We study the expected behavior of Betti numbers arrangements zeros random (distributed according to Kostlan distribution) polynomials in R P n $\mathbb {R}\mathrm{P}^n$ . Using a spectral sequence, we prove an asymptotically exact estimate on number connected components complement s $s$ such hypersurfaces also investigate same problem case where are defined by quadratic polynomials. In this cas...

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others...

The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline arrangements with contacts supported by a given network. In this paper, we construct the “brick polytope” of a network, o...

Annelid erythrocruorins are extracellular respiratory complexes assembled from 180 subunits into hexagonal bilayers. Cryo-electron microscopic experiments have identified two different architectural classes. In one, designated type I, the vertices of the two hexagonal layers are partially staggered, with one hexagonal layer rotated by about 16 degrees relative to the other layer, whereas in the...

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been studied extensively in the context of crossing number problems. We consider a natural class of simple topological drawings of complete bipartite graphs, in ...

Synaptic vesicles dock at active zones on the presynaptic plasma membrane of a neuron's axon terminals as a precondition for fusing with the membrane and releasing their neurotransmitter to mediate synaptic impulse transmission. Typically, docked vesicles are next to aggregates of plasma membrane-bound macromolecules called active zone material (AZM). Electron tomography on tissue sections from...

The testis of the donkey was completely descended into the scrotum around birth. It was covered by a thick tunica albuginea consisting of outer and inner fibrous layers in addition to middle vascular one. Discrete bundles of smooth muscle cells were demonstrated in the outer fibrous layer of the tunica albuginea. These cells give the tunica albuginea a contractile function, which may aid in spe...

Right atrial isomerism or left atrial isomerism is frequently diagnosed as situs ambiguous without further discrimination of the specific morbid anatomy. Thirty six cases of right atrial isomerism and seven cases of left atrial isomerism were collected from the records and pathological museum at the National Taiwan University Hospital. There was a necropsy report for 18 cases. In all patients o...

Abstract In this work, an experimental study on new series connection of two Ranque-Hilsch vortex tubes with generator materials, potential in seawater desalination was implemented, combined modification has not been studied open literature. Polycarbonate and Polyamide-Nylon 6 were tested compared as materials that enhance the heat transfer between air streams inside tube. Moreover, using prehe...