Results 1  10
of
309
Characterizing Algebraic Invariants by Differential Radical Invariants ⋆
"... Abstract We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This socalled differential radical characterization relies on a sound abstraction of the reachable set of solu ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
of solutions by the smallest variety that contains it. The characterization leads to a differential radical invariant proof rule that is sound and complete, which implies that invariance of algebraic equations over realclosed fields is decidable. Furthermore, the problem of generating invariant varieties
Differential Invariant Algebras of Lie Pseudo–Groups
, 2012
"... The aim of this paper is to describe, in as much detail as possible and constructively, the structure of the algebra of differential invariants of a Lie pseudogroup acting on the submanifolds of an analytic manifold. Under the assumption of local freeness ofasuitablyhighorder prolongationofthepse ..."
Abstract

Cited by 24 (12 self)
 Add to MetaCart
The aim of this paper is to describe, in as much detail as possible and constructively, the structure of the algebra of differential invariants of a Lie pseudogroup acting on the submanifolds of an analytic manifold. Under the assumption of local freeness ofasuitablyhighorder
A MachineChecked Proof of the Odd Order Theorem
"... This paper reports on a sixyear collaborative effort that culminated in a complete formalization of a proof of the FeitThompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework impleme ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
This paper reports on a sixyear collaborative effort that culminated in a complete formalization of a proof of the FeitThompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework
Extended Static Checking by Calculation using the Pointfree Transform
 Proc. LerNet ALFA Summer School Conf
, 2008
"... Abstract. The pointfree transform offers to the predicate calculus what the Laplace transform offers to the differential/integral calculus: the possibility of changing the underlying mathematical space so as to enable agile algebraic calculation. This paper addresses the foundations of the transfo ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
of the transform and its application to a calculational approach to extended static checking (ESC) in the context of abstract modeling. In particular, a calculus is given whose rules help in breaking the complexity of the proof obligations involved in static checking arguments. The close connection between
Anonymous Hierarchical IdentityBased Encryption (Without Random Oracles). In: Dwork
 CRYPTO 2006. LNCS,
, 2006
"... Abstract We present an identitybased cryptosystem that features fully anonymous ciphertexts and hierarchical key delegation. We give a proof of security in the standard model, based on the mild Decision Linear complexity assumption in bilinear groups. The system is efficient and practical, with sm ..."
Abstract

Cited by 119 (10 self)
 Add to MetaCart
not too many). The real difficulty is that each set of rerandomization components constitutes a fullfledged HIBE in its own right, which must be simulated together with its peers in the security proof (their number grows linearly with the maximal depth). Because these systems are not independent
Concurrent Kleene Algebra
"... A concurrent Kleene algebra offers, next to choice and iteration, operators for sequential and concurrent composition, related by an inequational form of the exchange law. We show applicability of the algebra to a partiallyordered trace model of program execution semantics and demonstrate its usefu ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
usefulness by validating familiar proof rules for sequential programs (Hoare triples) and for concurrent ones (Jones’s rely/guarantee calculus). This involves an algebraic notion of invariants; for these the exchange inequation strengthens to an equational distributivity law. Most of our reasoning has been
Baby Verma modules for rational Cherednik algebras
 Bull. London Math. Soc
"... Abstract. Symplectic reflection algebras arise in many different mathematical disciplines: integrable systems, Lie theory, representation theory, differential operators, symplectic geometry. In this paper, we introduce baby Verma modules for symplectic reflection algebras of complex reflection group ..."
Abstract

Cited by 57 (9 self)
 Add to MetaCart
of the representation theory and associated geometry of the rational Cherednik algebras at parameter t = 0. As an example, we use baby Verma modules to solve one problem posed by Etingof and Ginzburg and partially solve another, [5], and give an elementary proof of a theorem of Finkelberg and Ginzburg, [6]. 1. Notation
A generator system of invariant differential forms.
, 2002
"... We obtain a generator system of the algebra of GL(V)invariant differential forms on Endk(V). The proof uses the WeylSchur reciprocity. Let k be a field of characteristic zero and Mn(k) be the set of all n × n matrices with entries of elements of k. We consider GLn(k) adjoint action on Mn(k), i.e. ..."
Abstract
 Add to MetaCart
We obtain a generator system of the algebra of GL(V)invariant differential forms on Endk(V). The proof uses the WeylSchur reciprocity. Let k be a field of characteristic zero and Mn(k) be the set of all n × n matrices with entries of elements of k. We consider GLn(k) adjoint action on Mn(k), i
Invariance of tautological equations I: conjectures and applications
"... Abstract. The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the conjectures gives an efficient algorithm to calculate, conjecturally, all tautological equations using only finite dimensional linear algebra. Other applications ..."
Abstract

Cited by 23 (8 self)
 Add to MetaCart
Abstract. The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the conjectures gives an efficient algorithm to calculate, conjecturally, all tautological equations using only finite dimensional linear algebra. Other applications
Results 1  10
of
309