scholarly journals Generating Rational Loop Groups with Noncompact Reality Conditions

2013 ◽  
Vol 113 (2) ◽  
pp. 187 ◽  
Author(s):  
Oliver Goertsches
Keyword(s):  
Loop Group ◽  
Dimensional System ◽  
Loop Groups ◽  
Real Form ◽  
Reality Condition ◽  
Dressing Action

We find generators for the full rational loop group of ${\rm GL}(n,\mathsf{C})$ as well as for the subgroup consisting of loops that satisfy the reality condition with respect to the noncompact real form ${\rm GL}(n,\mathsf{R})$. We calculate the dressing action of some of those generators on the positive loop group, and apply this to the ZS-AKNS flows and the $n$-dimensional system associated to ${\rm GL}(n,\mathsf{R})/{\rm O}(n)$.

scholarly journals Micro-Rheological Changes of Red Blood Cells in the Presence of an Arterio-Venous Fistula or a Loop-Shaped Venous Graft in the Rat

2020 ◽  
Vol 11 ◽  
Author(s):  
Balazs Szabo ◽  
Bence Tanczos ◽  
Adam Varga ◽  
Barbara Barath ◽  
Souleiman Ghanem ◽  
...  
Keyword(s):  
Red Blood Cells ◽  
Blood Cells ◽  
Loop Group ◽  
Erythrocyte Aggregation ◽  
Rheological Parameters ◽  
Loop Groups ◽  
Access Methods ◽  
Minimal Impact ◽  
Hind Limbs ◽  
Venous Fistula

Introduction: In case of kidney failure, hemodialysis is the primary kidney replacement technique. Several vascular access methods used for the therapy, one of which is the arterio-venous fistula (AVF). In the AVF, the blood flow is altered, which can elevate the mechanical stress on the red blood cells (RBCs). This can affect the RBC hemorheological properties, and it can further cause systemic changes. To lower the turbulence and shear stress, we performed a loop-shaped arterio-arterial venous interposition graft (loop-shaped graft) to compare its effect to the conventional AVF.Materials and Methods: Thirty male Wistar were used (permission registration Nr.: 25/2016/UDCAW). The animals were randomly divided into sham-operated, AVF, and loop groups (n = 10/each). The superficial inferior epigastric vein (SIEV) was used to create the AVF and the loop-shaped graft. Blood samples were taken before/after the surgery and at the 1st, 3rd, and 5th postoperative weeks. We measured hemorhelogical, hematological, and blood gas parameters. The microcirculation of the hind limbs was also monitored using Laser Doppler fluxmetry.Results: Hematocrit, RBC count, and hemoglobin decreased by the 1st postoperative week. The erythrocyte aggregation values significantly increased in the fistula group by the 5th week (6.43 ± 2.31 vs. 13.60; p < 0.0001; vs. before operation). At the postoperative 1st week in the loop group, the values showed a significant decrease in RBC deformability. During the maturation period, dominantly at the 5th week, all values were normalized. The operated hind limb’s skin microcirculation significantly increased in the sham and loop group by the 1st week (39 ± 10.57 vs. 73.93 ± 1.97 BFU, p < 0.01). This increase wasn’t observed in the fistula group probably due to a steal-effect.Conclusion: Unlike in the loop group, in the presence of the fistula, several rheological parameters have changed. The loop-shaped graft had only minimal impact on micro-rheological parameters.

scholarly journals LOOP GROUPS, STRING CLASSES AND EQUIVARIANT COHOMOLOGY

2011 ◽  
Vol 90 (1) ◽  
pp. 109-127 ◽  
Author(s):  
RAYMOND F. VOZZO
Keyword(s):  
Lie Group ◽  
Differential Form ◽  
Equivariant Cohomology ◽  
Loop Group ◽  
Characteristic Classes ◽  
Loop Groups ◽  
Compact Lie Group ◽  
String Class ◽  
String Classes ◽  
Odd Dimensions

AbstractWe give a classifying theory for LG-bundles, where LG is the loop group of a compact Lie group G, and present a calculation for the string class of the universal LG-bundle. We show that this class is in fact an equivariant cohomology class and give an equivariant differential form representing it. We then use the caloron correspondence to define (higher) characteristic classes for LG-bundles and to prove a result for characteristic classes for based loop groups for the free loop group. These classes have a natural interpretation in equivariant cohomology and we give equivariant differential form representatives for the universal case in all odd dimensions.

scholarly journals Loop groups and noncommutative geometry

2017 ◽  
Vol 29 (09) ◽  
pp. 1750029
Author(s):  
Sebastiano Carpi ◽  
Robin Hillier
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Representation Theory ◽  
Noncommutative Geometry ◽  
Loop Group ◽  
Positive Energy ◽  
Loop Groups ◽  
Spectral Triples ◽  
Conformal Field ◽  
Coset Models

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level [Formula: see text] projective unitary positive-energy representations of any given loop group [Formula: see text]. The construction is based on certain supersymmetric conformal field theory models associated with [Formula: see text] in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.

COMPARISON OF METHODS OF SKELETAL FIXATION FOR SEVERELY INJURED DIGITS

Hand Surgery ◽  
2004 ◽  
Vol 09 (01) ◽  
pp. 63-69 ◽  
Author(s):  
Hi-Shan Cheng ◽  
Lok-Yan Wong ◽  
Lan-Fong Chiang ◽  
Iris Chan ◽  
Tak-Hing Yip ◽  
...  
Keyword(s):  
Functional Outcomes ◽  
Loop Group ◽  
Severely Injured ◽  
Comparison Of Methods ◽  
Loop Groups ◽  
Wire Loop ◽  
Non Union ◽  
Serious Injury ◽  
K Wires ◽  
Bony Fixation

Our objective is to compare the results of three different methods of osteosynthesis used in severely injured digits, namely the K-wire group, the K-wire & Wire-loop group and the Plate & Screws group. The results of 38 patients with 50 severely injured fingers managed between 1994 and 2000 were reviewed. Majority of them had serious injury caused by electric-saw and Zone III was the most common level of injury using Biemer's classification. Using the scoring system of Nakamura and Tamai, excellent and good results were obtained in 59.5% of the patients. The rate of bony complications was different among the three methods of osteosynthesis though the final functional outcomes were comparable. The rate of bony complications in this series was 20.4%, which included non-union (7), migration of K-wires (2) and infection (1). All occurred in K-wire and K-wire & Wire-loop groups. Plate & Screws, therefore, is the preferred method of bony fixation if further operation for non-union is to be avoided. This is more so for the proximal injuries.

scholarly journals PROJECTIVE LOOPS GENERATE RATIONAL LOOP GROUPS

2020 ◽  
pp. 1-27
Author(s):  
Gang Wang ◽  
Oliver Goertsches ◽  
Erxiao Wang
Keyword(s):  
Loop Group ◽  
Unitary Groups ◽  
Bäcklund Transformations ◽  
Loop Groups ◽  
Backlund Transformations ◽  
Generator Theorem ◽  
The Sacrifice ◽  
Physical Construction ◽  
Classical Construction

We generalize Uhlenbeck’s generator theorem of ${\mathcal{L}}^{-}\operatorname{U}_{n}$ to the full rational loop group ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{C}$ and its subgroups ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{R}$ , ${\mathcal{L}}^{-}\operatorname{U}_{p,q}$ : they are all generated by just simple projective loops. Recall that Terng–Uhlenbeck studied the dressing actions of such projective loops as generalized Bäcklund transformations for integrable systems. Our result makes a nice supplement: any rational dressing is the composition of these Bäcklund transformations. This conclusion is surprising in the sense that Lie theory suggests the indispensable role of nilpotent loops in the case of noncompact reality conditions, and nilpotent dressings appear quite complicated and mysterious. The sacrifice is to introduce some extra fake singularities. So we also propose a set of generators if fake singularities are forbidden. A very geometric and physical construction of $\operatorname{U}_{p,q}$ is obtained as a by-product, generalizing the classical construction of unitary groups.

scholarly journals Loop Groups and QNEC

2021 ◽  
Author(s):  
Lorenzo Panebianco
Keyword(s):  
Energy Condition ◽  
Adjoint Action ◽  
Loop Group ◽  
Null Energy Condition ◽  
Positive Energy ◽  
Exponential Map ◽  
Energy Tensor ◽  
Loop Groups ◽  
Positive Energy Representation ◽  
Simply Connected

AbstractWe construct and study solitonic representations of the conformal net associated to some vacuum Positive Energy Representation (PER) of a loop group LG. For the corresponding solitonic states, we prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound. As an intermediate result, we show that a Positive Energy Representation of a loop group LG can be extended to a PER of $$H^{s}(S^1,G)$$ H s ( S 1 , G ) for $$s>3/2$$ s > 3 / 2 , where G is any compact, simple and simply connected Lie group. We also show the existence of the exponential map of the semidirect product $$LG \rtimes R$$ L G ⋊ R , with R a one-parameter subgroup of $$\mathrm{Diff}_+(S^1)$$ Diff + ( S 1 ) , and we compute the adjoint action of $$H^{s+1}(S^1,G)$$ H s + 1 ( S 1 , G ) on the stress energy tensor.

A 60GHz-Band 3-Dimensional System-in-Package Transmitter Module with Integrated Antenna

2012 ◽  
Vol E95.C (7) ◽  
pp. 1141-1146 ◽  
Author(s):  
Noriharu SUEMATSU ◽  
Satoshi YOSHIDA ◽  
Shoichi TANIFUJI ◽  
Suguru KAMEDA ◽  
Tadashi TAKAGI ◽  
...  
Keyword(s):  
Band 3 ◽  
Dimensional System ◽  
3 Dimensional ◽  
Integrated Antenna
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