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Papers by William Meyerson

Research paper thumbnail of Lipschitz and biLipschitz Maps on Carnot Groups

Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is anothe... more Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of A of positive Hausdorff measure. We then construct Lipschitz maps from open sets in Carnot groups to Euclidean space that do not decrease dimension. Finally, we discuss two counterexamples to explain why Carnot group structure is necessary for these results.

Research paper thumbnail of ON THE ARITHMETIC OF CONGRUENCE MONOIDS

Research paper thumbnail of A theorem on accepted elasticity in certain local arithmetical congruence monoids

Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2009

We give necessary and sufficient conditions for a certain class of local arithmetical congruence ... more We give necessary and sufficient conditions for a certain class of local arithmetical congruence monoids (or ACMs) to have accepted elasticity.

Research paper thumbnail of On a result of James and Niven concerning unique factorization in congruence semigroups

Elemente Der Mathematik, 2007

The theory of non-unique factorizations in integral domains and monoids is a very active area of ... more The theory of non-unique factorizations in integral domains and monoids is a very active area of current research (see both [1] and [4] to view re-cent trends in this work). To demonstrate the phenomena of non-unique factorizations, we consider a result from the classical setting on uniqueness of factorizations by James and Niven [11]. We proceed as follows. Let N represent the natural numbers and suppose that M N is a multiplicative semigroup. M is called a congruence semigroup if there exists a natural number n such that

Research paper thumbnail of On the arithmetic of arithmetical congruence monoids

Colloquium Mathematicum, 2007

Let N represent the positive integers and N0 the nonnegative integers. If b 2 N and is a multipli... more Let N represent the positive integers and N0 the nonnegative integers. If b 2 N and is a multiplicatively closed subset of Zb = Z/bZ, then the set H = {x 2 N | x + bZ 2 } ( {1} is a multiplicative sub- monoid of N known as a congruence monoid. An arithmetical congruence monoid (or ACM) is

Research paper thumbnail of A THEOREM ON ACCEPTED ELASTICITY IN LOCAL ARITHMETICAL CONGRUENCE MONOIDS

We give necessary and sucient conditions for a certain class of local arithmetical congruence mon... more We give necessary and sucient conditions for a certain class of local arithmetical congruence monoids (or ACMs) to have accepted elasticity.

Research paper thumbnail of Significant Statistics: The Unwitting policy Making of Mathematically Ignorant Judges

... 1477 (1999), quoting Darrin R. Lehman, Richard O. Lempert & Richard E. Nisbett, The Effec... more ... 1477 (1999), quoting Darrin R. Lehman, Richard O. Lempert & Richard E. Nisbett, The Effects of Graduate Training on Reasoning: Formal Discipline and Thinking About ... 2001) (Due Process violated by lax prison security); Chavez v. Illinois State Police, 251 F.3d 612 (7th Cir. ...

Research paper thumbnail of Lipschitz and biLipschitz Maps on Carnot Groups

Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is anothe... more Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of A of positive Hausdorff measure. We then construct Lipschitz maps from open sets in Carnot groups to Euclidean space that do not decrease dimension. Finally, we discuss two counterexamples to explain why Carnot group structure is necessary for these results.

Research paper thumbnail of ON THE ARITHMETIC OF CONGRUENCE MONOIDS

Research paper thumbnail of A theorem on accepted elasticity in certain local arithmetical congruence monoids

Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2009

We give necessary and sufficient conditions for a certain class of local arithmetical congruence ... more We give necessary and sufficient conditions for a certain class of local arithmetical congruence monoids (or ACMs) to have accepted elasticity.

Research paper thumbnail of On a result of James and Niven concerning unique factorization in congruence semigroups

Elemente Der Mathematik, 2007

The theory of non-unique factorizations in integral domains and monoids is a very active area of ... more The theory of non-unique factorizations in integral domains and monoids is a very active area of current research (see both [1] and [4] to view re-cent trends in this work). To demonstrate the phenomena of non-unique factorizations, we consider a result from the classical setting on uniqueness of factorizations by James and Niven [11]. We proceed as follows. Let N represent the natural numbers and suppose that M N is a multiplicative semigroup. M is called a congruence semigroup if there exists a natural number n such that

Research paper thumbnail of On the arithmetic of arithmetical congruence monoids

Colloquium Mathematicum, 2007

Let N represent the positive integers and N0 the nonnegative integers. If b 2 N and is a multipli... more Let N represent the positive integers and N0 the nonnegative integers. If b 2 N and is a multiplicatively closed subset of Zb = Z/bZ, then the set H = {x 2 N | x + bZ 2 } ( {1} is a multiplicative sub- monoid of N known as a congruence monoid. An arithmetical congruence monoid (or ACM) is

Research paper thumbnail of A THEOREM ON ACCEPTED ELASTICITY IN LOCAL ARITHMETICAL CONGRUENCE MONOIDS

We give necessary and sucient conditions for a certain class of local arithmetical congruence mon... more We give necessary and sucient conditions for a certain class of local arithmetical congruence monoids (or ACMs) to have accepted elasticity.

Research paper thumbnail of Significant Statistics: The Unwitting policy Making of Mathematically Ignorant Judges

... 1477 (1999), quoting Darrin R. Lehman, Richard O. Lempert & Richard E. Nisbett, The Effec... more ... 1477 (1999), quoting Darrin R. Lehman, Richard O. Lempert & Richard E. Nisbett, The Effects of Graduate Training on Reasoning: Formal Discipline and Thinking About ... 2001) (Due Process violated by lax prison security); Chavez v. Illinois State Police, 251 F.3d 612 (7th Cir. ...

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