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The aim of this paper was to investigate intumescent coatings based on polyfurfuryl alcohol (PFA) resin as a binder benefiting from high char yield and low smoke emission. To this end, the coatings composition in terms of PFA binder resin, long oil alkyd plasticizing resin, TiO2 pigment, and flame-retardant additives (FR) was changed as input parameters according to a mixture design-of-experiments. The corresponding changes in the backside temperature of mild steel substrate (Tb), residual char expansion ratio, limiting oxygen index, and char residue (wt% @1000 °C) were studied as the response variables describing fire performance characteristics of the coatings. The results showed that the backside temperature of the plate increased and the expansion ratio decreased with increasing in the alkyd resin concentration. Also, the flame-retardant efficiency of coatings strongly depends on the content of FR additives. When the content of PFA and alkyd resin was increased at a high level (35 and 4 wt%, respectively), the Tb of the coated plates reached 415 °C rapidly, due to the cracking of the coating and the lower concentration of FR additives. However, the formula with higher FR content, i.e., 68 wt%, showed the lowest Tb value ca. 128 °C. Flame-retardant characteristics directly depended on the expansion ratio of the coatings and the morphology of the char layer remaining on the substrate after the flame test; therefore, coatings with a higher expansion ratio showed lower backside temperature. The findings were supported by examining of the remaining char morphology after a flame test by optical microscopy and validated by comparing the predicted and actual responses for optimization. The value of absolute relative deviation was obtained in the range of 1.6–7.9, which indicates a good agreement between the proposed and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on solving the generalized absolute value equations (GAVE). We present a new method named as modulus-based block triangular splitting iteration (MBTS) method based on the block matrix structure resulting from the transformation of the GAVE into two equations. This method is developed by decomposing the matrix into diagonal and triangular matrices, as well as applying a series of suitable combination and modification techniques. The advantage of the MBTS method is that it is not necessary to solve the inverse of the coefficient matrix of the linear equation system during each iteration, which greatly improves the computational speed and reduces its storage requirements. In addition, we present some convergent theorems proving by different techniques and the estimate of the required number of iteration steps. Furthermore, in the accompanying corollaries, we provide some estimations for choosing appropriate parameter values. Finally, we validated the effectiveness and efficiency of our newly developed method through two numerical examples of the GAVE. [ABSTRACT FROM AUTHOR]

Gabor phase retrieval is the problem of recovering a signal from the absolute values of Gabor transform, which has turned into a very active research area. In the paper, we define a generalized Paley–Wiener space, which is obtained by applying the special affine Fourier transform to L p ([ - B , B ]) (2 ≤ p ≤ ∞) and provide the uniqueness of the Gabor phase retrieval in the generalized Paley–Wiener space. When the window function ψ is the inverse special affine Fourier transform of ϕ = 2 1 4 e - π x 2 , we show that every signal in the generalized Paley–Wiener space can be uniquely recovered, up to a global sign, from its the magnitudes of Gabor measurement sampled on a rectangular lattice. Recently, Grohs, Liehr and Wellershoff studied the Gabor phase retrieval problems in the conventional Paley–Wiener space. The paper extends their results to the generalized Paley–Wiener space. Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the applied range of the Gabor phase retrieval. [ABSTRACT FROM AUTHOR]

Time series forecasting is an important application of many statistical methods. When it is appropriate to assume that the data may be projected towards the future based on the past history of the dataset, a preliminary examination is usually required to ensure that the data sequence is autocorrelated. This is a quite obvious assumption that has to be made and can be the object of a formal test of hypotheses. The most widely used test is the portmanteau test, i.e., a sum of the squared standardized autocorrelations up to an appropriate maximum lag (the truncation point). The choice of the truncation point is not obvious and may be data-driven exploiting supplementary information, e.g. the largest autocorrelation and the lag where such maximum is found. In this paper, we propose a portmanteau test with a truncation point equal to the lag of the largest (absolute value) estimated autocorrelation. Theoretical and simulation-based comparisons based on size and power are performed with competing portmanteau tests, and encouraging results are obtained. [ABSTRACT FROM AUTHOR]

The technique for order preference by similarity to ideal solution (TOPSIS) is a popular multi-attribute decision making method. However, the increasing uncertain information with probability and the psychological factor of regret aversion of experts in some complicated situations bring new challenges to the application of traditional TOPSIS. The probabilistic hesitant fuzzy set (P-HFS) is an effective tool to depict the hesitant fuzzy information with the corresponding probability, which can remain more information. In addition, the regret theory indicates that experts may care more about the regret values than the absolute values of alternatives under the fuzzy environment. This paper investigates a new probabilistic hesitant fuzzy TOPSIS (PHFTOPSIS) method based on the regret theory. We propose the corresponding concepts of utility function, reject–rejoice function and perceived utility value of the probabilistic hesitant fuzzy element (P-HFE). The maximum deviation model under the probabilistic hesitant fuzzy environment is presented to determine the weights of attributes. The detailed implementation process of the PHFTOPSIS method based on the regret theory is also provided. Moreover, we apply the proposed method to the investment strategy. Compared with earlier methods, the proposed method can consider both the probabilistic hesitant fuzzy information and regret aversion of experts at the same time in actual applications. A comparative analysis with traditional TOPSIS and probabilistic hesitant fuzzy weighted averaging (PHFWA) operator is further conducted to illustrate its advantages. [ABSTRACT FROM AUTHOR]

For the period of satellite altimetry observation 1993–2018, a comparison was made of estimates of the linear meridional shifts of the jet structure and variations in current intensity in the sector of the Antarctic Circumpolar Current (ACC) south of Africa (10° E–25° W), obtained on the basis of the parameters derived from the module of the absolute dynamic topography (ADT) gradient : directly , module of the velocity of geostrophic current |u| on the ocean surface, half of square of the ADT gradient , and specific kinetic energy . The analysis was carried out by a method developed earlier and refined in this paper using linear regression analysis. It is shown that qualitatively the characters of the meridional shifts (displacement of the curves of these parameters averaged over latitude and for each year) in latitude and the corresponding current intensity variations (i.e., variations in the parameters themselves) over 26-year observations, when calculated through each of the four parameters, turned out to be similar. The same similarity was obtained from the calculations with respect to the ADT scale. Meanwhile, the quantitative differences between calculations for different pairs of parameters can be significant even in the and pair. In quantitative terms, the absolute values of shifts of the jet structure and variations in the intensity of currents in the ACC band in the studied sector of the Southern Ocean generally increase from those linearly dependent on the ADT gradient module to quadratically dependent ones. [ABSTRACT FROM AUTHOR]

Consider a quantum cat map M associated with a matrix A ∈ Sp (2 n , Z) , which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of M on any nonempty open set in the position–frequency space satisfies a lower bound which is uniform in the semiclassical limit, under two assumptions: (1) there is a unique simple eigenvalue of A of largest absolute value and (2) the characteristic polynomial of A is irreducible over the rationals. This is similar to previous work (Dyatlov and Jin in Acta Math 220(2):297–339, 2018; Dyatlov et al. in J Am Math Soc 35(2):361–465, 2022) on negatively curved surfaces and (Schwartz in The full delocalization of eigenstates for the quantized cat map, 2021) on quantum cat maps with n = 1 , but this paper gives the first results of this type which apply in any dimension. When condition (2) fails we provide a weaker version of the result and discuss relations to existing counterexamples. We also obtain corresponding statements regarding semiclassical measures and damped quantum cat maps. [ABSTRACT FROM AUTHOR]

Newton-type methods have been successfully applied to solve the absolute value equation Ax − |x| = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix [A − I, A + I] is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs. [ABSTRACT FROM AUTHOR]

In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory Appl 169:705–712, 2016). [ABSTRACT FROM AUTHOR]

The letter is a response to comments made on a recently published paper about thrombocytopenia in the intensive care unit (ICU). The authors acknowledge that thrombocytopenia is a complex condition with various contributing factors and that its impact on prognosis may vary between different patient populations. The study focused on defining thrombocytopenia and its association with outcomes, rather than investigating its causes or management. The authors suggest that further research is needed to explore the association between thrombocytopenia and mortality in a broader ICU population and to gather randomized data on the use of platelet transfusions in ICU patients. [Extracted from the article]