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

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

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

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

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Pontine capillary telangiectasia as visualized on MR imaging causing a clinical picture resembling basilar-type migraine: a case report

A case of presumed pontine capillary telangiectasia in an 18-year-old woman with a clinical diagnosis of basilar-type migraine is reported. Since both are very rare diagnoses, this case provides some evidence to suggest that pontine capillary telangiectasia might cause a clinical picture resembling basilar-type migraine

On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions

We clarify the notion of the DS --- generalized Drinfeld-Sokolov --- reduction approach to classical ${\cal W}$-algebras. We first strengthen an earlier theorem which showed that an $sl(2)$ embedding ${\cal S}\subset {\cal G}$ can be associated to every DS reduction. We then use the fact that a \W-algebra must have a quasi-primary basis to derive severe restrictions on the possible reductions corresponding to a given $sl(2)$ embedding. In the known DS reductions found to date, for which the \W-algebras are denoted by ${\cal W}_{\cal S}^{\cal G}$-algebras and are called canonical, the quasi-primary basis corresponds to the highest weights of the $sl(2)$. Here we find some examples of noncanonical DS reductions leading to \W-algebras which are direct products of ${\cal W}_{\cal S}^{\cal G}$-algebras and `free field' algebras with conformal weights $\Delta \in \{0, {1\over 2}, 1\}$. We also show that if the conformal weights of the generators of a ${\cal W}$-algebra obtained from DS reduction are nonnegative $\Delta \geq 0$ (which isComment: 48 pages, plain TeX, BONN-HE-93-14, DIAS-STP-93-0

Representations of sl(2,?) in category O and master symmetries

We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries

Telomerase reverse transcriptase promoter mutations in bladder cancer: High frequency across stages, detection in urine, and lack of association with outcome

Background Hotspot mutations in the promoter of the gene coding for telomerase reverse transcriptase (TERT) have been described and proposed to activate gene expression. Objectives To investigate TERT mutation frequency, spectrum, association with expression and clinical outcome, and potential for detection of recurrences in urine in patients with urothelial bladder cancer (UBC). D