The First Main Theorem; Non-exceptional Branch Points; The Non-vanishing of the L th Derivative of Dirichlet’s Energy

2012 ◽  
pp. 47-68
Author(s):  
Anthony Tromba
Keyword(s):  
Branch Points ◽  
First Main Theorem

scholarly journals Actin-binding protein promotes the bipolar and perpendicular branching of actin filaments.

1980 ◽  
Vol 87 (3) ◽  
pp. 841-848 ◽  
Author(s):  
J H Hartwig ◽  
J Tyler ◽  
T P Stossel
Keyword(s):  
Actin Filaments ◽  
Actin Polymerization ◽  
Average Length ◽  
Binding Protein ◽  
Actin Binding ◽  
Branch Points ◽  
Heavy Meromyosin ◽  
Actin Binding Protein ◽  
Protein Dimers ◽  
Protein Molecules

Branching filaments with striking perpendicularity form when actin polymerizes in the presence of macrophage actin-binding protein. Actin-binding protein molecules are visible at the branch points. Compared with actin polymerized in the absence of actin-binding proteins, not only do the filaments branch but the average length of the actin filaments decreases from 3.2 to 0.63 micrometer. Arrowhead complexes formed by addition of heavy meromyosin molecules to the branching actin filaments point toward the branch points. Actin-binding protein also accelerates the onset of actin polymerization. All of these findings show that actin filaments assemble from nucleating sites on actin-binding protein dimers. A branching polymerization of actin filaments from a preexisting lattice of actin filaments joined by actin-binding protein molecules could generate expansion of cortical cytoplasm in amoeboid cells.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

scholarly journals Different Angiogenic Potentials of Mesenchymal Stem Cells Derived from Umbilical Artery, Umbilical Vein, and Wharton’s Jelly

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Lu Xu ◽  
Jianjun Zhou ◽  
Jingyu Liu ◽  
Yong Liu ◽  
Lei Wang ◽  
...  
Keyword(s):  
Stem Cells ◽  
Mesenchymal Stem Cells ◽  
Umbilical Vein ◽  
Wharton’S Jelly ◽  
Tube Length ◽  
Branch Points ◽  
Differentiation Potential ◽  
Wharton's Jelly ◽  
Allogeneic Cell Therapy ◽  
Perivascular Stem Cells

Human mesenchymal stem cells derived from the umbilical cord (UC) are a favorable source for allogeneic cell therapy. Here, we successfully isolated the stem cells derived from three different compartments of the human UC, including perivascular stem cells derived from umbilical arteries (UCA-PSCs), perivascular stem cells derived from umbilical vein (UCV-PSCs), and mesenchymal stem cells derived from Wharton’s jelly (WJ-MSCs). These cells had the similar phenotype and differentiation potential toward adipocytes, osteoblasts, and neuron-like cells. However, UCA-PSCs and UCV-PSCs had more CD146+ cells than WJ-MSCs (P<0.05). Tube formation assay in vitro showed the largest number of tube-like structures and branch points in UCA-PSCs among the three stem cells. Additionally, the total tube length in UCA-PSCs and UCV-PSCs was significantly longer than in WJ-MSCs (P<0.01). Microarray, qRT-PCR, and Western blot analysis showed that UCA-PSCs had the highest expression of the Notch ligand Jagged1 (JAG1), which is crucial for blood vessel maturation. Knockdown of Jagged1 significantly impaired the angiogenesis in UCA-PSCs. In summary, UCA-PSCs are promising cell populations for clinical use in ischemic diseases.

THE WATER-SOLUBLE POLYSACCHARIDES OF DERMATOPHYTES: IV. GALACTOMANNANS I FROM TRICHOPHYTON GRANULOSUM, TRICHOPHYTON INTERDIGITALE, MICROSPORUM QUINCKEANUM, TRICHOPHYTON RUBRUM, AND TRICHOPHYTON SCHÖNLEINII

1965 ◽  
Vol 43 (1) ◽  
pp. 30-39 ◽  
Author(s):  
C. T. Bishop ◽  
M. B. Perry ◽  
F. Blank ◽  
F. P. Cooper
Keyword(s):  
Aqueous Solutions ◽  
Copper Complexes ◽  
Trichophyton Rubrum ◽  
Periodate Oxidation ◽  
Structural Features ◽  
Water Soluble ◽  
Major Constituent ◽  
Branch Points ◽  
Terminal Units ◽  
Hydrolysis Of

A group of polysaccharides, called galactomannans I, were precipitated as their insoluble copper complexes from aqueous solutions of the crude polysaccharides obtained from each of the organisms designated in the title. The five galactomannans I were homogeneous under conditions of electrophoresis and ultracentrifugation and had high positive specific rotations. The major constituent monosaccharide was D-mannose; amounts of D-galactose ranged from nil for the polysaccharide from T. rubrum to 13% for that from T. schönleinii. Methylation and hydrolysis of the five galactomannans I yielded varying amounts of the following: 2,3,5,6-tetra-O-methyl-D-galactose (not present in the products from T. rubrum), 2,3,4,6-tetra-O-methyl-D-mannose, 2,3,4-tri-O-methyl-D-mannose, 2,4,6-tri-O-methyl-D-mannose, 3,4-di-O-methyl-D-mannose, and 3,5-di-O-methyl-D-mannose. Periodate oxidation results agreed with the methylation studies. The gross structural features of each galactomannan I appear to be the same, namely, a basic chain of 1 → 6 linked α-D-mannopyranose units for approximately every 22 of which there is a 1 → 3 linked α-D-mannopyranose residue. Branch points occur along the 1 → 6 linked chain at the C2 positions of the D-mannopyranose units and once in every 45 units at the C2 position of a 1 → 6 linked D-mannofuranose residue. The D-galactose in the polysaccharides is present exclusively as non-reducing terminal furanose units; non-reducing terminal units of D-mannopyranose are also present. The variations in the identities and relative amounts of the non-reducing terminal units were the only apparent differences in the gross structural features within this group of polysaccharides.

scholarly journals Identification of new branch points and unconventional introns in Saccharomyces cerevisiae

RNA ◽  
2016 ◽  
Vol 22 (10) ◽  
pp. 1522-1534 ◽  
Author(s):  
Genevieve M. Gould ◽  
Joseph M. Paggi ◽  
Yuchun Guo ◽  
David V. Phizicky ◽  
Boris Zinshteyn ◽  
...  
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Branch Points

Generalization of the Fahraeus principle for microvessel networks

1986 ◽  
Vol 251 (6) ◽  
pp. H1324-H1332 ◽  
Author(s):  
A. R. Pries ◽  
K. Ley ◽  
P. Gaehtgens
Keyword(s):  
Cross Sections ◽  
Flow Direction ◽  
Quantitative Information ◽  
Red Cells ◽  
Branch Points ◽  
Velocity Difference ◽  
Rat Mesentery ◽  
The Individual ◽  
Fahraeus Effect ◽  
Flow Cross

Microvessel hematocrits and diameters were determined in each vessel segment between bifurcations of three complete microvascular networks in rat mesentery. Classification of the segments as arteriolar, venular, or arteriovenular (av) was based on flow direction at branch points. Photographic and videomicroscopic mapping was used to obtain quantitative information on the architecture and topology of the networks. This topological information allowed the analysis of hematocrit distribution within a series of consecutive-flow cross sections, each of which carried the total flow through the network. The observed reduction of mean hematocrit in the more peripheral cross sections is explained by the presence of a “vessel” and a “network” Fahraeus effect. The vessel Fahraeus effect results from velocity difference between red cells and blood within the individual vessel segments due to the existing velocity and cell concentration profiles. The network Fahraeus effect is based on the velocity difference of red cells and blood caused by velocity and hematocrit heterogeneity between the vessels constituting any of the complete-flow cross sections. The network Fahraeus effect is found to account for approximately 20% of the total hematocrit reduction and increases toward the most distal cross sections.

scholarly journals Induction of myocardial infarcts of a predictable size and location by branch pattern probability-assisted coronary ligation in C57BL/6 mice

2004 ◽  
Vol 286 (3) ◽  
pp. H1201-H1207 ◽  
Author(s):  
Dongchoon Ahn ◽  
Linda Cheng ◽  
Chanil Moon ◽  
Harold Spurgeon ◽  
Edward G. Lakatta ◽  
...  
Keyword(s):  
Heart Disease ◽  
Coronary Artery ◽  
Left Coronary Artery ◽  
Left Ventricular ◽  
Myocardial Infarctions ◽  
Branch Points ◽  
Left Main ◽  
Uniform Size ◽  
Disease Research ◽  
Coronary Ligation

The ability to create experimental myocardial infarctions of reproducible size and location is tantamount to progress in multiple facets of ischemic heart disease research. Branches of the mouse left main descending coronary artery penetrate the myocardium close to their origin and require “blind” ligation. Our objective was to develop a technique for ligation of nonvisible coronary artery branches to permit the reliable creation of infarcts of uniformly small size and location. From latex castings of the left coronary artery of C57BL/6J mice ( n = 53), we calculated the highest probability for the location of branch points of two of three left ventricular (LV) branches distal to the origin of the left main descending artery. On the basis of these anatomic probabilities, we blindly ligated two areas that were likely to be locations of these nonvisible LV branches. We were successful in producing two types of small transmural myocardial infarctions (16.04 ± 3.64 and 4.68 ± 1.47% of the LV) in 57% of attempts. Thus our branch pattern probability-assisted method permits routine creation of small infarcts of uniform size in the mouse.

Peripheral intracranial aneurysms: management challenges in 60 consecutive cases

2009 ◽  
Vol 110 (1) ◽  
pp. 7-13 ◽  
Author(s):  
Eric S. Nussbaum ◽  
Michael T. Madison ◽  
James K. Goddard ◽  
Jeffrey P. Lassig ◽  
Leslie A. Nussbaum
Keyword(s):  
Intracranial Aneurysms ◽  
Artery Occlusion ◽  
Neurological Deficits ◽  
Parent Artery ◽  
Branch Points ◽  
Aneurysm Neck ◽  
Vertebrobasilar System ◽  
Parent Artery Occlusion ◽  
Major Branch ◽  
Proximal Occlusion

Object The authors report the management and outcomes of 55 patients with 60 intracranial aneurysms arising distal to the major branch points of the circle of Willis and vertebrobasilar system. Methods Between July 1997 and December 2006, the authors' neurovascular service treated 2021 intracranial aneurysms in 1850 patients. The database was reviewed retrospectively to identify peripherally located intracranial aneurysms. Aneurysms that were mycotic and aneurysms that were associated with either an arteriovenous malformation or an atrial myxoma were excluded from review. Results The authors encountered 60 peripheral intracranial aneurysms in 55 patients. There were 42 small, 7 large, and 11 giant lesions. Forty-one (68%) were unruptured, and 19 (32%) had bled. Fifty-three aneurysms were treated surgically by using direct clip reconstruction in 26, trapping or proximal occlusion with distal revascularization in 21, excision with end-to-end anastomosis in 3, and circumferential wrap/clip reconstruction in 3. Coils were used to treat 6 aneurysms, and 1 was treated by endovascular parent artery occlusion. Overall, 49 patients had good outcomes, 4 were left with new neurological deficits, and 2 died. Conclusions Peripherally situated intracranial aneurysms are rare lesions that present unique management challenges. Despite the fact that in the authors' experience these lesions were rarely treatable with simple clipping of the aneurysm neck or endovascular coil occlusion, preservation of the parent artery was possible in most cases, and the majority of patients had a good outcome.

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