Generalized q-Oscillators and their Hopf Structures

We study the relationships among the various forms of the $q$ oscillator algebra and consider the conditions under which it supports a Hopf structure. We also present a generalization of this algebra together with its corresponding Hopf structure. Its multimode extensions are also considered.Comment: 14 page

Classification of the quantum deformation of the superalgebra GL(1∣1)GL(1|1)

We present a classification of the possible quantum deformations of the supergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each $R$ matrix, one finds two inequivalent coproducts whether one chooses an unbraided or a braided framework while the corresponding structures are isomorphic as algebras. In the braided case, one recovers the classical algebra $gl(1|1)$ for suitable limits of the deformation parameters but this is no longer true in the unbraided case.Comment: 23p LaTeX2e Document - packages amsfonts,subeqn - misprints and errors corrected, one section adde

Coherent states for a quantum particle on a circle

The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a direct consequence of the Heisenberg algebra $[\hat \phi, \hat J]=i$, but it is more adequate for the study of the circlular motion.Comment: 23 pages LaTeX, uses ioplppt.st

Some remarks on the Gauss decomposition for quantum group GL_q(n)

In this letter some properties of the Gauss decomposition of quantum group $GL_q(n)$ with application to q-bosonization are considered.Comment: 11 page

I-21 Current therapeutic guidelines in Duchenne Muscular Dystrophy to prolong life

Duchenne's myopathy is an X-linked disease with well defined evolutionary phases, characterized by degradation of the walking function, development of evolutive scoliosis and progressive decline of the respiratory function leading patients to premature death. In 1985 Y. Rideau in France carried out a new global therapeutic strategy for treatment of lower limb deformities, scoliosis deformity and progressive restrictive syndrome. The indication for surgery at the lower limbs is made very early, at the onset of the first signs of disease. The procedures are carried out at the same time and always bilaterally; they include: (i) hip section of superficial flexors; (ii) iliotibial band resection; (iii) subcutaneous tenotomy of semitendineous and gracilis; (iv) subcutaneous lengthening of Achilles tendons. In the post-operative period, the patient begins exercises of active and passive mobility in few days and after three weeks recovers his performances; ambulation will remain almost normal for several years. A comparison of two groups of patients, the first precociously operated on the lower limbs, the other one not operated, shows better performances in the operated group. The indications for surgical treatment of Duchenne scoliosis must be made after the loss of ambulation and not too late, to avoid the concurrent respiratory restrictive syndrome makes the patient inoperable. Over ten years ago, in Poitiers, a specific instrumentation for Duchenne scoliosis was created, providing for cylindrical rods fixed by peduncular screws at the sacro-lumbar level. On the dorso-lumbar level, the rod becomes flat to allow more flexibility of the trunk. The complications observed in a group of 55 patients operated for scoliosis, consisted in 2 cases of breaking of rods and 1 superficial infection. The surgery approach in DMD has the double aim to prolong the time of the autonomous ambulation and to avoid the evolution of scoliosis, limiting the harmful effects of the scoliosis on the respiratory function. However, the surgery alone is unable to prolong the life expectancy in these patients, without treating the restrictive respiratory syndrome, first by nasal ventilation and then by elective tracheotomy, essential for the survival of the patient

q-Supersymmetric Generalization of von Neumann's Theorem

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom.Comment: 10 pages, Latex, HU-TFT-93-2

Molecular basis of FIR-mediated c-myc transcriptional control

The far upstream element (FUSE) regulatory system promotes a peak in the concentration of c-Myc during cell cycle. First, the FBP transcriptional activator binds to the FUSE DNA element upstream of the c-myc promoter. Then, FBP recruits its specific repressor (FIR), which acts as an on/off transcriptional switch. Here we describe the molecular basis of FIR recruitment, showing that the tandem RNA recognition motifs of FIR provide a platform for independent FUSE DNA and FBP protein binding and explaining the structural basis of the reversibility of the FBP-FIR interaction. We also show that the physical coupling between FBP and FIR is modulated by a flexible linker positioned sequentially to the recruiting element. Our data explain how the FUSE system precisely regulates c-myc transcription and suggest that a small change in FBP-FIR affinity leads to a substantial effect on c-Myc concentration.MRC Grant-in-aid U11757455

Field on Poincare group and quantum description of orientable objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincare group $G$. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group $\Pi =G\times G$. All such transformations can be studied by considering a generalized regular representation of $G$ in the space of scalar functions on the group, $f(x,z)$, that depend on the Minkowski space points $x\in G/Spin(3,1)$ as well as on the orientation variables given by the elements $z$ of a matrix $Z\in Spin(3,1)$. In particular, the field $f(x,z)$ is a generating function of usual spin-tensor multicomponent fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.Comment: 46 page

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well