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We prove the global space-time bound for the defocusing mass critical nonlinear Schrödinger equation on R 3 perturbed by a small multiplicative noise. The associated scattering behavior is also obtained. In addition to techniques from Fan and Xu (Global well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on R at L 2 regularity, 2018) and Fan and Zhao (On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise, 2020), the main new ingredients are the decomposition of the solution tailored for the bootstrap argument in this problem, and the incorporation of local smoothing norms to close the argument. We also prove the global space-time Strichartz estimate for the linear stochastic equation. It is a toy model of our nonlinear problem, but the bound itself is new and of its own interest. Furthermore, the proof we give for the linear model is more direct, and also illustrates the proof strategy for the nonlinear problem. [ABSTRACT FROM AUTHOR]

In group decision making, it is sensible to achive minimum consensus cost (MCC) because the consensus reaching process resources are often limited. In this endeavour, though, there are still two issues that require paying attention to: (1) the impact of decision rules, including decision weights and aggregation functions, on MCC; and (2) the impact of non-cooperative behaviors on MCC. Hence, this paper analytically reveals the decision rules to minimize MCC or maximize MCC. Furthermore, detailed simulation experiments show the joint impact of non-cooperative behavior and decisions rules on MCC, as well as revealing the effect of the consensus within the established MCC target. [ABSTRACT FROM AUTHOR]

The inertness of carbon felt as cathode is still one of the challenges encountered in the degradation of pollutants by electro-Fenton. In this study, we used a simple ultrasonic oxidation method to introduce oxygen-containing groups and defect carbons on carbon felt surface to improve the electro-Fenton performance. The modified carbon felts were prepared by ultrasonic treatment in three dilute solutions of HNO3, H2SO4, and HNO3–H2SO4. Ultrasound can provide an extra energetic environment to accelerate the oxidation process, while NO3− has stronger oxidation properties in the presence of excess H+, greatly increasing the amounts of C–O–C/C=O and C–C active sites on carbon felt surface. And an electro-Fenton system with modified CF as the cathode was used to degrade rhodamine B, and the factors affecting the degradation were discussed. The results showed that the modified cathode material was significantly more efficient in degrading rhodamine B, under the conditions of O2 flow rate of 0.3 L min−1, pH = 3, voltage of − 0.7 V, and addition of 0.2-mM Fe2+, HNO3–H2SO4 solution modified CF with 37% higher than that of the raw CF, and the decolorization rate reached 96% after 120 min. Modified carbon felt still has good degradation properties after 5 cycles. The CF was modified by ultrasonic oxidation technique to introduce oxygen-containing functional groups and C-sp3 on the surface of the carbon felt.Using this CF as a cathode for the degradation of RhB in an electro-Fenton system. [ABSTRACT FROM AUTHOR]

This paper concerns a two-product, multi-period nonstationary newsvendor model in which the inventory is not allowed to be carried between periods and each period the newsvendor is subject to a budget constraint and has to decide his order quantities on each product. The Weak Aggregating Algorithm (WAA) developed in computer science is an online learning method of prediction with expert advice; it makes decisions by considering all the experts advice, and each expert's weight is updated according to his performance in previous periods. Without making statistical assumption on future demand sequence, we propose newsvendor ordering policy by applying WAA to nonstationary ordering policy that can switch between different order quantities in all trading periods. Theoretically, we prove that the proposed ordering policy preserves great competitiveness when compared with the best nonstationary ordering policy with not too many switches. We consider both real-valued and integer-valued ordering policies. Numerical examples with different nonstationary demand types of product 1 illustrate the great competitive performance of the proposed ordering policy. It is found that as the budget increases, the order quantities on the two products and the ordering policy's cumulative gains increase. [ABSTRACT FROM AUTHOR]

The consistency test is a vital basis of the pairwise comparison method, which is performed to ensure that the decision maker is being logical in his/her pairwise comparisons. In the analytic hierarchy process, the pairwise comparison method with a fixed numerical scale has been employed. In this study, we provide a systematic review analysis regarding the inconsistency causes in the pairwise comparison method with a fixed numerical scale, and propose the paradoxes on Saaty’s consistency test in this pairwise comparison method. Meanwhile, based on the use of the consistency-driven linguistic methodology, we propose a novel approach from a perspective of the linguistic and numerical scale to deal with the inconsistency in the pairwise comparison method. [ABSTRACT FROM AUTHOR]