Spatial limit

METHOD OF DERICHE By resuming the model proposed by Canny, and relaxing the spatial limited support hypothesis, R. Deriche finds a more effective optimal edge operator and proposes a recursive implementation. 

Because of spatial limitations, only meso- and macrocycles possessing heteroatoms and/or subheterocycik rings ate reviewed in general, lactones, lactams, and cyclic imides have been excluded. In view of the delayed availability of some articles appearing in previous years, several have been incorporated. 

Block copolymers have been the focus of much interest during the last 30 years because their constituent blocks are generally immiscible, leading to a microphase separation. Since the different blocks are linked together by covalent bonds, the microphase separation is spatially limited and results in self-assembled structures whose characteristic sizes are of the order of a few times the radius of gyration, Rg, of the constituent blocks and thus range from ca. 10 to 100 nm [1],... 

Fig. 6.5 Comparison between NSE spectra at Q=0.1 A and T=473 K of both binary blends (filled circle and filled triangle), and those of the isotopic PDMS blends filled square). The solid lines result from a fit t with the dynamic structure factor for the Rouse model filled square) and of a spatially limited Rouse dynamics, as derived in [256] filled square and filled triangle). (Reprinted with permission from [255]. Copyright 2003)...

Space for estimation Estimation is a mathematical process whereas the main constraint on the orebody is the geological condition. Therefore, it is necessary to introduce the spatial limits of mineralization. For this project mineralization is not only limited by the vein but also it will be limited by the oxidized zone so that, the estimated space is that part of vein, which is located in oxidized atmosphere (Figure 6). 

The electrons in an atom surround the nucleus, but are constrained within given spatial limits, defined by atomic orbitals. Atomic orbitals describe the probability of finding an electron within a given space. We are unable to pin-point the electron at any particular time, but we have an indication that it will be within certain spatial limits. A farmer knows his cow is in a field, but, at any one time, he does not know precisely where it will be located. Even this is not a good analogy, because electrons do not behave as nice, solid particles. Their behaviour is in some respects like that of waves, and this can best be analysed through mathematics. 

The first issue can be addressed in two ways a primary ET species which has a large optical absorption cross-section can be chosen or arrays of molecules with large optical absorption cross-sections can be used as "antennas" that will efficiently collect and transport the electronic excitation energy to the primary ET species, in direct analogy to photosynthetic systems. While in the latter case it should be possible to develop systems with more efficient solar photon collection, the number of primary ET species will have to be reduced due to the spatial limitations, which will also reduce the potential electric current that can be produced by the system. Thus, questions related to the detailed molecular architecture of biomimetic solar energy conversion devices will have to address this issue, and it is quite likely that a number of compromises will have to be made before optimal design characteristics are obtained. 

Because of their well-defined porous structures and spatial limitations, zeolites and mesoporous aluminosilicates are shape-selective catalysts. The availability of... 

Opening of Ca channels of the endoplasmic reticulum by InsPj leads to an initial increase in free Ca by emptying the InsPs-sensitive Ca stores. As a consequence, a temporally and spatially limited increase in Ca is observed that can flow through the cell in the form of a Ca wave (review Berridge, 1993 Cooper et al., 1995). 

Why do we have to use an arbitrary value such as 95% to determine the spatial limitations of an orbital ... 

The study of confined quantum systems has attracted increasing attention from several research groups in the world due to the unusual physical and chemical properties exhibited by such systems when subject to spatial limitation. Such novel properties, not present in conventional materials, have marked a new era for the synthesis of modern materials - structured at the nanoscale - and leading to what is now called nanotechnology. 

As is the case with any scientific development with important technological consequences, basic research plays a fundamental role whereby appropriate models are designed to explore and predict the physical and chemical behavior of a system. A confined quantum system is a clear example where theory constitutes a cornerstone for explanation and prediction of new properties of spatially limited atoms, molecules, electrons, excitons, etc. Theoretical study of possible confined structures might also suggest and stimulate further experimental investigations. In essence, the design of novel materials with exceptional properties requires proper theoretical modeling. 

Despite the fact that at present many important regularities of PET processes across the membranes seem to be understood at a qualitative level, this turns out to be insufficient for PET across membranes to be controlled purposefully. For this, more detailed quantitative mechanistic studies are needed. In particular, more data are needed concerning the location of the photosensitizer and electron carriers inside the membrane, dynamics and spatial limits of their diffusion in the membrane, the actual role of electron tunneling in providing electron transfer across the hydrophobic core of the membrane. 

The second point implies that extended (100) terraces are more reactive towards 02 adsorption than the spatially limited terraces present on the stepped surfaces. Indeed for Ag(4 1 0) at E[ = 0.97 eY and 0 = 45°, S0 is four times larger when the trajectories point step up (31°), than when the molecules collide step down (at —59° the step heights are in shadow). Interestingly, the sticking probability... 

The relatively high activities of these catalysts can in most cases be attributed to the high dispersions of the active species. These are normally incorporated as cations via an ion-exchange process and thus remain bound onto the extensive inner surface of the zeolites by electrostatic forces. The selectivities observed, for example, in oligomerization reactions where, in general, dimers are formed in preference to higher oligomers, may be a direct consequence of the spatial limitations imposed on transition-state complexes within the small zeolite cavities. 

In proteins, all these different motions are localized within one macromolecule or a few molecules bound to each other. Thus, the space of motions is limited compared to the car race picture, just as if we were to explore the motions of selected parts of the engine and the cockpit during the race. Clearly, movements of the pistons and the crankshaft occur on a different time scale than that of the wheels or the full car, not to mention the driver-controlled steering wheel and transmission. In summary, molecular motions cover a wide range of time scales, occur in a spatially limited manner and, unlike cars and racing events, are not even directly observable. That is why we need sophisticated experimental techniques to characterize dynamics in biomacromolecules. 

Excluded volume determines space occupancy in biopolymer solutions. Competition between macromolecules for space in a mixed solution determines the phase separation threshold. In a dilute solution of biopolymers, macromolecules hardly interact with one another, individual macromolecules are independent of one another, and biopolymers are cosoluble. The effects of spatial limitations are enhanced by the transition from a dilute mixed solution, to a semi-dilute biopolymer solution where molecules come into contact with one another, interact, compete for the same space, and do not mix in all proportions. 

In addition, a detailed study of a metasomatized wall rock adjacent to an amphi-bole-pyroxenite dike has revealed that the contamination in " Nd/ " " Nd and Sr/ Sr is spatially limited to a distance of <25 cm from the dike (Bodinier et al., 2003). This distance is interpreted as the chromatographic front of neodymium and strontium since the infiltration of small volume melts probably occurred on a greater distance in the host peridotite, as attested by the enrichment of the highly incompatible elements observed at 25-80 cm from the dike (e.g., lanthanum and cerium, see Section... 

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