Oscillation and nonoscillation of Hill's equation with periodic damping

We prove new results on the oscillation and nonoscillation of the Hill's equation with periodic damping:

y″+p(t)y′+q(t)y=0,t?0,     

Blow-up solutions of nonlinear elliptic equations in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> with critical exponent <Emphasis Type="Italic">Dedicated to Philippe Dufour,whose exquisite horology artwork ‘‘Simplicity’’ inspires so much.</Emphasis>

For an integer n3 and any positive number , we establish the existence of smooth functions K on ⁿ {0} with |K–1|, such that the equation has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some situations K can be extended as a Lipschitz function on ⁿ . These provide counter-examples to a conjecture of C.-S. Lin when n>4, and a question of Taliaferro. Mathematics Subject Classification (2000)Primary 35J60; Secondary 53C21     

Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.     

Sensitivity enhancement of HCACO by using an HMQC magnetization transfer scheme

Previous theoretical calculations have demonstrated that the multiquantum relaxation rate of (1)H(alpha)-(13)C(alpha)(R(MQ)) is, on average, 1.3 +/- 0.4 or 1.7 +/- 0.6 times slower than the single-quantum relaxation rate of (13)C(alpha)(R(C)) for a sample with or without, respectively, amide protons. By taking advantage of this fact and by using the PEP sensitivity enhancement scheme, an HMQC version of the HCACO experiment has been developed. We demonstrate that this new experiment is 23 and 55% more sensitive than the original HSQC version of the HCACO experiment, at constant times of 7 and 27 ms, respectively, for a sample of the BC domain of the ciliary neurotrophic factor receptor protein dissolved in D(2)O at 20 degrees C.     

Vibrational entropy-driven dealloying of Mo(1 0 0) and W(1 0 0) surface alloys

The formation and stability of Cu, Ag and Au-induced c(2 × 2) alloys at the Mo(1 0 0) and W(1 0 0) surfaces have been investigated with low-energy electron microscopy and diffraction. The ordered alloys transform to disordered overlayer structures at elevated temperature. Comparison of the transformation temperatures with energetics obtained from first principles calculations reveals the vibrational entropic contribution to the system free energy that defines alloy thermal stability. Effective Debye temperatures for metal adatoms are determined that exhibit the expected mass and bond strength dependence.     

阿姆斯特朗电解液液桥的实验现象及断裂机理研究

阿姆斯特朗液桥是电流体力学领域中的一种有趣现象,它悬在空中抵抗重力流动的神奇状态引起了人们的广泛关注.近十几年来,去离子水液桥已经通过理论和实验得到深入研究,但是对于电解液液桥的研究依然十分有限.本文以Na2SO4电解液作为形成液桥的实验液体,利用高速摄相机和红外热像仪研究了电解液液桥的形成过程、焦耳效应、流动中的热气泡产生及其破碎导致的液桥断裂等现象,提出了不同于去离子水液桥的断裂机理,有助于进一步加深人们对液桥这一复杂现象的理解.     

用等效网络方法求均匀弹簧纵振动的本征频率

利用机电类比方法导出了均匀质量弹簧在几种特定边界条件下的本征频率方程,并给出了相应的本征频率公式。体现了等效网络理论分析机械振动问题的优越性。     

A dipicolinic acid tag for rigid lanthanide tagging of proteins and paramagnetic NMR spectroscopy

A new lanthanide tag was designed for site-specific labeling of proteins with paramagnetic lanthanide ions. The tag, 4-mercaptomethyl-dipicolinic acid, binds lanthanide ions with nanomolar affinity, is readily attached to proteins via a disulfide bond, and avoids the problems of diastereomer formation associated with most of the conventional lanthanide tags. The high lanthanide affinity of the tag opens the possibility to measure residual dipolar couplings in a single sample containing a mixture of paramagnetic and diamagnetic lanthanides. Using the DNA-binding domain of the E. coli arginine repressor as an example, it is demonstrated that the tag allows immobilization of the lanthanide ion in close proximity of the protein by additional coordination of the lanthanide by a carboxyl group of the protein. The close proximity of the lanthanide ion promotes accurate determinations of magnetic susceptibility anisotropy tensors. In addition, the small size of the tag makes it highly suitable for studies of intermolecular interactions.     

A Potential Alternative to Polystyrene: Ring-opening Terpolymerization of Different Epoxides with Phthalic Anhydride Using Metal-free Dual Catalysts

A series of semi-aromatic polyesters named as Poly(PO-CHO-PA) were facilely synthesized via ring-opening terpolymerization of biobased cyclohexane oxide(CHO)/propylene oxide(PO)/phthalic anhydride(PA) using economical U1/PPNCl as dual catalyst. The proportion of CHO-PA and PO-PA segments in polymer can be readily altered by changing the feed ratio of CHO/PO because the reactivity ratios of CHO and PO with PA calculated by Fineman-Ross method are comparable. All synthesized amorphous polyesters w...     

Anti-Hyperglycemic Effects of Refined Fractions from Cyclocarya paliurus Leaves on Streptozotocin-Induced Diabetic Mice

To identify the chemical components responsible for the anti-hyperglycemic effect of Cyclocarya paliurus (Batal.) Iljinsk (Juglandaceae) leaves, an ethanol extract (CPE) and a water extract (CPW) of C. paliurus leaves, as well as their total flavonoids (CPF), triterpenoids (CPT) and crude polysaccharides (CPP), were prepared and assessed on streptozotocin (STZ)-induced diabetic mice. After being orally administrated once a day for 24 days, CPF (300 mg/kg), CPP (180 mg/kg), or CPF+CPP (300 mg/kg CPF + 180 mg/kg CPP) treatment reversed STZ-induced body weight and muscle mass losses. The glucose tolerance tests and insulin tolerance tests suggested that CPF, CPP, and CPF+CPP showed anti-hyperglycemic effect in STZ-induced diabetic mice. Furthermore, CPF enhances glucose-stimulated insulin secretion in MIN6 cells and insulin-stimulated glucose uptake in C2C12 myotubes. CPF and CPP suppressed inflammatory cytokine levels in STZ-induced diabetic mice. Additionally, CPF and CPP improved STZ-induced diabetic nephropathy assessed by H&E staining, blood urea nitrogen content, and urine creatinine level. The molecular networking and Emperor analysis results indicated that CPF showed potential anti-hyperglycemic effects, and HPLC–MS/MS analysis indicated that CPF contains 3 phenolic acids and 9 flavonoids. In contrast, CPT (650 mg/kg) and CPC (300 mg/kg CPF + 180 mg/kg CPP + 650 mg/kg CPT) did not show anti-hyperglycemic effect. Taken together, polysaccharides and flavonoids are responsible for the anti-hyperglycemic effect of C. paliurus leaves, and the clinical application of C. paliurus need to be refined.