Is the formal energy of the mid-point rule convergent?

AbstractWe obtain some formulae for calculation of the coefficients of four special types of terms in τ2k, k = 1, 2, … (1−1 corresponding to four type of (2k + 1)-vertex free unlabeled trees, k = 1, 2, …, respectively), for a fixed step size τ, in the tree-expansion of the formal energy of the mid-point rule. And, we give an estimate of the difference between the formal energy H and the standard Hamiltonian H in some domain Ω under the assumptions 1.(i)|H is smooth and bounded in Ω, and2.(ii)|the absolute values of the coefficients of the terms in τ2k are uniformly bounded by ησ2k for some constants η ≥ 1, σ > 0 and for any k ≥ 1

Numerical study on aerodynamic characteristics of high-speed trains with considering thermal-flow coupling effects

In order to conduct in-depth researches on rationality of air conditioning system equipment of a high-speed train as well as its pipeline system design, working conditions of the air conditioning system and distribution of aerodynamic characteristics including pressure, velocity and temperature in high speed trains should be computed carefully at the design stage. Therefore, the finite volume method was used to solve a governing equation of computational fluid dynamics. The aerodynamic characteristics of pipelines of the air conditioning system and the complete high speed train were computed, so the indoor distribution of wind velocity, temperature and gas concentration (carbon oxide, carbon dioxide, nitrogen and so forth) was obtained. The flow field index and the thermal comfort index were used to evaluate the indoor thermal comfort degree. In this way, whether rationality of the air conditioning system design and indoor aerodynamic characteristic could satisfy requirements for design specifications can be analyzed. Results show that: Under winter or summer working conditions, wind velocity was relatively high at the passageway door, where the maximum wind velocity was more than 1 m/s and would make passengers uncomfortable. Air flow velocity outside comfortable regions was more than 0.05 m/s, satisfying UIC553 standards. Velocity distribution was basically the same indoors, where wind velocity was large at positions perpendicular to the air supply hole, and the maximum wind velocity was more than 1 m/s, but wind velocity was uniform in the passenger region, which was basically lower than 0.2 m/s and satisfied UIC553 standards. In summer and winter working conditions, distribution of pressure, velocity and temperature was not uniform, where the maximum temperature gradient was near the air inlet in the compartment. Air components in the compartment satisfied requirements for comfort. The most uncomfortable regions in the compartment were concentrated at the passageway. Air supply holes distributed symmetrically on the train roof caused high air flow intensity, high wind velocity, low temperature and high humidity at the passageway in the compartment, so the thermal comfort was low, and it is feasible to adjust the layout of air supply holes appropriately

Octa­aqua­bis(μ2-1H-pyrazole-3,5-di­carboxyl­ato)tricopper(II) tetra­hydrate

In the trinucler CuII complex mol­ecule of the title compound, [Cu3(C5HN2O4)2(H2O)8]·4H2O, the central CuII atom is located on an inversion centre and is coordinated in a distorted octa­hedral geometry. The equatorial sites are occupied by two N and two O atoms from two pyrazole-3,5-dicarboxyl­ate ligands and the axial positions are occupied by two water mol­ecules. The two other symmetry-related CuII atoms are penta­coordinated and assume a square-pyramidal geometry. In the crystal structure, coordinated and uncoordinated water mol­ecules and carboxyl­ate O atoms are linked by O—H⋯O hydrogen bonds

Protective effect of the daming capsule on impaired baroreflexes in STZ-induced diabetic rats with hyperlipoidemia

<p>Abstract</p> <p>Background</p> <p>The Daming capsule (DMC) is a traditional Chinese medicine used to treat hyperlipoidemia. Both clinic trials and studies on animal models have demonstrated that DMC is beneficial against diabetic symptoms. Impairment of the baroreflex can cause life-threatening arrhythmias and sudden cardiac death in patients with diabetes mellitus (DM). This study was designed to elucidate the effects of DMC on baroreflexes in streptozocin (STZ)-induced diabetic rats with hyperlipoidemia.</p> <p>Methods</p> <p>Wistar rats were randomly divided into three groups: untreated controls, rats pretreated STZ and high lipids (a diabetes model or DM rats), and DM rats treated with DMC. The baroreflex sensitivity was examined during intravenous injection of phenylephrine (PE) or sodium nitroprusside (SNP) and quantified by the change in heart rate over the change in mean arterial blood pressure (ΔHR/ΔMABP). Morphological remodeling of baroreceptors was analyzed by transmission electron microscopy (TEM). The mRNA levels and expression of GluR2 and a GABA_Areceptor subunit were measured by quantitative RT-PCR and Western blotting.</p> <p>Results</p> <p>Compared to untreated DM rats, DMC significantly elevated the ratio of ΔHR/ΔMABP by enhancing the compensatory reduction in HR (-ΔHR) in response to PE-induced hypertension (+ΔMABP) (<it>P </it>< 0.05). In the presence of SNP, DMC increased the ΔMABP (<it>P </it>< 0.05). In addition, DMC markedly shortened the duration of blood pressure changes elicited by PE or SNP in DM rats compared to the untreated DM group (<it>P </it>< 0.05). Electron microscopy revealed disrupted myelin sheaths, swollen ER, and lysed mitochondria in the nucleus ambiguous (NAm) DM rats. These signs of neuropathology were largely prevented by treatment with DMC for 30 days. Treatment with DMC elevated both mRNA and protein level of GluR2 in the NAm of DM rats, but had no effect on GABA_Areceptor expression.</p> <p>Conclusion</p> <p>The Daming capsule partially reversed the parasympathetic baroreflex impairment observed in STZ-induced diabetic rats with hyperlipoidemia. Treatment with DMC also prevented the degeneration of neurons and myelinated axons in the brain stem NAm and reversed the down-regulation of GluR2 mRNA. Rescue of NAm function may contribute to the medicinal properties of DMC in diabetic rats.</p

High Reversibility of Lattice Oxygen Redox in Na-ion and Li-ion Batteries Quantified by Direct Bulk Probes of both Anionic and Cationic Redox Reactions

The reversibility and cyclability of anionic redox in battery electrodes hold the key to its practical employments. Here, through mapping of resonant inelastic X-ray scattering (mRIXS), we have independently quantified the evolving redox states of both cations and anions in Na2/3Mg1/3Mn2/3O2. The bulk-Mn redox emerges from initial discharge and is quantified by inverse-partial fluorescence yield (iPFY) from Mn-L mRIXS. Bulk and surface Mn activities likely lead to the voltage fade. O-K super-partial fluorescence yield (sPFY) analysis of mRIXS shows 79% lattice oxygen-redox reversibility during initial cycle, with 87% capacity sustained after 100 cycles. In Li1.17Ni0.21Co0.08Mn0.54O2, lattice-oxygen redox is 76% initial-cycle reversible but with only 44% capacity retention after 500 cycles. These results unambiguously show the high reversibility of lattice-oxygen redox in both Li-ion and Na-ion systems. The contrast between Na2/3Mg1/3Mn2/3O2 and Li1.17Ni0.21Co0.08Mn0.54O2 systems suggests the importance of distinguishing lattice-oxygen redox from other oxygen activities for clarifying its intrinsic properties.Comment: 33 pages, 8 Figures. Plus 14 pages of Supplementary Materials with 12 Figure

The role of quality of care and attitude towards disability in the relationship between severity of disability and quality of life: findings from a cross-sectional survey among people with physical disability in China

Background: People with physical disability (PWPD) is the largest subgroup of people with disability (PWD) in China, but few studies have been conducted among this vulnerable population. The objective of this study was to investigate the level of quality of life (QoL), self-perceived quality of care and support (QOCS), severity of disability and personal attitude towards disability among people with physical disability in China, as well as to identify how QoL can be affected by severity of disability through QOCS and personal attitude towards disability among PWPD. Methods: A cross-sectional study was conducted among 1,853 PWPD in Guangzhou, China. Data were collected on participants’ QoL, QOCS, personal attitude towards disability and severity of disability. Structural equation modeling was used to examine the effects of the other variables on QoL. Results: Even with a mild disability (mean score:1.72), relatively low levels of QoL (mean score: 2.65- 3.22) and QOCS (mean score: 2.95 to 3.28), as well as unfavorable personal attitude towards disability (mean score: 2.75 to 3.36) were identified among PWPD. According to SEM, we found that the influence of severity of physical disability on QoL is not only exerted directly, but is also indirectly through QOCS and their personal attitudes towards disability, with QOCS playing a more important mediating role than PWPD’s attitudes towards their own disability. Conclusions: Unfavorable health status was identified among PWPD in China. Focusing on improvement of assistance and care services has the potential to substantially improve PWPD’s QoL. Further research should focus on understanding the needs and their current state of health care of PWPD in China thus being able to develop better interventions for them