Search

Purpose: To evaluate the distortion probability in impressions of completely dentate arches when different impression materials are used in relation to operator experience. Materials and Methods: A total of 28 students (Group A) and 7 dentists (Group B) performed three maxillary impressions on 28 participants, each using vinyl siloxane ether (VSE), polyether (PE), and irreversible hydrocolloid (IHC). Gypsum master casts were fabricated and subsequently digitized. Intraoral scans were taken as a control. Differences between master casts and intraoral scans were visualized with heatmaps, and planar deviations were investigated. If planar deviations > 120 µm were found, the impression was rated as "distorted." An additional superimposition using the casts from VSE or PE was performed to confirm the presence of distortions. The relative number of surfaces with distortions in each impression was calculated. The procedure was repeated for a distortion threshold of 500 µm. The statistical analyses included repeated measures ANOVA (RMA) and post hoc tests (a < .05). Results: When 120 µm was considered as the threshold for distortions, IHC impressions showed higher distortion probability than PE impressions in Group A (P = .003) and Group B (P < .0001). In Group B, PE showed a lower distortion probability than VSE (P = .02). There was no significant difference between the study groups (P = .42). Considering 500 µm as a threshold for distortions, there was no difference between impression materials (P = .17) or study groups (P = .53). Conclusions: There were no statistically significant differences in relation to operator experience. Different impression materials had a significant impact on distortion probability. PE impressions showed the lowest distortion probability. [ABSTRACT FROM AUTHOR]

The aim of this study is to reveal the spatial-temporal characteristics and influencing factors of the static and dynamic distribution of global cruise ships, against the backdrop of the COVID-19 pandemic, which has transformed the global cruise network from "lines" to "points". This study collected trajectory data for 292 cruise ships and data for 789 cruise ports worldwide from March 2020 to July 2021. Based on the relationship between port and navigation, port management rights research, and port geography theory, we analyzed the spatial distribution and spatiotemporal migration of cruise ships with ArcGIS tools. It was found that, compared with normal times, the distribution of cruise ships in regional markets, countries, and ports showed stronger spatial agglomeration characteristics and formed four types, which were mainly influenced by differences in cruise operators' fleet scale, positioning, and itinerary. With the improvement of the epidemic, cruise ships trended to gather at the cruise home port. During the COVID-19 pandemic, there was an obvious separation between the epidemic prevention country, flag country, and operator country. Operators were inclined to berth their cruise ships in the countries where cruise ships were registered, countries of operators, and ports with high integration. Rather than simply emphasizing the static state of the cruise shipping network, the global cruise geography under the COVID-19 pandemic reflects the right relationship between ports, cruise ships, and companies. This study provides a methodological framework for analyzing the cruise shipping network at the port level and has practical implications for micro-interpretation of the dotted cruise shipping network during the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Time domain finite difference methods have been widely used for wave‐equation modelling in exploration geophysics over many decades. When using time domain finite difference methods, it is desirable to use a larger time step so as to save numerical simulation time. The Lax–Wendroff method is one of the well‐known methods to allow larger time step without increasing the time grid dispersion. However, the Lax–Wendroff method suffers from more time consumption because there are more spatial derivatives required to be approximated by the finite difference operators. We propose a new finite difference scheme for the Lax–Wendroff method so as to reduce the numerical simulation time. Then we determine the finite difference operator coefficients and analyse the dispersion error of the proposed finite difference scheme for the Lax–Wendroff method. At last, we apply the proposed finite difference scheme for the Lax–Wendroff method to different velocity models. The numerical simulation results indicate that the proposed finite difference scheme for the Lax–Wendroff method can effectively suppress time grid dispersion and is more efficient compared to the traditional finite difference scheme for the Lax–Wendroff method. [ABSTRACT FROM AUTHOR]

Pitting is the preparation of a tree planting position. In South Africa, various contractors and grower companies have gradually adopted pitting machines over the past decade, to overcome the challenges of manual pitting, such as low productivity, poor ergonomics, and inconsistent pit quality. Even though most forestry stakeholders understand productivity requirements (e.g. pits/shift) from pitting machines, they are often unaware of productivity differences associated with different operators and work conditions. This study aimed to compare the operational productivity and pit quality achieved by different pitting machine operators under different site conditions. The experiment was conducted in two sub-compartments, with two different post-harvest slash treatments: broadcast burning or mulching (and pre-marking). Then, four operators were tasked to dig pits using the same equipment. Operator productivity was assessed by analyzing time study data, while pit quality was estimated by determining pit depth and diameter. The results indicated that Operator 4 performed significantly better on mulched sites (543 pits/PMH) than on burned sites (430 pits/PMH), while Operator 2 was the least productive with 261 and 253 pits/PMH in mulched and burned sites, respectively. The overall average productivity was 120 pits/PMH higher on mulched sites than on burned sites. Although work quality did not correlate with productivity, there were differences between operators on the mulched site. The proportion of good pits varied, but site preparation technique did not significantly affect pit quality. We conclude that operator experience significantly impacts productivity and that marking the pitting spots is important to ensure that the required number of pits per hectare is achieved. [ABSTRACT FROM AUTHOR]

Introduction. Recently, three-phase induction motor drives have been widely used in industrial applications; however, the feedback signal failures of current sensors can seriously degrade the operation performance of the entire drive system. Therefore, the motor drives require a proper solution to prevent current sensor faults and improve the reliability of the motor drive systems. The novelty of the proposed research includes integrating the current sensor fault-tolerant control (FTC) function according to enhanced technique into the field-oriented control loop for speed control of the motor drive system. Purpose. This research proposes a hybrid method involving a third difference operator and signal comparison algorithm to diagnose various types of current sensor faults as a positive solution to enhance the stability of the induction motor drive system. Methods. A hybrid method involving a third difference operator for the measured speed signals and a comparison algorithm between measured and estimated current signals are proposed to diagnose the current sensors’ health status in the fault-tolerant process. After determining the faulty sensor, the estimated current signals based on the Luenberger observer are used immediately to replace the defective sensor signal. Results. The current sensor is simulated with various failure types, from standard to rare failures, to evaluate the performance of the FTC method implemented in the MATLAB/Simulink environment. Simultaneously, a fault flag corresponding to a defective sensor should be presented as an indicator to execute the repair process for faulty sensors at the proper time. Practical value. Positive results have proven the feasibility and effectiveness of the proposed FTC integrated into the speed controller to improve reliability and ensure the stable operation of the induction motor drive system even under current sensor fault conditions. [ABSTRACT FROM AUTHOR]

The parabolic convection-diffusion-reaction problem is examined in this work, where the diffusion and convection terms are multiplied by two small parameters, respectively. The proposed approach is based on a fitted operator finite difference method. The Crank-Nicolson method on uniform mesh is utilized to discretize the time variables in the first step. Two-point Gaussian quadrature rule is used for further discretizing these semi-discrete problems in space, and the second order interpolation of the first derivatives is utilized. The fitting factor's value, which accounts for abrupt changes in the solution, is calculated using the theory of singular perturbations. The developed scheme is demonstrated to be second-order accurate and uniformly convergent. The proposed method's applicability is validated by two examples, which yielded more accurate results than some other methods found in the literatures. [ABSTRACT FROM AUTHOR]

Reverse-time migration (RTM) is widely regarded as one of the most accurate migration methods available today. A crucial step in RTM involves extending seismic wavefields forward and backward. Compared to the conventional central finite-difference (CFD) scheme, the combined compact difference (CCD) scheme offers several advantages, including a shorter difference operator and the suppression of numerical dispersion under coarse grids. These attributes conserve memory and enhance effectiveness while maintaining the same level of differential precision. In this article, we begin with the five-point eighth-order CCD scheme and utilize the least squares method and Lagrange multiplier method to optimize the difference coefficients. This optimization is guided by the concept of dispersion-relation-preserving (DRP). The result is the acquisition of an optimized combined compact difference (OCCD) scheme, further enhancing the ability to suppress numerical dispersion. We thoroughly compare and analyze dispersion relationships and stability conditions. In addition, we examine several crucial steps in the RTM of the second-order acoustic wave equation. These steps include absorption boundary conditions, boundary storage strategy, and Poynting vector imaging conditions. Finally, we apply both the CCD and OCCD schemes in the RTM of the layered model, graben model, and SEG/EAGE salt model. We compare these results with those obtained from CFD's RTM. Numerical findings demonstrate that, in contrast to the CFD scheme, the CCD scheme effectively suppresses numerical dispersion and enhances imaging accuracy. Moreover, the optimized OCCD scheme further improves the ability to suppress numerical dispersion and can obtain better imaging results, which is an effective RTM method suitable for coarse grid conditions. [ABSTRACT FROM AUTHOR]

In this paper, we introduced the gradient-enhanced fractional physics-informed neural networks (gfPINNs) for solving the forward and inverse problems of the multiterm time-fractional Burger-type equation. The gfPINNs leverage gradient information derived from the residual of the fractional partial differential equation and embed the gradient into the loss function. Since the standard chain rule in integer calculus is invalid in fractional calculus, the automatic differentiation of neural networks does not apply to fractional operators. The automatic differentiation for the integer order operators and the finite difference discretization for the fractional operators were used to construct the residual in the loss function. The numerical results demonstrate the effectiveness of gfPINNs in solving the multiterm time-fractional Burger-type equation. By comparing the experimental results of fractional physics-informed neural networks (fPINNs) and gfPINNs, it can be seen that the training performance of gfPINNs is better than fPINNs. [ABSTRACT FROM AUTHOR]

In this paper, high-order numerical algorithms for two classes of time-independent one-sided tempered fractional diffusion equations were studied. The time derivative was discretized by the backward difference formula, the space tempered fractional derivatives were discretized based on tempered weighted and shifted Grünwald difference operators combined with the quasi-compact technique, and the effective second-order numerical approximations of the left and right third-order Riemann-Liouville tempered derivatives were given, thus the detailed fourth-order numerical schemes of these two classes of equations were derived. With the energy method, we proved rigorously that the numerical schemes were stable and convergent with order O (τ + h 4) and were only related to the tempered parameter λ. Finally, some examples were given to verify the validity of the numerical schemes. [ABSTRACT FROM AUTHOR]

For the numerical solution of the singularly perturbed parabolic convection-diffusion equation with large time delays, a novel class of fitted operator finite difference method is constructed using the Mickens-type scheme. Since the perturbation param-eter is the source for the simultaneous occurrence of time-consuming and high-speed phenomena in physical systems that depend on present and past history, our study here is to capture the effect of the parameter on the boundary layer. The time derivative is suitably replaced by a Crank-Nicolson-based scheme, followed by the spatial derivative, which is replaced by a non-standard fitted operator scheme. First-order error bounds in space and second-order error bounds in time are established to provide numerical results. [ABSTRACT FROM AUTHOR]

There are exponential operators which are defined on the whole real line, namely, the Ismail–May operators (Tnf)(x)$$ \left({T}_nf\right)(x) $$, connected to 1+x2$$ 1&#x0002B;{x}&#x0005E;2 $$, and the Gauss–Weierstrass operators (Wnf)(x)$$ \left({W}_nf\right)(x) $$, connected with 1. Here we consider the composition Vn:=Tn∘Wn$$ {V}_n:&#x0003D; {T}_n\circ {W}_n $$ of these two operators and observe that the composition operator is not of exponential type operator. We find moment‐generating functions and moments of these operators and estimate some point‐wise convergence of these operators using the characteristic function. We also estimate quantitative Voronovskaya type asymptotic formula and error estimation. Also, the difference of the composition operators Vn$$ {V}_n $$ with its components Tn$$ {T}_n $$ and Wn$$ {W}_n $$ is estimated in terms of modulus of continuity. Finally, we provide some graphs to see visualize the convergence by considering the function x2e2x$$ {x}&#x0005E;2{e}&#x0005E;{2x} $$. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel explicit structure-preserving numerical method for solving nonlinear space-fractional Schrödinger equations based on the concept of the scalar auxiliary variable approach. Firstly, we convert the equations into an equivalent system through the introduction of a scalar variable. Subsequently, a semi-discrete energy-preserving scheme is developed by employing a fourth-order fractional difference operator to discretize the equivalent system in spatial direction, and obtain the fully discrete version by using an explicit relaxed Runge–Kutta method for temporal integration. The proposed method preserves the energy conservation property of the space-fractional nonlinear Schrödinger equation and achieves high accuracy. Numerical experiments are carried out to verify the structure-preserving qualities of the proposed method. [ABSTRACT FROM AUTHOR]

In this work, some properties of the general convolutional operators of general fractional calculus (GFC), which satisfy analogues of the fundamental theorems of calculus, are described. Two types of general fractional (GF) operators on a finite interval exist in GFC that are conventionally called the L-type and T-type operators. The main difference between these operators is that the additivity property holds for T-type operators and is violated for L-type operators. This property is very important for the application of GFC in physics and other sciences. The presence or violation of the additivity property can be associated with qualitative differences in the behavior of physical processes and systems. In this paper, we define L-type line GF integrals and L-type line GF gradients. For these L-type operators, the gradient theorem is proved in this paper. In general, the L-type line GF integral over a simple line is not equal to the sum of the L-type line GF integrals over lines that make up the entire line. In this work, it is shown that there exist two cases when the additivity property holds for the L-type line GF integrals. In the first case, the L-type line GF integral along the line is equal to the sum of the L-type line GF integrals along parts of this line only if the processes, which are described by these lines, are independent. Processes are called independent if the history of changes in the subsequent process does not depend on the history of the previous process. In the second case, we prove the additivity property holds for the L-type line GF integrals, if the conditions of the GF gradient theorems are satisfied. [ABSTRACT FROM AUTHOR]

In this paper, we propose two momentum-preserving finite difference schemes for solving one-dimensional Camassa–Holm equation with periodic boundary conditions. A two-level nonlinear difference scheme and a three-level linearized difference scheme are constructed by using the method of order reduction. For nonlinear scheme, we combine mid-point rule and a specific difference operator, which ensures that our obtained scheme is of second-order convergence in both temporal and spatial directions. For linearized scheme, we apply a linear implicit Crank–Nicolson scheme in the temporal direction, then unique solvability and momentum conservation are analysed in detail. Numerical experiments are provided for Camassa–Holm equation admitting different types of solutions, which demonstrate the convergence order and accuracy of the proposed methods coincide with theoretical analysis. Moreover, numerical results show that the nonlinear scheme exhibits better accuracy for mass conservation, while the linearized scheme is more time-saving in computation. [ABSTRACT FROM AUTHOR]

The Black–Scholes (B–S) equation has been recently extended as a kind of tempered time-fractional B–S equations, which becomes an interesting mathematical model in option pricing. In this study, we provide a fast numerical method to approximate the solution of the tempered time-fractional B–S model. To achieve high-order accuracy in space and overcome the weak initial singularity of exact solution, we combine the compact difference operator with L1-type approximation under nonuniform time steps to yield the numerical scheme. The convergence of the proposed difference scheme is proved to be unconditionally stable. Moreover, the kernel function in the tempered Caputo fractional derivative is approximated by sum-of-exponentials, which leads to a fast unconditionally stable compact difference method that reduces the computational cost. Finally, numerical results demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, inverse problems are studied for Sturm–Liouville difference operators having $ \frac {p^{2}-1/4}{m^{2}} $ p 2 − 1 / 4 m 2 type singularity. First, we define the Green's function and the corresponding Weyl function, some of their properties are investigated, and we give a method to find the potential function. Then we give the solution of the inverse nodal problem and present a constructive procedure for the solution of the inverse problem by using nodes. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the property of the meromorphic functions when it has shared values with its difference operators, from which we obtain the transcendence of the meromorphic functions, and then we prove that the meromorphic functions has the value distribution property, and finally we derive the expressions of the meromorphic functions. [ABSTRACT FROM AUTHOR]

In this paper, an $ H_{\infty } $ H ∞ negative imaginary static output feedback (SOF) controller is designed for a low frequency (LF) networked control system (NCS) with time-delays. A difference operator is introduced to deal with the time-delays in a feedback configuration via integral quadratic constraints (IQCs). Both $ H_{\infty } $ H ∞ performance and negative imaginariness are analysed via LF IQCs and a generalised Kalman–Yakubovich–Popov (GKYP) lemma. A two-stage algorithm is presented to obtain the $ H_{\infty } $ H ∞ negative imaginary SOF controller for the LF NCS with time-delays. Simulation results are given to show the effectiveness and superiority of the $ H_{\infty } $ H ∞ negative imaginary SOF controller. [ABSTRACT FROM AUTHOR]

We derived an explicit form of the Jacobian for discrete approximations of a nonlinear initial boundary value problems (IBVPs) in matrix-vector form. The Jacobian is used in Newton’s method to solve the corresponding nonlinear system of equations. The technique was exemplified on the incompressible Navier-Stokes equations discretized using summation-by-parts (SBP) difference operators and weakly imposed boundary conditions using the simultaneous approximation term (SAT) technique. The convergence rate of the iterations is verified by using the method of manufactured solutions. The methodology in this paper can be used on any numerical discretization of IBVPs in matrix-vector form, and it is particularly straightforward for approximations in SBP-SAT form. [ABSTRACT FROM AUTHOR]

In this work we solve initial-boundary value problems associated to coupled 2D parabolic singularly perturbed systems of convection-diffusion type. The analysis is focused on the cases where the diffusion parameters are small, distinct and also they may have different order of magnitude. In such cases, overlapping regular boundary layers appear at the outflow boundary of the spatial domain. The fully discrete scheme combines the classical upwind scheme defined on an appropriate Shishkin mesh to discretize the spatial variables, and the fractional implicit Euler method joins to a decomposition of the difference operator in directions and components to integrate in time. We prove that the resulting method is uniformly convergent of first order in time and of almost first order in space. Moreover, as only small tridiagonal linear systems must be solved to advance in time, the computational cost of our method is remarkably smaller than the corresponding ones to other implicit methods considered in the previous literature for the same type of problems. The numerical results, obtained for some test problems, corroborate in practice the good behavior and the advantages of the algorithm. [ABSTRACT FROM AUTHOR]

A complex single-valued neutrosophic (CSVN) set is a very useful tool to handle the uncertainty, inconsistency, and ambiguity of knowledge in a periodic framework. The Schweizer-Sklar (SS) t-norm (TN) and t-conorm (TCN) enhance the flexibility of a procedure for aggregation depending on its parameters, whereas the power aggregation(PA) operator prevents insufficient impact of excessively high or low arguments on the results. Based on the idea of Schweizer-Sklar power aggregation operators, this paper aims to propose a number of aggregation operators such as complex single-valued neutrosophic Schweizer-Sklar power weighted averaging (CSVNSSPWA), complex single-valued neutrosophic Schweizer-Sklar power ordered weighted averaging (CSVNSSPOWA). Weights determination to solve green supply chain management problems in the single valued neutrosophic context is accomplished through the Simple Multi-Attribute Rating Technique (SMART). Furthermore, an example is given to show the uniqueness of the proposed operator and the difference between the proposed work and previous research. [ABSTRACT FROM AUTHOR]

In this work, we consider the degenerate Frobenius-Euler-Genocchi polynomials utilizing the degenerate exponential function and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials utilizing the degenerate logarithm function. Then, we analyze some summation and addition formulas for these polynomials. In addition, we derive some correlations with degenerate Stirling numbers of both kinds and degenerate Frobenius-Euler polynomials. Moreover, we present difference and derivative operator rules for the generalized degenerate Frobenius-Euler-Genocchi polynomials. Lastly, we show certain zeros of both the degenerate Frobenius-Euler-Genocchi polynomials and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials and provide their beautifully graphical representations. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar (SAR) image change detection suffers from poor quality of the difference image and low detection accuracy. Hence, this paper proposes a SAR image change detection method based on a fused difference image and an optimized random forest scheme, termed LRN‐SSARF. Specifically, a fusion operator difference image LRN is proposed, which is generated using a weighted fusion of log‐ratio (LR), ratio (R), and normalized ratio (NoR). This difference image generation method reduces noise's influence. Then, the Otsu algorithm is applied to segment the difference image and select the training samples. The training samples are input into the random forest (RF) model optimised by the sparrow search algorithm (SSA) for training and classification. Finally, the region link is uesd to refine the detection results and generate the final result. The change detection results of six real SAR image scenes highlight that the proposed algorithm has a high detection accuracy, and affords appealing integrity and detailed information about the change regions. Specially, the detection accuracy advantage of the Bangladesh dataset is larger, with the accuracy and Kappa coefficient reaching 98.04% and 92.00%, much higher than the competitor methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ \Delta^{\jmath}_{\imath} and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m [(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m} for m = 0 m=0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 휆-statistical convergence, and generalized difference weak [ V , λ ] [\mathscr{V},\lambda] -convergence. [ABSTRACT FROM AUTHOR]

This paper employs the monotonicity analysis for non-negativity to derive a class of sequential fractional backward differences of Riemann–Liouville type a + 1 RL ∇ ν a RL ∇ α u (t) based on a certain subspace in the parameter space (0 , 1) × (0 , 1). Auxiliary and restriction conditions are included in the monotonicity results obtained in this paper and they confirm the monotonicity of the function on { a + 2 , a + 3 , ... }. A non-monotonicity result is also established based on the main conditions together with further dual conditions, and this confirms that the main theorem is almost sharp. Furthermore, we recast the dual conditions in a sing condition, and then we represent the sharpness result in a new corollary. Finally, numerical results via MATLAB software are used to illustrate the main mathematical results for some special cases. [ABSTRACT FROM AUTHOR]

In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of O (h 2 + k 2 + κ 2 + σ 2 + ρ 2) , where h, k and κ are space step for x, y and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution. [ABSTRACT FROM AUTHOR]

In this article, we investigate the use of a high-order compact finite difference method for solving a two-dimensional damped semilinear wave equation. We use a new iterative method that employs compact finite difference operators to approximate the second-order spatial derivatives and achieve fourth-order convergence. We establish the stability and convergence of the compact finite difference scheme in the sense of the discrete H 1 -norm. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some new truncated second main theorems by using the Jackson p -Casorati determinant, where the truncated counting functions are assigned varying weights. We specifically concentrate on the Jackson difference operator applied to zero-order holomorphic mappings intersecting a finite set of slowly moving targets in P n (C) . As an application, we prove a uniqueness theorem of meromorphic functions sharing some small functions with the Jackson-type counting functions. [ABSTRACT FROM AUTHOR]

The results in this paper are related to the existence of solutions to hybrid and non-hybrid discrete fractional three-point boundary value inclusion problems for the elastic beam equation. The development of our results is attributed to the use of the Caputo and difference operators. The existence results for the non-hybrid discrete fractional inclusion problem are established by using fixed point theory for multi-valued upper semi-continuous maps, and the case of the hybrid discrete fractional inclusion problem is treated by Dhage's fixed point theory. Additionally, we present two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper presents an efficient finite difference method for solving the time-fractional Cattaneo equation with spatially variable coefficients in two spatial dimensions. The main idea is that the original equation is first transformed into a lower system, and then the graded mesh-based fast L2- 1 σ formula and second-order spatial difference operator for the Caputo derivative and the spatial differential operator are applied, respectively, to derive the fully discrete finite difference scheme. By adding suitable perturbation terms, we construct an efficient fast second-order ADI finite difference scheme, which significantly improves computational efficiency for solving high-dimensional problems. The corresponding stability and error estimate are proved rigorously. Extensive numerical examples are shown to substantiate the accuracy and efficiency of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

We continue the program first initiated by Laptev, Schimmer, and Takhtajan [Geom. Funct. Anal. 26 (2016), pp. 288–305] and develop a modification of the technique introduced in that paper to study the spectral asymptotics, namely the Riesz means and eigenvalue counting functions, of functional difference operators H_0 = \mathcal {F}^{-1} M_{\cosh (\xi)} \mathcal {F} with potentials of the form W(x) = \left \lvert {x} \right \rvert ^pe^{\left \lvert {x} \right \rvert ^\beta } for either \beta = 0 and p > 0 or \beta \in (0, 2] and p \geq 0. We provide a new method for studying general potentials which includes the potentials studied by Laptev, Schimmer, and Takhtajan [Geom. Funct. Anal. 26 (2016), pp. 288–305] and [J. Math. Phys. 60 (2019), p. 103505]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics. [ABSTRACT FROM AUTHOR]

In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space ħ Z n . The current work is an extension of the previous work (Botchway et al. in J Funct Anal 278(11):108473, 33, 2020) and agrees with it in the limit of the parameter ħ → 1 . The various representations of the operators will be studied as well as the composition, transpose, adjoint and the link between ellipticity and parametrix of operators. We also give the conditions for the ℓ p , weighted ℓ 2 boundedness and ℓ p compactness of operators. We investigate the relation between the classical and semi-classical quantization in the spirit of Ruzhansky and Turunen (Pseudo-differential operators and symmetries. Pseudo-differential operators, vol 2. Theory and Applications, Birkhäuser, Basel, 2010; J Fourier Anal Appl 16(6):943–982, 2010) RTspsJFAA and employ its applications to Schatten–von Neumann classes on ℓ 2 (ħ Z n) . We establish Gårding and sharp Gårding inequalities, with an application to the well-posedness of parabolic equations on the lattice ħ Z n . Finally we verify that in the limiting case where ħ → 0 the semi-classical calculus of pseudo-differential operators recovers the classical Euclidean calculus, but with a twist. [ABSTRACT FROM AUTHOR]

In the space of square integrable functions on the positive semi-axis, two positive self-adjoint operators generated by a one-dimensional free Hamiltonian are constructed. These operators are employed to construct a pair of spectrally absolutely continuous bounded self-adjoint operators whose difference is an operator of rank 1. The perturbation determinant is used to find an explicit form of the M. G. Krein spectral shift function for this pair. It is shown that despite the Asmoothness of the perturbation in the sense of Hölder, the point λ = 1, where the spectral shift function has a discontinuity of the first kind, is not an eigenvalue of the perturbed operator. [ABSTRACT FROM AUTHOR]

The article starts from the challenge of the critical cases in difference operator stability for neutral functional differential equations (NFDE). Such cases occur in the NFDE associated to 1D$$ 1D $$ hyperbolic partial differential equations (PDE) dynamics in mechanical and hydraulic engineering. For some of such applications it resulted that the aforementioned critical (nonasymptotic) stability is connected to the character and level of the energy losses. It is shown that suitable choice of the losses to be taken into account can remove the critical stability properties and give the difference operator the asymptotic stability thus ensuring asymptotic stability for the system's dynamics and also other asymptotic properties. [ABSTRACT FROM AUTHOR]

Difference methods are widely used for the approximate solution of boundary value problems for partial differential equations. Grid approximations are most simply constructed when the computational domain is divided into rectangular cells. Typically, the grid nodes coincide with the vertices of the cells. In addition to such node-center approximations, grids with nodes at the centers of cells are also used. It is convenient to formulate boundary value problems in terms of invariant operators of vector (tensor) analysis, which are associated with corresponding grid analogs. In this work, analogs of the gradient and divergence operators are constructed on non-standard rectangular grids the nodes of which consist of both the vertices of the computational cells and their centers. The proposed approach is illustrated using approximations of a boundary value problem for a stationary two-dimensional convection–diffusion equation. The key features of constructing approximations for vector problems are discussed with a focus on applied problems of the mechanics of solids. [ABSTRACT FROM AUTHOR]

Combined endoscopic mucosal resection (EMR) with endoscopic Full thickness resection (EFTR) is an emerging technique that has been developed to target colorectal polyps larger than 2 cm. We performed a systematic review and meta-analysis to evaluate this technique for the resection of large colorectal lesions. We conducted a comprehensive search of multiple electronic databases from inception through August 2023, to identify studies that reported on hybrid FTR. A random-effects model was employed to calculate the overall pooled technical success, macroscopic complete resection, free vertical margins resection rate, adverse events, and recurrence on follow up. A total of 8 Study arms with 244 patients (30% women) were included in the analysis. The pooled technical success rate was 97% (95% CI 88%-100%, I2 = 79.93%). The pooled rate of macroscopic complete resection was achieved in 95% (95% CI 90%-99%, I2 = 49.98) with a free vertical margins resection rate 88% (95% CI, 78%-96%, I2 = 63.32). The overall adverse events rate was 2% (95% CI 0%-5%, I2 = 11.64) and recurrence rate of 6% (95% CI 2%-12%, I2=20.32). Combined EMR with EFTR is effective and safe for resecting large, and complex colorectal adenomas, offering a good alternative for high surgical risk patients. Regional heterogeneity was observed, indicating that outcomes may be impacted by differences in operator expertise and industry training certification across regions. Comparative studies that directly compare combined EMR with EFTR against alternative methods such as ESD and surgical resection are needed. [ABSTRACT FROM AUTHOR]

We introduce Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. We prove that they represent a commuting family of integral operators and also commute with Macdonald difference operators, which are gauge equivalent to the Ruijsenaars Hamiltonians of the quantum system. The proof of commutativity of the Baxter operators uses a hypergeometric identity on rational functions that generalize Ruijsenaars kernel identities. [ABSTRACT FROM AUTHOR]

Biological models for cardiac regeneration and remodeling, along with the effects of cytokines or chemokines during the therapy with mesenchymal stem cells after a myocardial infarction, are of crucial importance for understanding the complex underlying mechanisms. This paper presents a mathematical model composed of three coupled partial differential equations that describes the dynamics of stem cells, nutrients and chemokines, highlighting the fundamental role of the chemokines during the myocardial tissue regeneration process. The system is solved numerically using mimetic difference operators and the MOLE library for MATLAB. The results show the tissue regeneration process in the necrotic part closest to the cell implantation area. [ABSTRACT FROM AUTHOR]

Summary: In this study, the problem of preview tracking control (PTC) was considered with regard to the linear parameter periodic systems (LPPSs) subject to previewed signals. First, the difference operator approach was extended to derive an augmented error system (AES). As a result, the PTC problem was transformed into a stabilization problem via state/output feedback. Second, sufficient conditions guaranteeing the closed‐loop stability of the augmented error systems were derived, and the design of a periodic controller with preview actions was proposed through the approach of linear matrix inequalities (LMIs). Finally, a numerical simulation was performed to illustrate the effectiveness of the proposed periodic controller. [ABSTRACT FROM AUTHOR]

Copyright of Momento: Revista de Física is the property of Universidad Nacional de Colombia, Departamento de Fisica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Hepatitis B is a worldwide viral infection that causes cirrhosis, hepatocellular cancer, the need for liver transplantation, and death. This work proposed a mathematical representation of Hepatitis B Virus (HBV) transmission traits emphasizing the significance of applied mathematics in comprehending how the disease spreads. The work used an updated Atangana-Baleanu fractional difference operator to create a fractional-order model of HBV. The qualitative assessment and wellposedness of the mathematical framework were looked at, and the global stability of equilibrium states as measured by the Volterra-type Lyapunov function was summarized. The exact answer was guaranteed to be unique using the Lipschitz condition. Additionally, there were various analyses of this new type of operator to support the operator’s efficacy. We observe that the explored discrete fractional operators will be χ²-increasing or decreasing in certain domains of the time scale Nj := j, j +1,... by looking at the fundamental characteristics of the proposed discrete fractional operators along with χ-monotonicity descriptions. For numerical simulations, solutions were constructed in the discrete generalized form of the Mittag-Leffler kernel, highlighting the impacts of the illness caused by numerous causes. The order of the fractional derivative had a significant influence on the dynamical process utilized to construct the HBV model. Researchers and policymakers can benefit from the suggested model’s ability to forecast infectious diseases such as HBV and take preventive action. [ABSTRACT FROM AUTHOR]

In this research article, we investigates the value distribution of linear q-difference operators Lk(f, Δq,c) and Lk(g, Δq,c), for a transcendental entire functions of zero order. At the same time we also investigate the uniqueness problems when two linear q - difference operators of entire functions share one value with finite weight. Our results extends the previous theorems of existing studies [11], [12]. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear system of singularly perturbed differential equations of convectiondiffusion type with Dirichlet boundary conditions is considered on the interval [0,1]. Both components of the solution of the system exhibit boundary layers near t = 0. A new computational method involving classical finite difference operators, a piecewise-uniform Shishkin mesh and an algorithm based on the continuation method is developed to compute the numerical approximations. The computational method is proved to be first order convergent uniformly with respect to the perturbation parameters. Numerical experiments support the theoretical results. [ABSTRACT FROM AUTHOR]

The article develops the theory of stability of linear operator schemes for operator inequalities and nonlinear nonstationary initial–boundary value problems of mathematical physics with nonlinearities of unbounded growth. Based on sufficient conditions for the stability of A.A. Samarskii's two- and three-level difference schemes, the corresponding a priori estimates for operator inequalities are obtained under the condition of the criticality of the difference schemes under consideration, i.e., when the difference solution and its first time derivative are nonnegative at all nodes of the grid domain. The results obtained are applied to the analysis of the stability of difference schemes that approximate the Fisher and Klein–Gordon equations with nonlinear right-hand sides. [ABSTRACT FROM AUTHOR]

In this work, we are implementing some applications of Nevanlinna theory to entire functions that share a small function with two difference operators and we also generalize one of the results in the paper[3].. [ABSTRACT FROM AUTHOR]

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies. [ABSTRACT FROM AUTHOR]

This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathematical operator, namely, a fractional variable-order Caputo-like difference operator, is employed to establish the fractional form of the map with short memory. The numerical simulation results highlight its excellent dynamical behavior, revealing that the addition of the piecewise fractional order makes the memristive-based Duffing map even more chaotic. It is characterized by distinct features, including the absence of an equilibrium point and the presence of multiple hidden chaotic attractors. [ABSTRACT FROM AUTHOR]

The authors of this research paper have introduced a new method for solving Hamilton–Jacobi (HJ) equations called third-order weighted essentially nonoscillatory (WENO) method. This method uses exponential polynomials to construct numerical fluxes and smoothness indicators, which helps distinguish between singular and smooth regions more efficiently. The smoothness indicators are created using a finite difference operator that eliminates exponential polynomials. The numerical flux is constructed using an interpolation method based on exponential polynomials, which results in better outcomes around steep gradients. The new method maintains a high level of accuracy (i.e. three) in smooth regions, even near critical points. The authors have presented some numerical results to demonstrate the effectiveness of the new method and compared it with other WENO methods. [ABSTRACT FROM AUTHOR]

This work investigates the dynamics of discrete reaction-diffusion Gierer-Meinhardt system as mathematical models of biological pattern formation. We study the system's local asymptotic behaviour with and without the diffusion once developing the discrete integer variant of the well-known Gierer-Meinhardt model and proving that the model has a unique equilibrium. The requirements for the steady-state solution's local and global stability are found with the help of relevant approaches and the Lyapunov technique. Two large biological models and simulations are used throughout the work to validate the utility of the suggested technique. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the uniqueness problems of entire functions of finite order sharing two small functions with their difference operators and obtain three results. The results improve and generalize the results of Li et al. (Adv Differ Equ 390:1–9, 2017) in a large scale. [ABSTRACT FROM AUTHOR]