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Abstract Soft-tissue sarcomas (STS) emerges as formidable challenges in clinics due to the complex genetic heterogeneity, high rates of local recurrence and metastasis. Exploring specific targets and biomarkers would benefit the prognosis and treatment of STS. Here, we identified RCC1, a guanine-nucleotide exchange factor for Ran, as an oncogene and a potential intervention target in STS. Bioinformatics analysis indicated that RCC1 is highly expressed and correlated with poor prognosis in STS. Functional studies showed that RCC1 knockdown significantly inhibited the cell cycle transition, proliferation and migration of STS cells in vitro, and the growth of STS xenografts in mice. Mechanistically, we identified Skp2 as a downstream target of RCC1 in STS. Loss of RCC1 substantially diminished Skp2 abundance by compromising its protein stability, resulting in the upregulation of p27Kip1 and G1/S transition arrest. Specifically, RCC1 might facilitate the nucleo-cytoplasmic trafficking of Skp2 via direct interaction. As a result, the cytoplasmic retention of Skp2 would further protect it from ubiquitination and degradation. Notably, recovery of Skp2 expression largely reversed the phenotypes induced by RCC1 knockdown in STS cells. Collectively, this study unveils a novel RCC1-Skp2-p27Kip1 axis in STS oncogenesis, which holds promise for improving prognosis and treatment of this formidable malignancy.

Abstract We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.

Abstract Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let A 1 , A 2 , … , A N $A_{1}, A_{2},\ldots,A_{N}$ be N-variables monotone demi-continuous mappings from K N $K^{N}$ into X. Then: (1) the system of multivariate variational inequalities { 〈 A 1 ( x 1 , x 2 , … , x N ) , y 1 − x 1 〉 ≥ 0 , ∀ y 1 ∈ K , 〈 A 2 ( x 1 , x 2 , … , x N ) , y 2 − x 2 〉 ≥ 0 , ∀ y 2 ∈ K , ⋯ 〈 A N ( x 1 , x 2 , … , x N ) , y N − x N 〉 ≥ 0 , ∀ y N ∈ K , $$\textstyle\begin{cases} \langle A_{1}(x_{1},x_{2},\ldots,x_{N}), y_{1}-x_{1} \rangle\geq0, &\forall y_{1} \in K,\\ \langle A_{2}(x_{1},x_{2},\ldots,x_{N}), y_{2}-x_{2} \rangle\geq0, &\forall y_{2} \in K,\\ \cdots\\ \langle A_{N}(x_{1},x_{2},\ldots,x_{N}), y_{N}-x_{N} \rangle\geq0, &\forall y_{N} \in K,\\ \end{cases} $$ has a solution ( x 1 ∗ , x 2 ∗ , … , x N ∗ ) ∈ K N $(x_{1}^{*},x_{2}^{*},\ldots,x_{N}^{*}) \in K^{N}$ ; (2) the set of solutions of this system of multivariate variational inequalities is closed convex in K N $K^{N}$ ; (3) if A 1 , A 2 , … , A N $A_{1}, A_{2},\ldots,A_{N}$ are also strictly monotone, this system of multivariate variational inequalities has a unique solution.

This paper constructs the generalized viscosity implicit midpoint rule for nonexpansive mappings in Banach space. It obtains strong convergence conclusions for the proposed algorithm and promotes the related results in this field. Moreover, this paper gives some applications. Finally, the paper gives six numerical examples to support the main results.

This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space. Under certain conditions, this paper obtains the strong convergence results of the proposed algorithm and improves the relevant results of researchers in this field. In the end, this paper gives numerical examples to support the main results.

In recent years, the definition of relatively nonexpansive multivalued mapping and the definition of weak relatively nonexpansive multivalued mapping have been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive multivalued mappings and give two examples which are weak relatively nonexpansive multivalued mappings but not relatively nonexpansive multivalued mappings in Banach space 𝑙2 and 𝐿𝑝[0,1](1

The authors have obtained the following results: (1) the definition of uniformly closed countable family of nonlinear mappings, (2) strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, (3) two examples of uniformly closed countable families of nonlinear mappings and applications, (4) an example which is hemirelatively nonexpansive mapping but not weak relatively nonexpansive mapping, and (5) an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping. Therefore, the results of this paper improve and extend the results of Plubtieng and Ungchittrakool (2010) and many others.

Saewan and Kumam (2010) have proved the convergence theorems for finding the set of solutions of a general equilibrium problems and the common fixed point set of a family of closed and uniformly quasi-𝜙-asymptotically nonexpansive mappings in a uniformly smooth and strictly convex Banach space E with Kadec-Klee property. In this paper, authors prove the convergence theorems and do not need the Kadec-Klee property of Banach space and some other conditions used in the paper of S. Saewan and P. Kumam. Therefore, the results presented in this paper improve and extend some recent results.

The purpose of this article is to present a general viscosity iteration process {xn} which defined by xn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xn and to study the convergence of {xn}, where T is a nonexpansive mapping and A is a strongly positive linear operator, if {αn}, {βn} satisfy appropriate conditions, then iteration sequence {xn} converges strongly to the unique solution x*∈f(T) of variational inequality 〈(A−γf)x*,x−x*〉≥0, for all x∈f(T). Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. The results presented in this paper extend, generalize, and improve the results of Xu, G. Marino and Xu and some others.

The purpose of this paper is to prove strong convergence theorems for common fixed points of two countable families of relatively quasi nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalized -projection operator. In order to get the strong convergence theorems, a new iterative scheme by monotone hybrid method is presented and is used to approximate the common fixed points. Then, two examples of countable families of uniformly closed nonlinear mappings are given. The results of this paper modify and improve the results of Li et al. (2010), the results of Takahashi and Zembayashi (2008), and many others.

Let 𝑋 be a uniformly convex Banach space and 𝒮={𝑇(𝑠)∶0≤𝑠0𝐹(𝑇(𝑠))≠∅. Consider the iterative method that generates the sequence {𝑥𝑛} by the algorithm 𝑥𝑛+1=𝛼𝑛𝑓(𝑥𝑛)+𝛽𝑛𝑥𝑛+(1−𝛼𝑛−𝛽𝑛)(1/𝑠𝑛)∫𝑠𝑛0𝑇(𝑠)𝑥𝑛𝑑𝑠,𝑛≥0, where {𝛼𝑛}, {𝛽𝑛}, and {𝑠𝑛} are three sequences satisfying certain conditions, 𝑓∶𝐶→𝐶 is a contraction mapping. Strong convergence of the algorithm {𝑥𝑛} is proved assuming 𝑋 either has a weakly continuous duality map or has a uniformly Gâteaux differentiable norm.

The purpose of this paper is to present the notion of weak relatively nonexpansive multi-valued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces. The weak relatively nonexpansive multivalued mappings are more generalized than relatively nonexpansive multivalued mappings. In this paper, an example will be given which is a weak relatively nonexpansive multivalued mapping but not a relatively nonexpansive multivalued mapping. In order to get the strong convergence theorems for weak relatively nonexpansive multivalued mappings, a new monotone hybrid iteration algorithm with generalized (metric) projection is presented and is used to approximate the fixed point of weak relatively nonexpansive multivalued mappings. In this paper, the notion of multivalued resolvent of maximal monotone operator has been also presented which is a weak relatively nonexpansive multivalued mapping and can be used to find the zero point of maximal monotone operator.

The following main results have been given. (1) Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1)-L-Lipschitz mapping with condition 0

In recent years, the definition of weak relatively nonexpansive mapping has been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive mappings and give two examples which are weak relatively nonexpansive mappings but not relatively nonexpansive mappings in Banach space l2 and Lp[0,1] (1

The purpose of this paper is to introduce an iterative algorithm for finding a solution of quadratic minimization problem in the set of fixed points of a nonexpansive mapping and to prove a strong convergence theorem of the solution for quadratic minimization problem. The result of this article improved and extended the result of G. Marino and H. K. Xu and some others.

The purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings. Further, we apply our results to solve the equilibrium and optimization problems. The results of this paper improved and extended the results of W. Nilsrakoo and S. Saejung (2008) and some others in some respects.

Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 00. Let 0

The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings {Ti}i=1N, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others.

A new class of generalized nonlinear variational inclusions involving (A,η)-monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since (A,η)-monotonicity generalizes A-monotonicity and H-monotonicity, results obtained in this paper improve and extend many others.

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.

We show that the general variational inequalities are equivalent to the general Wiener-Hopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results improve and extend recent ones announced by many others.

We consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods. Our results include the previous results as special cases extend and improve the main results of R. U. Verma (2004), S. S. Chang et al. (2007), Z. Y. Huang and M. A. Noor (2007), and many others.

We modified the classic Mann iterative process to have strong convergence theorem for a finite family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend the results announced by many others.

Strong convergence theorems are obtained by hybrid method for modified composite implicit iteration process of nonexpansive mappings in Hilbert spaces. The results presented in this paper generalize and improve the corresponding results of Nakajo and Takahashi (2003) and others.

Strong convergence theorems are obtained from modified Halpern iterative scheme for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Kim, Xu, and some others.

In this paper, strong convergence theorem is obtained for the modified Noor iterations in the framework of uniformly smooth Banach spaces. Our results extend and improve the recent ones announced by Wittman, Kim, Xu, and some others.

Abstract Photothermal CO2 conversion to ethanol offers a sustainable solution for achieving net-zero carbon management. However, serious carrier recombination and high C-C coupling energy barrier cause poor performance in ethanol generation. Here, we report a Cu/Cu2Se-Cu2O heterojunction-nanosheet array, showcasing a good ethanol yield under visible–near-infrared light without external heating. The Z-scheme Cu2Se-Cu2O heterostructure provides spatially separated sites for CO2 reduction and water oxidation with boosted carrier transport efficiency. The microreactors induced by Cu2Se nanosheets improve the local concentration of intermediates (CH3* and CO*), thereby promoting C-C coupling process. Photothermal effect of Cu2Se nanosheets elevates system’s temperature to around 200 °C. Through synergizing electron and heat flows, we achieve an ethanol generation rate of 149.45 µmol g−1 h−1, with an electron selectivity of 48.75% and an apparent quantum yield of 0.286%. Our work can serve as inspiration for developing photothermal catalysts for CO2 conversion into multi-carbon chemicals using solar energy.

The western Pacific seamount area is abundant in both biological and mineral resources, making it a crucial location for international investigation of regional seabed resources. An essential stage in comprehending and advancing seamounts is gaining knowledge about the distribution characteristics and laws governing the seabed substrate. Deep-sea geological sampling is challenging because of the intricate nature of the deep-sea environment, resulting in increased difficulty in identifying and evaluating substrates. This study addresses the aforementioned issues by utilizing in-situ video footage obtained from the “Jiaolong” manned deep submersible and shipborne deep-water multibeam data. This data is used as a foundation for constructing a Western Pacific seamount areas substrate classification point set. Additionally, the paper introduces the mRMR-XGBoost substrate classification model. Substrate categorization in deep sea and mountainous regions has been successfully accomplished, yielding a classification accuracy of 92.5%. The classification experiments and box sampling results demonstrate that the mRMR-XGBoost substrate classification model proposed in this paper can efficiently use acoustic and optical data to accurately divide the substrate types in seamount areas, with better classification accuracy, when compared with commonly used machine learning models. It has a significant application value and the best classification effect on the two types of substrates: nodules and gravel substrates.

Safety is essential when building a strong transportation system. As a key development direction in the global railway system, the intelligent railway has safety at its core, making safety a top priority while pursuing the goals of efficiency, convenience, economy, and environmental friendliness. This paper describes the state of the art and proposes a system architecture for intelligent railway systems. It also focuses on the development of railway safety technology at home and abroad, and proposes the active safety method and technology system based on advanced theoretical methods such as the in-depth integration of cyber–physical systems (CPS), data-driven models, and intelligent computing. Finally, several typical applications are demonstrated to verify the advancement and feasibility of active safety technology in intelligent railway systems.