探讨带参数微分方程边值问题的解法

主要讨论带参数微分方程边值问题的逼近值及渐近值解法,并且利用基础解系、边值函数等概念,解决了带参数的微分方程中参数充分小的范围内解的变化趋势.     

多元函数的中值定理

将多元函数在有向光滑曲线上的增量与在某点处的方向导数联系起来得到一个多元函数的中值定理，并由此得到可用方向导数研究多元函数性质的一些结果     

Mox2 is a component of the genetic hierarchy controlling limb muscle development.

The skeletal muscles of the limbs develop from myogenic progenitors that originate in the paraxial mesoderm and migrate into the limb-bud mesenchyme. Among the genes known to be important for muscle development in mammalian embryos are those encoding the basic helix-loop-helix (bHLH) myogenic regulatory factors (MRFs; MyoD, Myf5, myogenin and MRF4) and Pax3, a paired-type homeobox gene that is critical for the development of limb musculature. Mox1 and Mox2 are closely related homeobox genes that are expressed in overlapping patterns in the paraxial mesoderm and its derivatives. Here we show that mice homozygous for a null mutation of Mox2 have a developmental defect of the limb musculature, characterized by an overall reduction in muscle mass and elimination of specific muscles. Mox2 is not needed for the migration of myogenic precursors into the limb bud, but it is essential for normal appendicular muscle formation and for the normal regulation of myogenic genes, as demonstrated by the downregulation of Pax3 and Myf5 but not MyoD in Mox2-deficient limb buds. Our findings show that the MOX2 homeoprotein is an important regulator of vertebrate limb myogenesis.     

fMRI evidence for objects as the units of attentional selection.

Contrasting theories of visual attention emphasize selection by spatial location, visual features (such as motion or colour) or whole objects. Here we used functional magnetic resonance imaging (fMRI) to test key predictions of the object-based theory, which proposes that pre-attentive mechanisms segment the visual array into discrete objects, groups, or surfaces, which serve as targets for visual attention. Subjects viewed stimuli consisting of a face transparently superimposed on a house, with one moving and the other stationary. In different conditions, subjects attended to the face, the house or the motion. The magnetic resonance signal from each subject's fusiform face area, parahippocampal place area and area MT/MST provided a measure of the processing of faces, houses and visual motion, respectively. Although all three attributes occupied the same location, attending to one attribute of an object (such as the motion of a moving face) enhanced the neural representation not only of that attribute but also of the other attribute of the same object (for example, the face), compared with attributes of the other object (for example, the house). These results cannot be explained by models in which attention selects locations or features, and provide physiological evidence that whole objects are selected even when only one visual attribute is relevant.     

A radiation hybrid map of the rat genome containing 5,255 markers.

A whole-genome radiation hybrid (RH) panel was used to construct a high-resolution map of the rat genome based on microsatellite and gene markers. These include 3,019 new microsatellite markers described here for the first time and 1,714 microsatellite markers with known genetic locations, allowing comparison and integration of maps from different sources. A robust RH framework map containing 1,030 positions ordered with odds of at least 1,000:1 has been defined as a tool for mapping these markers, and for future RH mapping in the rat. More than 500 genes which have been mapped in mouse and/or human were localized with respect to the rat RH framework, allowing the construction of detailed rat-mouse and rat-human comparative maps and illustrating the power of the RH approach for comparative mapping.     

The novel Cer-like protein Caronte mediates the establishment of embryonic left-right asymmetry.

In the chick embryo, left-right asymmetric patterns of gene expression in the lateral plate mesoderm are initiated by signals located in and around Hensen's node. Here we show that Caronte (Car), a secreted protein encoded by a member of the Cerberus/Dan gene family, mediates the Sonic hedgehog (Shh)-dependent induction of left-specific genes in the lateral plate mesoderm. Car is induced by Shh and repressed by fibroblast growth factor-8 (FGF-8). Car activates the expression of Nodal by antagonizing a repressive activity of bone morphogenic proteins (BMPs). Our results define a complex network of antagonistic molecular interactions between Activin, FGF-8, Lefty-1, Nodal, BMPs and Car that cooperate to control left-right asymmetry in the chick embryo.     

Munc13-1 is essential for fusion competence of glutamatergic synaptic vesicles.

Neurotransmitter release at synapses between nerve cells is mediated by calcium-triggered exocytotic fusion of synaptic vesicles. Before fusion, vesicles dock at the presynaptic release site where they mature to a fusion-competent state. Here we identify Munc13-1, a brain-specific presynaptic phorbol ester receptor, as an essential protein for synaptic vesicle maturation. We show that glutamatergic hippocampal neurons from mice lacking Munc13-1 form ultrastructurally normal synapses whose synaptic-vesicle cycle is arrested at the maturation step. Transmitter release from mutant synapses cannot be triggered by action potentials, calcium-ionophores or hypertonic sucrose solution. In contrast, release evoked by alpha-latrotoxin is indistinguishable from wild-type controls, indicating that the toxin can bypass Munc13-1-mediated vesicle maturation. A small subpopulation of synapses of any given glutamatergic neuron as well as all synapses of GABA (gamma-aminobutyric acid)-containing neurons are unaffected by Munc13-1 loss, demonstrating the existence of multiple and transmitter-specific synaptic vesicle maturation processes in synapses.     

Structure of Cdc42 in complex with the GTPase-binding domain of the 'Wiskott-Aldrich syndrome' protein.

The Rho-family GTP-hydrolysing proteins (GTPases), Cdc42, Rac and Rho, act as molecular switches in signalling pathways that regulate cytoskeletal architecture, gene expression and progression of the cell cycle. Cdc42 and Rac transmit many signals through GTP-dependent binding to effector proteins containing a Cdc42/Rac-interactive-binding (CRIB) motif. One such effector, the Wiskott-Aldrich syndrome protein (WASP), is postulated to link activation of Cdc42 directly to the rearrangement of actin. Human mutations in WASP cause severe defects in haematopoletic cell function, leading to clinical symptoms of thrombocytopenia, immunodeficiency and eczema. Here we report the solution structure of a complex between activated Cdc42 and a minimal GTPase-binding domain (GBD) from WASP. An extended amino-terminal GBD peptide that includes the CRIB motif contacts the switch I, beta2 and alpha5 regions of Cdc42. A carboxy-terminal beta-hairpin and alpha-helix pack against switch II. The Phe-X-His-X2-His portion of the CRIB motif and the alpha-helix appear to mediate sensitivity to the nucleotide switch through contacts to residues 36-40 of Cdc42. Discrimination between the Rho-family members is likely to be governed by GBD contacts to the switch I and alpha5 regions of the GTPases. Structural and biochemical data suggest that GBD-sequence divergence outside the CRIB motif may reflect additional regulatory interactions with functional domains that are specific to individual effectors.