In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unre...In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unreasonable setting of the characteristic of the system. Hereof, by means of nonstandard analysis, it is concluded that the advanced response arises from the course of Fourier analysis other than the transmission process of the signal.展开更多
For a given polyhedron K contain M, the notation RM（K） denotes a regular neighborhood of K in M. The authors study the following problem： find all pairs （m, k） such that if K is a compact k-polyhedron and M a PL ...For a given polyhedron K contain M, the notation RM（K） denotes a regular neighborhood of K in M. The authors study the following problem： find all pairs （m, k） such that if K is a compact k-polyhedron and M a PL m-manifold, then RM（f（K））≌RM（g（K）） for each two homotopic PL embeddings f,g ： K→M. It is proved that Rs^k＋2（Sk）≌/ S^k × D^2 for each k≥2 and some PL sphere S^k contain S^k＋2 （even for any PL sphere S^k contain S^k＋2 having an isolated non-locally flat point with the singularity S^k-1 contain S^k＋1 such that π1（S^k＋1 - S^k-1）≌/Z）.展开更多
文摘In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unreasonable setting of the characteristic of the system. Hereof, by means of nonstandard analysis, it is concluded that the advanced response arises from the course of Fourier analysis other than the transmission process of the signal.
基金Project supported by the Pierre Deligne Fund based on 2004 Balzan Prize in Mathematics,INTAS Grants(No.YSF-2002-393)the Russian Foundation for Basic Research(Nos.05-01-00993,04-01-00682,06-01-72551-NCNILa)+1 种基金President of the Russian Federation Grants(Nos.MD-3938.2005.1,NSH-1988.2003.1,MD-4729.2007.1)the Slovenian Research Agency(Nos.BI-RU/05-07-04,BI-RU/05-07-13).
文摘For a given polyhedron K contain M, the notation RM（K） denotes a regular neighborhood of K in M. The authors study the following problem： find all pairs （m, k） such that if K is a compact k-polyhedron and M a PL m-manifold, then RM（f（K））≌RM（g（K）） for each two homotopic PL embeddings f,g ： K→M. It is proved that Rs^k＋2（Sk）≌/ S^k × D^2 for each k≥2 and some PL sphere S^k contain S^k＋2 （even for any PL sphere S^k contain S^k＋2 having an isolated non-locally flat point with the singularity S^k-1 contain S^k＋1 such that π1（S^k＋1 - S^k-1）≌/Z）.
