Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

Design and construction of a two dimensional duct equipped with a wave generator and a variable coastal slope and an ocean wave energy conversion system (OWC)

The aims of this thesis were evaluation the type of wave channel, wave current, and effect of some parameters on them and identification and comparison between types of wave maker in laboratory situations. In this study, designing and making of two dimension channels (flume) and wave maker for experiment son the marine buoy, marine building and energy conversion systems were also investigated. In current research, the physical relation between pump and pumpage and the designing of current making in flume were evaluated. The related calculation for steel building, channels beside glasses and also equations of wave maker plate movement, power of motor and absorb wave(co astal slope) were calculated. In continue of this study, the servo motor was designed and applied for moving of wave maker’s plate. One Ball Screw Leaner was used for having better movement mechanisms of equipment and convert of the around movement to linear movement. The Programmable Logic Controller (PLC) was also used for control of wave maker system. The studies were explained type of ocean energies and energy conversion systems. In another part of this research, the systems of energy resistance in special way of Oscillating Water Column (OWC) were explained and one sample model was designed and applied in hydrolic channel at the Sheikh Bahaii building in Azad University, Science and Research Branch. The dimensions of designed flume was considered at 16 1.98 0. 57 m which had ability to provide regular waves as well as irregular waves with little changing on the control system. The ability of making waves was evaluated in our designed channel and the results were showed that all of the calculation in designed flume was correct. The mean of error between our results and theory calculation was conducted 7%, which was showed the well result in this situation. With evaluating of designed OWC model and considering of changes in the some part of system, one bigger sample of this model can be used for designing the energy conversion system model. The obtained results showed that the best form for chamber in exit position of system, were zero degree (0) in angle for moving below part, forty and five (45) degree in front wall of system and the moving forward of front wall keep in two times of height of wave.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

The Associations Between the Maladaptive Personality Dimensions of Neediness and Self-Criticism, Defense Styles, Selfobject Needs, and Attachment Styles in an Iranian Sample

The present study extends previous findings by examining whether defense styles, selfobject needs, attachment styles relate to Neediness and Self-Criticism, as maladaptive personality dimensions focused, respectively, on relatedness and self-definition in an Iranian sample. Three hundred and fifty two participants completed a socio-demographic questionnaire as well as the Persian forms of the Depressive Experiences Questionnaire, Experience of Close Relationships-Revised, Defense Style Questionnaire, Beck Depression Inventory–II and Selfobject Needs Inventory. Two Multiple Linear Regression Analyses, entering Self-criticism and Neediness as criterion variables, were computed. According to the results high Attachment anxiety, high Immature defenses, high depressive symptoms, and high need for idealization were related to self-criticism, and explained 47% of its variance. In addition, high attachment anxiety, low mature defenses, high neurotic defenses, high avoidance of mirroring, and low avoidance of idealization/twinship were related to neediness, and explained 40% of its variance. A Principal Component Analysis was performed, entering all the studied variables. Three factors emerged; one describing a maladaptive form of psychological functioning and two describing more mature modes of psychological functioning. The results are discussed in their implications for the understanding of neediness and self-criticism as maladaptive personality dimensions focused, respectively, on relatedness and self-definition.