Related papers: Mirror Principle IV
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.
The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
In this paper, we continue the study of almost squares and extend the result of the author's fourth paper of the series to almost squares with closer factors.
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…
New cases of the multiplicity conjecture are considered.
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
We show that the construction of mirror-reflective algebras inherits derived equivalences of gendo-symmetric algebras. More precisely, suppose A and B are gendo-symmetric algebras with both Ae and Bf faithful projective-injective left…
We highlight some facts about continued fractions of real cubic irrationalities. This may be thought as a small section in a textbook on continued fractions.
The present work consists of topics covered through a course currently taught by the author at SIMIS.
We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As…
We construct a subset $A$ of the unit disc with the following properties. (i) The set $A$ is the finite union of disjoint line segments. (ii) The shadow of $A$ is arbitrarily close to the shadow of the unit disc in "most" directions. (iii)…
In this article we introduce a group-theoretical point of view for the design of magnetic optical achromats based on symmetry. As examples we use two-cell repetitive achromats and four-cell achromats employing mirror symmetry.
Paper erroneously re-submitted as duplicte. Readers should look at math-ph/9909004.
This is the fourth part in the series of articles math.MG/0503397, math.MG/0503399, math.MG/0509512 where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations introduced in…
Problems in optimization and geometric probability are discussed, all connected with angles subtended at an observer's eye by an object at a distance. Several of these remain unsolved.
The contents of this manuscript has been moved to hep-ph/0412204.
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
We describe a simple geometrical derivation of the formula for reflection of light from a uniformly moving plane mirror directly from the postulates of special relativity.