Orientable case

The angle (p quantifies the in-plane direction, with cp = 0° corresponding to the direction along the stripe-like electrodes. For an alignment of the lamellae along the field direction (maximum azimuthal intensity distribution of the 2D Fourier transform intensity at (p = 90°), P) ranges from 0 to -0.5 with P2 = -0.5 corresponding to the fully oriented case. 

These differences in the magnitude of the measured absorbances are due to the redistribution of the transition dipoles in space, from a situation where all are in the x,y plane (e.g., vs(CH2), va(CH2) in an zSX-trans perpendicular orientation, case a,... 

It is convenient to distinguish between two types of literature search one concerned with a broad area of research, a method, a class of reactions, or a class of compounds and another concerned with information about a single chemical species or reaction. In the former, methodology-oriented case, you should begin by checking the review literature— specialized monographs (consult the subject catalog in the library), reference books,... 

It is easy to see how the various techniques mentioned above destabilize the ordinary pattern and operate on various psychological subsystems to push them toward extreme values of functioning. But where is the actual transition We do not know. Studies of hypnosis have generally paid little attention to the transition between hypnosis and waking. Some psychoanalytically oriented case studies 19 have reported marked transitional effects, but no study has tried to map the exact nature and extent of the quantum jump. 

Chang, Y.C., Dai, Y.C., Chow, N.H. Fibrolamellar hepatocellular carcinoma with a recurrence of classic hepatocellular carcinoma a case report and review of oriental cases. Hepato-Gastroenterol. 2003 50 1637-1640... 

In the uniaxially oriented case, the system is transversely isotropic and the dielectric constant tensor reduces to... 

The anisotropy of T, and Ti, have been little studied. The only comprehensive treatment of this has been given by McCall and co-workers,where results for tetrafluoroethylene-hexafluoropropylene copolymer fibres are presented, together with a theoretical treatment for the full orientation case. Any anisotropy in Ti was found to be minimal the anisotropy in Ti was comparable to that in Tj or the second moment, as would be expected on theoretical grounds. 

As a consequence of the central role that relations retain in object-relational data models, one crucial difference with respect to the object-oriented case is that the role played by object identity is relaxed to an optional, rather than mandatory, feature. Thus, an object-relational DBMS stands in an evolutionary path regarding relational ones, whereas object-oriented ones represent a complete break with the relational approach. In this context, notice that while a tuple of type constructor may allow a relation type to be supported, each tuple will have an identity, and attribute names will be explicitly needed to retrieve and interact with values. 

As in the object-oriented case, object-relational data models were first advocated in a concerted manner by a manifesto (Stonebraker et al., 1990) signed by prominent members of the research community. A book-length treatment is available in Stonebraker and Brown (1999). Any undergraduate textbook on Database Systems (e.g., Atzeni et al, 1999 Elmasri and Navathe, 2000) can be used to complement the treatment of this and the section that follows. 

In the object-oriented case, the separation between the languages used for data definition, querying and procedural... 

Thus, if a handle is glued to two distinct tori, Lemma 2.1.5 foUows for the orientable case. Let now a handle be glued to one torus (case 2). Now the tori... 

Now we proceed to the proof of Lemma 2.1.6. We begin with the orientable case. Let a round handle corresponding to a saddle circle be glued to distinct tori Ti and T2 along rings whose axes are noncontractible (by virtue of Lemma 2.1.5) circles 71 and 72, respectively. 

PROOF We begin with the orientable case. Lemmas 2.1.5, 2.1.6, and 2.1.7 imply that the manifold U S ) contains two tori, Pi = P-Ulifi and Pz = P-.UK2i which... 

The proof of the homological part of Theorem 2.1.1 is concluded as follows. If the integral is orientable, then r = 0, and therefore, under the condition that the group is finite (in Fig. 34b,c,d), there remain only graphs located on the right of the vertical dashed line, that is, m > 2. If the integral is nonorientable, then the homological assertions of the theorem follow from Lemma 2.1.14. The inequahty m H- r > 2 (under the condition that Hi is finite) is obviously equivalent to the inequality m 2 (in the orientable case) if each is considered to be a full torus see Lemma 2.1.14. 

One should double all the sides of the parallelepiped II2,..., Iljb+i. As a result, one obtains a new parallelepiped II extended in k directions. Now act with this parallelepiped II upon the point h. As a result, obtain a certain orbit Ti h). It is clear that now this orbit is represented (in action-angle variables on a Liouville torus) by a linear plane which is almost-closed after factorization of the cube to the torus. Farther arguments repeat those of the orientable case. This implies the lemma. 

Proof of Theorem 2.3.2 For simplicity we first consider the orientable case, that is, the case where the manifold Q does not involve nonoriented saddles. We will prove that rankfTi(Q,Z) ib, where k is the number of cuts necessary for transforming the initial graph into a branching one. Examine any cut. A small neighbourhood of this cut is a cylinder T xD. The manifold Q may be assumed to be obtained as a union of two of its submanifolds 1) k cylinders, 2) a connected manifold, which is a complement of the interior of the first submanifold. 

SGqUGntial Biaxial OriGntation. The standard process for sequential biaxial orientation is machine direction orientation followed by transverse orientation. This is a continuous process. The machine direction stretch occurs similar to the process described in the monoaxial section (Fig. 5). However, a second draw station is typically not present in this process. In the pure monoaxial orientation case, the process often tries to maximize the molecular orientation in the... 

If (M,oM) is an n-dimensional manifold with boundary an< Uc3M is a codimension 0 submanifold (which may be empty) of the boundary such that (M,U) is an (n-2)-dimensional geometric Poincare pair, and such that there is given a codimension 2 spine K c U, then the obstruction o (MrK) P -(II/W) obtained by Matsumoto H) (in the oriented case u = w = +1) for the existence of a codimension 2 spine (N,K) c(M,U) is the rel3 weak splitting obstruction along the zero section MCE(5) of an s -triangulation (defined as in Proposition 7.5.4)... 

In the case of homeotropic alignment the polar angle is equal to 90° and n is orthogonal to the surface. When the n lies in the plane of the surface (0 = 0°, planar alignment), two possible orientation cases exist ... 

Therefore, in the orientable case, the Poincare rotation number on the torus depends monotonically on (see Sec. 4.4). Typically, each rational rotation number corresponds to an interval of values of fi (a resonant zone). In the simplest case, there exist only two periodic orbits on the torus in the... 

---