Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues

We study the degenerate semilinear elliptic systems of the form -div(h1(x)∇u)=λ(a(x)u+b(x)v)+Fu(x,u,v),x∈Ω,-div(h2(x)∇v)=λ(d(x)v+b(x)u)+Fv(x,u,v),x∈Ω,u|∂Ω=v|∂Ω=0, where Ω⊂RN(N≥2) is an open bounded domain with smooth boundary ∂Ω, the measurable, nonnegative diffusion coefficients h1, h2 are allowed to vanish in Ω (as well as at the boundary ∂Ω) and/or to blow up in Ω¯. Some multiplicity results of solutions are obtained for the degenerate elliptic systems which are near resonance at higher eigenvalues by the classical saddle point theorem and a local saddle point theorem in critical point theory

The Neumann Problem for a Degenerate Elliptic System Near Resonance

This paper studies the following system of degenerate equations -divpx∇u+qxu=αu+βv+g1x,v+h1x, x∈Ω, -div(p(x)∇v)+q(x)v=βu+αv+g2(x,u)+h2(x), x∈Ω, ∂u/∂ν=∂v/∂ν=0, x∈∂Ω. Here Ω⊂Rn is a bounded C2 domain, and ν is the exterior normal vector on ∂Ω. The coefficient function p may vanish in Ω¯, q∈Lr(Ω) with r>ns/(2s-n),  s>n/2. We show that the eigenvalues of the operator -div(p(x)∇u)+q(x)u are discrete. Secondly, when the linear part is near resonance, we prove the existence of at least two different solutions for the above degenerate system, under suitable conditions on h1,h2,g1, and g2

New multiple positive solutions for elliptic equations with singularity and critical growth

In this note, the existence of multiple positive solutions is established for a semilinear elliptic equation −∆u = λ u γ + u 2 ∗−1 , x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω is a smooth bounded domain in RN (N ≥ 3), 2∗ = 2N N−2 , γ ∈ (0, 1) and λ > 0 is a real parameter. We show by the variational methods and perturbation functional that the problem has at least two positive solutions w0(x) and w1(x) with w0(x) < w1(x) in Ω

N′-(4-Hydr­oxy-3-methoxy­benzyl­idene)-4-methoxy­benzohydrazide monohydrate

In the title compound, C16H16N2O4·H2O, the dihedral angle between the two aromatic rings is 19.6 (2)°. In the crystal structure, mol­ecules are linked into a three-dimensional network by inter­molecular N—H⋯O, O—H⋯N and O—H⋯O hydrogen bonds

N′-(5-Bromo-2-hydr­oxy-3-methoxy­benzyl­idene)-4-hydr­oxy-3-methoxy­benzohydrazide dihydrate

In the title compound, C16H15BrN2O5·2H2O, the dihedral angle between the two aromatic rings is 2.9 (2)° and an intra­molecular O—H⋯N hydrogen bond is observed. One of the water mol­ecule is disordered over two positions, with occupancies of 0.83 (3) and 0.17 (3). In the crystal structure, mol­ecules are linked into a three-dimensional network by inter­molecular O—H⋯O, O—H⋯(O,O), O—H⋯N and N—H⋯O hydrogen bonds. π–π inter­actions involving Br-substituted benzene rings, with a centroid–centroid distance of 3.552 (3) Å are also observed

Sodium-Related Adaptations to Drought: New Insights From the Xerophyte Plant Zygophyllum xanthoxylum

Understanding the unusual physiological mechanisms that enable drought tolerance in xerophytes will be of considerable benefit because of the potential to identify novel and key genetic elements for future crop improvements. These plants are interesting because they are well-adapted for life in arid zones; Zygophyllum xanthoxylum, for example, is a typical xerophytic shrub that inhabits central Asian deserts, accumulating substantial levels of sodium (Na+) in its succulent leaves while growing in soils that contain very low levels of this ion. The physiological importance of this unusual trait to drought adaptations remains poorly understood, however. Thus, 2-week-old Z. xanthoxylum plants were treated with 50 mM NaCl (Na) for 7 days in this study in order to investigate their drought tolerance, leaf osmotic potential (Ψs) related parameters, anatomical characteristics, and transpiration traits. The results demonstrated that NaCl treatment significantly enhanced both the survivability and durability of Z. xanthoxylum plants under extreme drought conditions. The bulk of the Na+ ions encapsulated in plants was overwhelmingly allocated to leaves rather than roots or stems under drought conditions; thus, compared to the control, significantly more Na+ compared to other solutes such as K+, Ca2+, Cl-, sugars, and proline accumulated in the leaves of NaCl-treated plants and led to a marked decrease (31%) in leaf Ψs. In addition, the accumulation of Na+ ions also resulted in mesophyll cell enlargement and leaf succulence, enabling the additional storage of water; Na+ ions also reduced the rate of water loss by decreasing stomatal density and down-regulating stomatal aperture size. The results of this study demonstrate that Z. xanthoxylum has evolved a notable ability to utilize Na+ ions to lower Ψs, swell its leaves, and decrease stomatal aperture sizes, in order to enable the additional uptake and storage of water and mitigate losses. These distinctive drought adaption characteristics mean that the xerophytic plant Z. xanthoxylum presents a fascinating case study for the potential identification of important and novel genetic elements that could improve crops. This report provides insights on the eco-physiological role of sodium accumulation in xerophytes adapted to extremely arid habitats

A simulation study on the measurement of D0-D0bar mixing parameter y at BES-III

We established a method on measuring the \dzdzb mixing parameter $y$ for BESIII experiment at the BEPCII $e^+e^-$ collider. In this method, the doubly tagged $\psi(3770) \to D^0 \overline{D^0}$ events, with one $D$ decays to CP-eigenstates and the other $D$ decays semileptonically, are used to reconstruct the signals. Since this analysis requires good $e/\pi$ separation, a likelihood approach, which combines the $dE/dx$, time of flight and the electromagnetic shower detectors information, is used for particle identification. We estimate the sensitivity of the measurement of $y$ to be 0.007 based on a $20fb^{-1}$ fully simulated MC sample.Comment: 6 pages, 7 figure

Oncoprotein HCCR-1 expression in breast cancer is well correlated with known breast cancer prognostic factors including the HER2 overexpression, p53 mutation, and ER/PR status

<p>Abstract</p> <p>Background</p> <p>Oncoprotein HCCR-1 functions as a negative regulator of the p53 and contributes breast tumorigenesis. The serum HCCR-1 assay is useful in diagnosing breast cancer and mice transgenic for HCCR developed breast cancers. But it is unknown how <it>HCCR-1 </it>contributes to human breast tumorigenesis.</p> <p>Methods</p> <p>Oncogene HCCR-1 expression levels were determined in normal breast tissues, breast cancer tissues and cancer cell lines. We examined whether HCCR-1 protein expression in breast cancer is related to different biological characteristics, including ER, PR, p53 genotype, and HER2 status in 104 primary breast cancer tissues using immunohistochemical analyses.</p> <p>Results</p> <p>HCCR-1 was upregulated in breast cancer cells and tissues compared with normal breast tissues. In this study, overexpression of HCCR-1 was well correlated with known breast cancer prognostic markers including the presence of steroid receptors (ER and PR), p53 mutation and high HER2 overexpression. HCCR-1 was not detected in the ER-negative, PR-negative, p53 negative and low HER2 breast cancer tissues. These data indicate that the level of HCCR-1 in breast cancer tissues is relatively well correlated with known breast cancer factors, including the HER2 overexpression, p53 mutation, and ER/PR status.</p> <p>Conclusion</p> <p>Determination of HCCR-1 levels as options for HER2 testing is promising although it needs further evaluation.</p

Clinical characteristics of the autumn-winter type scrub typhus cases in south of Shandong province, northern China

<p>Abstract</p> <p>Background</p> <p>Before 1986, scrub typhus was only found endemic in southern China. Because human infections typically occur in the summer, it is called "summer type". During the autumn-winter period of 1986, a new type of scrub typhus was identified in Shandong and northern Jiangsu province of northern China. This newly recognized scrub typhus was subsequently reported in many areas of northern China and was then called "autumn-winter type". However, clinical characteristics of associated cases have not been reported.</p> <p>Methods</p> <p>From 1995 to 2006, all suspected scrub typhus cases in five township hospitals of Feixian county, Shandong province were enrolled. Indirect immunofluorescent assay (IFA) was used as confirmatory serodiagnosis test. Polymerase chain reaction (PCR) connected with restriction fragment length polymorphism (RFLP) and sequence analyses were used for genotyping of <it>O. tsutsugamushi </it>DNAs. Clinical symptoms and demography of confirmed cases were analyzed.</p> <p>Results</p> <p>A total of 480 scrub typhus cases were confirmed. The cases occurred every year exclusively between September and December with a peak occurrence in October. The case numbers were relatively higher in 1995, 1996, 1997, and 2000 than in other years. 57.9% of cases were in the group aged 21–50. More cases occurred in male (56%) than in female (44%). The predominant occupational group of the cases was farmers (85.0%). Farm work was reported the primary exposure to infection in 67.7% of cases. Fever, rash, and eschar were observed in 100.0%, 90.4%, and 88.5% of cases, respectively. Eschars formed frequently on or around umbilicus, abdomen areas, and front and back of waist (34.1%) in both genders. Normal results were observed in 88.7% (WBC counts), 84.5% (PLT counts), and 89.7% (RBC counts) of cases, respectively. Observations from the five hospitals were compared and no significant differences were found.</p> <p>Conclusion</p> <p>The autumn-winter type scrub typhus in northern China occurred exclusively from September to December with a peak occurrence in October, which was different from the summer type in southern China. In comparison with the summer type, complications associated with autumn-winter type scrub typhus were less severe, and abnormalities of routine hematological parameters were less obvious.</p