Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis

Numerical Algorithms - In this paper, the block generalized product-type bi-conjugate gradient (GPBi-CG) method for solving large, sparse nonsymmetric linear systems of equations with multiple...     

Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers

A numerical investigation of the mixed convection heat transfer from vertical helically coiled tubes in a cylindrical shell at various Reynolds and Rayleigh numbers, various coil‐to‐tube diameter ratios and non‐dimensional coil pitches was carried out. The particular difference in this study compared with other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid‐to‐fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell‐side mass flow rate on shell‐side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell‐side of the heat exchanger reasonably demonstrates the desired relation. Copyright © 2010 John Wiley & Sons, Ltd.     

Reflection Spaces and Corresponding Kinematic Structures

For a reflection space (P, Γ) [introduced in Karzel and Taherian (Results Math 59:213–218, 2011)] we define the notion “Reducible Subspace”, consider two subsets of ${\Gamma, \Gamma^{+} := \{a b\,|\, a,b \in P\}}$ and ${\Gamma^{-} := \{a b c\,|\, a, b, c \in P\}}$ and the map $$ \kappa : 2^{P} \to 2^{\Gamma^+} ; X \mapsto X \cdot X := \{xy\,|\, x,y \in X\}$$ We show, for each subspace S of (P, Γ), V := κ(S) is a v-subgroup (i.e. V is a subgroup of Γ⁺ with if ${\xi = xy \in V, \xi \neq 1}$ then ${x \cdot \overline{x,y}\subseteq V}$ ) if and only if S is reducible. Our main results are stated in the items 1–5 in the introduction.     

On Trigonometry in Beltrami–Klein Model of Hyperbolic Geometry

Ungar (Math. Appl. 49:187–221, 2005) employed the binary operation of Einsteins velocity addition to introduce into hyperbolic geometry the concepts of vectors, angles and trigonometry in full analogy with Euclidean geometry. We use the isomorphism between ${(\mathbb R,+,\cdot)}$ and ${((-1,1),\oplus,\otimes)}$ in Beltrami–Klein model of hyperbolic geometry for similar results.     

In‐situ polymerization of aliphatic‐aromatic polyamide nanocomposites in the presence of Halloysite nanotubes

Nanocomposites consisting of semi‐aromatic polyamide (PA) and pristine or alkali activated halloysite nanotubes (HNT or mHNT, respectively) were synthesized by the in‐situ interfacial polymerization method. The condensation reactions were carried out between isophthaloyl dichloride in hexane and triethylenetetramine in water containing different amounts of HNT or mHNT. The interactions and crystallinity of the nanocomposites were studied by Fourier transform infrared (FTIR) spectroscopy and X‐ray diffraction (XRD) analysis, respectively. Development of hydrogen bonds between the functional groups of PA and hydroxyl groups of nanotubes was indicated by FTIR spectroscopy. According to the XRD analysis, the addition of HNT and mHNT nanotubes increased the crystallinity of the PA. This was ascribed to the role of nanotubes as nucleating agents in the PA matrix. Thermal resistance and char residue of PA, as revealed by thermogravimetric analysis, were enhanced by incorporating both HNT and mHNT and the latter was more effective in this regard. Furthermore, while the addition of pristine HNTs decreased the glass transition temperature (Tg) of the PA, the Tg could be increased by about 5°C, in the presence of 5 wt% of mHNTs. Finally, the facilely activated mHNT nanotubes were found to be highly efficient in improving the thermal and structural properties of semi‐aromatic PAs.     

Elliptic Reflection Structures, K-Loop Derivations and Triangle-Inequality

This paper is a part of our general aim to study properties of elliptic and ordered elliptic geometries and then using some of these properties to introduce new concepts and develop their theories. If ${(P,\mathfrak{G}, \equiv,\tau)}$ denotes an elliptic geometry ordered via a separation ?? then there are polar points o and ?? and on the line ${ \overline{K} := \overline{\infty,o}}$ there can be established an operation ??+?? such that ${(\overline{K},+)}$ becomes a commutative group and the map ${ a^+ :\overline{K}\to \overline{K} ; x \mapsto a + x}$ is a motion on ${\overline{K}}$ . The separation ?? induces on ${\overline{K}}$ a cyclic order ?? with [o, e, ??] = 1 such that ${(\overline{K},+,\omega)}$ becomes a cyclic ordered group. For ${a,b \in K := \overline{K} {\setminus}\{\infty\}}$ we set ${a < b :\Longleftrightarrow [a,b,\infty] =1}$ and for all ${a\in K\,a < \infty}$ . Then (K,?<) is a totally ordered set. We show there is a surjective distance function: $$ \lambda : P \times P \to \overline{K}_+ := \{x \in \overline{K}\,|\,o \leq x\leq\infty\}, $$ with ?? ${\lambda(a,b) = \lambda(c,d) \ \Longleftrightarrow (a,b) \equiv (c,d)}$ ??. We prove in the first part of our project like (cf. Gr?ger in Mitt Math Ges Hamburg 11:441?C457, 1987) the following triangle-inequality: (cf. Theorem 8.2). If (a, b, c) is a triangle consisting of pairwise not polar points with ??(a, c), ??(b, c) < e then ??(a, b) ?? ??(a, c) + ??(b, c) < ??.     

On the Minkowski planes constructed by Artzy and Groh

The Minkowski planes constructed by R. Artzy and H. Groh [1] are characterized among the locally, connected and finite dimensional Minkowski planes as strongly semi-(p, w)-transitive Minkowski planes (see Theorem 2). The types of the Artzy-Groh planes in the typification of the Minkowski planes by M. Klein are determined (see Proposition 4). The second author was supported by a DAAD scholarship for a research visit at TU München. He sincerely thanks the Zentrum Mathematik der TU München for their hospitality.     

Antispasmodic effect of hydroalcoholic extract of Thymus vulgaris on the guinea-pig ileum

The effects of Thymus vulgaris hydroalcoholic extract on the contractile responses of the isolated guinea-pig ileum were investigated. Contraction changes in the terminal ileum of guinea pigs were monitored using a force displacement transducer amplifier connected to a physiograph. Thymus vulgaris extract inhibited the contractile responses in a dose-dependent manner and also decreased the amplitude of peristaltic waves. It is concluded that T. vulgaris has an antispasmodic action on guinea pig ileum by decreasing the amplitudes of the muscle contractions during peristalsis. The EC50 was calculated as 1.7 mg mL(-1). In guinea-pig ileum the extract led to an antispasmodic effect, possibly by affecting the anticholinergic and serotoninergic pathways.     

Groups with a ternary equivalence relation

We consider in a group \((G,\cdot )\) the ternary relation

$$\begin{aligned} \kappa := \{(\alpha , \beta , \gamma ) \in G^3 \ | \ \alpha \cdot \beta ^{-1} \cdot \gamma = \gamma \cdot \beta ^{-1} \cdot \alpha \} \end{aligned}$$

and show that \(\kappa \) is a ternary equivalence relation if and only if the set \( \mathfrak Z \) of centralizers of the group G forms a fibration of G (cf. Theorems 2, 3). Therefore G can be provided with an incidence structure

$$\begin{aligned} \mathfrak G:= \{\gamma \cdot Z \ | \ \gamma \in G , Z \in \mathfrak Z(G) \}. \end{aligned}$$

We study the automorphism group of \((G,\kappa )\), i.e. all permutations \(\varphi \) of the set G such that \( (\alpha , \beta , \gamma ) \in \kappa \) implies \((\varphi (\alpha ),\varphi (\beta ),\varphi (\gamma ))\in \kappa \). We show \(\mathrm{Aut}(G,\kappa )=\mathrm{Aut}(G,\mathfrak G)\), \(\mathrm{Aut} (G,\cdot ) \subseteq \mathrm{Aut}(G,\kappa )\) and if \( \varphi \in \mathrm{Aut}(G,\kappa )\) with \(\varphi (1)=1\) and \(\varphi (\xi ^{-1})= (\varphi (\xi ))^{-1}\) for all \(\xi \in G\) then \(\varphi \) is an automorphism of \((G,\cdot )\). This allows us to prove a representation theorem of \(\mathrm{Aut}(G,\kappa )\) (cf. Theorem 6) and that for \(\alpha \in G \) the maps

$$\begin{aligned} \tilde{\alpha }\ : \ G \rightarrow G;~ \xi \mapsto \alpha \cdot \xi ^{-1} \cdot \alpha \end{aligned}$$

of the corresponding reflection structure \((G, \widetilde{G})\) (with \( \tilde{G} := \{\tilde{\gamma }\ | \ \gamma \in G \}\)) are point reflections. If \((G ,\cdot )\) is uniquely 2-divisible and if for \(\alpha \in G\), \(\alpha ^{1\over 2}\) denotes the unique solution of \(\xi ^2=\alpha \) then with \(\alpha \odot \beta := \alpha ^{1\over 2} \cdot \beta \cdot \alpha ^{1\over 2}\), the pair \((G,\odot )\) is a K-loop (cf. Theorem 5).