In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can be computed, but (ii) globally they cannot (though we prove they are semi-computable). We also show that Smale’s horseshoe, the first example of a hyperboli...

We have developed a mathematical model for a tracheal ring that consists of a "horseshoe" of cartilage with its tips joined by a membrane. The ring is subjected to a uniform transmural pressure (Ptm) difference. The model was used to calculate the cross-sectional area (A) of the trachea. Whereas the mechanics of the deformation of the cartilage were analyzed using elastica theory, the posterior...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

Urinary tract infection, hydronephrosis, calculi, and tumor of the renal pelvis are knownas complications and multiple congenital anomalies can occur together with a horseshoe kidney (1). However, the occurrence of membranousnephropathy (MN) in a horseshoe kidney has been only reported in a few case reports (2, 3). Furthermore, horseshoe kidney and focal sclerosing glomerulonephritis were seen ...

We report a case of supernumerary kidney associated with horseshoe malformation. A 35-year-old man presented complaining of vague and intermittent left flank pain from few months ago. Ultrasonography of urinary tract showed bilateral hydronephrosis and was suggestive of the horseshoe anomaly. Further evaluation with Intravenous urography showed three renal moieties consisting of a horseshoe kid...

Beyond their commercial importance for LAL and bait, and their status as a living fossil, it is often asserted that horseshoe crabs play a vital role in the ecology of estuarine and coastal communities. How would the various ecological relationships involving horseshoe crabs be affected if these animals were no longer abundant? Attempts to understand and generalize the ecological importance of ...

Management of the horseshoe crab, Limulus polyphemus, is currently surrounded by controversy. The species is considered a multiple-use resource, as it plays an important role as bait in a commercial fishery, as a source of an important biomedical product, as an important food source for multiple species of migratory shorebirds, as well as in several other minor, but important, uses. Concern has...

Although premature separation of normally implanted placenta is considered the most serious complication of pregnancy, knowledge of uterine behaviour during this con­dition is meager, on the basis of electronic recording of intra-uterine pressure two type of contraction pattern has been identified.  In type I uterine tonus has values below 30mmHg  with a frequency of 4-9 contractions per 10 m...

Neuroblastoma is one of the commonest malignancy of childhood. Neuroblatoma in horseshoe kidney is an extremely rare condition. There is only one case of this tumour occurring in horseshoe kidney described in the literature. Recently we successfully treated a boy with neuroblastoma in horseshoe kidney.

Horseshoe kidney is a congenital anomaly characterized by medial fusion of the bilateral kidneys. Treatment for an abdominal aortic aneurysm (AAA) with a horseshoe kidney is a technical challenge because of the complex anatomy. We report a successful open surgical repair for a ruptured AAA with a horseshoe kidney. An aortic grafting was performed with division of the renal isthmus through a tra...