Unique constraint

Pickett et al. 1997) in MORE samples played an important role, not only to address the problem of magma transfer times, but also in the development of dynamic melting models able to sustain such disequilibria over long periods. In subduction zone volcanoes, the combined study of and Ra- °Th disequilibria place unique constraints on the... 

There are no primitives in Catalysis, only a set of basic object types that are defined in standard packages. Using exactly the same mechanisms, you can define your own basic types and packages of basic types suitable for your problem domain (see Figure A.2). Remember to add uniqueness constraints, which help define the meaning of object identity for your object type. There are frameworks, algebraic in nature, that capture even these basic recurring patterns. 

The probabilistic interpretation of these conditions is very similar to the interpretation of the (2, 2) conditions. The analysis is readily extended to higher-order densities, where one obtains / + 1 unique constraints on the / -matrix. 

Because of the unique operational and safety requirements of radiopharmaceutical synthesis, the motivation for the development of automated systems is clear. These unique constraints include short synthesis times and control from behind bulky shielding structures that make both access to and visibility of radiochemical processes and equipment difficult. The need for automated systems is particularly expressed for PET radiopharmaceutical synthesis, with the short-lived radionuclides emitting high-energy y photons at 511 keV. Automated synthesis systems require no direct human participation. The short half-lives of the PET radionuclides may require repeated synthesis during the day, thus being a potential radiation burden for the operator when not using automated systems. 

It is not required that such a column actually be used as an SQL key, but it is wise to do so. In this way, the SQL uniqueness constraints can help to ensure that the table is in first normal form. While this one column must be unique, it is entirely possible and even likely that some other data values will not be unique. For example, there are expected to be many compounds that coincidentally have the same logP. This does not violate first normal form. 

Another commonly used constraint is the uniqueness constraint. In previous examples, the column compound id was defined to be a unique integer. When the uniqueness constraint is used in a table holding a collection of compounds, it ensures that there can never be more than one compound with a particular compound id. This is essential if other data about a compound are stored in other tables that use compound id as a foreign key. Notice that this does not prevent two identical compounds... 

Once there is a unique, canonical SMILES available, this can be stored in a text column and a direct lookup for a specific structure can be done using the SQL = operator. If canonical SMILES is stored in a text column named cansmi, one can locate isopropyl alcohol using the SQL clause Where cansmi = CC(C) O. And because text data can be indexed in SQL, this lookup is extremely fast. In addition, SQL uniqueness constraints can be used to enforce data integrity when using canonical SMILES. 

It is possible to represent chirality in SMILES. This is essential to correctly define the appropriate enantiomer or stereoisomer. Many databases will contain isomers. It is possible to relate the various isomers of a structure by using their common canonical SMILES. This might be done by relaxing the uniqueness constraint on the cansmi column in a structure table, or by adding another table of stereoisomers that is related to the master table. Chirality may be used in SMARTS as well. 

One only needs to look at the examples of plug play simplicity provided by the universal serial bus (USB) and modem Ethernet networks in personal computers to realize that technology exists that could make the NeSSI vision a reality. However, that is not to say that an off-the-shelf solution exists. The NeSSI group has been working on defining and evaluating solutions that would fit into the somewhat unique constraints imposed by the chemical and petrochemical processing industries that are the main consumers for NeSSI systems. 

A sufficient condition for a unique Newton direction is that the matrix of constraint derivatives is of full rank (linear independence... 

The measurements do not close the constraints. Estimation of the parameter values against the actual measurements results in parameter values that are not unique. 

Note that since for each state E , d> assigns a unique successor state Eg, each column of the matrix consists of all zeroes except for a single 1 each row, on the other hand, is under no such constraint and can therefore have any number of I s. 

Notice that in this example, the speed of the packet is inversely proportional to the packet s spatial size. While there is certainly nothing unique about this particular representation, it is interesting to speculate, along with Minsky, whether it may be true that, just as the simultaneous information about position and momentum is fundamentally constrained by Heisenberg s uncertainty relation in the physical universe, so too, in a discrete CA universe, there might be a fundamental constraint between the volume of a given packet and the amount of information that can be encoded within it. 

For concreteness, let us suppose that the universe has a temporal depth of two to accommodate a Fi edkin-type reversibility i.e. the present and immediate past are used to determine the future, and from which the past can be recovered uniquely. The RUGA itself is deterministic, is applied synchronously at each site in the lattice, and is characterized by three basic dimensional units (1) digit transition, D, which represents the minimal informational change at a given site (2) the length, L, which is the shortest distance between neighboring sites and (3) an integer time, T, which, while locally similar to the time in physics, is not Lorentz invariant and is not to be confused with a macroscopic (or observed) time t. While there are no a priori constraints on any of these units - for example, they may be real or complex - because of the basic assumption of finite nature, they must all have finite representations. All other units of physics in DM are derived from D, L and T. 

Solving such a myopic deconvolution problem is much more difficult because its solution is highly non-linear with respect to the data. In effect, whatever are the expressions of the regularization terms, the criterion to minimize is no longer quadratic with respect to the parameters (due to the first likelihood term). Nevertheless, a much more important point to care of is that unless enough constraints are set by the regularization terms, the problem may not have a unique solution. 

Inverse problems are very common in experimental and observational sciences. Typically, they are encountered when a large number of parameters (as many as or more than measurements) are to be retrieved from measured data assuming a model of the data - also called the direct model. Such problems are ill-conditioned in the sense that a simple inversion of the direct model applied directly to the data yields a solution which exhibits significant, or even dominant, features which are completely different for a small change of the input data (for instance due to a different realization of the noise). Since the objective constraints set by the data alone are not sufficient to provide a unique and... 

Why are the oceans so depleted in these trace metals Certainly it is not for the lack of availability from rock weathering or because of constraints imposed by the solubility of any unique compound of these elements. The reason must lie in the dynamics of the system of delivery of the metals to the oceans and their subsequent behavior in an ocean that cannot be simulated by simple in vitro experiments involving homogeneous reaction kinetics. 

---