Cycles Avoiding a Color in Colorful Graphs

The Ramsey numbers of cycles imply that every 2‐edge‐colored complete graph on n vertices contains monochromatic cycles of all lengths between 4 and at least . We generalize this result to colors by showing that every k‐edge‐colored complete graph on vertices contains ‐edge‐colored cycles of all lengths between 3 and at least .     

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval‐valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval‐valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval‐valued intuitionistic fuzzy generalized weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016     

Transport numbers and ionic conduction of eutectic methacomposites {(1 ? x )MeWO4 · x WO3}) (Me = Sr, Ba; x = 0?0.55)

Transport numbers of oxygen ions, , in methacomposites (1 − x)MeWO₄ · xWO₃, where Me = Sr and Ba and x = 0−0.55, are determined in the temperature interval 600 to 900°C by a method of the emf of an oxygen-air galvanic cell. It is demonstrated that the region of small contents of the additive (x ≤ 0.2) is predominantly characterized by oxygen-ion conduction ( = 1), which gives way to electronic conduction (t _e = 1) at x > 0.35. It is confirmed once again that subeutectic compositions (1 − x)MeWO₄ · xWO₃ where Me = Sr and Ba and x = 0−0.2 belong in the class of ion-conducting methacomposites. The threshold of percolation of electronic conduction (t _e ≥ 0.5, < 0.5) occurs at x _t ≥ 0.3. Dependences of the transport numbers of the oxygen ions on the volume ratio between components in both composites resemble one another; specifically, the threshold composition contains nearly 20 vol % of WO₃. The dramatic amplification (by 1–1.5 orders of magnitude) of the ionic conductivity in the methacomposites occurs at small contents of tungstic oxide (x ≤ 0.01). A chemical transport removal of excess tungstic oxide, which is segregated in the form of the surface compound MeW-s, from the surface of the MeWO₄ grains destroys MeW-s, leading to a 10–15-fold drop of the ionic conductance. At x ≥ 0.05, the oxygen-ion conductance in the methacomposites is practically independent of their composition. A model for the formation and architecture of the methacomposites is qualitatively modified. The modified model takes into account doubled surface activity and mobility of the MeW-s phase with respect to MeWO₄ and WO₃. Original Russian Text ? N.N. Pestereva, A.Yu. Zhukova, A. Ya. Neiman, 2007, published in Elektrokhimiya, 2007, Vol. 43, No. 11, pp. 1379–1386.     

A New Method Based on Time-Varying Filtering Intrinsic Time-Scale Decomposition and General Refined Composite Multiscale Sample Entropy for Rolling-Bearing Feature Extraction

The early fault diagnosis of rolling bearings has always been a difficult problem due to the interference of strong noise. This paper proposes a new method of early fault diagnosis for rolling bearings with entropy participation. First, a new signal decomposition method is proposed in this paper: intrinsic time-scale decomposition based on time-varying filtering. It is introduced into the framework of complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN). Compared with traditional intrinsic time-scale decomposition, intrinsic time-scale decomposition based on time-varying filtering can improve frequency-separation performance. It has strong robustness in the presence of noise interference. However, decomposition parameters (the bandwidth threshold and B-spline order) have significant impacts on the decomposition results of this method, and they need to be artificially set. Aiming to address this problem, this paper proposes rolling-bearing fault diagnosis optimization based on an improved coyote optimization algorithm (COA). First, the minimal generalized refined composite multiscale sample entropy parameter was used as the objective function. Through the improved COA algorithm, optimal intrinsic time-scale decomposition parameters based on time-varying filtering that match the input signal are obtained. By analyzing generalized refined composite multiscale sample entropy (GRCMSE), whether the mode component is dominated by the fault signal is determined. The signal is reconstructed and decomposed again. Finally, the mode component with the highest energy in the central frequency band is selected for envelope spectrum variation for fault diagnosis. Lastly, simulated and experimental signals were used to verify the effectiveness of the proposed method.     

基于弹性变分模态分解的癫痫脑电信号分类方法

癫痫脑电信号分类对于癫痫诊治具有重要意义.为了实现病灶性与非病灶性癫痫脑电信号的分类,本文利用弹性网回归重构变分模态分解算法,提出弹性变分模态分解算法并将其应用到所提癫痫脑电信号分类方法中.该方法先将原信号分割成多个子信号,并对各子信号进行弹性变分模态分解,然后从分解后的不同变分模态函数中提取精细复合多尺度散布熵作为特征,最后利用支持向量机进行分类.针对癫痫脑电的公共数据集,最终的实验结果表明,准确率、灵敏度和特异度三个性能指标分别达到92.54%,93.22%和91.86%.     

First-principles calculations on ferroelectricity and lattice dynamics of Type-II multiferroic SmMn2O5

In this work, we report on the structural, electronic, and ferroelectric properties of SmMn₂O₅ by using first-principles density functional theory plus on-site Coulomb interaction (DFT + U) calculations. A thorough analysis was preformed to reveal the competing characteristics of different high-temperature (T) phases and the polarization mechanism in the low-T multiferroic phase. We show that the structural characteristics of the high-T phases have a strong influence on the low-T multiferroicity. In addition to the spin-induced lattice distortion that reduces substantially the purely electronic ferroelectricity, the dominant polarization mechanism in low-T SmMn₂O₅ still originates from the electronic polarization. By performing mode decomposition of the Hellmann–Feynman forces and the lattice distortion induced by the q = (0.5, 0, 0) magnetic order, we find that the Raman-active A_g mode characterized by the Mn⁴⁺O₆ octahedron distortion and synergistic displacement of Mn³⁺ and Sm ions is of primary importance, while the infrared (IR)-active B_2u mode plays a secondary role. These findings provide a theoretical foundation for future studies concerning the enhanced magnetoelectric effects of SmMn₂O₅ due to its pure exchange–striction mechanism.     

Resolutions of monomial ideals of projective dimension 1

We show that a monomial ideal I in a polynomial ring S has projective dimension ≤ 1 if and only if the minimal free resolution of S∕I is supported on a graph that is a tree. This is done by constructing specific graphs which support the resolution of the S∕I. We also provide a new characterization of quasi-trees, which we use to give a new proof to a result by Herzog, Hibi, and Zheng which characterizes monomial ideals of projective dimension 1 in terms of quasi-trees.     

Computation methods for combinatorial sums and Euler‐type numbers related to new families of numbers

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order. We can show that these numbers are related to the well‐known numbers and polynomials such as the Stirling numbers of the second kind and the central factorial numbers, the array polynomials, the rook numbers and polynomials, the Bernstein basis functions and others. In order to derive our new identities and relations for these numbers, we use a technique including the generating functions and functional equations. Finally, we give not only a computational algorithm for these numbers but also some numerical values of these numbers and the Euler numbers of negative order with tables. We also give some combinatorial interpretations of our new numbers. Copyright © 2016 John Wiley & Sons, Ltd.     

Hankel transforms of generalized Motzkin numbers

We study Hankel transform of the sequences (u,l,d),t, and the classical Motzkin numbers. Using the method based on orthogonal polynomials, we give closed‐form evaluations of the Hankel transform of the aforementioned sequences, sums of two consecutive, and shifted sequences. We also show that these sequences satisfy some interesting convolutional properties. Finally, we partially consider the Hankel transform evaluation of the sums of two consecutive shifted (u,l,d)‐Motzkin numbers. Copyright © 2017 John Wiley & Sons, Ltd.