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1. The semigroup analogue of the Pontrjagin duality theorem was first studied in [1]. In that paper, it was shown that a necessary and sufficient condition for duality in discrete abelian semigroups is that the semigroup be a union of groups and have an identity element. Such semigroups we shall call inverse semigroups. For compact abelian topological semigroups it was shown in [1] that the separation of points by semicharacters is a sufficient condition for duality in an inverse semigroup with identity. In [2] it was shown that, in any topological abelian semigroup, a necessary condition for duality is that the semigroup be an inverse semigroup with identity and continuous inversion. In this paper we obtain necessary and sufficient conditions that semicharacters separate points in a topological abelian inverse semigroup with identity which is compact, or locally compact with continuous inversion. In the compact case we obtain the same result as has been given by Sneperman [5], using different methods. 1.1. DEFINITION. An abelian semigroup is a nonempty set S together with a map m: (x, y)-*xy on SXS to S, such that x(yz) = (xy)z and xy =yx for all x, y and z in S. If S is a Hausdorff topological space and the mapping m is continuous, S is called a topological abelian semigroup. 1.2. DEFINITION. A semicharacter X of a topological abelian semigroup S is a bounded, continuous, complex-valued function on S, not identically zero, satisfying x(xy) =x(x)x(y) for all x and y in S. We denote the set of semicharacters of S by SA. We endow SA with the compact open topology. The following facts aretobefoundin [1], [3]or [4]. 1.3. If S has an identity element, S^ becomes a topological abelian semigroup, when endowed with the operation of pointwise multiplication. 1.4. If S has an identity element, and is discrete, S^ is a compact abelian semigroup [1, 3.1 ]. 1.5. We call S an abelian inverse semigroup if S is an abelian semigroup which is a union of groups. If S is a topological, abelian inverse semigroup with an identity element then S"" is of the same type. Further, if S is compact then S^ is discrete [1, 6.11.

Sufficient conditions are given so that all solutions of the nonlinear differential equation u ″ + φ ( t , u , u ′) u ′ + p ( t ) gf ( u ) g ( u ′) = h ( t , u , u ′) are continuable to the right of an initial t -value t 0 ⩾ 0. These conditions are then extended so that all solutions u of the equation in question together with their derivative u ′ are bounded for t ⩾ t 0 .

Free jejunal transfer is a useful alternative for the reconstruction of defects of the pharynx and cervical esophagus. We describe 17 patients who received free jejunal grafts between 1980 and 1984 at the Eastern Virginia Medical School. The rationale and indications for the procedure are discussed. We emphasize certain technical considerations and improvements.

Encouraged by their experience since 1978 with blunt esophagectomy and gastric reconstruction in the management of pharyngolaryngeal malignancy, the authors have extended their use of this technique to the management of thoracic esophageal cancer. A study of 43 blunt esophageal resections is presented; 23 were performed in the management of pharyngolaryngeal cancer, and 20 were performed (22 attempted) for the resection of intrathoracic esophageal cancer. In the first group, two deaths occurred secondary to liver failure in cirrhotic patients with moist ascites. One death occurred due to anastomotic leak in the neck of a patient with laryngeal cancer treated with extended mediastinal dissection and tracheal resection for surgical and radiation failure. Two tracheal injuries occurred; one could be managed through the neck, and one required thoractomy for repair. In the 20 resections performed for intrathoracic cancer, there were no deaths, no tracheal injuries, and one chest was explored for bleeding in the splenic bed, which decompressed itself into the right chest. The overall mortality was 7.5%. The evaluation emphasizes: The applicability of this technique for the management of esophageal problems at all levels. The safety of the technique, particularly in the typical population with advanced aged and severe underlying medical illness. Good functional results with palliation and/or cure. The benefit of intact mediastinal pleura in avoiding certain thoracic complications. The authors conclude that blunt esophagectomy is a safe resection procedure with limited morbidity and mortality, and that gastric reconstruction is reliable and affords excellent functional results. They are encouraged to continue management of panesophageal cancer with this technique.

The accelerating effect of acids and bases on various reactions in organic chemistry, such as those which involve hydrolysis, condensation, isomerisation etc. represents the oldest and most widely studied type of homogeneous catalysis in solution.1