Of object variables

For an array of object variables, you must use a different approach to obtain the upper or lower bounds of the array indices, thus ... 

First, one can check whether a randomly compiled test set is within the modeling space, before employing it for PCA/PLS applications. Suppose one has calculated the scores matrix T and the loading matrix P with the help of a training set. Let z be the characteristic vector (that is, the set of independent variables) of an object in a test set. Then, we first must calculate the scores vector of the object (Eq. (14)). 

Many process simulators come with optimizers that vary any arbitrary set of stream variables and operating conditions and optimize an objective function. Such optimizers start with an initial set of values of those variables, carry out the simulation for the entire flow sheet, determine the steady-state values of all the other variables, compute the value of the objective function, and develop a new guess for the variables for the optimization so as to produce an improvement in the objective function. 

There are several mathematical methods for producing new values of the variables in this iterative optimization process. The relation between a simulation and an optimization is depicted in Eigure 6. Mathematical methods that provide continual improvement of the objective function in the iterative... 

In real-life problems ia the process iadustry, aeady always there is a nonlinear objective fuactioa. The gradieats deteroiiaed at any particular poiat ia the space of the variables to be optimized can be used to approximate the objective function at that poiat as a linear fuactioa similar techniques can be used to represent nonlinear constraints as linear approximations. The linear programming code can then be used to find an optimum for the linearized problem. At this optimum poiat, the objective can be reevaluated, the gradients can be recomputed, and a new linearized problem can be generated. The new problem can be solved and the optimum found. If the new optimum is the same as the previous one then the computations are terminated. 

Constrained Derivatives—Equality Constrained Problems Consider minimizing the objective function F written in terms of n variables z and subject to m equahty constraints h z) = 0, or... 

Optimization of Unconstrained Olnective Assume the objective Func tion F is a function of independent variables i = r. A computer program, given the values for the independent variables, can calculate F and its derivatives with respect to each Uj. Assume that F is well approximated as an as-yet-unknown quadratic function in u. 

First, we must realize that many variables exist in any structural design. We can make a list of structural variables such as sizes, lengths of objects, materials, laminae orientations, and so on. those variables all have influence just as column length, moment of inertia, and Young s modulus influence column-buckling loads. The complete list of design variables will be called the vector Xj, and that vector will have N components. That list constitutes the definition of the structural configuration. 

Everything in Swarm is an object with three main characteristics Name, Data and Rules. An object s Name consists of an ID that is used to send messages to the object, a type and a module name. An object s Data consists of whatever local data (i.e. internal state variables) the user wants an agent to possess. The Rules are functions to handle any messages that are sent to the object. The basic unit of Swarm is a swarm a collection of objects with a schedule of event over those objects. Swarm also supplies the user with an interface and analysis tools. 

Object in this section is to review how rheological knowledge combined with laboratory data can be used to predict stresses developed in plastics undergoing strains at different rates and at different temperatures. The procedure of using laboratory experimental data for the prediction of mechanical behavior under a prescribed use condition involves two principles that are familiar to rheologists one is Boltzmann s superposition principle which enables one to utilize basic experimental data such as a stress relaxation modulus in predicting stresses under any strain history the other is the principle of reduced variables which by a temperature-log time shift allows the time scale of such a prediction to be extended substantially beyond the limits of the time scale of the original experiment. 

In this context it is the separation of solids from water by forcing the water through a porous filter media. The objective is typically to reduce the level of TDS in the water and often to reduce both the size of the particle remaining and the turbidity of the water. Filtration efficiency and quality is a function of many variable factors, although filtration is usually carried out at relatively low velocities, where velocity and pressure drop are directly related to each other. Typically a sand filter will remove a high percentage of particles above a diameter of 20 to 30 pm, whereas dual or multimedia filtration is required to remove particles down to a diameter of 10 to 20... 

---