A Sufficient Condition for Nilpotency in a Finite Group

It is shown that finite groups in which the order of the product of every pair of elements of co-prime order is the product of the orders, is nilpotent

Correlation functions of twist fields from Ward identities in the massive Dirac theory

We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion point, and it is well-known that their vacuum two-point functions are determined by integrable differential equations. We extend part of this result to more general quantum states (pure or mixed) and to certain descendents, showing that some two-point functions are determined by the sinh-Gordon differential equations whenever there is translation and parity invariance, and the density matrix is the exponential of a bilinear expression in fermions. We use methods involving Ward identities associated to the copy-rotation symmetry in a model with two independent, anti-commuting copies. Such methods were used in the context of the thermally perturbed Ising quantum field theory model. We show that they are applicable to the Dirac theory as well, and we suggest that they are likely to have a much wider applicability to free fermion models in general. Finally, we note that our form-factor study of descendents twist fields combined with a CFT analysis provides a new way of evaluating vacuum expectation values of primary U(1) twist fields: by deriving and solving a recursion relation.Comment: 31 page

Control of corn diseases in Illinois

"In cooperation with Office of Cereal Crops and Diseases, Bureau of Plant Industry, U.S. Department of Agriculture.

The Emperor Has No Clothes: Confronting the DC Circuit’s Usurpation of SEC Rulemaking Authority

In The Emperor Has No Clothes: Confronting the D.C. Circuit’s Usurpation of SEC Rulemaking Authority, Professor James D. Cox of Duke University School of Law & Benjamin J.C. Baucom, recent law clerk to Justice Don R. Willett of the Supreme Court of Texas, argue “that the level of review invoked by the D.C. Circuit in Business Roundtable and its earlier decisions is dramatically inconsistent with the standard enacted by Congress.” They conclude “that the D.C. Circuit has assumed for itself a role opposed to the one Congress prescribed for courts reviewing SEC rules.

A generic operational simulation for early design civil unmanned aerial vehicles

Contemporary aerospace programmes often suffer from large cost overruns, delivery delays and inferior product quality. This is caused in part by poor predictive quality of the early design phase processes with regards to the operational environment of a product. This paper develops the idea of a generic operational simulation that can help designers to rigorously analyse and test their early product concepts. The simulation focusses on civil Unmanned Air Vehicle products and missions to keep the scope of work tractable. The research agenda is introduced along with ideas, initial results and future work. Designers specify details about their product, its environment and anticipated operational procedures. The simulation returns information that can help to estimate the value of the product using the value-driven design approach. Information will include recurring and non-recurring mission cost items. The research aim is to show that an operational simulation can improve early design concepts, thereby reducing delays and cost overruns. Moreover, a trade-off between mission fidelity and model generality is sought along with a generic ontology of civil Unmanned Air Vehicle missions and guidelines about capturing operational informatio

Well-posedness for the diffusive 3D Burgers equations with initial data in H1/2H^{1/2}

In this note we discuss the diffusive, vector-valued Burgers equations in a three-dimensional domain with periodic boundary conditions. We prove that given initial data in $H^{1/2}$ these equations admit a unique global solution that becomes classical immediately after the initial time. To prove local existence, we follow as closely as possible an argument giving local existence for the Navier--Stokes equations. The existence of global classical solutions is then a consequence of the maximum principle for the Burgers equations due to Kiselev and Ladyzhenskaya (1957). In several places we encounter difficulties that are not present in the corresponding analysis of the Navier--Stokes equations. These are essentially due to the absence of any of the cancellations afforded by incompressibility, and the lack of conservation of mass. Indeed, standard means of obtaining estimates in $L^2$ fail and we are forced to start with more regular data. Furthermore, we must control the total momentum and carefully check how it impacts on various standard estimates.Comment: 15 pages, to appear in "Recent Progress in the Theory of the Euler and Navier--Stokes Equations", eds. J.C. Robinson, J.L. Rodrigo, W. Sadowski and A. Vidal-L\'opez, Cambridge University Press, 201

Twisted modules for vertex operator algebras and Bernoulli polynomials

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. This is explained through results in the general theory of vertex operator algebras, including a new identity, which we call ``modified weak associativity.'' This paper is an announcement. The detailed proofs will appear elsewhere.Comment: 15 pages, LaTeX, Revised version (to appear in I.M.R.N.