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The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V (r) = �1r 8 + �2r 3 + �3r 2 + �3r 1 + �2r 3 + �1r 4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schrodinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r ! 1 and r ! 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions ofthe stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schrodinger equation; and lastly, they discuss the solutions and make conclusions.

The fate of neural stem cells (NSCs), including their proliferation, differentiation, survival, and death, is regulated by multiple intrinsic signals and the extrinsic environment. We had previously reported that 5-aminoimidazole-4-carboxamide-1-beta-D-ribofuranoside (AICAR) directly induces astroglial differentiation of NSCs by activation of the Janus kinase (JAK)/Signal transducer and activator of transcription 3 (STAT3) pathway independently of AMP-activated protein kinase (AMPK). Here, we reported the observation that AICAR inhibited NSC proliferation and its underlying mechanism. Analysis of caspase activity and cell cycle showed that AICAR induced G1/G0 cell cycle arrest in NSCs, associated with decreased levels of poly(ADP-ribose) polymerase, phospho-retinoblastoma protein (Rb), and cyclin D but did not cause apoptosis. Iodotubericidin and Compound C, inhibitors of adenosine kinase and AMPK, respectively, or overexpression of a dominant-negative mutant of AMPK, but not JAK inhibitor, were able to reverse the anti-proliferative effect of AICAR. Glucose deprivation also activated the AMPK pathway, induced G0/G1 arrest, and suppressed the proliferation of NSCs, an effect associated with decreased levels of phospho-Rb and cyclin D protein. Furthermore, Compound C and overexpression of dominant-negative AMPK in C17.2 NSCs could block the glucose deprivation-mediated down-regulation of cyclin D and partially reverse the suppression of proliferation. These results suggest that AICAR and glucose deprivation might induce G1/G0 cell cycle arrest and suppress proliferation of NSCs via phospho-Rb and cyclin D down-regulation. AMPK, but not JAK/STAT3, activation is key for this inhibitory effect and may play an important role in the responses of NSCs to metabolic stresses such as glucose deprivation.

We present a new detecting scheme of high-frequency gravitational waves (HFGWs) in the GHz band, the scheme consists of a high-quality-fact or open microwave cavity, a static magnetic field passing through the cavity and an electromagnetic (EM) normal mode stored in the cavity It is found that under the resonant condition first-and second-order perturbation EM effects have almost the same detecting sensitivity to the HFGWs in the GHz band (h ~ 10−26, ν ~ 5 GHz), but the former contains more information from the HFGWs. We also provide a very brief review for possible improving way of the sensitivity This scheme would be highly complementary to other schemes of detecting the HFGWs.

We present a class of new exact solutions in string cosmology theory, and the solutions describe a homogeneous but anisotropic plane-symmetric string universe within the framework of Bianchi type-I cosmology. Some solutions previously discussed are included in the class of exact solutions as the special cases. Our result may provide further quantitative description and theoretical basis for the string cosmology model.

The purpose of our study was to assess the alteration of the brainstem raphe (BR) on transcranial sonography (TCS) in depression patients with or without Parkinson's disease (PD) and to explore whether the different changes of BR could reflect an increasing impairment of raphe structures. TCS was performed in patients with PD, depression with PD, depression only, and controls. Using the red nucleus as an internal standard, the BR was rated semi-quantitatively from grades 1-4 with grades 1-3 determined as abnormal. The rate of abnormal BR (≤grade 3) was found to be only 10 % in patients with PD (4/40) and 5 % in control patients (2/40). The rate of abnormal raphe was significantly higher (p < 0.05) in patients with both depression and PD (85 %, 34/40) or patients with depression only (87.5 %, 35/40). TCS of the raphe in most patients with mild depression scored grade 3, while those with moderate depression scored grade 2-3, and those with severe depression scored grade 1. The different BR echogenicity score reflected an increasing impairment of raphe structures in depression patients with or without PD (p < 0.05). TCS provides a good tool for assessing depression, more severe depressive symptoms were associated with different aspects in TCS studies.

The epoxide opening with BF3·OEt2 followed by cleavage of the aldehyde group of the resulting β-ketoaldehyde furnishes deoxybenzoins which give the title furans after HBr-promoted ring closure.

Preclinical and clinical studies demonstrated that the inhibition of cholinergic supersensitivity through nicotinic antagonists and partial agonists can be used successfully to treat depressed patients, especially those who are poor responders to selective serotonin reuptake inhibitors (SSRIs). In our effort to develop novel antidepressant drugs, LF-3-88 was identified as a potent nicotinic acetylcholine receptor (nAChR) partial agonist with subnanomolar to nanomolar affinities for β2-containing nAChRs (α2β2, α3β2, α4β2, and α4β2*) and superior selectivity away from α3β4 - (K i > 10(4) nmol/L) and α7-nAChRs (K i > 10(4) nmol/L) as well as 51 other central nervous system (CNS)-related neurotransmitter receptors and transporters. Functional activities at different nAChR subtypes were characterized utilizing (86)Rb(+) ion efflux assays, two-electrode voltage-clamp (TEVC) recording in oocytes, and whole-cell current recording measurements. In mouse models, administration of LF-3-88 resulted in antidepressive-like behavioral signatures 15 min post injection in the SmartCube® test (5 and 10 mg/kg, i.p.; about 45-min session), decreased immobility in the forced swim test (1-3 mg/kg, i.p.; 1-10 mg/kg, p.o.; 30 min pretreatment, 6-min trial), and decreased latency to approach food in the novelty-suppressed feeding test after 29 days chronic administration once daily (5 mg/kg but not 10 mg/kg, p.o.; 15-min trial). In addition, LF-3-88 exhibited a favorable profile in pharmacokinetic/ADME-Tox (absorption, distribution, metabolism, excretion, and toxicity) assays. This compound was also shown to cause no mortality in wild-type Balb/CJ mice when tested at 300 mg/kg. These results further support the potential of potent and selective nicotinic partial agonists for use in the treatment of depression.

We consider the resonant response of a Gaussian beam passing through a static magnetic field to a high-frequency relic gravitational wave (GW). It is found that under the synchroresonance condition, the first-order perturbative electromagnetic energy fluxes will contain a ``left circular wave'' and a ``right circular wave'' around the symmetrical axis of the Gaussian beam, but the perturbative effects produced by the + and × polarization of the GW have a different physical behaviour. For the high-frequency relic GW with νg = 1010 Hz, h = 10-30, recently expected by the quintessential inflationary models, the corresponding perturbative photon flux passing through the region 10-2 m2 would be expected to be 104 s-1. This is the largest perturbative photon flux we have recently analysed and estimated using the typical laboratory parameters.

By using the general expressions of energy-momentum pseudo-tensor of the cylindrical gravitational waves (GW) given by Rosen and Virbhadra in Cartesian coordinates, the concrete forms of energy density and radiative energy flux of the pulse cylindrical GW are obtained. Their physical properties, suitable range and asymptotic behaviour are considered. It is found that: For the region in which space radial coordinates to origin are greater than the pulse width of the pulse cylindrical GW, the energy density and radiative energy flux of the outward travelling pulse cylindrical GW propagating along a light-cone are positive definite. However, for the region in which the space radial coordinates are less than the pulse width, there is no guarantee for the positive definite property of the radiative energy flux of the outward travelling wave. Moreover, we show that the asymptotic behaviour of the energy and energy flux densities of the pulse cylindrical GW and that of the Riemann curvature tensor have good self-consistancy in space-like, time-like and null infinity regions.

Starting with the Einstein equation of weak gravitational field, a new scheme of generating high frequency gravitational wave by composite toroidal electromagnetic resonant system is discussed. The system is a composite toroidal electromagnetic resonant cavity consisting of a vacuum and a dielectric regions. In the focal region of the cavity under the condition of allowable ohmic losses in the cavity walls, the amplitude of the standing gravitational wave is almost two orders of magnitude higher than that in usual cavity with the same volume. A concrete numerical calculation shows that a composite toroidal electromagnetic resonant system with a volume 2 × 108 cm3 could generate the standing gravitational wave with an amplitude h = 10-33, wavelength λg = 40 cm in its focal region. This is comparable to the typical order of magnitude of several astrophysical sources, and it would be displayed by electromagnetic detection due to very high frequency.

Preclinical and clinical studies demonstrated that the inhibition of cholinergic supersensitivity through nicotinic antagonists and partial agonists can be used successfully to treat depressed patients, especially those who are poor responders to selective serotonin reuptake inhibitors (SSRIs). In our effort to develop novel antidepressant drugs, LF-3-88 was identified as a potent nicotinic acetylcholine receptor (nAChR) partial agonist with subnanomolar to nanomolar affinities for β2-containing nAChRs (α2β2, α3β2, α4β2, and α4β2*) and superior selectivity away from α3β4 - (K i10(4) nmol/L) and α7-nAChRs (K i10(4) nmol/L) as well as 51 other central nervous system (CNS)-related neurotransmitter receptors and transporters. Functional activities at different nAChR subtypes were characterized utilizing (86)Rb(+) ion efflux assays, two-electrode voltage-clamp (TEVC) recording in oocytes, and whole-cell current recording measurements. In mouse models, administration of LF-3-88 resulted in antidepressive-like behavioral signatures 15 min post injection in the SmartCube® test (5 and 10 mg/kg, i.p.; about 45-min session), decreased immobility in the forced swim test (1-3 mg/kg, i.p.; 1-10 mg/kg, p.o.; 30 min pretreatment, 6-min trial), and decreased latency to approach food in the novelty-suppressed feeding test after 29 days chronic administration once daily (5 mg/kg but not 10 mg/kg, p.o.; 15-min trial). In addition, LF-3-88 exhibited a favorable profile in pharmacokinetic/ADME-Tox (absorption, distribution, metabolism, excretion, and toxicity) assays. This compound was also shown to cause no mortality in wild-type Balb/CJ mice when tested at 300 mg/kg. These results further support the potential of potent and selective nicotinic partial agonists for use in the treatment of depression.

In our continued efforts to develop α4β2-nicotinic acetylcholine receptor (nAChR) partial agonists as novel antidepressants having a unique mechanism of action, structure-activity relationship (SAR) exploration of certain isoxazolylpyridine ethers is presented. In particular, modifications to both the azetidine ring present in the starting structure 4 and its metabolically liable hydroxyl side chain substituent have been explored to improve compound druggability. The pharmacological characterization of all new compounds has been carried out using [(3)H]epibatidine binding studies together with functional assays based on (86)Rb(+) ion flux measurements. We found that the deletion of the metabolically liable hydroxyl group or its replacement by a fluoromethyl group not only maintained potency and selectivity but also resulted in compounds showing antidepressant-like properties in the mouse forced swim test. These isoxazolylpyridine ethers appear to represent promising lead candidates in the design of innovative chemical tools containing reporter groups for imaging purposes and of possible therapeutics.

Despite their discovery in the early 20th century and intensive study over the last twenty years, nicotinic acetylcholine receptors (nAChRs) are still far from being well understood. Only a few chemical entities targeting nAChRs are currently undergoing clinical trials, and even fewer have reached the marketplace. In our efforts to discover novel and truly selective nAChR ligands, we designed and synthesized a series of chiral cyclopropane-containing α4β2-specific ligands that display low nanomolar binding affinities and excellent subtype selectivity, while acting as partial agonists at α4β2-nAChRs. Their favorable antidepressant-like properties were demonstrated in the classical mouse forced swim test. Preliminary ADMET studies and broad screening towards other common neurotransmitter receptors were also carried out to further evaluate their safety profile and eliminate their potential off-target activity. These highly potent cyclopropane ligands possess superior subtype selectivity compared to other α4β2-nAChR agonists reported to date, including the marketed drug varenicline, and therefore may fully satisfy the crucial prerequisite for avoiding adverse side effects. These novel chemical entities could potentially be advanced to the clinic as new drug candidates for treating depression.

The first total synthesis of lathyranoic acid A (1) was accomplished stereoselectively in a linear sequence of 20 steps and an overall yield of 1.4%. This modular synthesis featured a cyclic, stereocontrolled Cu-catalyzed intramolecular cyclopropanation to construct the cis-cyclopropane unit, a Grubbs metathesis to construct the γ-substituted cyclopentenone moiety, and an anion-mediated conjugate addition.

The community of nitrifiers cultivated with reject water were investigated by fluorescent in situ hybridization (FISH) performed with 16S rRNA-targeted oligonucleotide probes, and the kinetic properties such as temperature correction factor tauN and the half saturation coefficient K(N) were also investigated. The results showed that the percentage of ammonia oxidizing bacteria (AOB) and nitrite oxidizing bacteria (NOB) in the activated sludge was 15.7% +/- 3.7% and 12.9% +/- 3.2%, Nitrosomonas europaea-Nitrosococcus mobilis lineage were the dominant AOB, Nitrobacter spp. were the dominant NOB. The temperature correction factors of ammonium utilized rate (AUR) and nitrite utilized rate (NUR) were 1.092 and 1.061 respectively; the K(N) of AOB and NOB were (1.60 +/- 0.29) mg/L (NH4(+) -N), (2.78 +/- 0.30) mg/L (NO2(-) -N) respectively.

AMPK is a potential target of metabolic diseases including obesity and type 2 diabetes. The activation of AMPK can lead to an increase of glucose uptake into muscle, decreased gluconeogenesis in liver, increased fatty acid oxidation in muscle and liver, decreased fatty acid synthesis in liver and adipose tissue, and increase mitochondrial biogenesis. Until now, many efforts from industrial and academia have been focused on searching novel agents that activate AMPK directly or indirectly. This review will discuss recent advances in the search for novel therapeutic agents that mediate their activity via AMPK activation.

Sequencing batch reactor, treating simulated municipal wastewater for N removal and operated at near the minimum SRT (solids retention time) for nitrification (in reactor 2), was seeded daily with nitrifying biomass accumulated with reject water (in reactor 1) came from Xi' an Dengjiacun wastewater treatment plant. Comparison of the nitrification ability, the characteristics of the activated sludge before seeding and after seeding was made. The experiment result shows that, the maximum nitrification rate of the activated sludge in the reactor 1 reached 81.4 mg/(L x h). The effluent concentration of NH4+ -N of the reactor 2 decreased at a rate of 0.992 mg/(L x d) (R2 = 0.903), and the maximum nitrification rate increased 1.36 times. Once seeding was terminated, the effluent concentration of NH4+ -N increased at a rate of 1.956 mg/(L x d) (R2 = 0.999), and nitrification caused by seeding was not completely disappeared after seeding was stopped for 34 d. The amount and varieties of protozoa and the value of SVI in the reactor seeded with nitrifiers increased during the initial time of seeding, but were recovered when the reactor 2 reached stable state.

AMP-activated protein kinase (AMPK) serves as an energy sensor and is considered a promising drug target for treatment of type II diabetes and obesity. A previous report has shown that mammalian AMPK alpha1 catalytic subunit including autoinhibitory domain was inactive. To test the hypothesis that small molecules can activate AMPK through antagonizing the autoinhibition in alpha subunits, we screened a chemical library with inactive human alpha1(394) (alpha1, residues 1-394) and found a novel small-molecule activator, PT1, which dose-dependently activated AMPK alpha1(394), alpha1(335), alpha2(398), and even heterotrimer alpha1beta1gamma1. Based on PT1-docked AMPK alpha1 subunit structure model and different mutations, we found PT1 might interact with Glu-96 and Lys-156 residues near the autoinhibitory domain and directly relieve autoinhibition. Further studies using L6 myotubes showed that the phosphorylation of AMPK and its downstream substrate, acetyl-CoA carboxylase, were dose-dependently and time-dependently increased by PT1 with-out an increase in cellular AMP:ATP ratio. Moreover, in HeLa cells deficient in LKB1, PT1 enhanced AMPK phosphorylation, which can be inhibited by the calcium/calmodulin-dependent protein kinase kinases inhibitor STO-609 and AMPK inhibitor compound C. PT1 also lowered hepatic lipid content in a dose-dependent manner through AMPK activation in HepG2 cells, and this effect was diminished by compound C. Taken together, these data indicate that this small-molecule activator may directly activate AMPK via antagonizing the autoinhibition in vitro and in cells. This compound highlights the effort to discover novel AMPK activators and can be a useful tool for elucidating the mechanism responsible for conformational change and autoinhibitory regulation of AMPK.

Neural stem cell differentiation and the determination of lineage decision between neuronal and glial fates have important implications in the study of developmental, pathological, and regenerative processes. Although small molecule chemicals with the ability to control neural stem cell fate are considered extremely useful tools in this field, few were reported. AICAR is an adenosine analog and extensively used to activate AMP-activated protein kinase (AMPK), a metabolic "fuel gauge" of the biological system. In the present study, we found an unrecognized astrogliogenic activity of AICAR on not only immortalized neural stem cell line C17.2 (C17.2-NSC), but also primary neural stem cells (NSCs) derived from post-natal (P0) rat hippocampus (P0-NSC) and embryonic day 14 (E14) rat embryonic cortex (E14-NSC). However, another AMPK activator, Metformin, did not alter either the C17.2-NSC or E14-NSC undifferentiated state although both Metformin and AICAR can activate the AMPK pathway in NSC. Furthermore, overexpression of dominant-negative mutants of AMPK in C17.2-NSC was unable to block the gliogenic effects of AICAR. We also found AICAR could activate the Janus kinase (JAK) STAT3 pathway in both C17.2-NSC and E14-NSC but Metformin fails. JAK inhibitor I abolished the gliogenic effects of AICAR. Taken together, these results suggest that the astroglial differentiation effect of AICAR on neural stem cells was acting independently of AMPK and that the JAK-STAT3 pathway is essential for the gliogenic effect of AICAR.

To investigate the apoptosis in vascular smooth muscle cell (VSMC) induced by oxidated low-density lipoprotein cholesterol (ox-LDL), and to discuss the relative mechanism of the apoptosis of VSMC.The growth index of VSMC of Wistar rat was determined. By using trypan blue to count sustaining cells, the proliferative effect of ox-LDL on culturing VSMC was observed. With flow cytometer, the apoptosis of VSMC induced by ox-LDL and the inhibitory effect of cyclooxygenase-2 (COX-2) inhibitor NS-398 on apoptosis were determined.After VSMC grew normally in culture, ox-LDL in concentrations of 35 mg/L and 50 mg/L could advance the growth period of VSMC to between 12 and 24 hours, and the proliferation of VSMC were obvious. The proliferation of VSMC induced by ox-LDL were inhibited by NS-398. The rate of apoptosis of VSMC in ox-LDL and NS-398 groups were higher than that of normal control.ox-LDL could induce an obvious proliferation of VSMC in culture. Although NS-398 can decrease the proliferation of VSMC, it could enhance ox-LDL to induce apoptosis.

Various cosmology models, brane oscillation scenarios, interaction of interstellar plasma with intense electromagnetic radiation, and even high-energy physics experiments (e.g., Large Hadron Collider (LHC)) all predict high frequency gravitational waves (HFGWs, i.e., high-energy gravitons) in the microwave band and higher frequency region, and some of them have large energy densities. Electromagnetic (EM) detection to such HFGWs would be suitable due to very high frequencies and large energy densities of the HFGWs. We review several typical EM detection schemes, i.e., inverse Gertsenshtein effect (G-effect), coupling of the inverse G effect with a coherent EM wave, coupling of planar superconducting open cavity with a static magnetic field, cylindrical superconducting closed cavity, and the EM sychro-resonance system, and discuss related minimal detectable amplitudes and sensitivities. Furthermore, we give some new ideas and improvement ways enhancing the possibility of measuring the HFGWs. It is shown that there is still a large room for improvement for those schemes to approach and even reach up the requirement of detection of HFGWs expected by the cosmological models and high-energy astrophysical process.

According to the Einstein-Tolman expression of the energy-momentum pseudo-tensor (EMPT), we calculate the EMPT of cylindrical gravitational waves (CGW) of both the polarized states (BPS) in cylindrical polar coordinates and Cartesian coordinates. We find that Cartesian coordinates are the more suitable coordinates to describe the CGW of BPS.

The displaying condition of strength, phase and polarization states of high-frequency relic gravitational waves (HFRGWs) in electromagnetic (EM) detecting systems is studied. It is shown that the displaying condition depends not only on the sensitivity of EM detecting systems and the amplitudes of HFRGWs, but also on the phase, the polarization states of HFRGWs and their matching to the EM detecting systems. In order to display simultaneously the strength, phase and polarization states of the resonant "monochromatic component" of HFRGWs, an important necessary condition is the utilization of two or more different EM detectors.

We calculate the unpolarized differential cross section in magnetic dipole field, electric dipole field and uniform electrostatic and magnetostatic fields, respectively,by the Feynman perturbation technique. It is found that in electric dipole field, the differential cross section vanishes in both the same and the opposite propagating directions of the photon flux. In the magnetic dipole field the differential cross section generally has non-vanishing values in both directions,but when the propagating direction of photon flux is parallel to the magnetic dipole vector, the differential cross section is equal to zero. In the uniform electrostatic and magnetostatic fields, non-vanishing differential cross sections occur in the same and opposite propagating directions of the photon flux, but in the latter case it is weaker than in the former. When the mass of axion approaches to zero,the above process shows similar characters as the conversion of the photons to the gravitons.

Gaussian beam resonance system (GBRS) opens a very important window for detection of relic stochastic high frequency gravitational waves (HFGWs) of early universe. The results of calculation show that the first-order perturbation photon flux produced by this system has no observable effect when the GWs frequency is different from that of Gaussian beam. The first-order perturbation photon flux produced by GBRS will be reduced by several orders of magnitude when the propagation direction of GWs is different from that the positive direction of the symmetrical axis of Gaussian beam, i. e., GBRS only responds to relic HFGWs that propagate along a specific direction. Therefore, GBRS have a useful selective effect with respect to the frequency and propagation direction of relic HFGWs.

First-order and second-order perturbations to the energy of Gaussian beam by a doubly polarized weak gravitational plane wave in static magnetic fields are discussed.The results of numerical estimation show that the perturbation to Gaussian beams by weak gravitational plane waves is very small,i.e.the total energy of the background fields would not change obviously in the influence of gravitational waves,but the perturbative power flux produced in the local region may be observable.