On Fuzzy Probability Theory

Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition.     

Special Features of the Correlation between the Uranium–Oxygen Interatomic Distances and the Frequencies of the Valence Vibrations of the UO2 2+ Group in Complex Compounds of Uranyl

We considered the factors due to which the dependences between the uranium–oxygen distances R ₀ and the frequencies of valence vibrations _as for complex compounds of uranyl are described by two independent expressions generally represented by equations of the type R ₀ = a + b_as ^–2/3 (b > 0) with the coefficients a and b differing in the regions R ₀ < 0.178 nm and R ₀ > 0.178 nm. It is shown that the reason is that there is a mutual effect of the ligands in the uranyl complex responsible for different partial contributions of the uranium orbitals and of the atoms of the first coordination sphere to the chemical bonding.     

Beatings in the Spin Echo Signal in Media Having a Doublet Structure of the Spectrum

We have obtained an analytical expression for the twopulse echo signal arising in nonresonant excitation of a condensed medium with a nonuniformly broadened spectrum of doublet structure by two pulses of an electromagnetic field of different durations and of the same amplitude. It is shown that in the case where the differences between the carrying frequency of exciting pulses and the central frequencies of the spectral lines differ considerably, beatings are formed in the signal of the twopulse echo. The rate of decay of the amplitude of these beatings is found to depend only on the time of reversible and irreversible relaxation, and their circular frequency is determined by the shift of the spectral lines relative to each other. A technique for separate determination of the inhomogeneous width of the lines and time of the irreversible transverse relaxation is suggested which is based on the analysis of the twopulse echo signal beatings.     

Influence of magnetic powders on the tribological performance of a novel magnetic brake material

By adding magnetic powders into matrix material, it has been proved to be a creative approach to improve tribological properties of brake materials. In this paper, a novel magnetic brake material with Nd–Fe–B and nano-Fe₃O₄ was developed, and the influential mechanism of these two magnetic powders and their content on the friction and wear performance was deeply discussed. Firstly, some experiments were carried out to investigate the tribological performance and influential mechanisms of four groups of brake pad samples with different magnetic powders. Furthermore, based on these results, further experiments for investigating the influence that Nd–Fe–B contents have on the tribological properties were conducted. According to the theoretical analysis about experiments, it was concluded that nano-Fe₃O₄ is beneficial to promote the formation of friction film and has certain lubricant effects. However, Nd–Fe–B has double effects on the formation of friction film. It will have positive effects when its content is less than a certain value. Otherwise, it will destroy the structure of friction film. Conclusively, it is believed that this study will be significantly valuable and meaningful for developing new brake materials and improving safety reliability of mechanical brakes.     

Improved synthesis of polyfluorinated l-lysine for 19F NMR-based screening

Polyfluorinated N-α-Fmoc--Boc-l-lysine represents the best-in-class among a set of polyfluorinated amino acids (PFAs) which are useful tools for ¹⁹F NMR-Based Screening. In this communication, optimized reaction conditions that allowed for the multi-gram preparation of this unnatural amino acid are reported.     

Manifestation of Extracoordination in the Resonance Raman Spectra of Water‐Soluble Cation Co‐Porphyrins

Resonance Raman spectra (RRS) of Co(II) and Co(III)5,10,15,20tetrakis(4Nmethylpyridinium)porphyrin ((Co^II(TmpyP4), and Co^III(TMPyP4)) in aqueous solutions at different pH as well as in organic solvents (methanol, ethanol, DMSO, DMF) are obtained. The increased sensitivity of the oscillation frequencies ₂, ₄, ₈, and ₆ — the markers of the oxidation state of a metal — to the nature of an axial ligand has been revealed. For Co^III(TmpyP4), the shifts of the indicated frequencies in extracoordination have turned out to be twofold larger than those for Co^II(TmpyP4). The spectral effects observed are related to different electron influence of the extraligands on the system of the porphyrin ring. In the case of Co(III)porphyrin, interaction of the d orbitals of the metal and the e _g ^*orbitals of the macrocycle is more efficient since its ionic radius is smaller than for the Co(II)complex. For Co^III(TmpyP4), a linear correlation between the oscillation frequencies ₂, ₄, ₈, and ₆ and the experimental Gutmann parameters characterizing the electronacceptor properties of solvents is found.     

用近红外无损肌氧及运动心率检测技术评定100 m极量强度运动对心脏冲击影响

利用连续双波长近红外光技术测量肌肉中血红蛋白含氧量的变化情况,同时应用运动心率无线实时采集设备,设计了检测实时肌肉组织血氧含量和瞬时心率实验方案,对6名健康男性进行了100 m跑同步实测实验。实验表明,肌肉组织氧合血红蛋白浓度在100 m跑结束后继续降低,达到最低值的时刻滞后于运动结束时刻的时间为(6.65±1.10)s;心率则在运动结束后继续上升,达到最高值的时刻滞后于运动结束时刻的时间为(8.00±1.57)s。这些结果显示了双波长近红外光组织氧测试技术和运动心率无线实时采集系统能够正确检测极量强度运动时的血氧参数和心率,揭示了极量强度运动过程中肌肉中氧运输与消耗的过程及其与心率之间的动力学特征。     

Commutativity of the Arens product in lattice ordered algebras

Let be an Abelian Archimedean lattice ordered algebra. The order bidual furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the up-down-up approximation of positive elements in the order continuous order bidual by elements in the canonical image of in Components of positive elements in are characterized and the result is applied to the Arens product of -and almost -algebras.     

A Strong Law for Mixing Random Variables

A sharp almost sure bound is derived for limit points of average sum of weakly dependent random variables, which ensures strong laws of large numbers for and -mixing random variables, without assumptions on rate of tending to zero of and -mixing parameters _n and _n.     

On K‐Theory of Simplicial Rings and Degreewise Constructions

We give a measure of the difference between Waldhausen's definition of the Ktheory of a simplicial ring and the definition we obtain by extending Quillen's definition degreewise. This has computational advantages as the degreewise Ktheory sometimes is simpler to work with.