A Residue Theorem for Malcev-neumann Series
نویسنده
چکیده
In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal series that are related by a change of variables. We obtain simple conditions for when a change of variables is possible, and find that the two related formal series in fact belong to two different fields of Malcev-Neumann series. The multivariate Lagrange inversion formula is easily derived and Dyson’s conjecture is given a new proof and generalized.
منابع مشابه
Malcev-Neumann series and the free field
After reviewing some aspects of Cohn’s theory of the free field, we give another proof of a theorem of Lewin: the subfield of rational elements in the field of Malcev-Neumann series on the free group is isomorphic to the free field.
متن کاملA Generalization of Stanley’s Monster Reciprocity Theorem
By studying the reciprocity property of linear Diophantine systems in light of Malcev-Neumann series, we present in this paper a new approach to and a generalization of Stanley’s monster reciprocity theorem. A formula for the “error term” is given in the case when the system does not have the reciprocity property. We also give a short proof of Stanley’s reciprocity theorem for linear homogeneou...
متن کاملOn a class of systems of n Neumann two-point boundary value Sturm-Liouville type equations
Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.
متن کاملDamage identification of structures using second-order approximation of Neumann series expansion
In this paper, a novel approach proposed for structural damage detection from limited number of sensors using extreme learning machine (ELM). As the number of sensors used to measure modal data is normally limited and usually are less than the number of DOFs in the finite element model, the model reduction approach should be used to match with incomplete measured mode shapes. The second-order a...
متن کاملAbout Levi-malcev Theorem for Homogeneous Bol Algebras
The fundamental ideas of the applicability of Levi-Malcev Theorem for Bol algebras, which plays a basic role in structural theory are outlined
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004