EXISTENCE OF SOLUTIONS TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.     

Triple-period partial misfit dislocations at the InN/GaN (0001) interface: A new dislocation core structure for III-N materials

The lattice-misfit InN/GaN (0001) interface supports a triangular network of α-core 90° partial misfit dislocations. These misfit dislocations provide excellent strain relief. However, in their unreconstructed form the dislocation contains numerous high-energy N dangling bonds, which must be eliminated by reconstructing the dislocation core. Existing single-period (SP) and double-period (DP) dislocation reconstruction models eliminate these dangling bonds via a like-atom dimerization, such as N-N dimers. However, we show that these N–N dimers are unstable for the III-N materials, so an entirely new reconstruction mechanism is needed. A “triple-period” (TP) structural model is developed which eliminates N dangling bonds via the formation of N vacancies instead of N-N dimers. The model contains no N–N (or III–III) bonds, fully bonds all N atoms to four group-III neighboring atoms, and satisfies the “electron counting rule” by transferring charge from In dangling bonds to Ga dangling bonds.     

Zur Elektronenstruktur metallorganischer Komplexe der f‐Elemente. 64 Äußert sich die zwitterionische Natur des Triphenylphosphanoxid‐Liganden auch in seinen spektrochemischen Eigenschaften?

Electronic Structures of Organometallic Compounds of f Elements. 64 Does the Zwitterionic Nature of the Triphenylphosphine Oxide Ligand Manifest itself in its Spectrochemical Properties? The triphenylphosphine oxide mono adducts of the moiety tris(η⁵‐cyclopentadienyl)lanthanide(III) (Ln(Cp)₃; Ln = Pr ( 1 ), La ( 2 )) were synthesized and structurally characterized. The Ln–O distances of these compounds are noticeably shorter than those of the corresponding THF adducts. A crystal field (CF) analysis of the optical spectra of 1 leads to a low absolute value of the quadratic CF parameter which is comparable with those of [Pr(Cp)₃(L)]^? adducts with anionic bases but not with [Pr(Cp)₃(MeTHF)]. Reasons for the latter finding are presented.     

Sydowiols A–C: Mycobacterium tuberculosis protein tyrosine phosphatase inhibitors from an East China Sea marine-derived fungus, Aspergillus sydowii

Chemical analysis of an East China Sea marine-derived fungus, Aspergillus sydowii (MF357) returned three new tris-pyrogallol ethers, sydowiols A–C (1–3), and two known bis-pyrogallol ethers, violaceols I (4) and II (5). Structures were assigned on the basis of detailed spectroscopic analysis and by consideration of symmetry. Sydowiols A (1) and C (3) were responsible for the inhibitory activity detected in the crude fungal extract against Mycobacterium tuberculosis protein tyrosine phosphatase A (PtpA).     

A Berry--Esseen theorem for weakly negatively dependent random variables and its applications

Summary We provide uniform rates of convergence in the central limit theorem for linear negative quadrant dependent (LNQD) random variables. Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\{X_{n},\allowbreak n\ge1\}$ be a LNQD sequence of random variables with $EX_{n}=0$, set $S_{n}=\sum_{j=1}^{n}X_{j}$ and $B_{n}^{2}=\Var\, (S_{n})$. We show that \begin{gather*} \sup_{x} \left|P\left(\frac{S_{n}}{B_{n}}<x\right)-\Phi(x)\right|= O\bigg(n^{-\delta/(2+3\delta)}\vee \frac{n^{3\delta^{2}/(4+6\delta)}}{B^{2+\delta}_{n}} \sum_{i=1}^{n} E{|X_{i}|}^{2+\delta}\bigg) \end{gather*} under finite $(2+\delta)$th moment and a power decay rate of covariances. Moreover, by the truncation method, we obtain a Berry--Esseen type estimate for negatively associated (NA) random variables with only finite second moment. As applications, we obtain another convergence rate result in the central limit theorem and precise asymptotics in the law of the iterated logarithm for NA sequences, and also for LNQD sequences.     

Small molecule microarray screening methodology based on surface plasmon resonance imaging

In order to increase the scope and utility of small molecule microarrays (SMMs) we have combined SMMs and SPRi to screen small molecule antagonists against protein targets. Several small molecules, including immunosuppressive drugs (rapamycin and FK506) and reported inhibitors (FOBISIN and Blapsin) of 14-3-3ζ proteins have been used to validate this technology. Furthermore, a small library of isatin derivatives have been synthesized and screened on developed platform against 14-3-3ζ protein. Three molecules, derived from the endogenous intermediate isatin termed, FZIB-35, FZIB-36 and FZIB-38 were identified as novel inhibitors which shows significant interaction with 14-3-3ζ. A mutation in the binding groove of 14-3-3ζ, (K49E), almost abolishes the binding of these compounds to 14-3-3ζ protein. To exclude the probability of false positives, two more purified proteins (PtpA and BirA) were also tested. Furthermore, in order to confirm the binding pocket specificity, competition assay against R18 peptide was also carried out on presented platform. We show that SMMs in combination with SPRi are a powerful method to identify lead compounds in high throughput manner without the need to develop an activity based assay.     

Rosenthal type inequalities forB-valued strong mixing random fields and their applications

Some inequalities for moments of partial sums of aB -valued strong mixing field are established and their applications to the weak and strong laws of large numbers and the complete convergences are discussed. Project supported by the National Natural Science Foundation of China (Grant No. 19701011) and China Postdoctoral Science Foundation.     

Precise rates in the law of the logarithm in the Hilbert space

Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X₁+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,

     

Function of ROC4 in the Efficient Repair of Photodamaged Photosystem II in Arabidopsis†

ROC4 is the only cyclophilin in the chloroplast stroma. Here, we used the T‐DNA knockout mutant of roc4 to study the physiological role of ROC4 in vivo in Arabidopsis thaliana. Our results showed that ROC4 is not required for the biogenesis and functional operation of photosystem II (PSII). However, growth in greenhouse and PSII activity, as detected by photoinhibition measurements showed increased sensitivity to high light irradiance in the mutant. In the presence of chloroplast protein synthesis inhibitor lincomycin, which blocks de novo protein synthesis and thus the repair of PSII, wild‐type and mutant plants showed a similar extent of inactivation of PSII activity. The recovery of PSII activity in roc4 leaves from photoinhibition is also impaired compared with that of wild‐type plants. Immunoblot analysis showed that the degradation of PSII reaction center proteins occurred at a similar rate in the presence of lincomycin in wild‐type and mutant plants. Thus, these results suggest that ROC4 functions in the repair of photodamaged PSII.