A note on double lacunary statistical $$\sigma$$-convergence of fuzzy numbers

Quite recently, Sava? (Appl Math Lett 21:134–141, 2008), defined the lacunary statistical analogue for double sequence \(X=\{X_{k,l}\}\) of fuzzy numbers as follows: a double sequence \(X=\{X_{k,l}\}\) is said to be lacunary P-statistically convergent to \(X_{0}\) provided that for each \(\epsilon >0\)

$ P-\lim_{r,s}\frac{1}{h_{r,s}}\left | \{(k,l)\in I_{r,s}: d(X_{k,l },X_0)\geq \epsilon\}\right|= 0. $

In this paper we introduce and study double lacunary \(\sigma\)-statistical convergence for sequence of fuzzy numbers and also we get some inclusion theorems.

     

高密度脉冲电流对2024铝合金凝固组织的影响

研究了把高密度脉冲电流以外部瞬间能量和环境作功的形式注入到凝固过程中的高熔点2024铝合金熔体以细化其凝固组织，结果表明，高密度脉冲电流可以显著细化其凝固组织，讨论了高密度脉冲电流细化凝固组织的机理，指出了需要进一步解决的新问题。     

Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.     

新版Auto CAD计算机辅助设计在我公司氯碱设计中的应用

随着计算机技术及外围设备的提高和完善 ,计算机辅助设计和计算机辅助工程技术得到了日益广泛应用 ,绘图技术也得到了很大的发展 ,并已成为工程制图发展的必然趋势。我公司应用美国ＡＵＴＯＤＥＳＫ公司推出的新版ＡｕｔｏＣＡＤ2 0 0 2中文版本 ,是当前国际上最为先进和流行的绘图软件之一 ,具有以下增强功能。1　新增设计中心图库 ,在绘图过程中 ,可边绘图 ,边自动将所绘单元图储存在设计中心库中 ,这样可重复和快速使用相同或相近单元图 ,或在绘制新图时 ,可从中心库中随时提取相同或相近单元图形来绘制新图。其次 ,在绘图过程中 ,也可把…     

Study on the properties of crosslinking of poly(ethylene oxide) and hydroxyapatite–poly(ethylene oxide) composite

This study covers the crosslinking of poly(ethylene oxide) (PEO) and its composite with calcium hydroxyapatite (HA), their mechanical and swelling properties, and morphology. Sheets of the composites of PEO (two different grades with M_v: 5 × 10⁶ and 2 × 10⁵) and HA and neat PEO were prepared by compression molding. The prepared composite and PEO (0.1‐mm‐thick) sheets were crosslinked with exposure of UV‐irradiation in the presence of a photoinitiator, acetophenone (AP). This simple method for crosslinking, induced by UV‐irradiation in the presence of AP, yielded PEO with gel content up to 90%. Gel content, equilibrium swelling ratio, and mechanical and morphological properties of the low molecular weight polyethylene oxide (LMPEO)–HA crosslinked and uncrosslinked composites were evaluated. Although the inclusion of HA into LMPEO inhibits the extent of crosslinking, the LMPEO–HA composite with 20% HA by weight shows the highest gel content, with appreciable equilibrium swelling and mechanical strength. The growth of HA in simulated body fluid solutions on fractured surfaces of LMPEO and also LMPEO–HA was found to be very favorable within short times. The dimensional stability of these samples was found to be satisfactory after swelling and deposition experiments. The good compatibility between the filler hydroxyapatite and poly(ethylene oxide) makes this composite a useful tissue‐adhesive material. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 488–496, 2003     

Statistical prediction of fracture parameters of concrete and implications for choice of testing standard

This article shows how the fracture energy of concrete, as well as other fracture parameters such as the effective length of the fracture process zone, critical crack-tip opening displacement and the fracture toughness, can be approximately predicted from the standard compression strength, maximum aggregate size, water-cement ratio, and aggregate type (river or crushed). A database, consisting of 238 test data, is extracted from the literature and tabulated, and approximate mean prediction formulae calibrated by this very large data set are developed. A distinction is made between (a) the fracture energy, G_f, corresponding to the area under the initial tangent of the softening stress-separation curve of cohesive crack model, which governs the maximum loads of structures and is obtained by the size effect method (SEM) or related methods (Jenq-Shah two-parameter method and Karihaloo's effective crack model, ECM) and (b) the fracture energy, G_F, corresponding to the area under the complete stress-separation curve, which governs large postpeak deflections of structures and is obtained by the work-of-fracture method (WFM) proposed for concrete by Hillerborg. The coefficients of variation of the errors in the prediction formulae compared to the test data are calculated; they are 17.8% for G_f and 29.9% for G_F, the latter being 1.67 times higher than the former. Although the errors of the prediction formulae taking into account the differences among different concretes doubtless contribute significantly to the high values of these coefficients of variation, there is no reason for a bias of the statistics in favor of G_f or G_F. Thus, the statistics indicate that the fracture energy based on the measurements in the maximum load region is much less uncertain than that based on the measurement of the tail of the postpeak load-deflection curve. While both G_f and G_F are needed for accurate structural analysis, it follows that if the testing standard should measure, for the sake of simplicity, only one of these two fracture energies, then G_f is preferable.     

Use of ultrasonic energy in reactive dyeing of cellulosic fabrics

The use of ultrasonic energy in dyeing cotton fabrics with monochlorotriazine and vinylsulphone reactive dyes has been studied spectrophotometrically. The dyeings carried out conventionally and by the use of ultrasonic techniques were compared in terms of percentage exhaustion, total amount of dye transferred to the washing bath after dyeing, fastness properties and colour values of the dyed materials. Overall results have shown that the use of ultrasound in reactive dyeing of cellulosic fabrics can result in energy savings, less water consumption, increased depth of colour and better process conditions.     

Activities of MFI-Supported Rhenium Catalysts for the Aromatization of Methane: Effect of Cationic Form of the Inorganic Carrier

MFI type inorganic carrier was used in two different cationic forms, hydrogen and calcium respectively. MFI-supported molybdenum and rhenium catalysts were prepared. The activities of the catalysts were compared for the aromatization reaction of methane. Higher activity values were attained with the catalysts supported on HZSM-5. Aromatics were also observed with the catalysts supported on CaZSM-5, despite their deficiency in acid sites. Highly dispersed rhenium is expected to be formed with the use of the inorganic carrier in calcium form. On the other hand, lower reaction rates were observed with rhenium supported on CaZSM-5, in spite of the improved dispersion of the active rhenium species on this catalyst. This was interpreted in terms of the critical role of the acid sites in the conversion of methane to aromatics, compared to the improved dispersion of the active metal.     

Crack Growth in Solid Oxide Fuel Cell Materials: From Discrete to Continuum Damage Modeling

This paper addresses the damage and fracture issues of glass and ceramic materials used in solid oxide fuel cells. Analyses of an internal crack and of an interface crack between dissimilar materials were conducted using a modified boundary layer modeling approach. In this approach, fracture is allowed to occur in a small process window situated at an initial crack tip. Elastic displacement crack-tip fields are prescribed as remote boundary conditions. Crack propagation was first modeled discretely. Next, a continuum damage mechanics (CDM) model for brittle materials was developed to capture damage and crack growth in the process window. In particular, the damage model was applied to a glass-ceramic material that had been developed in-house for sealing purposes. Discrete and continuum damage solutions were then compared. Finally, the CDM model was used to determine the crack propagation direction as a function of a mode mixity measure.     

Łukasiewicz logic and Riesz spaces

We initiate a deep study of Riesz MV-algebras which are MV-algebras endowed with a scalar multiplication with scalars from \([0,1]\) . Extending Mundici’s equivalence between MV-algebras and \(\ell \) -groups, we prove that Riesz MV-algebras are categorically equivalent to unit intervals in Riesz spaces with strong unit. Moreover, the subclass of norm-complete Riesz MV-algebras is equivalent to the class of commutative unital C \(^*\) -algebras. The propositional calculus \({\mathbb R}{\mathcal L}\) that has Riesz MV-algebras as models is a conservative extension of ?ukasiewicz \(\infty \) -valued propositional calculus and is complete with respect to evaluations in the standard model \([0,1]\) . We prove a normal form theorem for this logic, extending McNaughton theorem for ? ukasiewicz logic. We define the notions of quasi-linear combination and quasi-linear span for formulas in \({\mathbb R}{\mathcal L},\) and relate them with the analogue of de Finetti’s coherence criterion for \({\mathbb R}{\mathcal L}\) .