Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

Tracking intracavernously injected adipose-derived stem cells to bone marrow.

The intracavernous (i.c.) injection of stem cells (SCs) has been shown to improve erectile function in various erectile dysfunction (ED) animal models. However, the tissue distribution of the injected cells remains unknown. In this study we tracked i.c.-injected adipose-derived stem cells (ADSCs) in various tissues. Rat paratesticular fat was processed for ADSC isolation and culture. The animals were then subject to cavernous nerve (CN) crush injury or sham operation, followed by i.c. injection of 1 million autologous or allogeneic ADSCs that were labeled with 5-ethynyl-2-deoxyuridine (EdU). Another group of rats received i.c. injection of EdU-labeled allogeneic penile smooth muscle cells (PSMCs). At 2 and 7 days post injection, penises and femoral bone marrow were processed for histological analyses. Whole femoral bone marrows were also analyzed for EdU-positive cells by flow cytometry. The results show that ADSCs exited the penis within days of i.c. injection and migrated preferentially to bone marrow. Allogenicity did not affect the bone marrow appearance of ADSCs at either 2 or 7 days, whereas CN injury reduced the number of ADSCs in bone marrow significantly at 7 but not 2 days. The significance of these results in relation to SC therapy for ED is discussed

Single transverse-spin asymmetry in Drell-Yan lepton angular distribution

We calculate a single transverse-spin asymmetry for the Drell-Yan lepton-pair's angular distribution in perturbative QCD. At leading order in the strong coupling constant, the asymmetry is expressed in terms of a twist-3 quark-gluon correlation function T_F^{(V)}(x_1,x_2). In our calculation, the same result was obtained in both light-cone and covariant gauge in QCD, while keeping explicit electromagnetic current conservation for the virtual photon that decays into the lepton pair. We also present a numerical estimate of the asymmetry and compare the result to an existing other prediction.Comment: 15 pages, Revtex, 5 Postscript figures, uses aps.sty, epsfig.st

The fractional quantum Hall effect in infinite layer systems

Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases host ``one and a half'' dimensional surface phases in which motion in one direction is chiral. We offer a general analysis of conduction in the latter by combining sum rule and renormalization group arguments, and find that when interlayer tunneling is marginal or irrelevant they are chiral semi-metals that conduct only at T > 0 or with disorder.Comment: RevTeX 3.0, 4p., 2 figs with epsf; reference to the detailed companion paper cond-mat/0006506 adde

Virtual photon fragmentation functions

We introduce operator definitions for virtual photon fragmentation functions, which are needed for reliable calculations of Drell-Yan transverse momentum ($Q_T$) distributions when $Q_T$ is much larger than the invariant mass $Q$. We derive the evolution equations for these fragmentation functions. We calculate the leading order evolution kernels for partons to fragment into a unpolarized as well as a polarized virtual photon. We find that fragmentation functions to a longitudinally polarized virtual photon are most important at small $z$, and the fragmentation functions to a transversely polarized virtual photon dominate the large $z$ region. We discuss the implications of this finding to the J/$\psi$ mesons' polarization at large transverse momentum.Comment: Latex, 19 pages including 6 figures. An error in the first version has been corrected, and references update

Improving information filtering via network manipulation

Recommender system is a very promising way to address the problem of overabundant information for online users. Though the information filtering for the online commercial systems received much attention recently, almost all of the previous works are dedicated to design new algorithms and consider the user-item bipartite networks as given and constant information. However, many problems for recommender systems such as the cold-start problem (i.e. low recommendation accuracy for the small degree items) are actually due to the limitation of the underlying user-item bipartite networks. In this letter, we propose a strategy to enhance the performance of the already existing recommendation algorithms by directly manipulating the user-item bipartite networks, namely adding some virtual connections to the networks. Numerical analyses on two benchmark data sets, MovieLens and Netflix, show that our method can remarkably improve the recommendation performance. Specifically, it not only improve the recommendations accuracy (especially for the small degree items), but also help the recommender systems generate more diverse and novel recommendations.Comment: 6 pages, 5 figure

Composition-Diamond lemma for λ\lambda-differential associative algebras with multiple operators

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K$ with multiple operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words

Raman Spectroscopy Characterization of Aqueous Vanadate Species Interaction with Aluminum Alloy 2024-T3 Surfaces

Raman spectroscopy and electrochemical techniques were used to characterize the interactions of aqueous NaVO_3/NaCl and NH_4VO_3/oxalic acid with AA 2024-T3. The interaction of aqueous NaVO_3 with Cu^0 and Cu_2O was characterized. At potential values similar to the OCP of AA 2024-T3 in dilute NaCl, aqueous NaVO_3 formed a polyvanadate film on Cu_2O and formed little or no vanadate film on Cu^0. Treatment of AA 2024-T3 with basic, aqueous NaVO_3/NaCl resulted in a polyvanadate film on copper-rich intermetallic particles and the formation of monovanadates on the matrix. Treatment of AA 2024-T3 with acidic, aqueous NH_4VO_3/oxalic resulted in the formation of monovanadates on the matrix and provided no evidence of vanadate species on copper-rich particles. AA 2024-T3 samples pretreated with either aqueous vanadate salt solution displayed modest cathodic inhibition soon after treatment but inhibition degraded with aging. The formation of polymerized vanadates species on copper-rich particles supports the cathodic inhibition mechanism. The presence of vanadate species on copper-rich particles pretreated with aqueous NaVO_3/NaCl containing predominantly tetrahedral vanadates versus the lack of evidence for similar species on particles treated with aqueous NH_4VO_3/oxalic acid containing predominantly octahedral vanadates supports the importance of tetrahedrally coordinated vanadate species for corrosion inhibition