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Localized corrosion often occurs on steel members due to paint peeling led from insufficient durability of the coating material or human collision, which may significantly reduce the load carrying capacity and safety performance of the structures. The effects of the parameters such as localized corrosion penetration, circumferential corrosion ratio, longitudinal corrosion ratio, slenderness ratio and eccentricity of mechanical behaviors of locally corroded circular steel tubes under compression were studied experimentally and numerically. Based on the test results and the finite element analysis, a calculation method was proposed for predicting load carrying capacity of the corroded specimen under compression. It is found that localized corrosion did not change the failure modes of test specimens, and all of them failed in the limit point buckling mode. The factors affecting the degradation of load carrying capacity and stiffness of localized corrosion specimens from high to low were corrosion time, circumferential corrosion ratio and longitudinal corrosion ratio. The most unfavorable localized corrosion modes of load carrying capacity and stiffness were H3L3-270 and H3L1-270, respectively. The load carrying capacity degradation of members increases with the increase of the localized corrosion ratio, circumferential corrosion ratio and longitudinal corrosion ratio, while decreases with the increase of the eccentricity. The formula proposed can be used to predict the load carrying capacity of locally corroded circular steel tube members under compression.

In this paper, some new theorems for various cyclic contractions are established in Gb-metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic α-ψφ-contractive mappings in Gb-metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results.

The aim of this paper is to propose a new φ -coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ -coupled fixed point and modified F -control function. Our obtained results are applied to derive some φ -coupled fixed point theorems in partial metric spaces and quasi-metric spaces, respectively. Some applications to matrix equations and integral equations are also presented so as to illustrate our results.

The tension between unitarity and wave-packet collapse is an annoying problem in quantum mechanics, while a breakthrough was made by Zurek recently from the point of view of information transfer. In this paper, we reconsider Zurek's derivation in the setting of generalized probabilistic theories (GPT), and establish that actionable information about a system can be repeatedly passed on to other systems only when the chosen states of the system have mutual zero fidelity. This may be interpreted as an extension of Zurek's result to GPT.

This paper investigated on the performance of slender concrete-filled carbon fiber-reinforced polymer (CFRP)–PVC tubular columns under axial compression. Four specimens with different slenderness ratios were firstly carried out to explore their performance and failure modes under axial compressive loads in laboratory. Secondly, a nonlinear finite element model (NFEM) was developed to analyze the relation between loads and deformation, and the analytical values were compared with the experimental results. After the efficiency of NFEM was verified, the parametric analyses varying the number of CFRP layer, concrete compressive strength and the slenderness ratio were conducted by the NFEM, and the ultimate bearing capacity formula as well as the relation model of the stability coefficient (φ) versus slenderness ratios (λ) were proposed. To validate the efficiency, ultimate bearing capacity was compared among the experimental results, NFEM analytical values and the prediction by the proposed formula. The results indicate that not only the developed NFEM can effectively depict the varying process of the loads and deformation in details, but also the proposed ultimate bearing capacity formula is reasonable and reliable in the fast prediction of the bearing capacity for slender concrete-filled CFRP–PVC tubular columns. It is beneficial to widely apply such new type composite columns in pile foundation or corrosion environments.

When A ∈ B ( H ) and B ∈ B ( K ) are given, we denote by M C the operator acting on the infinite dimensional separable Hilbert space H ⊕ K of the form M C = ( A C 0 B ) . In this paper, we first give some necessary and sufficient conditions for M C to be a left invertible operator (an upper semi-Weyl, upper semi-Fredholm) operator for some C ∈ B ( K , H ) , which extend the corresponding results in Cao et al. (2006) [4] , Cao and Meng (2005) [5] , Hwang and Lee (2001) [12] and Li and Du (2006) [15] . Then we present some counter-examples.