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26 February 2026, Volume 46 Issue 1 Previous Issue   

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Normalized Solutions to a $p$-Laplacian Equation with an $L^2$ Constraint: The Mass Supercritical Case Yulu Tian, Dengshan Wang, Liang Zhao Acta mathematica scientia,Series A. 2026, 46 (1):  1-30.  Abstract ( 68 )   RICH HTML   PDF (750KB) ( 91 )   Save References | Related Articles | Metrics

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Quasi-Periodicity and Uniqueness of Meromorphic Functions with $Ac$-Shared Functions Keqi Hu, Qingcai Zhang Acta mathematica scientia,Series A. 2026, 46 (1):  31-57.  Abstract ( 38 )   RICH HTML   PDF (709KB) ( 69 )   Save The paper focuses on the quasi-periodicity of meromorphic functions with $Ac$-shared functions. At the latter part of the paper, we give a uniqueness theorem for quasi-periodic functions. The proofs of the uniqueness theorem of additive quasi-periodic function are simplified by converting some equations into vectors and using MATLAB for some tedious procedures. Figures and Tables | References | Related Articles | Metrics

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The Hardy Operator on $L^2(\mathbb{R})$ Ran Li, Chengjia Zhang Acta mathematica scientia,Series A. 2026, 46 (1):  58-68.  Abstract ( 48 )   RICH HTML   PDF (601KB) ( 36 )   Save In this paper, we study the Hardy operator $H_{\mathbb{R}} $ defined on the space $ L^2(\mathbb{R})$. By introducing an orthogonal basis associated with Laguerre polynomials, we prove that the operator $ I - H_{\mathbb{R}} $ acts as an isometric shift on $ L^2(\mathbb{R})$. We further analyze the properties of its adjoint and establish that $ I - H_{\mathbb{R}}^*$ is also an isometric shift, satisfying $(I - H_{\mathbb{R}})(I - H_{\mathbb{R}}^*) = I,$ which implies that the operator norm of $ H_{\mathbb{R}}$ is 2. Moreover, we investigate the spectral structure of $H_{\mathbb{R}} $ in detail, proving that its spectrum lies on the circle in the complex plane centered at $ (1,0)$ with radius 1, and that $ H_{\mathbb{R}}$ has an empty point spectrum. Finally, we generalize the definition of the Hardy operator by considering a weighted version and demonstrate its application to solving certain first-order differential equations. References | Related Articles | Metrics

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Periodic Solutions of Second-Order Evolution Equations with Weak Damping in Hilbert Spaces Yongxiang Li, Yun Gao Acta mathematica scientia,Series A. 2026, 46 (1):  69-79.  Abstract ( 21 )   RICH HTML   PDF (547KB) ( 41 )   Save In this paper, the existence and uniqueness of periodic solutions for the second-order evolution equation with weak damping in a Hilbert space $H$ $$ u''(t)+2c u'(t)+Au(t)=f(t, u(t)),\quad t\in \mathbb{R} $$ are discussed, where $ A: D(A)\subset H\to H$ is a positive definite self-adjoint operator with a compact resolvent in $H$, $f: \mathbb{R}\times H\to H$ is continuous, $f(t, x)$ is $\omega$-periodic in $t$, and $c>0$ is the damping coefficient. By applying the semigroup theory of linear operators and fixed-point theorem, we obtain existence and uniqueness results of $\omega$-periodic weak solution and classical solution of the equations. References | Related Articles | Metrics

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Landweber Iterative Method for a Time Fractional Inverse Diffusion Problem Yunze Liu, Lixin Feng Acta mathematica scientia,Series A. 2026, 46 (1):  80-93.  Abstract ( 29 )   RICH HTML   PDF (966KB) ( 106 )   Save In this paper, an inverse diffusion problem with the Caputo fractional derivative in time is considered. We prove that such a problem is ill-posed and apply the Landweber iteration method. The selection criteria for the number of iterations (regularization parameter) under both prior and posterior conditions are provided respectively, along with a rigorous mathematical proof of the convergence of the method. Finally, a numerical example is given to illustrate the effectiveness of this method. Figures and Tables | References | Related Articles | Metrics

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Projection Algorithm for Hierarchical Variational Inequality Problem and Fixed Point Problem in Hilbert Space Jiayu Liu, Xinghui Gao, Luhan Dan Acta mathematica scientia,Series A. 2026, 46 (1):  94-107.  Abstract ( 27 )   RICH HTML   PDF (711KB) ( 37 )   Save This paper introduces a novel multi-step inertial regularization algorithm in Hilbert spaces, designed to solve the common solution of hierarchical variational inequality problems and quasi-non expansive mapping fixed-point problems. Under certain conditions, the strong convergence theorem for this iterative sequence generated by the algorithm is established. Finally, a numerical example is provided to demonstrate that this algorithm is more efficient than the existing ones. Figures and Tables | References | Related Articles | Metrics

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Long-Time Asymptotics of the Nonlocal Positive Flow Short-Pules Equation Wenhao Liu, Yufeng Zhang Acta mathematica scientia,Series A. 2026, 46 (1):  108-129.  Abstract ( 21 )   RICH HTML   PDF (700KB) ( 107 )   Save The nonlocal positive flow short-pules equation is first proposed based on the nonlinear transverse oscillation of elastic beam under tension in physics. By the nonlinear steepest descent method, the long-time asymptotics of the solution of the Cauchy problem for the equation is discussed. Starting from the WKI-type Lax pair it satisfies, the corresponding basic Riemann-Hilbert problem and reconstruction formula for the solution are established. Through a series of deformations such as reorientation, extending, cuting and rescaling, the basic Riemann-Hilbert problem is transformed into the model Riemann-Hilbert problem that can be solved using parabolic cylinder functions. Finally, the long-time asymptotics of the solution of the nonlocal positive flow short-pules equation is obtained. Figures and Tables | References | Related Articles | Metrics

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Traveling Wave Solutions and Spreading Speed for a Nonlocal Lotka-Volterra Competition System with Seasonal Succession Jun Sheng, Haiqin Zhao Acta mathematica scientia,Series A. 2026, 46 (1):  130-142.  Abstract ( 24 )   RICH HTML   PDF (616KB) ( 45 )   Save This paper investigates a nonlocal Lotka-Volterra competition model with seasonal succession. The existence of a monostable traveling waves connecting two semi-trivial equilibria is proven by using the theory of monotone semiflows. Meanwhile, we obtain the rightward spreading speed, we establish the existence of the minimal wave speed for rightward traveling waves and its coincidence with the rightward spreading speed. References | Related Articles | Metrics

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Spatiotemporal Dynamics Analysis of a Leslie-Gower Predator-Prey System with Multiple Interactions Zhengwu Yang, Min Xiao, Ying Zhou, Jie Ding, Jing Zhao, Rutkowski Leszek Acta mathematica scientia,Series A. 2026, 46 (1):  143-156.  Abstract ( 28 )   RICH HTML   PDF (2853KB) ( 41 )   Save Current studies on predator-prey systems mainly consider single interaction mechanisms, which cannot fully characterize the complex ecological interactions between populations. Therefore, this paper establishes a cross-diffusion predator-prey system incorporating multiple interaction mechanisms including fear effects, saturation effects, intraspecific competition, and predator interference, based on the Beddington-DeAngelis functional response function and modified Leslie-Gower terms. For the non-diffusion system, we analyze the stability of positive equilibrium points and the Hopf bifurcation conditions induced by prey intraspecific competition. For the diffusion system, we derive the conditions for Turing instability and focus on investigating how various interaction mechanisms affect the formation and evolution of Turing patterns. The results demonstrate that changing the intensity of interaction mechanisms (such as fear effects) and cross-diffusion coefficients can lead to transitions between different Turing patterns, while different interaction mechanisms can also alter the system stability and the stabilization rate of Turing patterns to varying degrees. The results indicate that interactions between predators and prey, along with cross-diffusion, significantly impact the dynamical behavior of the system. Figures and Tables | References | Related Articles | Metrics

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Periodic Traveling Waves for a Delayed SIR System with Nonlocal Dispersal Mengxuan Jia, Yunrui Yang Acta mathematica scientia,Series A. 2026, 46 (1):  157-173.  Abstract ( 26 )   RICH HTML   PDF (627KB) ( 35 )   Save The periodic traveling waves for a class of delayed SIR system with nonlocal dispersal are considered. Firstly, the basic reproduction number $\Re_{0}$ is defined by the method of subalgebraic operators. Secondly, the existence of periodic traveling waves of the system when the basic reproduction number $\Re_{0}>1$ is established based on the non-compactness Kuratowski measure theory and the asymptotic fixed point theorem. Finally, the non-existence of periodic traveling waves when the basic reproduction number $\Re_{0}<1$ is investigated using the method of contradiction proof and the analysis technique. References | Related Articles | Metrics

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Unique Continuation Properties of Weighted Degenerate Elliptic Equation with Singular Potential Guangwei Du, Feixue Wei Acta mathematica scientia,Series A. 2026, 46 (1):  174-189.  Abstract ( 22 )   RICH HTML   PDF (613KB) ( 29 )   Save In this paper, we consider the following second order variable coefficient weighted degenerate elliptic equation with singular potential constituted by Generalized Baouendi-Grushion vector fields $$ - \sum\limits_{i,j = 1}^N {{X_j}({a_{ij}}(x,y){X_i}u)} + V(x,y)u = 0,$$ where $$\lambda {\left| \eta \right|^2}w \leqslant \left\langle {A\eta,\eta } \right\rangle \leqslant {\lambda ^{ - 1}}{\left| \eta \right|^2}w,\ \ A = {({a_{ij}})_{N \times N}},$$ $w$ is a weight function related to quasi distance. By using the weighted Hardy inequality, Rellich type identity and the estimates of Dirichlet energy, we first get the monotonicity of the frequency function of the weak solutions. Then the doubling and unique continuation properties of the weak solutions are obtained. References | Related Articles | Metrics

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Existence of Nontrivial Solution of Klein-Gordon-Maxwell Systems with Critical or Supercritical Nonlinearity Xin Sun, Yu Duan, Jiu Liu Acta mathematica scientia,Series A. 2026, 46 (1):  190-199.  Abstract ( 22 )   RICH HTML   PDF (597KB) ( 31 )   Save This article concerns the following Klein-Gordon-Maxwell system $$\begin{cases}-\Delta u+ V(x)u-(2\omega+\phi)\phi u=\lambda |u|^{s-2}u+ f(u), & x\in \mathbb{R}^{3},\\\Delta \phi=(\omega+\phi)u^2, & x\in \mathbb{R}^{3},\end{cases}$$ where $\omega> 0$ is a constant, $\lambda> 0$ is a real parameter, $s\geq6$. When $V, f$ satisfy suitable conditions and $\lambda$ is relatively small, existence of nontrivial solution can be proved via variational methods and Moser iteration. The result in this paper completes some recent works concerning research on solutions of this system. References | Related Articles | Metrics

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Global Existence and Large Time Behavior of Strong Solutions for Three-Dimensional Compressible Liquid Crystals in a Bounded Domain Xiaohan Pi, Qiuju Xu Acta mathematica scientia,Series A. 2026, 46 (1):  200-214.  Abstract ( 26 )   RICH HTML   PDF (578KB) ( 31 )   Save In this paper, the initial boundary value problem of a three-dimensional compressible nematic liquid crystal flows is studied. The global existence and large time behavior of a strong solution on a bounded domain is obtained when the initial value is close to a equilibrium state in $H^2$ Sobolev space. References | Related Articles | Metrics

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Global Well-Posedness of Strong Solutions to Compressible Magnetohydrodynamic System with Large Initial Data in 3D Bounded Domains Mingyu Zhang Acta mathematica scientia,Series A. 2026, 46 (1):  215-237.  Abstract ( 21 )   RICH HTML   PDF (604KB) ( 34 )   Save The three-dimensional (3D) compressible magnetohydrodynamic system is studied in a bounded rectangular domain with slip boundary condition for the velocity field and perfect conduction for the magnetic field. For the regular initial data with large energy, the global well-posedness of strong solutions to the initial-boundary-value problem of this system is obtained. References | Related Articles | Metrics

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Optical Soliton Resonances and Soliton Molecules for the Hiorta Equation Pingping Zeng, Pingan Zeng, Lu Liu Acta mathematica scientia,Series A. 2026, 46 (1):  238-248.  Abstract ( 30 )   RICH HTML   PDF (2408KB) ( 39 )   Save Soliton resonance and soliton molecules play a significant role in the study of optics, physics, and fluid mechanics. This paper systematically investigates the soliton resonance and soliton molecule properties of the Hirota equation in the context of nonlinear optical systems. First, based on the Lax pair, the $N$-fold Darboux transformation of the Hirota equation is constructed, from which the exact analytical expressions of the $N$-soliton solutions are derived. Subsequently, by adjusting the spectral parameters and initial phase parameters, novel soliton resonance and soliton molecule solutions of the Hirota equation are constructed, and their dynamical characteristics are analyzed. The research results indicate that localized soliton resonance can evolve into soliton molecules, with soliton molecules being the limiting form of localized soliton resonance. Furthermore, the study reveals that the energy carried by solitons exhibits a growth trend during the formation of soliton resonance and soliton molecules. It also demonstrates that the spatiotemporal evolution patterns of soliton molecules become increasingly complex as the soliton order increases. Meanwhile, the wave density of soliton molecules is positively correlated with the coefficients of higher-order dispersion and higher-order nonlinear terms. These findings provide new theoretical insights into the soliton dynamics of the Hirota equation and contribute to a better understanding of soliton interaction mechanisms in nonlinear optical systems. Figures and Tables | References | Related Articles | Metrics

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Approximate Controllability of Riemann-Liouville Fractional Semilinear Evolution Systems Cuiyun Shi, Maojun Bin Acta mathematica scientia,Series A. 2026, 46 (1):  249-258.  Abstract ( 15 )   RICH HTML   PDF (556KB) ( 39 )   Save In this paper, We discuss Riemann-Liouville fractional evolution differential systems in Banach spaces. Firstly, the existence of $C_{1-\alpha}$-mild solutions for the Riemann-Liouville fractional evolution differential equations are established in Banach spaces. Secondly, we make some general assumptions to guarantee the approximate controllability of the associated Riemann-Liouville fractional evolution systems is also formulated and proved. In the end, an example is given to illustrate our main results. References | Related Articles | Metrics

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Stability and Spectral Analysis of Nonuniform Transmission Line Equations Le Zhang, Dongxia Zhao, Jingwen Wang, Jiaojiao Zhang Acta mathematica scientia,Series A. 2026, 46 (1):  259-269.  Abstract ( 16 )   RICH HTML   PDF (790KB) ( 28 )   Save This article applies Riemann coordinate transformation and coordinate scaling to non-uniform transmission line equations, and establishes a class of hyperbolic PDE-PDE coupled systems with variable coefficients. Assuming that the control input voltage of the boundary condition remains constant, the proportional feedback boundary condition of the system is obtained. Then rewrite the closed-loop system into the form of abstract evolution equations, and use the semigroup method and equivalent norm theorem to obtain the dissipativity conditions of feedback control parameters, ensuring the dissipativity of system operators. Finally, spectral analysis was conducted on the system operators, and the asymptotic expression of the eigenvalues was derived using the matrix operator pencil method. Figures and Tables | References | Related Articles | Metrics

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Algebraic Degeneration of One-Dimension Non-Recurrent Diffusion Processes Leilei Gan, Yifei Hao, Yingzhe Wang Acta mathematica scientia,Series A. 2026, 46 (1):  270-285.  Abstract ( 20 )   RICH HTML   PDF (583KB) ( 33 )   Save Algebraic degeneration in $L^2$ sense is studied for non-recurrent diffusion process on a semi-line. The sufficient and necessary conditions are presented under two boundary conditions. The similar conclusions are also proved on the real line. The conclusions are applied to two examples, yielding precise results. References | Related Articles | Metrics

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The Joint Limiting Distribution of the Upper and the Lower Extreme Order Statistics with Random Sample Size Ying Tao, Zuoxiang Peng, Zhongquan Tan Acta mathematica scientia,Series A. 2026, 46 (1):  286-304.  Abstract ( 22 )   RICH HTML   PDF (636KB) ( 35 )   Save Motivated by the paper of Vasudeva (Metrika, 2024, 87: 571-584), this paper studied the joint limiting distribution of the upper and the lower extreme order statistics with random sample size. Let $\{X_{n}, n\geq1\}$ be a sequence of random variables and $N(n)$ be a sequence of positive integer random variables. Under some conditions, we derive first the joint limiting distribution of $M_{N(n)} =\max\left \{X_{1}, X_{2}, \cdots, X_{N(n)} \right \}$ and $W_{N(n)} =\min\left \{ X_{1}, X_{2}, \cdots, X_{N(n)} \right \}$ and then we extended the result to the case of the upper and the lower extreme order statistics. The obtained results extended that of Vasudeva (Metrika, 2024, 87: 571-584). References | Related Articles | Metrics

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Sharp Large Deviations of the Non-Stationary Ornstein-Uhlenbeck Process with Linear Drift Qinwen Li, Shoujiang Zhao Acta mathematica scientia,Series A. 2026, 46 (1):  305-317.  Abstract ( 16 )   RICH HTML   PDF (544KB) ( 43 )   Save The Ornstein-Uhlenbeck (O-U) process, as an important diffusion process, plays a significant role in fields such as statistics, finance, and physics. In this paper, the sharp large deviations of the maximum likelihood estimation for the O-U process with linear drift in the explosive cases are studied by change of measure, and a refined characterization of the tail probability is obtained. As an application, the large deviation principle is obtained. The results demonstrate that the maximum likelihood estimations of the O-U process with and without linear drift in the explosive cases have the same large deviations. References | Related Articles | Metrics

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Finite Element Calculation of a Steady-State Variable Dielectric Poisson-Nernst-Planck Equations Bingjie Zhang, Ruigang Shen Acta mathematica scientia,Series A. 2026, 46 (1):  318-326.  Abstract ( 18 )   RICH HTML   PDF (652KB) ( 33 )   Save The Variable Dielectric Poisson-Nernst-Planck (VDPNP) equations are models that describe ion transport behavior in electrolyte solutions. These equations extend the classical Poisson-Nernst-Planck (PNP) equations by introducing a dependence of the dielectric constant on ion concentration, which allows for a better description of the complex dynamic processes in electrolyte solutions. To investigate the impact of the VDPNP equations on system interactions, this paper first solves the VDPNP model using the Gummel finite element method. Subsequently, numerical simulations of nanopore systems are performed. The simulation results show that, in mixed solutions, the traditional PNP equations cannot distinguish between sodium and potassium ions based on concentration, whereas the VDPNP models can clearly differentiate between sodium and potassium ions. Furthermore, the distinguishing effect becomes more pronounced as the surface charge increases. Figures and Tables | References | Related Articles | Metrics

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An Adaptive Momentum-Accelerated Two-Point Gradient Method for Solving Ill-Posed Inverse Problems Xianting Xiao, Qinglong He Acta mathematica scientia,Series A. 2026, 46 (1):  327-342.  Abstract ( 17 )   RICH HTML   PDF (1262KB) ( 46 )   Save The Landweber iterative regularization method is an effective approach for solving nonlinear ill-posed inverse problems. However, its convergence speed is often slow, which greatly limits its practical applications. An adaptive two-point gradient method with momentum (ATPGM) is proposed to accelerate the classic Landweber method. The main idea of the ATPGM is that the momentum is introduced into the gradient direction of the two-point gradient method, thus it can take full advantage of the previous gradients information, resulting in a highly fast convergence.The convergence and regularity of ATPGM are given. In numerical experiments, we test the numerical performance of ATPGM, based on one-dimensional and two-dimensional elliptic parameter identification problems. A comprehensive comparision between the Landweber iterative regularization method, the two-point gradient method (TPG) and ATPGM is also presented. The numerical results show that ATPGM performs little better in terms of iterations and running time. Numerical results also show that ATPGM is not sensitive to noise in terms of iterations. Figures and Tables | References | Related Articles | Metrics

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European Maximal Call Options Pricing in a Multidimensional Jump Diffusion Market Model Under a Fuzzy Environment Hongwei Liu, Yajun Wang, Pengcheng Ma Acta mathematica scientia,Series A. 2026, 46 (1):  343-358.  Abstract ( 22 )   RICH HTML   PDF (706KB) ( 36 )   Save In this paper, the uncertainty of the multidimensional European maximal call option is characterized by a combination of fuzziness and stochasticity. The pricing formulas for the correspond-ing European maximal call option are given by L$\acute{\rm e}$vy-It$\hat{\rm o}$ formula, when the logarithm of the jump amplitude is with fuzzy normal sum and fuzzy double exponential distribution. A clarity number is given by weighted probability averaging in the valuation of the fuzzy option. Finally, the effects of the variation of the main parameters and different models on the pricing of the European maximal call option are analyzed by numerical simulation. Figures and Tables | References | Related Articles | Metrics

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An Entropy of an Extended Map of Amenable Group Actions Yuan Lian, Hongjun Liu Acta mathematica scientia,Series A. 2026, 46 (1):  359-365.  Abstract ( 26 )   RICH HTML   PDF (520KB) ( 46 )   Save The study of group actions and the corresponding entropy theory in topological spaces is very important in mathematical physics and topology. Factor map is a key concept in the study of the structural theory of measure preserving dynamical systems. Conditional entropy, on the other hand, quantitatively characterises the complexity of factor map. In this paper, we calculate the conditional entropy of a class of extended maps in the dynamical system for amenable group actions, and its value is zero. References | Related Articles | Metrics

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Sharing Quantum Nonlocality in Noisy Star Networks Shan Liu, Kan He, Feng Zhang Acta mathematica scientia,Series A. 2026, 46 (1):  366-376.  Abstract ( 32 )   RICH HTML   PDF (1611KB) ( 45 )   Save Bell nonlocality sharing of quantum systems is a basic feature of quantum mechanics. The nonlocality sharing ability of network quantum states is stronger than bell nonlocality, and the structure of network quantum states is more complex. In practical applications, the error of quantum entanglement generation and the noise in the process of quantum measurement will lead to the decay of nonlocality sharing. This article explores the sufficient conditions for the persistence of nonlocality sharing with noise under unilateral and multilateral measurements in star networks, and analyzes the impact of different noise conditions on the persistence of nonlocality sharing in star networks. In particular, this paper also applies the above conclusions to the specific bilocal scenarios: with two independent sources, one central party and two edge parties. Figures and Tables | References | Related Articles | Metrics