Fourth order Superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials

A study is presented of two-dimensional superintegrable systems separating in Cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the momenta. All quantum mechanical potentials that do not satisfy any linear differential equation are found. They do however satisfy nonlinear ODEs. We show that these equations always have the Painlev\'e property and integrate them in terms of known Painlev\'e transcendents or elliptic functions.Comment: 36 page

Two-dimensional superintegrable systems from operator algebras in one dimension

We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on a one-dimensional phase space, a natural Hamiltonian $H$ and a polynomial of order $N$ in the momentum $p.$ We assume that their Poisson commutator $\{H,K\}$ vanishes, is a constant, a constant times $H$, or a constant times $K$. In the quantum case $H$ and $K$ are operators and their Lie commutator has one of the above properties. We use two copies of such $(H,K)$ pairs to generate two-dimensional superintegrable systems in the Euclidean space $E_2$, allowing the separation of variables in Cartesian coordinates. All known separable superintegrable systems in $E_2$ can be obtained in this manner and we obtain new ones for $N=4.

Role of the homeobox HESX1/HESX1 in forebrain and pituitary development in mouse and human

The homeobox gene Hesx1 encodes a transcriptional repressor that is required, within the anterior neural plate of the vertebrate embryo, for normal forebrain and pituitary development. Hesx1'' mice display variable defects, affecting midline telencephalic commissural tracts, the eyes and the pituitary gland. In humans, mutations in HESX1 are associated with hypopituitarism and septo-optic dysplasia (SOD), a condition characterised by pituitary abnormalities in association with midline telencephalic structure and optic nerve defects. In this thesis, a dual approach was used, in order to gain insights into HESX1 function. Firstly, a yeast two-hybrid screen identified DNMT1, LONP2, SRFBP1, SAFB1 and ZFP592 as protein partners of HESX1. Mapping of the interacting regions indicated that different domains of HESX1 are involved in each of these interactions. The five proteins co-localise with HESX1 in the nucleus and their transcripts are co-expressed with Hesxl in mouse embryos. Furthermore, these interactions are disrupted by various HESX1 mutations. The binding with DNMT1 was characterised in more detail, since this protein has a crucial role in gene silencing through its DNA methylation properties. Thus this interaction suggests a novel mechanism for the repressing activity of HESX1. Secondly, gene targeting was used to generate two knock-in mouse models, based on two autosomal recessive human HESX1 mutations, I26T and R160C. I26T has been associated with anterior pituitary hypoplasia in a patient, whilst R160C was identified in two siblings with SOD. Hesxl embryos display fully penetrant pituitary defects with frequent occurrence of eye abnormalities, whereas the telencephalon develops normally. HesxlR160C/R160C embryos display more severe forebrain and pituitary defects that are identical to those observed in Hesxl' ' mice. These data indicate that Hesxl-I26T is a hypomorphic allele, whereas Hesxl-R160C yields a null allele and consequently causes a more severe phenotype in mice and humans

Post anesthetic shivering in children: incidence and causative factors

چکیده: زمینه و هدف: بیماران در طی بیهوشی حرارت از دست می دهند و پیدایش لرز روشی برای مقابله با آن است. تاکنون مطالعات متعددی در مورد لرز در بالغین انجام شده، ولی میزان این مطالعات در کودکان محدود است. لذا این مطالعه با هدف بررسی شیوع لرز پس از بیهوشی در کودکان و عوامل مربوط به آن انجام شد. روش بررسی: در این مطالعه توصیفی - تحلیلی ٢٠٠ کودک سه ماهه تا چهارده ساله در اطاق بهبودی از نظر عوامل زمینه ای، دریافت پیش داروی بیهوشی، روش بیهوشی، مدت زمان بیهوشی، درجه حرارت بیمار در اطاق بهبودی و درجه حرارت اطاق بهبودی مورد بررسی قرار گرفتند. پس از جمع آوری داده ها با کمک پرسشنامه، اطلاعات با استفاده از تست های آماری کای دو و اسپیرمن مورد تجزیه و تحلیل قرار گرفتند. یافته ها: تعداد کل موارد مشاهده شده لرز ٧ (١٤ نفر) بود. شیوع لرز در بیهوشی استنشاقی (6/13) به صورت معنی دار بیشتر از بیهوشی وریدی (صفر) بود (05/0

Fiscal consolidation in a low inflation environment: pay cuts versus lost jobs

We construct a model of a monetary union to study fiscal consolidation in the Periphery of the euro area, through cuts in public sector wages or hiring when the nominal interest rate is constrained at its lower bound. Consolidation induces a positive wealth effect that increases demand, as well as a reallocation of workers towards the private sector, which together boost private activity. However, in a low inflation environment, demand is suppressed and the private sector is not able to absorb the additional workers. Comparing the two instruments, cuts in public hiring increase unemployment persistently in this environment, while wage cuts reduce it. Regions with higher mobility of labour between the two sectors are able to consolidate more effectively. Price flexibility is also key at the zero lower bound: for a higher degree of price rigidity in the Periphery, consolidation becomes harder to achieve. Consolidations can be self-defeating when the public good is productive, or a complement to private consumption