Burgess bounds for short mixed character sums

This paper proves nontrivial bounds for short mixed character sums by introducing estimates for Vinogradov's mean value theorem into a version of the Burgess method.Comment: 20 page

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.Comment: 63 page

AGRICULTURE AND RURAL DEVELOPMENT: LESSONS FOR CHRISTIAN GROUPS COMBATING PERSISTENT POVERTY

Persistent poverty is one of the core challenges faced by Christians and by development scholars and practitioners alike. There is no question that Jesus was concerned about the poor - both materially and spiritually. From his first public address in the Synagogue in Nazareth, His home town, where He concluded by saying that He had come to "preach good news to the poor" (Luke 4:18), Jesus lived the gospel in word and deed. We, as Christian men and women, whether researchers or practitioners, are called to do no less. When Jesus made His parting remarks to His disciples, He said (John 20:21) "As the Father has sent me, I am sending you." emphasizing that we are to do likewise. This concern permeates the Old and New Testament, another example being the words of the prophet Micah (6:8): "He has showed you, O man, what is good. And what does the LORD require of you? To act justly and to love mercy and to walk humbly with your God." We are here to think through together some of the implications of this mandate for ourselves as researchers and practitioners. More specifically, to consider how the work we do as researchers can inform our work in the field as practitioners in such a way as to more effectively help those who are materially poor.Community/Rural/Urban Development, O1, Q12, Q18,

Constructing transportable behavioural models for nonlinear electronic devices

We use radial basis functions to model the input--output response of an electronic device. A new methodology for producing models that accuratly describe the response of the device over a wide range of operating points is introduced. A key to the success of the method is the ability to find a polynomial relationship between the model parameters and the operating points of the device.Comment: The file is in Revtex, it is 7 pages (two collumn format) with 13 figures in eps forma

Coulomb blockade in a Si channel gated by an Al single-electron transistor

We incorporate an Al-AlO_x-Al single-electron transistor as the gate of a narrow (~100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET). Near the MOSFET channel conductance threshold, we observe oscillations in the conductance associated with Coulomb blockade in the channel, revealing the formation of a Si single-electron transistor. Abrupt steps present in sweeps of the Al transistor conductance versus gate voltage are correlated with single-electron charging events in the Si transistor, and vice versa. Analysis of these correlations using a simple electrostatic model demonstrates that the two single-electron transistor islands are closely aligned, with an inter-island capacitance approximately equal to 1/3 of the total capacitance of the Si transistor island, indicating that the Si transistor is strongly coupled to the Al transistor.Comment: 3 pages, 4 figures, 1 table; typos corrected, minor clarifications added; published in AP