The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry

An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS_5xS^5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S-matrix in the generalized rapidity plane.Comment: 27 pages, no figures; v2: sign typo fixed in (24), everything else unchange

Canonical transformations in three-dimensional phase space

Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J. Mod. Phys.

A peptide with N-terminal histidine and C-terminal isoleucine amide (PHI) and vasoactive intestinal peptide (VIP) are copackaged in myenteric neurones of the guinea pig ileum.

When cytoplasmic extracts of the myenteric plexus of guinea pig ileum are submitted to centrifugal density gradient separation in a zonal rotor, conditions which separate storage particles containing substance P, somatostatin and VIP from each other, PHI copurifies with VIP. The two immunoreactivities cannot be separated by particle exclusion chromatography, which depends on size rather than density. It is concluded that the posttranslational cleavage of the propeptide or precursor to PHI and VIP occurs after packaging into these storage particles

Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type

We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of genus one and two with many automorphisms. In the genus one case we find new addition formulae for the equianharmonic and lemniscate cases, and in genus two we find some new addition formulae for a number of curves, including the Burnside curve.Comment: 19 pages. We have extended the Introduction, corrected some typos and tidied up some proofs, and inserted extra material on genus 3 curve

The eVALuate study: two parallel randomised trials, one comparing laparoscopic with abdominal hysterectomy, the other comparing laparoscopic with vaginal hysterectomy

OBJECTIVE: To compare the effects of laparoscopic hysterectomy and abdominal hysterectomy in the abdominal trial, and laparoscopic hysterectomy and vaginal hysterectomy in the vaginal trial. DESIGN: Two parallel, multicentre, randomised trials. Setting 28 UK centres and two South African centres. Participants 1380 women were recruited; 1346 had surgery; 937 were followed up at one year. PRIMARY OUTCOME: outcome Rate of major complications. RESULTS: In the abdominal trial laparoscopic hysterectomy was associated with a higher rate of major complications than abdominal hysterectomy (11.1% v 6.2%, P = 0.02; difference 4.9%, 95% confidence interval 0.9% to 9.1%) and the number needed to treat to harm was 20. Laparoscopic hysterectomy also took longer to perform (84 minutes v 50 minutes) but was less painful (visual analogue scale 3.51 v 3.88, P = 0.01) and resulted in a shorter stay in hospital after the operation (3 days v 4 days). Six weeks after the operation, laparoscopic hysterectomy was associated with less pain and better quality of life than abdominal hysterectomy (SF-12, body image scale, and sexual activity questionnaires). In the vaginal trial we found no evidence of a difference in major complication rates between laparoscopic hysterectomy and vaginal hysterectomy (9.8% v 9.5%, P = 0.92; difference 0.3%, − 5.2% to 5.8%), and the number needed to treat to harm was 333.We found no evidence of other differences between laparoscopic hysterectomy and vaginal hysterectomy except that laparoscopic hysterectomy took longer to perform (72 minutes v 39 minutes) and was associated with a higher rate of detecting unexpected pathology (16.4% v 4.8%, P = < 0.01). However, this trial was underpowered. CONCLUSIONS: Laparoscopic hysterectomy was associated with a significantly higher rate of major complications than abdominal hysterectomy. It also took longer to perform but was associated with less pain, quicker recovery, and better short term quality of life. The trial comparing vaginal hysterectomy with laparoscopic hysterectomy was underpowered and is inconclusive on the rate of major complications; however, vaginal hysterectomy took less time

Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites

We calculate the bulk contribution for the doubly degenerated largest eigenvalue of the transfer matrix of the eight vertex model with an odd number of lattice sites N in the disordered regime using the generic equation for roots proposed by Fabricius and McCoy. We show as expected that in the thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change

Differential constraints and exact solutions of nonlinear diffusion equations

The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries

Past and future blurring at fundamental length scale

We obtain the $\kappa$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2\kappa)$. The functions also indicate a smearing of the light cone. These results favor the interpretation of $q$ as a fundamental length scale below which the concept of a point in spacetime should be substituted by the concept of a fuzzy region of radius $q$, as proposed long ago by Heisenberg.Comment: Essentially, this is the version published in the Phys. Rev. Lett. 105, 211601 (2010). It has 4 pages and contains 2 figure

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure

Exact and simple results for the XYZ and strongly interacting fermion chains

We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects