6,527 results
Search Results
2. Generalized focal surfaces of spacelike curves lying in lightlike surfaces.
- Author
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Liu, Siyao and Wang, Zhigang
- Subjects
PAPER arts ,SPHERES ,CUSP forms (Mathematics) ,EDGES (Geometry) - Abstract
The main work of this paper is to investigate two kinds of generalized focal surfaces and two kinds of evolutes generated by spacelike curve γ lying in lightlike surfaces in Minkowski three‐space. Applying the method of unfolding theory in singularity theory to our study, it is shown that there exist the cuspidal edge and the swallowtail types of singularities in each of two classes of generalized focal surfaces under certain conditions; the only cusps will appear in each of evolutes. Two new geometric invariants are presented to classify the singularities of generalized focal surfaces and evolutes. Much more importantly, we reveal the correspondence among the geometric invariants, the types of singularities on generalized focal surfaces and evolutes, the singularities of two kinds of evolutes, and the contact of γ with the osculating spheres. Finally, several examples are presented to demonstrate the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. Comment on the paper "A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms, Mohamed Dilmi, Mourad Dilmi, Hamid Benseridi, Mathematical Methods in the Applied Sciences 2019, 42:6505‐6521".
- Author
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Pantokratoras, Asterios
- Subjects
NONLINEAR equations ,APPLIED sciences ,STRAINS & stresses (Mechanics) - Abstract
There is no correct form of the term HT ht in the literature. In Physics it is not allowed to add quantities with different units and the term HT ht is wrong. [Extracted from the article]
- Published
- 2023
- Full Text
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4. (CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications.
- Author
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Cortés, Juan Carlos, Navarro‐Quiles, Ana, Romero, José‐Vicente, and Roselló, María‐Dolores
- Subjects
PROBABILITY density function ,LOGISTIC functions (Mathematics) ,MATHEMATICAL models ,EQUATIONS ,DIFFERENTIAL equations ,RANDOM variables ,TECHNOLOGY transfer ,STOCHASTIC processes - Abstract
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
5. Comment on the paper "Entropy generation in nanofluid flow of Walters‐B fluid with homogeneous‐heterogeneous reactions, Sumaira Qayyum, Tasawar Hayat, Sumaira Jabeen, Ahmed Alsaedi, Mathematical Methods in the Applied Sciences 2020, 43: 5657–5672"
- Author
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Pantokratoras, Asterios
- Subjects
APPLIED sciences ,FLUID flow ,NANOFLUIDICS - Abstract
Some errors exist in the above paper. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
6. Comment on the paper "Interaction of delta shock waves for the Chaplygin Euler equations of compressible fluid flow with split delta functions, Yu Zhang, Yanyan Zhang, Jinhuan Wang Mathematical Methods in the Applied Sciences, 2018; 41:7678–7697".
- Author
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Pantokratoras, Asterios
- Subjects
EULER equations ,FLUID flow ,SHOCK waves - Abstract
The equations studied in the above paper are dimensionally incorrect. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
7. (CMMSE paper) A finite‐difference model for indoctrination dynamics.
- Author
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Medina‐Guevara, M. G., Vargas‐Rodríguez, H., and Espinoza‐Padilla, P. B.
- Subjects
INDOCTRINATION ,DIFFERENCE equations ,LINEAR equations ,SMALL groups - Abstract
In this work, a system of non‐linear difference equations is employed to model the opinion dynamics between a small group of agents (the target group) and a very persuasive agent (the indoctrinator). Two scenarios are investigated: the indoctrination of a homogeneous target group, in which each agent grants the same weight to his (or her) partner's opinion and the indoctrination of a heterogenous target group, in which each agent may grant a different weight to his or her partner's opinion. Simulations are performed to study the required times by the indoctrinator to convince a group. Initially, these groups are in a consensus about a doctrine different to that of the ideologist. The interactions between the agents are pairwise. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
8. Generation of Escher‐like spiral drawings in a modified hyperbolic space.
- Author
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Chung, Kwok Wai, Ouyang, Peichang, Nicolas, Alain, Cao, Shiyun, Bailey, David, and Gdawiec, Krzysztof
- Subjects
SYMMETRY groups ,GRAPHIC artists ,WALLPAPER ,SYMMETRY ,CONFORMAL mapping ,HYPERBOLIC geometry - Abstract
Dutch graphic artist M.C. Escher created many famous drawings with a deep mathematical background based on wallpaper symmetry, hyperbolic geometry, spirals, and regular polyhedra. However, he did not attempt any spiral drawings in hyperbolic space. In this paper, we consider a modified hyperbolic geometry by removing the condition that a geodesic is orthogonal to the unit circle in the Poincaré model. We show that spiral symmetry and the similarity property exist in this modified geometry so that the creation of uncommon hyperbolic spiral drawings is possible. To this end, we first establish the theoretical foundation for the proposed method by deriving a contraction mapping and a rotation for constructing modified hyperbolic spiral tilings (MHSTs) and introduce symmetry groups to analyze the structure of MHSTs. Then, to embed a pre‐designed wallpaper template into the tiles, we derive a one‐to‐one mapping between a tile of MHST and a rectangle. Finally, we specify some technical implementation details and give a gallery of the resulting MHST drawings. Using existing wallpaper templates, the proposed method is able to generate a great variety of exotic Escher‐like drawings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
9. Stability analysis of discretized structure systems based on the complex network with dynamics of time‐varying stiffness.
- Author
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Wang, Chaoyu and Wang, Yinhe
- Subjects
TIME-varying networks ,DYNAMIC stability ,DYNAMIC models - Abstract
The stability analysis of dynamic continuous structural system (DCSS) has often been investigated by discretizing it into several low‐dimensional elements. The integrated results of all elements are employed to describe the whole dynamic behavior of DCSS. In this paper, DCSS is regarded as the complex dynamic network with the discretized elements as the dynamic nodes and the time‐varying stiffness as the dynamic link relations between them, by which the DCSS can be regarded to be the large‐scale system composed of the node subsystem (NS) and link subsystem (LS). Therefore, the dynamic model of DCSS is proposed as the combination of dynamic equations of NS and LS, in which their state variables are coupled mutually. By using the model, this paper investigates the stability of DCSS. The research results show that the state variables of NS and LS are uniformly ultimately bounded (UUB) associated with the synthesized coupling terms in LS. Finally, the simulation example is utilized to demonstrate the validity of method in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
10. Well‐posedness of quantum stochastic differential equations driven by fermion Brownian motion in noncommutative Lp‐space.
- Author
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Jing, Guangdong, Wang, Penghui, and Wang, Shan
- Subjects
- *
STOCHASTIC differential equations , *STOCHASTIC control theory , *FERMIONS , *STOCHASTIC systems , *BROWNIAN motion , *TIME perspective - Abstract
This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space Lp(풞) for 2≤p<∞$$ 2\le p<\infty $$. First, we investigate the existence and uniqueness of Lp$$ {L}^p $$‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of Lp$$ {L}^p $$‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
11. Scattering properties of the nonlinear eigenvalue‐dependent Sturm‐Liouville equations with sign‐alternating weight and jump condition.
- Author
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Coskun, Nimet
- Subjects
- *
STURM-Liouville equation , *DIFFERENTIAL operators , *RESOLVENTS (Mathematics) , *SCATTERING (Mathematics) - Abstract
This paper aims to investigate the scattering function and discrete spectrum of the impulsive Sturm‐Liouville type differential operator with a turning point and nonlinear eigenparameter‐dependent boundary condition. Using hyperbolic type representations of the fundamental solutions, the operator's discrete spectrum was constructed. We presented asymptotic equations for the fundamental solutions and the Jost function. Finally, we stated an example to demonstrate the paper's major points. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. Hyers–Ulam–Rassias stability of fractional delay differential equations with Caputo derivative.
- Author
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Benzarouala, Chaimaa and Tunç, Cemil
- Abstract
This paper is devoted to the study of Hyers–Ulam–Rassias (HUR) stability of a nonlinear Caputo fractional delay differential equation (CFrDDE) with multiple variable time delays. We obtain two new theorems with regard to HUR stability of the CFrDDE on bounded and unbounded intervals. The method of the proofs is based on the fixed point approach. The HUR stability results of this paper have indispensable contributions to theory of Ulam stabilities of CFrDDEs and some earlier results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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13. Stability analysis and numerical approximate solution for a new epidemic model with the vaccination strategy.
- Author
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Movahedi, Fateme
- Subjects
- *
NUMERICAL solutions to differential equations , *SMALLPOX , *BASIC reproduction number , *VACCINATION , *EPIDEMICS , *MEASLES vaccines , *DIFFERENTIAL equations - Abstract
In this paper, we introduce a new mathematical epidemic model with the effect of vaccination. We formulate a Susceptible-High risk-Infective-Recovered-Vaccinated (SHIRV) model in which the susceptible individuals with a higher probability of being infected (H) are selected as a separate class. We study the dynamical behavior of this model and define the basic reproductive number, R0. It is proved that the disease-free equilibrium is asymptotically stable if R0 < 1, and it is unstable if R0 1. Also, we investigate the existence and stability of the endemic equilibrium point analytically. For the system of differential equations of the SHIRV model, we give an approximating solution by using the Legendre-Ritz-Galerkin method. Finally, we study the influence of vaccination on measles and smallpox, two cases of the epidemic, using the proposed method in this paper. Numerical results showed that choosing high-risk people for vaccination can prevent them from getting infected and reduce mortality in the community. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Exact delay range for the stabilization of linear systems with input delays.
- Author
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Lin Li and Ruilin Yu
- Subjects
- *
LINEAR systems , *ARITHMETIC series , *STABILITY of linear systems , *EIGENVALUES , *MULTIPLICITY (Mathematics) - Abstract
This paper is concerned with the exact delay range making input-delay systems unstabilizable. The exact range means that the systems are unstabilizable if and only if the delay is within this range. Contributions of this paper are to characterize the exact range and to present a computation method to derive this range. It is shown that the above range is related to unstable eigenvalues of the system matrix. In the discrete-time case, if none of the eigenvalues of the system matrix is a unit root, then the above range is a finite set. If there exist some eigenvalues which are unit roots, this range may be a finite set or may be composed of several arithmetic progressions. When this range contains finite elements, the number of these elements is bounded by the geometric multiplicities of eigenvalues. When this range contains arithmetic progressions, the number of such progressions is bounded by the above multiplicities. On the other hand, our results can provide an upper bound for the well-known delay margin, which is the maximal delay value achievable by a robust controller to stabilize systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Geometric regularity criteria for the Navier-Stokes equations in terms of velocity direction.
- Author
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Skalak, Zdenek
- Subjects
- *
NAVIER-Stokes equations , *BOUSSINESQ equations , *VELOCITY , *VORTEX motion - Abstract
In this paper, we are inspired by a famous result by Constantin and Fefferman who proved that a simple geometrical assumption on the direction of the vorticity leads to the regularity of weak solutions of the 3D Navier-Stokes equations. We show that the same result can be achieved if the vorticity direction is replaced by the velocity direction. We further strengthen this result and prove that in fact it is not necessary to consider the velocity direction in all close space points but only in the points whose distance equals to a small positive number dependant on the data. In the second part of the paper, we extend a result by Berselli and Córdoba concerning the role of the helicity for the regularity of the weak solutions of the Navier-Stokes equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Well‐posedness and error analysis of wave equations with Markovian switching.
- Author
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Li, Jiayang and Wang, Xiangjun
- Abstract
Compared to traditional partial differential equation modeling methods, Markov switching models can accurately capture the abrupt changes or jumps that complex systems often experience in the real world. In this paper, we propose a novel wave equation model with Markovian switching to represent complex systems with state‐jumping phenomena better, and the well‐posedness of the model is proved. In addition, a numerical method with non‐uniform grids is also proposed for the proposed model to simulate the data in realistic situations, which is based on the use of finite element discretization in space and central difference discretization in time. Finally, we conduct several experiments to analyze the errors and stability of the proposed model and the traditional model. The results show that the Markov switching model proposed in this paper has a smaller error than the traditional models while ensuring stability and can more accurately simulate the state jump phenomena of real‐world systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Global existence and blowup of solutions for nonlinear Love equation.
- Author
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Dung, Dao Bao and Tran Vu, Ngo
- Abstract
In this paper, we are concerned with the nonlinear Love equation, which describes some sort of “propagation process” in physics. Firstly, we establish the local existence and uniqueness of the solution by using the contraction mapping principle and the regularity theory for the elliptic problem. Secondly, we construct a family of potential wells to obtain a threshold for the existence of global solutions and blowup in a finite time of the solution in both cases with subcritical and critical initial energy. Additionally, we provide the decay rate of the global solution and estimate the lifespan of a blow‐up solution. Moreover, at the supercritical initial energy level, we provide a sufficient condition for initial data leading to blow‐up results. This paper, along with the previous work of A. N. Carvalho, J. Cholewa, Local well‐posedness, asymptotic behavior, and asymptotic bootstrapping for a class of semilinear evolution equations of the second order in time, Trans. Amer. Math. Soc. 361 (5) (2009) 2567‐2586, provides us with a comprehensive and systematic study of the dynamic behavior of the solution to the nonlinear Love equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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18. The impact of demography in a model of malaria with transmission‐blocking drugs.
- Author
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Ouifki, Rashid, Banasiak, Jacek, and Tchoumi, Stéphane Yanick
- Abstract
In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Error analysis for discontinuous Galerkin method for time‐fractional Burgers' equation.
- Author
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Maji, Sandip and Natesan, Srinivasan
- Abstract
The primary goal of this paper is to suggest a fully discrete numerical solution approach for the time‐fractional Burgers' equation. This paper will consider the fractional derivative in the Caputo sense. The time derivative of this equation will be discretized using the L2‐type discretization formula. The spatial variable is approximated by using the nonsymmetric interior penalty discontinuous Galerkin method. The proposed method is globally and unconditionally stable. The accuracy of the solution is evaluated using a convergence analysis. Computational experiments further confirm the accuracy and stability of the suggested strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Corrigendum to a fractional sideways problem in a one‐dimensional finite‐slab with deterministic and random interior perturbed data.
- Author
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Duc Trong, Dang, Thi Hong Nhung, Nguyen, Dang Minh, Nguyen, and Nhu Lan, Nguyen
- Abstract
In a lot of engineering applications, one has to recover the temperature of a heat body having a surface that cannot be measured directly. This raises an inverse problem of determining the temperature on the surface of a body using interior measurements, which is called the sideways problem. Many papers investigated the problem (with or without fractional derivatives) by using the Cauchy data u(x0,t),ux(x0,t)$$ u\left({x}_0,t\right),{u}_x\left({x}_0,t\right) $$ measured at one interior point x=x0∈(0,L)$$ x={x}_0\in \left(0,L\right) $$ or using an interior data u(x0,t)$$ u\left({x}_0,t\right) $$ and the assumption limx→∞u(x,t)=0$$ {\lim}_{x\to \infty }u\left(x,t\right)=0 $$. However, the flux ux(x0,t)$$ {u}_x\left({x}_0,t\right) $$ is not easy to measure, and the temperature assumption at infinity is inappropriate for a bounded body. Hence, in the present paper, we consider a fractional sideways problem, in which the interior measurements at two interior point, namely, x=1$$ x=1 $$ and x=2$$ x=2 $$, are given by continuous data with deterministic noises and by discrete data contaminated with random noises. We show that the problem is severely ill‐posed and further constructs an a posteriori optimal truncation regularization method for the deterministic data, and we also construct a nonparametric regularization for the discrete random data. Numerical examples show that the proposed method works well. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Mittag‐Leffler stability of neural networks with Caputo–Hadamard fractional derivative.
- Author
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Demirci, Elif, Karakoç, Fatma, and Kütahyalıoglu, Aysen
- Abstract
In this paper, a Hopfield‐type neural network system with Caputo–Hadamard fractional derivative is discussed. The importance of the existence of the equilibrium point in the analysis of artificial neural networks is well known. Another important investigation is the stability properties. So, the stability of a neural network system is dealt with in the present paper. First, a theorem that asserts the existence and uniqueness of the equilibrium point of the system is proven. Later, the conditions that ensure the Mittag‐Leffler stability of the equilibrium point is obtained by using the Lyapunov's direct method. In addition, an example is given with numerical simulations to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Probabilistic analysis of a class of compartmental models formulated by random differential equations.
- Author
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Bevia, Vicente J., Carlos Cortés, Juan, Luisovna Pérez, Cristina, and Villanueva, Rafael‐Jacinto
- Abstract
This paper deals with the probabilistic analysis of a class of compartmental models formulated via a system of linear differential equations with time‐dependent non‐homogeneous terms. For the sake of generality, we assume that initial conditions and rates between compartments are random variables with arbitrary distributions while the source terms defining the flows entering the compartments are stochastic processes. We then take extensive advantage of the so‐called random variable transformation (RVT) technique to determine the first probability distribution of the solution of such a randomized model under very general hypotheses. In the simplest but relevant case of time‐independent source terms, we also obtain the probability distribution of the equilibrium, which is a random vector. Furthermore, we first particularize the aforementioned results for different types of integrable source terms that permit obtaining an explicit solution of the compartmental model: random constants, a train of Dirac delta impulses with random intensities, and a Wiener process. Secondly, we show an alternative approach based on the Liouville–Gibbs equation, which is useful when dealing with source terms that do not admit a closed‐form primitive. All the previous theoretical results are first illustrated through several numerical examples and simulations where a wide range of different probability distributions are assumed for the model parameters. The paper concludes by applying a compartmental model that describes the dynamics of oral drug administration through multiple chronologically spaced doses using synthetic data generated according to pharmacological references. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. On the jerk and snap in motion along non‐lightlike curves in Minkowski 3‐space.
- Author
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Elsharkawy, Ayman, Cesarano, Clemente, and Alhazmi, Hadil
- Abstract
In this paper, we study the jerk vector that is the rate of change of the acceleration vector over time. In three‐dimensional space, the decomposition of the jerk vector is a new concept in the field. This decomposition expresses the jerk vector as the sum of three unique components in specific directions: the tangential direction, the radial direction in the osculating plane, and the radial direction in the rectifying plane. The snap vector is the rate of change of the jerk vector over time. In this paper, the authors examine non‐relativistic particles moving along non‐lightlike Frenet curves at low speeds compared to the speed of light in Minkowski 3‐space. They resolve the jerk and snap vectors using Frenet–Serret frames. Additionally, the cases for motion along non‐lightlike Frenet planar curves in the Minkowski 3‐space are given as corollaries. To help understand these results, the paper provides some illustrative examples [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Simulating variable‐order fractional Brownian motion and solving nonlinear stochastic differential equations.
- Author
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Samadyar, Nasrin and Ordokhani, Yadollah
- Abstract
Stochastic differential equations (SDEs) are very useful in modeling many problems in biology, economic data, turbulence, and medicine. Fractional Brownian motion (fBm) and variable‐order fractional Brownian motion (vofBm) are suitable alternatives to standard Brownian motion (sBm) for describing and modeling many phenomena, since the increments of these processes are dependent of the past and for H>12$$ \mathcal{H}>\frac{1}{2} $$ these increments have the property of long‐term dependence. Classical mathematical techniques such as Ito's calculus do not work for stochastic computations on fBm and vofBm due to they are not semi‐Martingale for H(ξ)≠12$$ \mathcal{H}\left(\xi \right)\ne \frac{1}{2} $$. Therefore, solving these equations is much more difficult than solving SDEs with sBm. On the other hand, these equations do not have an analytical solution, so we have to use numerical methods to find their solution. In this paper, a computational approach based on hybrid of block‐pulse and parabolic functions (HBPFs) has been introduced for simulating vofBm and solving a modern class of SDEs. The mechanism of this approach is based on stochastic and fractional integration operational matrices, which transform the intended problem to a nonlinear system of algebraic equations. Thus, the complexity of solving the mentioned problem is reduced significantly. Also, convergence analysis of the expressed method has been theoretically examined. Finally, the accuracy and efficiency of the proposed algorithm have been experimentally investigated through some test problems and comparison of obtained results with results of previous papers. High accurate numerical results are obtained by using a small number of basic functions. Therefore, this method deals with smaller matrices and vectors, which is one of the most important advantage of our suggested method. Also, presenting an applicable procedure to construct vofBm is another innovation of this work. To gain this aim, at first, discretized sBm is generated via fundamental features of this process, and afterward, block‐pulse functions (BPFs) and HBPFs are utilized for simulating discretized vofBm. Finally, spline interpolation method has been employed to provide a continuous path of vofBm. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Separation method of semifixed variables together with integral bifurcation method for solving generalized time‐fractional thin‐film equations.
- Author
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Rui, Weiguo and He, Weijun
- Abstract
It is well known that investigation on exact solutions of nonlinear fractional partial differential equations (PDEs) is a very difficult work compared with integer‐order nonlinear PDEs. In this paper, based on the separation method of semifixed variables and integral bifurcation method, a combinational method is proposed. By using this new method, a class of generalized time‐fractional thin‐film equations are studied. Under two kinds of definitions of fractional derivatives, exact solutions of two generalized time‐fractional thin‐film equations are investigated respectively. Different kinds of exact solutions are obtained and their dynamic properties are discussed. Compared to the results in the existing references, the types of solutions obtained in this paper are abundant and very different from those in the existing references. Investigation shows that the solutions of the model defined by Riemann–Liouville differential operator converge faster than those defined by Caputo differential operator. It is also found that the profiles of some solutions are very similar to solitons, but they are not true soliton solutions. In order to visually show the dynamic properties of these solutions, the profiles of some representative exact solutions are illustrated by 3D graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse.
- Author
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Kumar Sharma, Om Prakash, Vats, Ramesh Kumar, and Kumar, Ankit
- Subjects
- *
DIFFERENTIAL inclusions , *SET-valued maps , *CAPUTO fractional derivatives , *STOCHASTIC systems , *STOCHASTIC analysis , *FRACTIONAL calculus - Abstract
This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. B‐almost periodic solutions in finite‐dimensional distributions for octonion‐valued stochastic shunting inhibitory cellular neural networks.
- Author
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Huo, Nina and Li, Yongkun
- Subjects
- *
EXPONENTIAL stability , *STOCHASTIC processes , *CAYLEY numbers (Algebra) , *DIFFERENTIAL inequalities - Abstract
In this paper, we consider a class of octonion‐valued stochastic shunting inhibitory cellular neural networks with delays. First, we give an estimate of the distance between two different moments of finite‐dimensional distributions of a stochastic process. Then, based on this and by using fixed point theorems and inequality techniques, we establish the existence and global exponential stability of Besicovitch almost periodic (B$$ \mathcal{B} $$‐almost periodic for short) solutions in finite‐dimensional distributions for this kind of networks. Our results are new even if the networks we consider in the paper are real‐valued ones. At the same time, the method proposed in this paper can be applied to study the existence of Besicovitch almost periodic solutions in finite‐dimensional distributions for other types of stochastic neural networks. Finally, an example is given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. On the Cauchy problem for semilinear σ‐evolution equations with time‐dependent damping.
- Author
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Sevki Aslan, Halit and Anh Dao, Tuan
- Subjects
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EQUATIONS , *LINEAR equations , *CAUCHY problem , *BLOWING up (Algebraic geometry) - Abstract
In this paper, we would like to consider the Cauchy problem for semilinear σ$$ \sigma $$‐evolution equations with time‐dependent damping for any σ≥1$$ \sigma \ge 1 $$. Motivated strongly by the classification of damping terms in some previous papers, the first main goal of the present work is to make some generalizations from σ=1$$ \sigma =1 $$ to σ>1$$ \sigma >1 $$ and simultaneously to investigate decay estimates for solutions to the corresponding linear equations in the so‐called effective damping cases. For the next main goals, we are going not only to prove the global well‐posedness property of small data solutions but also to indicate blow‐up results for solutions to the semilinear problem. In this concern, the novelty which should be recognized is that the application of a modified test function combined with a judicious choice of test functions gives blow‐up phenomena and upper bound estimates for lifespan in both the subcritical case and the critical case, where σ$$ \sigma $$ is assumed to be any fractional number. Finally, lower bound estimates for lifespan in some spatial dimensions are also established to find out their sharp results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Oscillation criterion for Euler type half‐linear difference equations.
- Author
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Hasil, Petr and Veselý, Michal
- Subjects
- *
LINEAR equations , *OSCILLATIONS , *DIFFERENCE equations - Abstract
We consider general classes of Euler type linear and half‐linear difference equations, which are conditionally oscillatory. Applying the adapted Riccati technique, we improve known oscillation criteria for these equations. More precisely, our presented main criterion is the full oscillatory counterpart of a non‐oscillation criterion. Thus, in this paper, we enlarge the set of conditionally oscillatory Euler type difference equations. We highlight that our results are new even for linear equations with periodic coefficients. This fact is documented by simple examples of such equations at the end of this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Research on evolution dynamics of urban rail transit network based on allometric growth relationship.
- Author
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Zhang, Zehua, Feng, Shumin, Jia, Huihui, Liu, Hao, Yang, Chao, and Kang, Maohua
- Subjects
- *
CONSTRUCTION planning - Abstract
Each stage of the construction of the rail transit network has unique dynamic characteristics. It can provide recommendations for rail transit network planning and phased construction by evaluating the degree of evolution of the urban rail transit network and dividing the evolution stages precisely. Starting from the allometric growth relationship between transfer nodes and ordinary nodes in the urban rail transit network, this paper defines the evolution level of the rail transit network and the growth rate difference between transfer nodes and ordinary nodes and deduces the dynamic logistic equation of URT network evolution level using the mathematical derivative and logarithmic relationship. This paper reveals the dynamic law of the evolution process of the urban rail transit network at a theoretical level, analyzes the dynamic evolution process on this basis, determines the threshold for phasing the evolution stage, and divides it into four evolution stages. Finally, the results of the theoretical derivation are validated by the evolution data of the Beijing Rail Transit Network (1984–2020) over 45 years. The verification results are substantially congruent with the conclusions of the theoretical derivation, demonstrating the accuracy of the theoretical model and its practical usefulness in directing the building of the rail transit network. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. Boundary value problems for nonlinear second‐order functional differential equations with piecewise constant arguments.
- Author
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Buedo‐Fernández, Sebastián, Cao Labora, Daniel, and Rodríguez‐López, Rosana
- Subjects
- *
NONLINEAR boundary value problems , *FUNCTIONAL differential equations , *BOUNDARY value problems , *LINEAR differential equations , *DELAY differential equations - Abstract
In this paper, we consider a class of nonlinear second‐order functional differential equations with piecewise constant arguments with applications to a thermostat that is controlled by the introduction of functional terms in the temperature and the speed of change of the temperature at some fixed instants. We first prove some comparison results for boundary value problems associated to linear delay differential equations that allow to give a priori bounds for the derivative of the solutions, so that we can control not only the values of the solutions but also their rate of change. Then, we develop the method of upper and lower solutions and the monotone iterative technique in order to deduce the existence of solutions in a certain region (and find their approximations) for a class of boundary value problems, which include the periodic case. In the approximation process, since the sequences of the derivatives for the approximate solutions are, in general, not monotonic, we also give some estimates for these derivatives. We complete the paper with some examples and conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. An accelerated projection‐based parallel hybrid algorithm for fixed point and split null point problems in Hilbert spaces.
- Author
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Arfat, Yasir, Kumam, Poom, Khan, Muhammad Aqeel Ahmad, and Sa Ngiamsunthorn, Parinya
- Subjects
- *
PARALLEL algorithms , *HILBERT space , *MONOTONE operators - Abstract
The purpose of the present paper is to construct a common solution of the split null point problem associated with the maximal monotone operators and the fixed point problem associated with a finite family of k‐demicontractive operators in Hilbert spaces. We compute the optimal common solution via inertial parallel hybrid algorithm under a suitable set of control conditions. The viability of parallel implementation of the algorithm is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. On a m(x)$$ m(x) $$‐polyharmonic Kirchhoff problem without any growth near 0 and Ambrosetti–Rabinowitz conditions.
- Author
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Harrabi, Abdellaziz, Karim Hamdani, Mohamed, and Fiscella, Alessio
- Abstract
In this paper, we study a higher order Kirchhoff problem with variable exponent of type M∫Ω|Dru|m(x)m(x)dxΔm(x)ru=f(x,u)inΩ,Dαu=0,on∂Ω,for eachα∈ℝNwith|α|≤r−1,$$ \left\{\begin{array}{ll}M\left({\int}_{\Omega}\frac{{\left|{\mathcal{D}}_ru\right|}^{m(x)}}{m(x)} dx\right){\Delta}_{m(x)}^ru=f\left(x,u\right)& \mathrm{in}\kern0.30em \Omega, \\ {}{D}^{\alpha }u=0,\kern0.30em & \mathrm{on}\kern0.30em \mathrm{\partial \Omega },\kern0.30em \mathrm{for}\ \mathrm{each}\kern0.4em \alpha \in {\mathrm{\mathbb{R}}}^N\kern0.4em \mathrm{with}\kern0.4em \mid \alpha \mid \le r-1,\end{array}\right. $$ where Ω⊂ℝN$$ \Omega \subset {\mathrm{\mathbb{R}}}^N $$ is a smooth bounded domain, r∈ℕ∗,m∈C(Ω‾),1
- Published
- 2024
- Full Text
- View/download PDF
34. The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions.
- Author
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Ndiaye, Ameth and Özdemir, Zehra
- Subjects
- *
CAYLEY numbers (Algebra) , *MINKOWSKI space , *HYPERSURFACES , *GAUSSIAN curvature , *OPTICAL fibers , *VECTOR fields - Abstract
In this paper, we define three types of 2‐ruled hypersurfaces in the Minkowski 4‐space 피14. We obtain Gaussian and mean curvatures of the 2‐ruled hypersurfaces of type‐1 and type‐2 and some characterizations about its minimality. We also deal with the first Laplace–Beltrami operators of these types of 2‐ruled hypersurfaces in 피14. Moreover, the importance of this paper is the definition of these surfaces by using the octonions in 피14. Thus, this is a new idea and makes the paper original. We give an example of 2‐ruled hypersurface constructed by octonion, and we visualize the projections of the images with MAPLE program. Furthermore, the optical fiber can be defined as a one‐dimensional object embedded in the four‐dimensional Minkowski space 피14. Thus, as a discussion, we investigate the geometric evolution of a linearly polarized light wave along an optical fiber by means of the 2‐ruled hypersurfaces in a four‐dimensional Minkowski space. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. An analysis of the convergence problem of a function of hexagonal Fourier series in generalized Hölder norm using Hausdorff operator.
- Author
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Nigam, H. K. and Kumar Sah, Manoj
- Subjects
- *
GENERALIZED spaces , *HAUSDORFF spaces , *CONTINUOUS functions , *FOURIER series - Abstract
In the present paper, we obtain the results on the degree of convergence of an H$$ H $$‐periodic continuous function in generalized Hölder spaces using Hausdorff operator with monotonically non‐decreasing and monotonically non‐increasing rows of its hexagonal Fourier series. Some important corollaries are also deduced from our main theorems. Applications of main theorems are also obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. On stable solutions of a weighted elliptic equation involving the fractional Laplacian.
- Author
-
Quynh Nguyen, Thi and Tuan Duong, Anh
- Subjects
- *
ELLIPTIC equations , *LAPLACIAN operator , *LIOUVILLE'S theorem , *MATHEMATICS - Abstract
In this paper, we study the following fractional Choquard equation with weight (−Δ)su=1|x|N−α∗h(x)|u|ph(x)|u|p−2uinℝN,$$ {\left(-\Delta \right)}^su=\left(\frac{1}{{\left|x\right|}^{N-\alpha }}\ast h(x){\left|u\right|}^p\right)h(x){\left|u\right|}^{p-2}u\kern0.5em \mathrm{in}\kern0.5em {\mathrm{\mathbb{R}}}^N, $$where 0
2s,p>2,α>0$$ 02s,p>2,\alpha >0 $$ and h$$ h $$ is a positive weight function satisfying h(x)≥C|x|a$$ h(x)\ge C{\left|x\right|}^a $$ at infinity, for some a≥0$$ a\ge 0 $$. We establish, in this paper, a Liouville type theorem saying that if maxN−4s−2a,0<α- Published
- 2024
- Full Text
- View/download PDF
37. A linearized approach for solving differentiable vector optimization problems with vanishing constraints.
- Author
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Antczak, Tadeusz
- Subjects
- *
CONVEX functions - Abstract
In this paper, two mathematical methods are used for solving a complex multicriteria optimization problem as the considered convex differentiable vector optimization problem with vanishing constraints. First of them is the linearized approach in which, for the original vector optimization problem with vanishing constraints, its associated multiobjective programming problem is constructed at the given feasible solution. Since the aforesaid multiobjective programming problem constructed in the linearized method is linear, one of the existing methods for solving linear vector optimization problems is applied for solving it. Thus, the procedure for solving the considered differentiable vector optimization problems with vanishing constraints is presented in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. A simple formula of the magnetic potential and of the stray field energy induced by a given magnetization.
- Author
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Boulmezaoud, Tahar Zamene
- Subjects
- *
MAGNETIZATION , *LANDAU-lifshitz equation , *SPECIAL functions - Abstract
The primary aim of this paper is the derivation and a proof of a simple and tractable formula for the stray field energy in micromagnetic problems. The formula is based on an expansion in terms of a special family of recently discovered functions. It remains valid even if the magnetization is not of constant magnitude or if the sample is not geometrically bounded. The paper continues with a direct and important application which consists in a fast summation technique of the stray field energy. The convergence of this method is established, and its efficiency is proved by various numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. A necessary and sufficient condition for the global existence of solutions to nonlinear reaction‐diffusion equations on the half‐spaces in ℝN.
- Author
-
Chung, Soon‐Yeong and Hwang, Jaeho
- Subjects
- *
NONLINEAR equations , *REACTION-diffusion equations , *CONTINUOUS functions - Abstract
In this paper, we study the existence and nonexistence of the global solutions to nonlinear reaction‐diffusion equations ut(x,t)=Δu(x,t)+ψ(t)f(u(x,t)),(x,t)∈Ω×(0,∞),u(·,0)=u0(x),x∈Ω,u(x,t)=0,(x,t)∈∂Ω×(0,∞),$$ \left\{\begin{array}{ll}{u}_t\left(x,t\right)=\Delta u\left(x,t\right)+\psi (t)f\left(u\left(x,t\right)\right),& \left(x,t\right)\in \Omega \times \left(0,\infty \right),\\ {}u\left(\cdotp, 0\right)={u}_0(x),& x\in \Omega, \\ {}u\left(x,t\right)=0,& \left(x,t\right)\in \mathrm{\partial \Omega}\times \left(0,\infty \right),\end{array}\right. $$where Ω$$ \Omega $$ is the half‐space ℝKN$$ {\mathrm{\mathbb{R}}}_K^N $$, ψ$$ \psi $$ is a nonnegative continuous function, and f$$ f $$ is a locally Lipschitz function with some additional properties. The purpose of this paper is to give a necessary and sufficient condition for the existence of global solutions as follows: There is no global solution for any nonnegative and nontrivial initial data u0∈C0(Ω)$$ {u}_0\in {C}_0\left(\Omega \right) $$ if and only if ∫1∞ψ(t)tN+K2fϵt−N+K2dt=∞$$ {\int}_1^{\infty}\psi (t){t}^{\frac{N+K}{2}}f\left(\epsilon \kern0.1em {t}^{-\frac{N+K}{2}}\right) dt=\infty $$ for every ϵ>0$$ \epsilon >0 $$. In fact, we introduce a very special curve in ℝKN$$ {\mathrm{\mathbb{R}}}_K^N $$x^(t):=t,⋯,t⏟K‐times,xK+1,⋯,xN,t>0,$$ \hat{x}(t):= \left(\underset{K\hbox{-} \mathrm{times}}{\underbrace{\sqrt{t},\cdots, \sqrt{t}}},{x}_{K+1},\cdots, {x}_N\right),t>0, $$to obtain the lower bound of decay of the heat semigroup, which is essential to prove the main result. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. A necessary and sufficient condition for the global existence of solutions to nonlinear reaction‐diffusion equations on the half‐spaces in ℝN.
- Author
-
Chung, Soon‐Yeong and Hwang, Jaeho
- Subjects
NONLINEAR equations ,REACTION-diffusion equations ,CONTINUOUS functions - Abstract
In this paper, we study the existence and nonexistence of the global solutions to nonlinear reaction‐diffusion equations ut(x,t)=Δu(x,t)+ψ(t)f(u(x,t)),(x,t)∈Ω×(0,∞),u(·,0)=u0(x),x∈Ω,u(x,t)=0,(x,t)∈∂Ω×(0,∞),$$ \left\{\begin{array}{ll}{u}_t\left(x,t\right)=\Delta u\left(x,t\right)+\psi (t)f\left(u\left(x,t\right)\right),& \left(x,t\right)\in \Omega \times \left(0,\infty \right),\\ {}u\left(\cdotp, 0\right)={u}_0(x),& x\in \Omega, \\ {}u\left(x,t\right)=0,& \left(x,t\right)\in \mathrm{\partial \Omega}\times \left(0,\infty \right),\end{array}\right. $$where Ω$$ \Omega $$ is the half‐space ℝKN$$ {\mathrm{\mathbb{R}}}_K^N $$, ψ$$ \psi $$ is a nonnegative continuous function, and f$$ f $$ is a locally Lipschitz function with some additional properties. The purpose of this paper is to give a necessary and sufficient condition for the existence of global solutions as follows: There is no global solution for any nonnegative and nontrivial initial data u0∈C0(Ω)$$ {u}_0\in {C}_0\left(\Omega \right) $$ if and only if ∫1∞ψ(t)tN+K2fϵt−N+K2dt=∞$$ {\int}_1^{\infty}\psi (t){t}^{\frac{N+K}{2}}f\left(\epsilon \kern0.1em {t}^{-\frac{N+K}{2}}\right) dt=\infty $$ for every ϵ>0$$ \epsilon >0 $$. In fact, we introduce a very special curve in ℝKN$$ {\mathrm{\mathbb{R}}}_K^N $$x^(t):=t,⋯,t⏟K‐times,xK+1,⋯,xN,t>0,$$ \hat{x}(t):= \left(\underset{K\hbox{-} \mathrm{times}}{\underbrace{\sqrt{t},\cdots, \sqrt{t}}},{x}_{K+1},\cdots, {x}_N\right),t>0, $$to obtain the lower bound of decay of the heat semigroup, which is essential to prove the main result. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Issue Information.
- Subjects
COPYRIGHT ,RESEARCH papers (Students) ,PERIODICAL subscriptions - Abstract
No abstract is available for this article. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. Editorial of Applied Geometric Algebras in Computer Science and Engineering (AGACSE 21).
- Author
-
Vašík, Petr, Hitzer, Eckhard, and Lavor, Carlile
- Subjects
COMPUTER science ,COMPUTER engineering ,ALGEBRA ,COMPUTER engineers ,QUANTUM cryptography ,MEASUREMENT errors ,CLIFFORD algebras - Abstract
This document is an editorial summarizing the Applied Geometric Algebras in Computer Science and Engineering (AGACSE) conference held in Brno, Czech Republic in September 2021. The conference aimed to promote the use of geometric algebra in fields such as image processing, robotics, and quantum computing. The conference proceedings were published in the journal Mathematical Methods in the Applied Sciences. The editorial provides a list of accepted papers, covering topics such as applied geometry, technological applications, algebra, and quantum phenomena. One specific paper explores the use of geometric algebra in teaching rotations through neural networks. The document is a compilation of research papers showcasing the applications of geometric algebra in various fields, including robotics, control systems, image processing, cryptography, and physics. Each paper presents a specific problem or application and proposes a unique approach or solution using geometric algebra. The authors compare their methods with existing techniques and provide mathematical analysis to support their claims. Overall, the papers demonstrate the versatility and effectiveness of geometric algebra in different domains. [Extracted from the article]
- Published
- 2024
- Full Text
- View/download PDF
43. A stochastic predator–prey model with distributed delay and Ornstein–Uhlenbeck process: Characterization of stationary distribution, extinction, and probability density function.
- Author
-
Zhang, Xinhong, Yang, Qing, and Jiang, Daqing
- Subjects
PROBABILITY density function ,ORNSTEIN-Uhlenbeck process ,PREDATION ,STATIONARY processes ,STOCHASTIC models ,BRANCHING processes ,STOCHASTIC systems - Abstract
As the evolution of species relies on not only the current state but also the past information, it is more reasonable and realistic to take delay into an ecological model. This paper deals with a stochastic predator–prey model that considers the distribution delay and assume that the intrinsic growth rate and the death rate in the model are governed by Ornstein–Uhlenbeck process to simulate the random factors in the environment. Based on the existence and uniqueness of the global solution to the model and the boundedness of the p$$ p $$ order moments of the solution, several conditions are established to analyze the survival of the species. Specifically, a criteria for the existence of the stationary distribution to the stochastic system is established by constructing some suitable Lyapunov functions. And the analytical expression of the probability density function of the model around the quasi‐equilibrium is obtained. Furthermore, the extinction of species in the model is also explored. Finally, numerical simulations are carried out to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Time‐delay compensation‐based robust control of mechanical manipulators: Operator‐theoretic analysis and experiment validation.
- Author
-
Song, Geun Il and Kim, Jung Hoon
- Subjects
ROBUST control ,MANIPULATORS (Machinery) ,EXPONENTIAL stability ,TORQUE control ,TORQUE - Abstract
This paper provides a new robust control approach to uncertain mechanical manipulators in the computed torque framework. With respect to the fact that model uncertainties occurring from the framework could make the overall system unstable although the resulting nominal plant is stabilized, this paper develops a readily applicable method for estimating such uncertain elements. More precisely, we propose a time‐delay compensation method, by which prior values relevant to the model uncertainties in a sufficiently small time instant are used for such an estimation. The theoretical effectiveness of the proposed method is validated by establishing the two different arguments on operator‐theoretic exponential stability and Lypaunov‐based disturbance input‐to‐state stability. Finally, some simulation and experiment results are provided to demonstrate the overall arguments developed in this paper for both the theoretical and practical aspects. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Corrigendum to "Mathematical modelling of the semi‐Markovian random walk processes with jumps and delaying screen by means of a fractional order differential equation" [Math. Meth. Appl. Sci. 41(18) (2018). https://doi.org/10.1002/mma.5328 ].
- Author
-
Bandaliyev, Rovshan A., Nasirova, Tamilla I., and Omarova, Konul K.
- Subjects
STOCHASTIC processes ,RANDOM walks ,FRACTIONAL differential equations ,JUMP processes ,MATHEMATICAL models - Abstract
In the paper mentioned in the title, we studied the semi‐Markovian random walk processes with jumps and delaying screen in zero. More precisely, we obtained a mathematical modeling of the semi‐Markov random walk processes with a delaying screen in zero, given in general form by means of fractional differential equation. In this note, we provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Multiplicity of nontrivial solutions for p‐Kirchhoff type equation with Neumann boundary conditions.
- Author
-
Wang, Weihua
- Subjects
NEUMANN boundary conditions ,MULTIPLICITY (Mathematics) ,EQUATIONS - Abstract
This paper is concerned with the multiplicity results to a class of p$$ p $$‐Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by the abstract linking lemma due to Brézis and Nirenberg. We obtain the twofold results in subcritical and critical cases, which is a meaningful addition and completeness to the known results about Kirchhoff equation. At the same time, this paper also gives a method to deal with p$$ p $$‐Laplacian, Kirchhoff equation, and some Kirchhoff type equation in a unified variational framework. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. Long‐time dynamics for the radial focusing fractional INLS.
- Author
-
Majdoub, Mohamed and Saanouni, Tarek
- Subjects
LORENTZ spaces ,LAPLACIAN operator ,BLOWING up (Algebraic geometry) ,NONLINEAR equations - Abstract
We consider the following fractional NLS with focusing inhomogeneous power‐type nonlinearity: i∂tu−(−Δ)su+|x|−b|u|p−1u=0,(t,x)∈ℝ×ℝN,$$ i{\partial}_tu-{\left(-\Delta \right)}^su+{\left|x\right|}^{-b}{\left|u\right|}^{p-1}u=0,\kern0.30em \left(t,x\right)\in \mathrm{\mathbb{R}}\times {\mathrm{\mathbb{R}}}^N, $$where N≥2$$ N\ge 2 $$, 1/2
- Published
- 2023
- Full Text
- View/download PDF
48. Robust uniform stability criteria for fractional‐order gene regulatory networks with leakage delays.
- Author
-
Arjunan, Mani Mallika, Anbalagan, Pratap, and Al‐Mdallal, Qasem
- Subjects
STABILITY criterion ,LEAKAGE ,HOPFIELD networks ,GENE regulatory networks - Abstract
In this paper, we aim to establish the uniform stability criteria for fractional‐order time‐delayed gene regulatory networks with leakage delays (FOTDGRNL). First, we establish the existence and uniqueness of the considered systems by using the Banach fixed point theorem. Second, the delay‐dependent uniform stability and robust uniform stability of FOFGRNLT are investigated with the help of certain analysis techniques depending on equivalent norm techniques. Finally, the paper comes up with two numerical examples to justify the applicability of our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. A new model for investigating the transmission of infectious diseases in a prey‐predator system using a non‐singular fractional derivative.
- Author
-
Ghanbari, Behzad
- Subjects
INFECTIOUS disease transmission ,COMPUTATIONAL biology ,PREDATION ,DIFFERENTIAL equations ,FRACTIONAL calculus - Abstract
During past decades, the study of the interaction between predator and prey species has become one of the most exciting topics in computational biology and mathematical ecology. In this paper, we aim to investigate the stability of a diseased model of susceptible, infected prey and predators around an internal steady state. To this end, the fractional derivatives based on the Mittag‐Leffler kernels in the Liouville‐Caputo concept has been taken into consideration. The existence and uniqueness of the acquired solutions to the model are also studied in this paper. In order to investigate the effects of the fractional‐order along with other existing parameters in the model, several possible scenarios have been examined. As it is seen in the proposed graphical simulations, the employed fractional operator is capable of capturing all anticipated theoretical features of the model. The numerical technique employed in this contribution is precise and efficient and can be easily adopted to investigate many fractional‐order models in biology. It is found that new proposed operators of fractional‐order can describe the real‐world phenomena even better than integer‐order differential equations because of their memory‐related properties. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. Incremental subgradient algorithms with dynamic step sizes for separable convex optimizations.
- Author
-
Yang, Dan and Wang, Xiangmei
- Subjects
CONVEX functions ,ASSIGNMENT problems (Programming) ,ALGORITHMS ,PROBLEM solving - Abstract
We consider the incremental subgradient algorithm employing dynamic step sizes for minimizing the sum of a large number of component convex functions. The dynamic step size rule was firstly introduced by Goffin and Kiwiel [Math. Program., 1999, 85(1): 207‐211] for the subgradient algorithm, soon later, for the incremental subgradient algorithm by Nedic and Bertsekas in [SIAM J. Optim., 2001, 12(1): 109‐138]. It was observed experimentally that the incremental approach has been very successful in solving large separable optimizations and that the dynamic step sizes generally have better computational performance than others in the literature. In the present paper, we propose two modified dynamic step size rules for the incremental subgradient algorithm and analyse the convergence and complexity properties of them. At last, the assignment problem is considered and the incremental subgradient algorithms employing different kinds of dynamic step sizes are applied to solve the problem. The computational experiments show that the two modified ones converges dramatically faster and more stable than the corresponding one in [SIAM J. Optim., 2001, 12(1): 109‐138]. Particularly, for solving large separable convex optimizations, we strongly recommend the second one (see Algorithm 3.3 in the paper) since it has interesting computational performance and is the simplest one. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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