The November Meeting in Milwaukee
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چکیده
s of papers presented at the meeting follow. Those with t after the abstract number were presented by title. In the case of joint papers, the name of the author who read the paper is followed by (p). Mr. Ornstein was introduced by Professor Irving Kaplansky and Professor L. V. Toralballa by Professor J. W. T. Youngs. ALGEBRA AND THEORY OF NUMBERS 123/. K. T. Chen: Integration of paths—geometric invariants and a generalized Baker-Hausdorff formula. Let the path « in the affine w-space R be given by #»««»•(*), * = 1, • • • , m, a^t^b. Starting from the line integral fad(i) Œ fadxi, one defines inductively, for p^2, fad(ii, • • • , iP) ~f%[fatd(ii, • • • , ip-i)]dca (f) where a} denotes the portion of a. with the parameter ranging from a to t. The integral remains unchanged when a undergoes a translation. It is further observed that the totality of fad{ii, • • • , ip)t with p fixed, forms a pth order tensor associated with a under linear transformations of R. If all fad(ii, • • • , iP) = 0 for pSr, then a is said to be of lower central class r, which is an affine invariant of a. The paths of lower central class 1 are characterized by being closed; and those of lower central class 2, by enclosing zero algebraic area when projected on any plane in R. Let X\, • • • , Xm be noncommutative indeterminates. Define 0 ( a ) ! + £ ƒ « d(i)Xi-h£,fad(it j)XiXi+Y,f<A& h k)XiXjXk
منابع مشابه
Proceedings of the First MEFOMP International Conference of Medical Physics: November 2-4, 2011, Shiraz, Iran
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