General solution of one-dimensional,time dependent coupled heat flow systems

A new, powerful method of analysis, involving the combined use of finite integral transform and finite element techniques, is presented for the solution of time dependent heat flow systems composed of many one-dimensional elements connected through the nodes. This method leads to an eigenvalue problem which is not of the conventional Sturm-Liouville type. A procedure for the determination of the eigenvalues is described. The solution obtained is in the form of an infinite series and contains quasi-steady and transient terms. The general solution obtained can be applied in the mathematical modelling of many engineering applications such as the determination of the penetration of the daily temperature cycle into buildings, the analysis of heat transfer in array of extended surfaces in compact heat exchangers, and many others.     

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.

     

An isogeometrical approach to structural topology optimization by optimality criteria

The Isogeometric Analysis (IA) method is applied for structural topology optimization instead of finite elements. For this purpose, a control point based Solid Isotropic Material with Penalization (SIMP) method is employed and the material density is considered as a continuous function throughout the design domain and approximated by the Non-Uniform Rational B-Spline (NURBS) basis functions. To prevent the formation of layouts with porous media, a penalization technique similar to the SIMP method is used. For optimization an optimality criteria is derived and implemented. A few examples are presented to demonstrate the performance of the method. It is shown that, dissimilar to the element based SIMP topology optimization, the resulted layouts by this method are independent of the number of the discretizing control points and checkerboard free.     

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.     

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.     

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 \({\mathbb R}{\mathcal L}\) .     

Hierarchy-Debug: a scalable statistical technique for fault localization

Considering the fact that faults may be revealed as undesired mutual effect of program predicates on each other, a new approach for localizing latent bugs, namely Hierarchy-Debug, is presented in this paper. To analyze the vertical effect of predicates on each other and on program termination status, the predicates are fitted into a logistic lasso model. To support scalability, a hierarchical clustering algorithm is applied to cluster the predicates according to their presence in different executions. Considering each cluster as a pseudo-predicate, a distinct lasso model is built for intermediate levels of the hierarchy. Then, we apply a majority voting technique to score the predicates according to their lasso coefficients at different levels of the hierarchy. The predicates with relatively higher scores are ranked as fault relevant predicates. To provide the context of failure, faulty sub-paths are identified as sequences of fault relevant predicates. The grouping effect of Hierarchy-Debug helps programmers to detect multiple bugs. Four case studies have been designed to evaluate the proposed approach on three well-known test suites, Space, Siemens, and Bash. The evaluations show that Hierarchy-Debug produces more precise results compared with prior fault localization techniques on the subject programs.     

Effects of dowels produced from various materials on withdrawal strength in MDF and Pb

Wood dowels are commonly used in the construction furniture, but little information is available about the additive effects of dowels on the ultimate withdrawal strength of single or multidowel joints. This study was carried out to determine the tensile strength of 10‐mm‐diameter dowels produced from medium‐density fiberboard (MDF), plywood, scotch pine (Pinus sylvestris L.), and beech (Fagus orientalis lipsky), bonded parallel and vertical to the surface of MDF and particleboard (Pb) with poly(vinyl acetate) (PVAc) and Desmodur‐VTKA (D‐VTKA). Tensile strength was applied to the dowels according to the procedure in the ASTM‐D 1037 standard. The effects of dowel species, direction of tensile, composite material, and type of adhesive on tensile strength were determined. The results showed that the highest tensile strength was obtained in beech dowels bonded vertically with PVAc adhesive to the surface of MDF at 7.91 N/mm². If the dowels used in furniture production are subjected to great tensile strength, beech dowels bonded with PVAc adhesive on MDF should be used. However, when dowels produced from MDF and plywood waste are used, they also can produce positive results. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 531–535, 2003     

Synthesis and properties of chitosan-modified poly(vinyl butyrate)

Modification of chitosan by grafting of vinyl butyrate was carried out in homogeneous phase using potassium persulfate as redox initator and 1.5% acetic acid as solvent. The percent grafting and grafting efficiency were analysed and the high grafting efficiency up to 94% was observed. The effects of reaction variables such as monomer concentration, initiator concentration, temperature and reaction time were investigated. It was observed that the solubility of chitosan was markedly reduced after grafting with vinyl butyrate. The grafted product is insoluble in common organic solvents as well in dilute organic and inorganic acids. Characterization of the graft copolymers were carried out by using Fourier Transform Infrared Spectroscopy (FTIR), Differential Scanning Calorimetry (DSC) and Scanning Electron Microscopy (SEM) technics. Characteristic signal of carbonyl group was observed at 1,731 cm⁻¹ which belongs to the poly vinyl butyrate segments in the graft copolymer. The melting transition of the chitosan main chain in the copolymer shifted to 124°C from its original value 101°C. In addition to these, we have also studied topology of the graft copolymer and the SEM micrograph showed continuous homogenous matrix which means there is no phase separation.     

A new hardening rule for metallic foam plasticity

Metallic foams are a class of porous materials widely used in the industry because of their advantages. In recent years, extensive studies on the behavior of these materials have been conducted. Several constitutive equations have also been presented and applied. This study proposes a new constitutive equation that predicts metallic foam behavior using the stress–strain curve in uniaxial compression. The proposed model offers a new functionality for work hardening and is evaluated for both isotropic and combined hardening. The constitutive equations are implemented in MATLAB and integrated using return mapping algorithm. The material parameters are identified using genetic algorithm and through a comparison of the experimental and numerical results. The aluminum foams discussed in this paper are the commercially available types, Foaminal and Alporas. The comparison of numerical and experimental results indicate that this new constitutive equation predicts foam behavior in a reasonable manner. Moreover, a good agreement is observed between the experimental and computational curves.