. By studying these properties, deeper understanding of the relationship between the position of order statistics and the resulting residual Tsallis entropy is gained.

We here investigate the dynamical behavior of a fractional-order predator-prey system with anti-predator behavior and Holling IV type functional response. First we study the non-negativity, existence, uniqueness, and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, and prove the existence of a supercritical Hopf bifurcation in the system. After providing numerical simulations to illustrate the conclusions theoretically derived, by summarizing those various analytical results obtained, we finally present three interesting conclusions that can contribute to better understanding and preservation of ecological systems.

Elucidating physicochemical processes in the degradation of pollutants may optimize their removal from water sources. This work presents a set of elementary steps in the photocatalytic degradation of carbamazepine (CBZ), assuming a steady state approximation in an Advanced Oxidation Process (AOP) combining short-wave ultraviolet radiation (UVC), homogeneous reagent (H₂O₂) and heterogeneous (TiO₂) catalyst. Elementary steps include excitation of both reagent/catalysts by UVC photons, adsorption of CBZ on the excited TiO₂, or its oxidation by hydroxyl radicals. Assuming the steady state approximation on the intermediate products (excited TiO₂, CBZ- excited TiO₂ complex, and hydroxyl radicals), leads to rate laws for degradation of CBZ, in which UVC radiation, TiO₂, and H₂O₂ are pseudo first order at all concentrations or intensities having no direct influence on CBZ pseudo-order, whereas CBZ shifts from pseudo first order at low concentrations to pseudo-zero order at high concentrations. Several experiments to test the mechanism were conducted, by varying CBZ, H₂O₂, and TiO₂ concentrations, and UVC radiation intensities. Measured results indeed fit the suggested mechanism for the first three, but irradiation intensity appears to shift CBZ influence from pseudo-second to pseudo-first order with increased intensities. Corrected elementary steps are proposed to fit the results.

Malaysia implemented a movement control order (MCO) to curb the spread of the SARS-CoV-2 virus in March 2020. Despite healthcare services remaining operational, rising COVID-19 infections and MCO restrictions have forced healthcare professionals to seek a compromise between service capacity and standard operating procedure compliance. A cross-sectional survey was conducted among public and private sector doctors, dentists and pharmacists to determine how lockdown measures impacted healthcare services. Responses from 413 doctors, 193 dentists, and 163 pharmacists were analysed. Pharmacy services remained mostly unaffected throughout the MCO. In contrast, operational capacities for surgical and dental services were severely affected during the MCO. All service sectors reported restricting patients or accompanying individuals at the workplace, reductions in staffing capacity, and shortened patient contact time at various degrees. Many pharmacy and medical participants reported supplying extended medication supplies to patients. Adoption of virtual healthcare services was generally poor. All private service sectors suffered financial losses ranging between 59 to 75%. Periodic assessments of the healthcare system throughout the pandemic are required to identify which patients have their treatment compromised so that healthcare managers and policy makers can plan and implement appropriate interventions that help alleviate pressure within the health system.

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

^{We consider the collective pricing orders in a minimum supply chain that is composed of a monopolistic manufacturer and many retailers that belong to the same chain store firm. The retailers have the freedom to raise or lower the local price. The chain store firm sets up the commercial rules for local retail stores to maximize its total payoff. The monopolistic manufacturer firm controls the total quantity supplied for the market to achieve maximum benefits. We applied the two dimensional Ising model in statistical physics to map the collective distribution of microscopic strategy of local retailers into the macroscopic total payoff of the chain store firm. The local stores choose to raise the price or lower the price based their own mind when the supply in market surpasses the demand. When the supply in market is far less than the demand, the stores synchronously raise prices, even though a local store only have the incomplete information of their nearest neighboring supermarket. We find the critical equation for the balance point between the action of supplier and the action of chain store management based on game theory and statistical physics. The critical equation can identify the Nash equilibrium point of the non-cooperative game between the manufacturer and the chain-store seller, and reveal different levels of collective operations. This statistical physics method also holds for more complicate supply chains and economic systems.}

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.

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.