A Barker sequence is a binary sequence for which all non-trivial aperiodic autocorrelations are at most 1 in magnitude. An old conjecture due to Turyn asserts that there is no Barker sequence of length greater than 13. In 1961, Turyn and Storer gave an elementary, though somewhat complicated, proof that this conjecture holds for odd lengths. We give a new and simpler proof of this result.

Extracting useful features from a scene is an essential step in any computer vision and multimedia data analysis task. Though progress has been made in past decades, it is still quite difficult for computers to comprehensively and accurately recognize an object or pinpoint the more complicated semantics of an image or a video. Thus, feature extraction is expected to remain an active research ar...

Though controversy exists regarding the utility of pulmonary artery catheters (PAC), their use persists in select patients. Knotting of these catheters upon insertion is a rare but serious complication. We present 2 cases of coagulopathic patients undergoing orthotopic liver transplantation complicated by PAC knotting on attempted line placement. Both knotted PAC were successfully removed nonsu...

Although a large number of concerted thermal 1,3-migrations of a group-14 element have been known, their mechanistic aspects are rather complicated. Following the WoodwardHoffmann rules, 1) suprafacial 1,3-migration with retention at the migrating center (suprafacial-retention) is symmetryforbidden; antarafacial-retention and suprafacial-inversion processes are allowed, though they are usually ...

Laparoscopic Nissen fundoplication is the current standard surgical option for complicated GERD and symptomatic hiatal hernia. Though comparable in safety, short-term efficacy, and patient satisfaction when compared with open operation, laparoscopic Nissen fundoplication has demonstrated shorter hospital stays and recuperative times. Commonly reported complications include gastric or esophageal...

Innovations in conformal mapping continue to extend this classical technique to more complicated configurations, and surveys of the various techniques available are given in Ref. [7] and Ref. [1]. Some specific recommendations of techniques and tools are given in Ref. [7]. Conformal systems have advantage the of introducing the fewest additional terms in transformed partial differential equatio...

We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some self-similarity phenomena in irrational triangular billiards. Our analysis illustrates the surprising fact that billiards on a triangle near a V...

The pathophysiology and fundamental etiologic mechanism of inflammatory bowel disease (IBD) is not well understood even though therapeutic regimens and drugs are rapidly evolutionary. IBD has complicated connections with genetic, immunologic, gut microbial, environmental, and nutritional factors. It is not clearly well known to the physicians how to feed, what nutrients are more helpful, and wh...

Mid-esophageal diverticula are rare entities. Only symptomatic patients usually receive surgical treatment. Esophageal leakage is one of the most common complications after these procedures. Though in literature, operative management is the preferred treatment for esophageal fistula, conservative approach is described in case of small leaks. We report a case of an operated giant mid-esophageal ...