Abstract Previously we have shown how measurements of static magnetic susceptibility χ c (T) YBa 2 Cu 3 O 6+x single crystals for fields applied along the -axis, and ab in ab-plane , can give useful information about their thermodynamic properties which are still being hotly debated. SQUID magnetometry above superconducting (s/c) transition temperature T is used larger crystals, while piezoleve...

From ab initio quality calculations on model systems, we conclude that in unliganded Fe-porphyrin the FE lies in the plane for both the high-spin (q) and intermediate-spin (t) states. Thus, the high-spin d6 Fe is not too big to fit into the porphyrin plane (as often suggested). We find the q state lower for a porphyrin hole radius greater than 1.94 A and the t state lower for smaller sizes. For...

1. Introduction. 4 will denote the space of all plane paths w, so that w is a short way of denoting the curve z(t, (o) = {x(t, w), y(t, (o)} (0 < t < + oc). We assume that there is a probability measure ,u defined on a Borel field 9 of (measurable) subsets of S2, so that the system (Q, 3~ 7_ " u) forms a mathematical model for Brownian paths in the plane. [For details of the definition of ,u, s...

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle α to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 < α < π/2) in the case x < 0 with t < 0, and diverging pendent rivulets (when π/2 < α < π) in the case x > 0 with t > 0, where x denotes a coordinate me...

The cell rotation graph D(G) on the strongly connected orientations of a 2-edge-connected plane graph G is de5ned. It is shown that D(G) is a directed forest and every component is an in-tree with one root; if T is a component of D(G), the reversions of all orientations in T induce a component of D(G), denoted by T−, thus (T; T−) is called a pair of in-trees of D(G); G is Eulerian if and only i...

For any connected abstract graph G, the tree graph T (G) is the graph that has one vertex for each spanning tree of G and an edge joining trees R and S whenever R is obtained from S by a single edge exchange. R. L. Cummings proved in [C] that T (G) is hamiltonian; see also [S] for a short proof. A geometric variation that has been studied is the following: For a set P of points in general posit...

We study curves on a surface whose position vectors lie in the plane generated by any two among ?T, ?N and ?T ? . find distance function, tangential, normal binormal components of such obtain condition for its invariancy under isometry surfaces.

1 Billiards and related systems 1.1 Polygonal outer billiards in the hyperbolic plane The outer billiard about a convex polygon P in the plane R 2 is a piece-wise isometry, T , of the exterior of P defined as follows: given a point x outside of P , find the support line to P through x having P on the left, and define T (x) to be the reflection of x in the support vertex. See [10, 35]. Figure 1:...

0.1. 2D. In the context of linear algebra a plane is a two-dimensional real vector space. A basis for a plane consists of any two vectors E1,E2 which span the plane. ‘Spanning’ means that any vector v⃗ in the plane can be written as v⃗ = uE1 + vE2 with u, v ∈ R. It is a theorem that for two vectors in the plane “spanning” is equivalent to being “linearly independent”. The ‘linearly independent pa...

plane and mulberry trees play a crucial role in purifying the polluted air in tehran as a majorcity. in this research, 13 main districts of tehran city were chosen as study area. 20 completely healthy planeand mulberry species were selected in similar ecological conditions and age range. the uptake of cd and pbwas determined using spectrophotometry, whereas the chlorophyll content was measured ...