Topology of multiple log transforms of 4-manifolds

Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, from that we deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of E(1) # 5(-CP^2) differs from the original one by a codimension zero simply connected Stein submanifold M_{p,q}, which are therefore examples of infinitely many Stein manifolds that are exotic copies of each other (rel boundaries). Furthermore, by a similar method we produce infinitely many simply connected Stein submanifolds Z_{p} of E(1)_{p,2} # 2(-CP^2)$ with the same boundary and the second Betti number 2, which are (absolutely) exotic copies of each other; this provides an alternative proof of a recent theorem of the author and Yasui [AY4]. Also, by using the description of S^2 x S^2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that multiple log transforms along the tori in these cusps do not change smooth structure of S^2 x S^2.Comment: Updated, with 17 pages 21 figure

Topological quantum D-branes and wild embeddings from exotic smooth R^4

This is the next step of uncovering the relation between string theory and exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges in IIA string theory. We construct wild embeddings of spheres and relate them to a class of topological quantum Dp-branes as well to KK theory. These branes emerge when there are non-trivial NS-NS H-fluxes where the topological classes are determined by wild embeddings S^2 -> S^3. Then wild embeddings of higher dimensional $p$-complexes into S^n correspond to Dp-branes. These wild embeddings as constructed by using gropes are basic objects to understand exotic smoothness as well Casson handles. Next we build C*-algebras corresponding to the embeddings. Finally we consider topological quantum D-branes as those which emerge from wild embeddings in question. We construct an action for these quantum D-branes and show that the classical limit agrees with the Born-Infeld action such that flat branes = usual embeddings.Comment: 18 pages, 1 figur

Liouville Vortex And φ4\varphi^{4} Kink Solutions Of The Seiberg--Witten Equations

The Seiberg--Witten equations, when dimensionally reduced to \bf R^{2}\mit, naturally yield the Liouville equation, whose solutions are parametrized by an arbitrary analytic function $g(z)$. The magnetic flux $\Phi$ is the integral of a singular Kaehler form involving $g(z)$; for an appropriate choice of $g(z)$ , $N$ coaxial or separated vortex configurations with $\Phi=\frac{2\pi N}{e}$ are obtained when the integral is regularized. The regularized connection in the \bf R^{1}\mit case coincides with the kink solution of $\varphi^{4}$ theory.Comment: 14 pages, Late

Effect of Ankaferd Blood Stopper on Early Bone Tissue Healing in Extraction Sockets: An Experimental In vivo Study

Purpose: To investigate the effect of Ankaferd blood stopper (ABS) on early bone healing of extraction sockets in rats.Method: Twenty-eight male Wistar rats were divided into four groups. The maxillary right first molar tooth of the rats was extracted under general anesthesia. Two groups (C-1, n = 6 and C-2, n = 6) received saline solutions in the extraction sockets immediately and one day after the extraction, respectively, while two groups (A-1, n = 8 and A-2, n = 8) received ABS. The rats in A-1 and C-1 groups were sacrificed after 7 days of post-extraction while the rats in A-2 and C-2 groups were sacrificed after 28 days. Bone samples were taken from the maxillas, and tissues were prepared for histopathological analysis. Osteoid tissue (OT), mineralized bone tissue (MT), remaining area (RA), and inflammatory cell infiltration (ICI) were determined. The histomorphometric results were analyzed statistically using analysis of variance (ANOVA).Results Osteoid formation was highest in C-1 group (39.71 ± 9.68, p < 0.05). Differences in OT among other groups were not significant (p > 0.05). MT was higher in C-2 group (47.73 ± 12.15) than in other groups (p < 0.05). RA was highest in C-1 group (59.95 ± 12.75). ICI was significantly lower in control (C1 and C-2) groups than in ABS (A-1 and A-2) groups (p < 0.05).Conclusion: ABS administered topically to extraction sockets immediately after extraction has no effect on bone healing; in fact, ABS increases inflammation in vivo

Constructions of generalized complex structures in dimension four

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-manifolds, both simply and non-simply connected, which are neither complex nor symplectic

Online Advice Taking: Examining the Effects of Self-Efficacy, Computerized Sources, and Perceived Credibility

The Internet offers limitless advice on a multitude of products and services. The quality of the advice varies and is inherently a matter of human judgment. To help users determine the quality of advice and whether to use the advice, design features of web sites include information about the type and credibility of the advice source. This research examines how characteristics of the online user (i.e., self-efficacy) and characteristics of the advice source (i.e., type and credibility) affect advice taking in an online investing context. A laboratory experiment provides evidence that users with higher levels of self-efficacy are less likely to take advice than those with lower levels of self-efficacy. Results also suggest users given highly credible advice are more likely to take the advice compared to users who receive advice with dubious credibility. The implications are discussed

Solutions of the Einstein-Dirac and Seiberg-Witten Monopole Equations

We present unique solutions of the Seiberg-Witten Monopole Equations in which the U(1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component, and the 4-manifold is a product of two Riemann surfaces of genuses p_1 and p_2. There are p_1 -1 magnetic vortices on one surface and p_2 - 1 electric ones on the other, with p_1 + p_2 \geq 2 p_1 = p_2= 1 being excluded). When p_1 = p_2, the electromagnetic fields are self-dual and one also has a solution of the coupled euclidean Einstein-Maxwell-Dirac equations, with the monopole condensate serving as cosmological constant. The metric is decomposable and the electromagnetic fields are covariantly constant as in the Bertotti-Robinson solution. The Einstein metric can also be derived from a K\"{a}hler potential satisfying the Monge-Amp\`{e}re equations.Comment: 22 pages. Rep. no: FGI-99-

Witten's conjecture and Property P

Let K be a non-trivial knot in the 3-sphere and let Y be the 3-manifold obtained by surgery on K with surgery-coefficient 1. Using tools from gauge theory and symplectic topology, it is shown that the fundamental group of Y admits a non-trivial homomorphism to the group SO(3). In particular, Y cannot be a homotopy-sphere.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper7.abs.html Version 5: links correcte

Benchmarking of Different Powder-Bed Metal Fusion Processes for Machine Selection in Additive Manufacturing

In the last decade, additive manufacturing has gained significant interest for direct part production and started to change the way companies manufacture products; even in very demanding sectors like aerospace. The biggest challenge for a wider industrial acceptance still stands as the need for more reliable, repeatable and precise machines for additive manufacturing. This paper presents a comprehensive benchmarking study for the selection of an additive manufacturing machine for powder-bed metal fusion process, i.e. Selective Laser Melting or Direct Metal Laser Sintering or Laser Cusing. Four different machine vendors for the same technology to be employed for aeroengine part manufacturing using Inconel 625 powder have been involved for comparing different machine specifications. Many aspects such as dimensional accuracy, surface quality, need of support structures, density, hardness and process limits (minimum wall thickness, overhang surfaces, inclinations and curvatures, etc.) are addressed in the paper. The state-of-the-art in machines for powder-bed metal fusion process is presented aiming at understanding the current limitations of the technology available today.Mechanical Engineerin