Quasi-exact solutions for guided modes in two-dimensional materials with tilted Dirac cones.

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given one-dimensional (1D) potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a 2D Dirac material possessing tilted, anisotropic Dirac cones. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as 8-Pmmn borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.

Coronary artery-left ventricular fistula.

Coronary artery-left ventricular fistulae are exceedingly rare and to date only 19 cases have been reported in the literature. We describe another four cases which we encountered recently. The first patient was a 10-year-old asymptomatic Indian male who was referred because of a to-and-fro murmur. Haemodynamic and angiographic studies revealed an aneurysmally enlarged right coronary draining into the left ventricle. The fistula was ligated and the patient has remained well over a 21/2-year follow-up period. The second patient was a 13-year-old asymptomatic Chinese female referred also because of a to-and-fro murmur. Haemodynamic and angiographic studies showed a grossly enlarged right coronary artery draining into the left ventricle. This patient refused operation and has remained well over a 2-year follow-up period. The third patient was a 43-year-old Chinese male who presented with a 3-year history of angina pectoris and was admitted to hospital because of crescendo angina. The resting electrocardiogram showed marked ischaemic changes and the treadmill exercise stress test was also positive. Selective coronary angiography showed markedly dilated right and left coronary arteries. Multiple fistulae from the three major coronary arteries were seen to communicate with the left ventricle. It was elected to treat this patient medically with propranolol. He has remained well over a 6-month follow-up period. The fourth patient was a 5-year-old asymptomatic Chinese girl. Cardiac catheterization and selective coronary angiography revealed marked dilatation of the branches of the left coronary artery which communicated via a maize of fine vessels into the left ventricle. This patient has remained well over a 5-year follow-up period. The clinical presentation, investigations and treatment of coronary artery-left ventricular fistula are discussed and the literature regarding this subject is reviewed.

Formes frustes of Marfan's syndrome presenting with severe aortic regurgitation. Clinicogenetic study of 18 families.

Eighteen patients who presented with severe aortic regurgitation and dilatation of the ascending aorta were found to be formes frustes of Marfan's syndrome and formed the basis for this clinicogenetic study. All had aortic valve replacement and reconstruction of part of the ascending aorta. The diagnosis was confirmed by histological examination of the aortic tissue. There were 126 first degree relatives; 85 were living and 67 (78-8%) of these were examined. Limited information was available about 32 of the 41 relatives who had died. No relative had the classical clinical features of Marfan's syndrome but stigmata of the disease were found in 25 (37-3%) of the 67 first degree relatives examined. In 21, the abnormality was confined to the cardiovascular system, the skeleton, or the eye, but in 4, abnormalities involved 2 systems. Cardiovascular abnormalities affecting the aortic valve or aortic wall were present in 6 (9-0%) of the 67 first degree relatives examined. One or more of the skeletal indices measured (height-span difference, metacarpal index, phalangeal index) was abnormal in 18 (26-9%) and ocular abnormalities were found in 5 of 51 (9-8%) examined. There were no relatives with dislocation of the lens or iridodonesis. Using strict diagnostic criteria, a minimum of 37-3 per cent of the first degree relatives examined were affected; this involved 12 of the 18 families studied. There was nothing in our data to suggest that the formes frustes of the disease had a different mode of inheritance from the classical syndrome.