In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

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.

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.

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.

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.

This paper is concerned about the novel exact solitons to the truncated M-fractional (1+1)-dimensional non-linear generalized Bretherton model with arbitrary constants . This model is used to explain the resonant nonlinear interaction between the waves in different phenomenon, including fluid dynamics, plasma physics, ocean waves, and many others. A series of exact solitons, including bright, dark, periodic, singular, singular-bright, singular-dark, and other solitons are obtained by applying the extended sinh-Gordon equation expansion (EShGEE), and the modified (G′/G2)-expansion tech- niques. A novel definition of Fractional derivative provides the solutions distinct from the present solutions. Mathematica software is used to obtain, and verify the solutions. The solutions are shown through 2-D, 3-D, and density plots. The stability process is performed to verify that the solutions are exact and accurate. The modulation instability is used to determine the steady-state stable results to the corresponding equation.

In this paper, a small wind power generator is proposed with a new straight shape stator and rotor. The advantages of the proposed structure are introduced through a comparison between the basic and the proposed models. By comparing the pole slot combination of the proposed generator, the combination with optimal cogging torque characteristics was selected. The electromagnetic characteristics of proposed shape are analyzed for design variables using a finite element analysis (FEA) of ANSYS Maxwell. The final model of the proposed structure is designed by considering cogging torque and the generator electromagnetic characteristics. The electromagnetic and structural simulations of the final model are performed to satisfy the required performance of generator and mechanical safety. To verify the FEA results of the final model, a prototype is manufactured, experimented, and compared with the FEA results.

Our main goal is here to make a comparative analysis between the well-known MOND theory and a more recent model called κ-model. An additional connection, between the κ-model and two other novel MOND-type theories: Newtonian Fractional-Dimension Gravity (NFDG) and Refracted Gravity (RG), is likewise presented. All these models are built to overtake the DM paradigm, or at least to strongly reduce the dark matter content. Whereas they rely on different formalisms, however, all four seem to suggest that the universal parameter, a0, appearing in MOND theory could intrinsically be correlated to either the sole baryonic mean mass density (RG and κ-model) and/or to the dimension of the object under consideration (NFDG and κ-model). We could then confer to the parameter a0 a more flexible status of multiscale parameter, as required to explain the dynamics together in galaxies and in galaxy clusters. Eventually, the conformal gravity theory (CFT) also seems to have some remote link with the κ-model, even though the first one is an extension of general relativity, and the second one is Newtonian in essence. The κ-model has been tested on a small sample of spiral galaxies and in galaxy clusters. Now we test this model on a large sample of galaxies issued from the SPARC database.

The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

Single-fluid electrospinning creates nanofibers from molten polymer solutions with active ingredients. The study utilized a combination of a fractional factorial design and a Box-Behnken design to examine crucial factors among a multitude of parameters and to optimize the electrospinning conditions that impact the fiber mats' morphology and entrapment efficiency of the Senna alata leaf extract. The findings indicated that the shellac content had the greatest impact on both fiber diameter and bead formation. The optimum electrospinning conditions were identified as a voltage of 24 kV, a solution feed rate of 0.8 mL/h, and a shellac-extract ratio of 38.5:3.8. These conditions produced nanosized fibers with a diameter of 306 nm, a low bead-to-fiber ratio of 0.29, and an extract entrapment efficiency of 96% within the fibers. The biphasic profile of optimized nanofibers was confirmed through an in vitro release study. This profile consisted of an initial burst release of 88% within the first hour, which was succeeded by a sustained release pattern surpassing 90% for the next 12 h, as predicted by zero-order release kinetics. The optimized nanofibers demonstrated antimicrobial efficacy against diverse pathogens, suggesting promising applications in wound dressings and protective textiles.

Although Sugarcane bagasse ash (SCBA) has good cementitious property, previous researchers have primarily aimed to improve the mechanical performance of conventional concrete or cement-based composites. Research is lacking on ultra-high performance concrete (UHPC), especially regarding tensile self-sensing properties. This paper aimed to comprehensively evaluate the SCBA effect on the UHPC’s mechanical, electrical, and tensile self-sensing properties. The results showed that SCBA below the critical incorporation concentration (CIC) improved the UHPC’s mechanical properties compared to steel fibers alone. Furthermore, adding 3.0wt% SCBA remarkably enhanced the UHPC mechanical properties where the compressive, flexural, and tensile strengths increased by 13.1%, 17.4%, and 20.6%, respectively. The SCBA content of 0.3wt% achieved the maximum UHPC electrical resistivity since values smaller or greater than this content decreased the resistivity. The SCBA-enhanced UHPC showed better tensile stress-sensing performance than UHPC without SCBA due to improved linearity and reversibility, lower hysteresis, higher sensitivity, and superior repeatability. UHPC with 0.3wt% SCBA achieved the best linearity, while UHPC with 0.9wt% SCBA showed the highest sensitivity, lowest hysteresis, and best repeatability. Overall, the content of 0.9wt% SCBA is the best in improving the overall mechanical, electrical, and tensile self-sensing performance.

We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.

This research paper is about to obtain new soliton solutions to the M-fractional (1+1)-dimensional nonlinear Westervelt model by utilizing $\exp_a$ function and modified simplest equation techniques. The gained solutions involving dark, bright, periodic, dark-bright and other solitons. These results have many applications in wave propagation of sound waves, high amplitude in medical imaging and therapy. Achieved results are verified by Mathematica tool and the effect of M-fractional derivative on the solutions is explained through 2-Dimensional, 3-Dimensional and contour plots. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

White noise is fundamentally linked to many processes, it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise.

In magneto-photoluminescence (magneto-PL) spectra of quasi-two dimensional islands (quantum dots) having seven electrons and Wigner-Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts and jumps of the energy of the emission components for filling factors >1 (B<10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock-Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, Majorana anyon origin of the states having even , i.e., composite fermions, which provide new opportunities for topological quantum computing.

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense

In clinical diagnostics and longitudinal studies, the reproducibility of MRI assessments is of high importance in order to detect pathological changes, but developments in MRI hard- and software often outrun extended periods of data acquisition and analysis. This could potentially introduce artefactual changes or mask pathological alterations. However, if and how changes of MRI hardware, scanning protocols or preprocessing software affect complex neuroimaging outcomes from e.g. diffusion weighted imaging (DWI) remains largely understudied. We therefore compared DWI outcomes and artefact severity of 121 healthy participants (age range 19-54 years) who underwent two matched DWI protocols (Siemens product and Center for Magnetic Resonance Research sequence) at two sites (Siemens 3T Magnetom Verio and Skyra^fit). After different preprocessing steps, fractional anisotropy (FA) and mean diffusivity (MD) maps,obtained by tensor fitting, were processed with tract-based spatial statistics (TBSS). Inter-scanner and inter-sequence variability of skeletonised FA values reached up to 5% and differed largely in magnitude and direction across the brain. Skeletonised MD values differed up to 14% between scanners. We here demonstrate that DTI outcome measures strongly depend on imaging site and software, and that these biases vary between brain regions. These regionally inhomogeneous biases may exceed and considerably confound physiological effects such as ageing, highlighting the need to harmonise data acquisition and analysis. Future studies thus need to implement novel strategies to augment neuroimaging data reliability and replicability.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

Exact and soliton type solutions have great importance in propagation of surface waves, fluid dynamics, optics, and many other elds of nonlinear sciences. In this study, the explicit and exact soliton type solutions for two space-time fractional Equal- Width (FEW) equations with conformable derivative are procured via the hyperbolic function approach. The wave type solutions are represented in some hyperbolic and trigonometric functions.

Speckle noise corrupt the major part of ultrasound image, because of which the quality deteriorate and loss of valuable information leads to false diagnosis. A large community of images like synthetic aperture radar (SAR) image, Synthetic image, and simulated ultrasound image, require despeckling at pre-processing stage for better processing. Cleaning the speckle from image and preserving the edge details is a vital task. Nowadays not only despeckling is considered as an important process but also preserving information at boundary and edges of image is also important. As most of the algorithms able to remove speckle noise but fails to preserve the details of edges. This paper covers several recent methods for removal of speckle noise along with various metrics opted for comparisons. The distinctive part of this paper is, a mathematical and parametric review has been done. Also a table is also included which summarizes the entire paper.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

Arduino microcontrollers are being used for a wide range of technological and biomedical applications such as image classification, computer vision, brain-computer interaction and vision experiments. Here I present a new cost-effective mini-device based on RGB LED flicker stimulation for the assessment of polychromatic temporal resolution of visual function. The visual device configuration allows for relative luminance thresholding, mono- and polychromatic critical flicker fusion frequency assessment. The results demonstrate the steady white visual perception of a trichromatic flicker stimulus beyond the critical flicker fusion frequency, as predicted by Talbot´s law for monochromatic stimuli. The trichromatic critical flicker fusion frequency (tFCC) depends on the relative luminance threshold at the light-adaptation level. Finally, wavefront measurements demonstrate that high-order aberrations improve the temporal resolution of visual function.

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

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.

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.

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 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.

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.

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).

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.

In this paper, we establish the existence and uniqueness results of the fractional Navier-Stokes evolution equation using the Banach fixed point theorem, where the fractional order β is in the form of the Atangana-Baleanu Caputo fractional order. The iterative method combined with the Laplace transform and Sumudu transform are employed to find the exact and approximate solutions of the fractional Navier-Stokes equation of a one-dimensional problem of unsteady flow of a viscous fluid in a tube. Mathematica software is used to present the solutions graphically.

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

The Stepped Frequency Waveform (SFW) is commonly employed in radar technology to synthesize wideband signals through the aggregation of narrow-band pulses, thereby achieving high-resolution range profiles without the need to increase the radar's instantaneous bandwidth. However, the inherent large time-bandwidth product of SFW introduces substantial ranging errors and energy dispersion, which significantly hinders its efficacy in detecting high-speed objects. This paper introduces a pioneering velocity estimation technique utilizing the fractional Fourier transform (FrFT) to address these limitations. Leveraging the characteristic of the Doppler signal from a moving target, which manifests as a chirp signal with a rate proportional to the target's velocity, the FrFT is utilized for precise velocity estimation. Subsequent to this, velocity compensation is applied using the deduced metrics, followed by the application of the inverse fast Fourier transform (iFFT) to pinpoint the target's exact location. To optimize the computational efficiency of determining the FrFT's optimal order, we propose an iterative algorithm founded on the golden section search method. The effectiveness of the proposed approach is verified by simulation data, and the results demonstrate that the proposed approach can accurately estimate the velocity and the range of the high-speed targets with a relatively low computational complexity.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

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.

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.

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.

Analyzing the impacts of urban landscape patterns on the thermal environment has become one of the key research areas in addressing urban heat islands (UHI) and improving the living environment. A case study was carried out in Fuzhou, Fujian Province of China, to quantify the spatial patterns of urban landscape and land surface temperature (LST) in different development areas. The contribution of the thermal environment and the factors influencing the heterogeneity of LST were analyzed and discussed. In this study, bi-temporal Landsat imagery was selected to calculate LST, percent impervious surface area (ISA), and fractional vegetation cover (FVC). The urban area was further divided into three concentric urban zones, ranging from the city center to the urban periphery, based on urban development densities. The spatial pattern of LST and its variance were analyzed and compared between different zones and different dates. The thermal environment contribution of different zones was also quantified to indicate the change in urban landscape pattern resulting from urban expansion in different zones. Furthermore, Geodetector was used to explore the single factors and interaction factors controlling the spatial patterns of LST in each zone. The results showed that (ⅰ) Urban expansion primarily increased in zone 2 and zone 3, and the areal proportion of high and sub-high LST areas increased from 56.11% and 21.08% to 62.03% and 32.49% in zone 2 and zone 3, respectively, from 2004 to 2021; (ⅱ) The heat effect contribution of zones 2 and 3 reached from 75.16% in 2004 to 89.40% in 2021, indicating that the increase of ISA with >LSTmean was more pronounced in zone 3 and zone 2 during the period; (ⅲ) The driving factors of LST spatial distribution were regionally different because of the different landscape patterns, and the explanatory power for the heterogeneity of LST in zone 1 was weaker than that in zone 2 and zone 3 in the study area; (ⅳ) The interaction of different factors had a higher explanatory power on the spatial distribution of LST than a single factor in each zone because the distributions of land cover types are heterogeneous in urban area. The results of the study can be used to improve urban planning for urban ecology and UHI mitigation.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

The fractional telegraph partial differential equation with fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplace method is used to find the exact solution of this equation. Stability inequalities are proved for the exact solution. Difference schemes for the implicit finite method are constructed. The implicit finite method is used to deal with modelling the fractional telegraph differential equation defined by Caputo fractional of Atangana-Baleanu (AB) derivative for different interval. Stability of difference schemes for this problem is proved by the matrix method. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

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

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

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.

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.

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.

This article aims to explore the existence and stability of solutions to differential equations involving a regularized ψ−Hilfer fractional derivative, which, compared to standard ψ−Hilfer fractional derivatives, provide a clear physical interpretation when dealing with initial conditions. We discovered that the regularized ψ−Hilfer fractional derivative can be represented as the inverse operation of the ψ−Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a regularized ψ−Hilfer fractional derivative. Additionally, we applied the Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a regularized ψ−Hilfer fractional derivative, and further discussed Ulam-Hyers-Rassias stability and semi-Ulam-Hyers-Rassias stability of these solutions. Finally, we illustrated our results through case studies.

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.

Coronary artery lesions (CALs) after Kawasaki disease present complex coronary hemodynamics. We investigated the relationship between coronary fractional flow reserve (FFR), myocardial blood flow reserve (MFR), and myocardial blood flow volume fraction (MBF), and their clinical usefulness in CALs after Kawasaki disease. Nineteen patients (18 male, 1 female) who underwent cardiac catheterization and 13N-ammonia positron emission tomography, with 24 coronary artery branches, were included. Five branches had inconsistent FFR and MFR values, two had normal FFR but abnormal MFR, and three had abnormal FFR and normal MFR. The abnormal MFR group had significantly higher MBF at rest than the normal group (0.86±0.13 vs. 1.08±0.09, p=0.001). The abnormal FFR group had significantly lower MBF at adenosine loading than the normal group (2.23±0.23 vs. 1.88±0.29, p=0.021). The three branches with abnormal FFR only had stenotic lesions, but the MFR may have been normal because blood was supplied by collateral vessels. Combining FFR, MFR, and MBF will enable a more accurate assessment of peripheral coronary circulation and stenotic lesions in CALs and help determine treatment strategy and timing of intervention.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

The evolution of integrable classical systems leads to conserved quantities and vanishing Poisson brackets. In contrast, such invariants do not exist in the dynamics of non-integrable systems, which include (but are not limited to) deterministic models with long-term chaotic behavior. The object of this review is to briefly survey the mathematical background of nonintegrability and its role in the physics unfolding well-above the Standard Model (SM) scale.

Suitable measures of grazing impacts on ground cover, that enable separation of the effects of climatic variations, are needed to inform land managers and policy makers across the arid rangelands of the Northern Territory of Australia. This work developed and tested a time-series, change-point detection method for application to time series of vegetation fractional cover derived from Landsat data to identify irregular and episodic ground-cover growth cycles. These cycles were classified to distinguish grazing impacts from that of climate variability. A measure of grazing impact was developed using a multivariate technique to quantify the rate and degree of ground cover change. The method was successful in detecting both long term (> 3 years) and short term (< 3 years) growth cycles. Growth cycle detection was assessed against rainfall surplus measures indicating a relationship with high rainfall periods. Ground cover change associated with grazing impacts was also assessed against field measurements of ground cover indicating a relationship between both field and remotely sensed ground cover. Cause and effects between grazing practices and ground cover resilience can now be explored in isolation to climatic drivers. This is important to the long term balance between ground cover utilisation and overall landscape function and resilience.