241 research outputs found
Two-Generator Free Kleinian Groups and Hyperbolic Displacements
The Theorem, proved by Culler and Shalen, states that every point in
the hyperbolic 3-space is moved a distance at least by one of the
non-commuting isometries or provided that and
generate a torsion-free, discrete group which is not co-compact and contains no
parabolic. This theorem lies in the foundation of many techniques that provide
lower estimates for the volumes of orientable, closed hyperbolic 3-manifolds
whose fundamental group has no 2-generator subgroup of finite index and, as a
consequence, gives insights into the topological properties of these manifolds.
In this paper, we show that every point in the hyperbolic 3-space is moved a
distance at least by one of the isometries in
when and satisfy the conditions given in
the Theorem.Comment: 43 Pages. 2 figures. Almost completely rewritten in line with the
referee's recommendations. By Lemma 4.10, suggested by the referee, the
proofs of many lemmas are substantially shortened. The main theorem, Theorem
5.1, is reproved with a more geometric approac
Symmetric Decompositions of Free Kleinian Groups and Hyperbolic Displacements
In this paper, it is shown that every point in the hyperbolic 3-space is
moved at a distance at least by one of
the isometries of length at most in a 2-generator Klenian group
which is torsion-free, not co-compact and contains no parabolic. Also
some lower bounds for the maximum of hyperbolic displacements given by
symmetric subsets of isometries in purely loxodromic finitely generated free
Kleinian groups are conjectured.Comment: 62 pages, 3 Figures, Comments are welcom
Jorgensen's Inequality and Purely Loxodromic 2-Generator Free Kleinian Groups
Let and be two non--commuting isometries of the hyperbolic
--space so that is a purely
loxodromic free Kleinian group. For and ,
let denote the distance between and . Let
and be the mid-points of the shortest geodesic segments connecting
the axes of , and , respectively. In
this manuscript it is proved that if for every
and
, then Above
is the unique real root of the polynomial that is greater than . Also generalisations of this
inequality for finitely generated purely loxodromic free Kleinian groups are
conjectured.Comment: A contradiction with Theorem 4.1 in v3, named as Theorem 4.2 in this
version, arose while rephrasing of Theorem 4.2 in v3. This was fixed by
restating Theorem 4.2, which was named as Theorem 4.3 in this version. Lemma
4.1 is due to the anonymous referee. Conjecture 4.2 was also restated
accordingly. No changes occurred in the computations otherwise. 26 pages, 3
Figure
TRANSATLANTIC TRADE AND INVESTMENT PARTNERSHIP (TTIP): IMPACT AND CORRELATION ANALYSIS BASED ON TRADE AND INVESTMENT BETWEEN TURKEY AND EU, AND THE USA
The main objective of this study is to ascertain the importance and necessity of Turkey, based on trade and investment, in TTIP agreement as a partner country with both European Union (EU) and the USA. Here, it uses secondary data sources — Central Bank of the Republic of Turkey (CBRT) and Turkish Statistical Institute — from 2001 to 2016. To obtain vibrant findings, the study introduces two statistical analyses: correlation and regression. In addition, it elucidates descriptive analysis for comprehending the general trade and investment scenario. The results derived from correlation suggest that there is a strong positive correlation between Turkey’s total foreign trade and its export to and import from EU and the USA, Turkey’s total FDI and EU’s FDI in Turkey, as well as Turkey’s total FDI and the USA’s FDI in Turkey. In addition, a strong positive correlation has been found between Turkey’s total resident FDI in abroad and Turkey’s FDI in EU and the USA. On the other hand, the regression results indicate that Turkey’s trade and investment with EU and the USA have a significant impact on Turkey’s total foreign trade and investmen
Interplay between physical cleaning, membrane pore size and fluid rheology during the evolution of fouling in membrane bioreactors
[EN] Fouling is one of the most pressing limitations during operation of membrane bioreactors, as it increases operating costs and is the cause of short membrane lifespans. Conducting effective physical cleanings is thus essential for keeping membrane operation above viable performance limits. The nature of organic foulants present in the sludge and the membrane properties are among the most influential factors determining fouling development and thus, efficiency of fouling mitigation approaches. The role of other factors like sludge viscosity on fouling is still unclear, given that contradictory effects have been reported in the literature. In the present study we use a new research approach by which the complex interplay between fouling type, levels of permeate flux, membrane material and feed properties is analyzed, and the influence of these factors on critical flux and membrane permeability is evaluated. A variety of systems including activated sludge and model solutions with distinct rheological behavior has been investigated for two membranes differing in pore size distribution. We present a novel method for assessing the efficiency of fouling removal by backwash and compare it with the efficiency achieved by means of relaxation. Results obtained have proven that backwash delays development of critical fouling as compared with relaxation and reduces fouling irreversibility regardless of fluid rheology. It was shown that backwash is especially effective for membranes for which internal fouling is the main cause of loss in permeability. Nonetheless, we found out that for membranes with tight pores, both relaxation and backwash are equally effective. The critical flux decreases significantly for high-viscosity fluids, such as activated sludge. This effect is mainly caused by an intensified concentration polarization at the feed side rather than by internal fouling events. However, membrane permeability has been proven to rely more on the permeate viscosity than on the feed viscosity: poor rejection of organic fractions showcasing high viscosity causes an acute decline in membrane permeability as a consequence of increased shear stress inside the membrane pores. (C) 2018 Elsevier Ltd. All rights reserved.M.W. acknowledges the support through an Alexander-von-Humboldt Professorship. M.C. Marti-Calatayud acknowledges the support to Generalitat Valenciana through the funding APOSTD2017. M.C. Marti-Calatayud thanks the contributions of Sybille Hanisch, Sanchita Khandelwal and Sara Vivanco. This work was supported by the German Federal Ministry of Education and Research (BMBF) through the project BRAMAR (02WCL1334A). We thank Synder Filtration for the supplied membranesMartí Calatayud, MC.; Schneider, S.; Yüce, S.; Wessling, M. (2018). Interplay between physical cleaning, membrane pore size and fluid rheology during the evolution of fouling in membrane bioreactors. Water Research. 147:393-402. https://doi.org/10.1016/j.watres.2018.10.017S39340214
Measurement of the profiles of disorder-induced localized resonances in photonic crystal waveguides by local tuning
Near the band edge of photonic crystal waveguides, localized modes appear due
to disorder. We demonstrate a new method to elucidate spatial profile of the
localized modes in such systems using precise local tuning. Using deconvolution
with the known thermal profile, the spatial profile of a localized mode with
quality factor () is successfully reconstructed with a resolution of
m
Lasing from single, stationary, dye-doped glycerol/water microdroplets located on a superhydrophobic surface
We report laser emission from single, stationary, Rhodamine B-doped
glycerol/water microdroplets located on a superhydrophobic surface. In the
experiments, a pulsed, frequency-doubled Nd:YAG laser operating at 532 nm was
used as the excitation source. The microdroplets ranged in diameter from a few
to 20 um. Lasing was achieved in the red-shifted portion of the dye emission
spectrum with threshold fluences as low as 750 J/cm2. Photobleaching was
observed when the microdroplets were pumped above threshold. In certain cases,
multimode lasing was also observed and attributed to the simultaneous lasing of
two modes belonging to different sets of whispering gallery modes.Comment: to appear in Optics Communication
One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula
In \cite{Mul} one-parameter planar motion was first introduced and the
relations between absolute, relative, sliding velocities (and accelerations) in
the Euclidean plane were obtained. Moreover, the relations
between the Complex velocities one-parameter motion in the Complex plane were
provided by \cite{Mul}. One-parameter planar homothetic motion was defined in
the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in
the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion
is defined in the Hyperbolic plane. Some characteristic properties about the
velocity vectors, the acceleration vectors and the pole curves are given.
Moreover, in the case of homothetic scale identically equal to 1, the
results given in \cite{Yuc} are obtained as a special case. In addition, three
hyperbolic planes, of which two are moving and the other one is fixed, are
taken into consideration and a canonical relative system for one-parameter
planar hyperbolic homothetic motion is defined. Euler-Savary formula, which
gives the relationship between the curvatures of trajectory curves, is obtained
with the help of this relative system
Common coeliacomesenteric trunk: a computed tomography radiological study
Background: There is an increasing trend for administration of invasive radiological interventions, laparoscopic surgery, and transplantation procedures in recent years, and determining the vascular variations prior to these procedures is crucially important. Coeliacomesenteric trunk (CMT) is among these variations. This study aimed to retrospectively evaluate this rare anomaly by computed tomography (CT). Materials and methods: A total of 1000 CT angiography images were analysed retrospectively, and the patients with mesenteric and coeliac arteries arising from the abdominal aorta with a single root were identified. The level that CMT arose, and its branching patterns were determined individually for all patients. Results: Ten patients (6 males and 4 females) with a mean age of 50.2 years (17–87 years) had CMT in CT images. Conclusions: The knowledge of variations in the CMT prior to vascular or laparoscopic interventions will contribute to early intervention in case of a complication, or to avoid from a potential damage
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