Fields of definition of finite hypergeometric functions

Finite hypergeometric functions are functions of a finite field ${\bf F}_q$ to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential sums and were introduced independently by John Greene and Nick Katz in the 1980's. They have many properties in common with their analytic counterparts, the hypergeometric functions. One restriction in the definition of finite hypergeometric functions is that the hypergeometric parameters must be rational numbers whose denominators divide $q-1$. In this note we use the symmetry in the hypergeometric parameters and an extension of the exponential sums to circumvent this problem as much as posssible.Comment: 8 page

Interpolated sequences and critical LL-values of modular forms

Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for $\zeta(3)$ in terms of a critical $L$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $L$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $L$-values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor

A split-cavity design for the incorporation of a DC bias in a 3D microwave cavity

We report on a technique for applying a DC bias in a 3D microwave cavity. We achieve this by isolating the two halves of the cavity with a dielectric and directly using them as DC electrodes. As a proof of concept, we embed a variable capacitance diode in the cavity and tune the resonant frequency with a DC voltage, demonstrating the incorporation of a DC bias into the 3D cavity with no measurable change in its quality factor at room temperature. We also characterize the architecture at millikelvin temperatures and show that the split cavity design maintains a quality factor $Q_\text{i} \sim 8.8 \times 10^5$, making it promising for future quantum applications

Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

Log Fano varieties over function fields of curves

Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite set of points on the base curve.Comment: 18 page

Deep Brain Stimulation of the Pallidum is Effective and Might Stabilize Striatal D2 Receptor Binding in Myoclonus–Dystonia

Purpose: To assess clinical efficacy of deep brain stimulation (DBS) of the pallidum in Myoclonus–Dystonia (M–D) patients, and to compare pre- and post-operative striatal dopamine D2 receptor availability. Methods: Clinical parameters were scored using validated rating scales for myoclonus and dystonia. Dopamine D2 receptor binding of three patients was studied before surgery and approximately 2 years post-operatively using 123-I-iodobenzamide Single Photon Emission Computed Tomography. Two patients who did not undergo surgery served as controls. Results: Clinically, the three M–D patients improved 83, 17, and 100%, respectively on the myoclonus rating scale and 78, 23, and 65% on the dystonia rating scale after DBS. Dopamine D2 receptor binding did not change after surgery. In the two control subjects, binding has lowered further. Conclusion: These findings confirm that DBS of the pallidum has beneficial effects on motor symptoms in M–D and suggest this procedure might stabilize dopamine D2 receptor binding

Study on Solar KANG Heating System for Cold Areas

AbstractThe current rural traditional heated kang cannot meet people's increasing requirements of comfort and environmental protection. This paper propose solar kang heating system in cold regions. System performance and heating effect were analyzed. We selected two typical rooms. One was set in traditional kang, and the other one was solar Kang type. Using temperature recording instrument and 64 roads inspection instrument and other instruments, we test the indoor temperature and the kang surface temperature of two rooms. Solar kang thermal resistance, heat storage, heat dissipation and heating effect were analyzed and compared. The results of the study show this system have the smaller fluctuation, more comfort while alleviating the kang surface overheat or super-cooling problem. It satisfied the requirements of indoor thermal comfort. The warming rate is 5.17°C/h, and the cooling rate is 3.01°C/h. These are slower than traditional Huokang speed. It improved the heat storage capacity of kang body with surface heat dissipation 1237W. Average temperature of the solar kang heating room was improved 3.28°C. It gets the smaller indoor temperature fluctuation. PMV values are concentrated about -0.5, and this basically meet the requirements of the user comfort

MEN-2 Syndrome: The Value of Screening and Central Registration; A Study of Six Kindreds in The Netherlands

Since 1975, six families with the MEN-2A syndrome including 66 patients have been identified in The Netherlands. All these patients underwent thyroidectomy for C-cell hyperplasia and/or medullary thyroid carcinoma (MTC); eight were symptomatic (Group A), 51 were relatives of patients found to be affected (Group B), and seven had had a negative screening test that became positive (Group C). To assess the effect of screening, we compared these groups with respect to the occurrence of metastatic MTC at thyroidectomy and the results of the postoperative calcitonin (CT) tests. We found that 87% of Group A, 37% of Group B; and none of Group C had metastatic disease at surgery. The cure rates in these three groups with MEN-2A, as determined by stimulated CT measurement, was 0%, 51%, and 100%, respectively. From these results it may be concluded that screening can lead to the detection of MTC at an earlier stage which in turn could permit curative treatment and improvement of both prognosis and life expectancy. The need for supervision of affected families by central registration to guarantee the continuity of screening is stressed

Gauge Theory Wilson Loops and Conformal Toda Field Theory

The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.Comment: 17 pages, 3 figures; references added