Asymptotic Formulas for Two Continued Fractions in Ramanujan's Lost Notebook

On page 45 of his lost notebook, Ramanujan recorded two asymptoticformulas for two continued fractions involving the Riemann zeta-functionand Dirichlet L-functions. The paper proves a more general theoremand derives Ramanujan's claims as a corollary of the theorem.     

Combined in-situ SAXS/WAXS and HRTEM study on crystallization of (Cu60Co40)1 − xZrx metallic glasses

CuZr as well as CoZr are well known metallic glass-formers in a wide compositional range. Since the binary Cu-Co system exhibits a metastable liquid-liquid miscibility gap, i.e. Cu and Co tend to separate from each other, the ternary Cu-Co-Zr system is a promising candidate to form phase separated glass-glass composites. In this work (Cu₆₀Co₄₀)_1 − xZr_x metallic glasses with relatively low Zr contents of x = 37 and x = 32 were prepared by melt spinning and investigated by in-situ small-angle and wide-angle X-ray scattering (SAXS/WAXS) and differential scanning calorimetry (DSC). Certain heat treated samples were additionally investigated by high-resolution transmission electron microscopy (HRTEM). Even for x = 32 there are no indications for any kind of phase separation in the as-quenched state within experimental resolution, i.e. the critical temperature T_c for a liquid-liquid phase separation has already decreased from 1556 K for binary Cu₆₀Co₄₀ to a temperature below the glass transition temperature T_g = 762(5)K found for (Cu₆₀Co₄₀)₆₈Zr₃₂. Combined in-situ SAXS/WAXS and HRTEM investigations reveal that thermal annealing also does not induce an amorphous-amorphous phase separation. Instead the formation of nano crystallites of a so far unknown Cu-rich/Zr-poor phase with relatively low activation energy for crystallization E_a = 116(7) kJ/mol at temperatures far below the crystallization temperature deduced from DSC measurements is observed.     

Understanding a time reversal process in Lamb wave propagation

This study investigates the time reversal process (TRP) of Lamb wave signals which are transmitted and received by piezoelectric transducers bonded on plate-like structures. A number of previous studies have paid attention to spatial and temporal refocusing capability of an original excitation through the TRP in highly dispersive and complex media. However, when the TRP is applied to Lamb waves in a homogeneous regular waveguide, the refocusing capability is limited due to permanent residual side bands even if the duration of the time reversed signal increases. Based on the reciprocity of elastodynamics and linear piezoelectricity, theoretical interpretation is conducted for the main and residual side bands of the reconstructed signal in the time domain. In particular, the interpretation includes the temporal effect of velocity and amplitude dispersions, the existence of multimodes, and the reflections from boundaries during the TRP. Then, numerical and experimental tests are conducted to validate the theoretical findings of this paper. Practical issues for the successful implementation of the TRP of Lamb waves are briefly addressed as well.     

Effect of apex strake incidence-angle on the vortex development and interaction of a double-delta wing

The vortex flow characteristics of a sharp-edged delta wing with an apex strake was investigated through the visualization and particle image velocimetry (PIV) measurement of the wing-leeward flow region, and the wing-surface pressure measurement. The wing model was a flat-plate, and 65°-sweep cropped-delta wing with sharp leading edges. The apex strake was also a flat-plate wing with a cropped-delta shape of 65°/90° sweep, and it can change its incidence angle. The flow Reynolds number was 2.2 × 10⁵ for the flow visualization and 8.2 × 10⁵ for the PIV and wing-surface pressure measurements. The physics of the vortex flow in the wing-leeward flow region and the suction-pressure distribution on the wing upper-surface were interrelated and analyzed. The effect of a positive (negative) strake incidence-angle was the upward movement of the strake and wing vortices away from (downward movement of the strake and wing vortices toward) the wing-upper surface and the delayed (enhanced) coiling interaction between them. This change of vortex flow characteristics projected directly on the suction pressure distribution on the wing upper-surface.     

Numerical investigation of hydroplaning characteristics of three-dimensional patterned tire

Hydroplaning characteristics of patterned tire on wet road are investigated by making use of finite volume and finite element methods. A detailed 3-D patterned tire model is constructed by our in-house modeling program and the rainwater flow is considered as incompressible and inviscid. Meanwhile, the fluid–structure interaction between the highly complicated tire tread and the rainwater flow is effectively treated by the general coupling method. Through the numerical experiments, the rainwater flow drained through tire grooves, hydrodynamic pressure and contact force are investigated and compared with those of the three-grooved tire model.     

Adaptive Multiuser Detection Based on RBF Networks in Impulsive Noise CDMA Channels

With increasing need for capacity in mobilecellular communications, code division multiple accesshas been viewed as the technique to meet this goal.However, the conventional receiver suffers frommultiuser interference and the near-far effect. Toalleviate this problem, various multiuser receivers havebeen proposed. They have been shown to enhance theperformance of the conventional receiver with respect to capacity and interference rejection. Butthese receivers, intended for Gaussian noise channels,can fail in other environments such as impulsive noiseconditions. A possible solution is to exploit the advantages of neural networks. A neuralnetwork's ability to reject non-Gaussian noise can beutilized to implement multiuser receivers that rejectboth impulsive noise and multiuser interference.Following this logic, this paper considers nonadaptivemultiuser receiver and adaptive multiuser receiver basedon radial basis function neural networks. Simulations ofthese receivers show results that are superior to previously studied multiuser receivers, withrespect to practicality and performance.     

Wavelength dependent performance of a wavelength converter based oncross-gain modulation and birefringence of a semiconductor opticalamplifier

By exploiting pump-induced birefringence in addition to cross-gain modulation, we have obtained improved extinction ratio and reduced optical power penalties for a wavelength converter using a semiconductor optical amplifier. In the probe beam wavelength range of 1528-1566 nm, while extinction ratios and power penalties of a conventional wavelength converter are found to be 4.5-9.2 dB and -0.5-2.1 dB, those of the proposed converter are 6.6-10 dB and -0.7-1.0 dB, respectively. The proposed converter shows better performance for all wavelengths in the range examined for both extinction ratio and power penalty. Especially, more improvements have been obtained in the longer wavelength     

Microhydration effects on the electronic spectra of protonated polycyclic aromatic hydrocarbons: [naphthalene-(H2O)(n = 1,2)]H+

Vibrational and electronic spectra of protonated naphthalene (NaphH(+)) microsolvated by one and two water molecules were obtained by photofragmentation spectroscopy. The IR spectrum of the monohydrated species is consistent with a structure with the proton located on the aromatic molecule, NaphH(+)-H(2)O. Similar to isolated NaphH(+), the first electronic transition of NaphH(+)-H(2)O (S(1)) occurs in the visible range near 500 nm. The doubly hydrated species lacks any absorption in the visible range (420-600 nm) but absorbs in the UV range, similar to neutral Naph. This observation is consistent with a structure, in which the proton is located on the water moiety, Naph-(H(2)O)(2)H(+). Ab initio calculations for [Naph-(H(2)O)(n)]H(+) confirm that the excess proton transfers from Naph to the solvent cluster upon attachment of the second water molecule.     

An Fc variant with two mutations confers prolonged serum half-life and enhanced effector functions on IgG antibodies

The pH-selective interaction between the immunoglobulin G (IgG) fragment crystallizable region (Fc region) and the neonatal Fc receptor (FcRn) is critical for prolonging the circulating half-lives of IgG molecules through intracellular trafficking and recycling. By using directed evolution, we successfully identified Fc mutations that improve the pH-dependent binding of human FcRn and prolong the serum persistence of a model IgG antibody and an Fc-fusion protein. Strikingly, trastuzumab-PFc29 and aflibercept-PFc29, a model therapeutic IgG antibody and an Fc-fusion protein, respectively, when combined with our engineered Fc (Q311R/M428L), both exhibited significantly higher serum half-lives in human FcRn transgenic mice than their counterparts with wild-type Fc. Moreover, in a cynomolgus monkey model, trastuzumab-PFc29 displayed a superior pharmacokinetic profile to that of both trastuzumab-YTE and trastuzumab-LS, which contain the well-validated serum half-life extension Fcs YTE (M252Y/S254T/T256E) and LS (M428L/N434S), respectively. Furthermore, the introduction of two identified mutations of PFc29 (Q311R/M428L) into the model antibodies enhanced both complement-dependent cytotoxicity and antibody-dependent cell-mediated cytotoxicity activity, which are triggered by the association between IgG Fc and Fc binding ligands and are critical for clearing cancer cells. In addition, the effector functions could be turned off by combining the two mutations of PFc29 with effector function-silencing mutations, but the antibodies maintained their excellent pH-dependent human FcRn binding profile. We expect our Fc variants to be an excellent tool for enhancing the pharmacokinetic profiles and potencies of various therapeutic antibodies and Fc-fusion proteins.Subject terms: Antibody therapy, Molecularly targeted therapy, Drug development