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.

     

Investigating the influence of tool shape during FSW of aluminum alloy via CFD analysis

This paper describes the application of the CFD code, Comsol Multiphysics, to modeling the 3-D metal flow in friction stir welding of AA 2024-T3 aluminum alloy in order to investigate the influence of tool shape over the metal flow. Heat transfer and non-Newtonian flow equations were solved simultaneously. The results from the benchmark experiments found in the literature were used for validation purposes. Scrolled shoulders and threaded pins were given as kinematic boundary conditions. This made the computational problem an easy one. A welding engineer can predict the metal flow around the tool with different scrolls and threads under any welding conditions without making expensive experiments. Investigation of the velocity field before actual welding can save a lot of engineering hours.     

The Impact of the Azo-Chromophore Sort on the Features of the Supramolecular Azopolyimide Films Desired to Be Used as Substrates for Flexible Electronics

High-performance supramolecular polyimide systems were synthesized via a simple and innovative approach using two types of azo-chromophores, leading to concomitant special properties: high thermostability, the ability to be processed in the form of films with high flexibility, adequate morphological features, and good structuring capacity via phase mask ultraviolet (UV) laser irradiation, induced by the presence of the azo groups (–N=N–). The dimension and the anisotropy degree of the micro/nano patterns obtained on the surface of the flexible films (determined by atomic force microscopy) depend on the azo-dye type used in the supramolecular azopolyimide synthesis, which were higher when the azo-chromophore containing a –cyano group (–C≡N) was used. The molecular dynamics method, an excellent tool for an in-depth examination of the intermolecular interactions, was used to explain the morphological aspects. Energetic, dynamic and structural parameters were calculated for the two systems containing azo-chromophores, as well as for the pristine polymer system. It was highlighted that the van der Waals forces make a major contribution to the intermolecular interactions. The results from the combination of the dynamic analysis and the concentration profile explain the better mobility of the polyimide chains with a maximum content of azo groups in the cis configuration compared to the other systems. Taking all these data into account, the surfaces of the films can be tuned as required for the proposed applications, namely as substrates for flexible electronis.     

Effects of pretreatment and various operating parameters on permeate flux and quality during ultrafiltration of apple juice

The central composite design with a quadratic model was used to investigate the effect of temperature (20–40 °C) and transmembrane pressure (TMP) (100–300 kPa) as well as pretreatment with gelatin and bentonite (0:0–300:1500 mg L^?1) on permeate flux and fouling resistance during ultrafiltration of apple juice. The changes in some physicochemical properties were also investigated. Pretreatment of apple juice with gelatin and bentonite and an increase in the temperature and TMP significantly improved the permeate flux. In general, physicochemical properties of apple juice other than polyphenolics were not affected by the applied parameters. Using 150 mg L^?1 of gelatin and 750 mg L^?1 of bentonite for fining significantly reduced the total phenolic content and so did the fouling resistance. Fouling resistance also decreased with increasing temperature, and increasing pressure increased the fouling resistance.     

Study of thermal behavior of polyimides containing pendent-substituted azobenzene units

Thermal stability and degradation kinetic of the polyimides containing pendent-substituted azobenzene units were investigated by thermogravimetric analysis in nitrogen at different heating rates. Freeman–Carroll, Coats–Redfern and Flynn–Wall–Ozawa methods were utilized to obtain the kinetic parameters (activation energy E _a, pre-exponential factor A and order of reaction n) or variation of activation energy with conversion degree from thermogravimetric and derivative thermogravimetric curves. The thermogravimetric analysis revealed that the decomposition of azopolyimides proceeds in three or four stages, regardless of heating rate.     

Transmission- and side-detection configurations in ultrasound-modulated optical tomography of thick biological tissues

Ultrasound-modulated optical tomography of thick biological tissues was studied based on speckle-contrast detection. Speckle decorrelation was investigated with biological tissue samples of various thicknesses. Images of optically absorbing objects buried in biological tissue samples with thicknesses up to 50 mm were obtained in a transmission-detection configuration. The image contrast was more than 30%, and the spatial resolution was approximately 2 mm. In addition, a side-detection scheme along with two specific configurations were examined, and the advantages were demonstrated. Experimental results implied feasibility of applying the ultrasound-modulation technique to characterize optical properties in inhomogeneous biological tissues.     

Electrical characteristics of an organic thin copolymer/p-Si Schottky barrier diode

We have fabricated a poly(aniline-3-methyl thiophene) organic thin material on p-Si substrate by placing a solution of copolymer in acetonitrile on top of a p-Si substrate and then evaporating the solvent. The electrical and interface state density properties of the poly(aniline-3-methyl thiophene) copolymer/p-Si/Al diode have been investigated through methods using current-voltage (I-V), Cheung's, and a modified Norde's function. Good agreement was observed with the values of barrier height as obtained from all of these methods. The diode shows a non-ideal I-V behavior with an ideality factor greater than unity, which could be ascribed to the interfacial layer, interface states and series resistance. The interface state density of diode was determined using the forward-bias I-V characteristic technique at room temperature, and it decreases exponentially with bias from 1.39 × 10¹⁶ cm⁻² eV⁻¹ in (0.06 − E_v) eV to 4.86 × 10¹⁵ cm⁻² eV⁻¹ in (0.51 − E_v) eV.     

Initiation system effects in the cationic copolymerization of tetrahydrofuran (THF)

Summary Macromonomeric peroxy initiator, poly tetrahydrofuran (poly-THF=inimer) were synthesized via cationic polymerization of THF by the mono- (t-BuBP) and tetra-bromo methyl benzoyl peroxides (BDBP)/ZnCl₂ initiating system. The macromonomers were characterized by ¹H-NMR, IR, and GPC techniques. Methyl methacrylate (MMA) polymerization initiated by poly-THF inimers at 80°C and different times in bulk gave crosslinked poly-THF-b-polymethyl methacrylate block copolymers. Swelling ratios of the crosslinked block copolymers obtained by taking in same amounts of poly-THF inimer and MMA monomer in CHCl₃ were decreased versus time. It was compared the results obtained from t-BuBP-, BDBP-ZnCl₂ initiating systems with t-BuBP-, BDBP-AgSbF₆ initiating systems for THF monomer. Poly(THF-b-MMA) crosslinked block copolymers containing undecomposed peroxide groups initiated the thermal polymerization of styrene, S, were used to obtain poly(THF-b-MM_A-b-S) crosslinked multicomponent copolymers at 90°C. The crosslinked multi component copolymers were investigated sol-gel analysis and swelling ratios in CHCl₃. "Active" poly(THF-b-MM_A) having peroxygen group were used in the free radical coupling reaction of poly butadien (Poly Bd). Poly(THF-b-MM_A)-polybutadien crosslinked blend soluble graft copolymers were obtained. Received: 31 July 2001/Revised version: 16 June 2002/ Accepted: 5 July 2002