On the Integrability of the Abel and of the Extended Liénard Equations

Acta Mathematicae Applicatae Sinica, English Series - We present some exact integrability cases of the extended Liénard equation y″ + f(y)(y′)n + k(y)(y′)m + g(y)y′ +...     

On Ivády’s bounds for the gamma function and related results

Periodica Mathematica Hungarica - We prove that the inequality $$\begin{aligned} \Gamma (x+1)\le \frac{x^2+\beta }{x+\beta } \end{aligned}$$ holds for all $$x\in [0,1]$$ , $$\beta \ge {\beta...     

The effects of sensory hearing loss on cochlear filter times estimated from auditory brainstem response latencies.

Derived-band auditory brainstem responses (ABRs) were obtained in 43 normal-hearing and 80 cochlear hearing-impaired individuals using clicks and high-pass noise masking. The response times across the cochlea [the latency difference between wave V's of the 5.7- and 1.4-kHz center frequency (CF) derived bands] were calculated for five levels of click stimulation ranging from 53 to 93 dB p.-p.e. SPL (23 to 63 dB nHL) in 10-dB steps. Cochlear response times appeared to shorten significantly with hearing loss, especially when the average pure tone (1 to 8 kHz) hearing loss exceeded 30 dB. Examination of derived-band latencies indicates that this shortening is due to a dramatic decrease of wave V latency in the lower CF derived band. Estimates of cochlear filter times in terms of the number of periods to maximum response (Nmax) were calculated from derived-band latencies corrected for gender-dependent cochlear transport and neural conduction times. Nmax decreased as a function of hearing loss, especially for the low CF derived bands. The functions were similar for both males and females. These results are consistent with broader cochlear tuning due to peripheral hearing loss. Estimating filter response times from ABR latencies enhances objective noninvasive diagnosis and allows delineation of the differential effects of pathology on the underlying cochlear mechanisms involved in cochlear transport and filter build-up times.     

The energy dependence of nuclear reaction cross sections

The reaction cross section σ_R^pA(E) for proton-nucleus collisions varies with energy as the total cross section σ_t^pN(E) does for proton-nucleon scattering in the energy regime 100 MeV ? E ?400 GeV. We propose several empirical relations, and test them by a χ² analysis of various data. Within the framework of Glauber theory, the parameters in the relations can be linked to the cross section for a single inelastic collision.     

Differential cross-sections for pp → π−π+, K−K+ between 0.8 and 2.4 GeV/c

We present measurements from a spark chamber experiment of the differential cross-sections for $\text{p}$p → π^?π⁺, K^?K⁺ at 20 momenta in the range 0.8–2.4 GeV/c (c.m. energy 2.02 to 2.57 GeV). The c.m. angular range was $\text{?0.95 <}\text{cos}\text{θ}{}^1\text{< 0.95}$. There are about 2000π^?π⁺ events and about 300 K^?K⁺ events at each momentum.     

The A 1Σ+ → X 1Σ+ bands of the isotopic lithium hydrides

In order to obtain a better understanding of the X¹Σ⁺ ground state and the A¹Σ⁺ state potential energy curves of lithium hydride and to examine in detail the concept of “mass-reduced quantum numbers” for both an ordinary (X¹Σ⁺) and an anomalous (A¹Σ⁺) electronic state, the emission spectra of the A¹Σ⁺ → X¹Σ⁺ bands of the isotopic lithium hydrides and deuterides were photographed in the 3000–5000-Å region with a 3.4-m Ebert Spectrograph. The bands found involved v″ = 0 to 7 to various v′ = 0 to 17 for ⁶LiH, and v″ = 0 to 7 to various v′ = 1 to 16 for ⁶LiD. Additional bands involving v″ = 4 and 5 were also found for ⁷LiH. The vibrational-rotational spectroscopic analysis of ⁷LiH, ⁶LiH, and ⁶LiD are reported here, as are the reanalyses of the ⁷LiH and ⁷LiD data reported by Crawford and Jorgensen. New Rydberg-Klein-Rees (RKR) A¹Σ⁺ and X¹Σ⁺ potential curves have been constructed for each individual molecule and are reported, but detailed isotopic comparisons will be reported in subsequent publications.     

Computer graphics-assisted applications of first-order chemical kinetics in the determination of inorganic complexes complexes

Computer graphics-assisted applications of first-order chemical kinetics are applied to absorbance data from spectrophotometric measurements of the decomposition of di-μ-hydroxobis[dioxalatocobaltate(III)] (at pH 4.0) and trioxalatocobaltate(III) (in 1.0 M perchloric acid) in order to estimate the purity of the complexes. A program called KINFIR is used.     

Synthesis of Biomorphic ZrO2-CeO2 Nanostructures by Silkworm Silk Template

以桑蚕丝为模板制备多级生物形态结构ZrO₂-CeO₂. 整个合成过程是由桑蚕丝模板的导向作用决定的. 分析结果表明ZrO₂-CeO₂结晶良好,呈多级网络中空纤维结构,直径为16～28μm,800 oC煅烧后ZrO₂-CeO₂晶粒尺寸约为14 nm.