Dynamic processes definition

The chemical world is often divided into measurers and makers of molecules. This division has deep historic roots, but it artificially impedes taking advantage of both aspects of the chemical sciences. Of key importance to all forms of chemistry are instruments and techniques that allow examination, in space and in time, of the composition and characterization of a chemical system under study. To achieve this end in a practical manner, these instruments will need to multiplex several analytical methods. They will need to meet one or more of the requirements for characterization of the products of combinatorial chemical synthesis, correlation of molecular structure with dynamic processes, high-resolution definition of three-dimensional structures and the dynamics of then-formation, and remote detection and telemetry. 

One could go on with examples such as the use of a shirt rather than sand reduce the silt content of drinking water or the use of a net to separate fish from their native waters. Rather than that perhaps we should rely on the definition of a chemical equilibrium and its presence or absence. Chemical equilibria are dynamic with only the illusion of static state. Acetic acid dissociates in water to acetate-ion and hydrated hydrogen ion. At any instant, however, there is an acid molecule formed by recombination of acid anion and a proton cation while another acid molecule dissociates. The equilibrium constant is based on a dynamic process. Ordinary filtration is not an equilibrium process nor is it the case of crystals plucked from under a microscope into a waiting vial. 

We study next the dynamical irreducibility condition which appeared in the definition of the transport operator. It eliminates from this quantity the reducible collision processes where the particles coming from infinity interact, recede to an infinite distance from one another, and then interact again. We define an extended transport operator from which the irreducibility condition is eliminated and which involves this time the reducible collisions. The relation between the transport operator and the extended transport operator is made explicit by means of a correspondence between the dynamical processes and the Mayer graphs for equilibrium. In this respect, we demonstrate, in these graphs, the importance of the role of the articulation points. 

So far, the concept of time has entered the discussion only in the form of the qualitative definition given in Section V.F it has not entered in any quantitative way, and, until it does, there can be no discussion of dynamical processes. 

However, the same difficulty that observers meet in defining a cluster exist for theorists to define clusters in a numerical simulation typical numerical simulations handled several millions dark matter particle and a similar number of gas particle when hydro-dynamical processes are taken into account the actual distribution of dark matter, at least on non linear scales is very much like a fractal, for which the definition of an object is somewhat conventional Different algorithms are commonly used to define clusters. Friend of friend is commonly used because of its simplicity, however its relevance to observations is very questionable, especially for low mass systems. On the analytical side... 

The dynamic variable J x is orthogonal [22-24] to the longitudinal total mass-current density Jk = Ju,p- This makes especially convenient the theoretical treatment of dynamical processes in small k region, where the collective type of the dynamics prevails [22-24], Using the definition (43), the Eqs. (39)—(42) can be easily rewritten for new set of dynamic variables, so that we obtain ... 

In this section we describe some of the essential features of fractal functions starting from the simple dynamical processes described by functions that are fractal (such as the Weierstrass function) and that are continuous everywhere but are nowhere differentiable. This idea of nondifferentiability leads to the introduction of the elementary definitions of fractional integrals and fractional derivatives starting from the limits of appropriately defined sums. We find that the relation between fractal functions and the fractional calculus is a deep one. For example, the fractional derivative of a regular function yields a fractal function of dimension determined by the order of the fractional derivative. Thus, the changes in time of phenomena that are best described by fractal functions are probably best described by fractional equations of motion, as well. In any event, this latter perspective is the one we developed elsewhere [52] and discuss herein. Others have also made inquiries along these lines [70] ... 

Evolution of process instances is inherent to dynamic task nets. The process meta model is designed such that planning and enactment may be interleaved seamlessly. Evolution of process definitions is performed at the level of packages. To maintain traceability, packages are submitted to version control. 

Our approach to interorganizational cooperation in development processes builds on the definition of dynamic process views onto development processes as its foundation [175-177]. Dynamic process views support better visibility management for process elements carried out within an organization. 

Dynamic process views are located at the process view layer above. Parts of the overall process within each organization are made externally visible by the definition and publication of one or more process view definitions. These process view definitions are subscribed by other organizations, where the respective private processes are extended with the contents of the corresponding view instances. In our approach, the remote process view elements are directly embedded into the private task nets to allow... 

Some other researchers like Finkelstein [669] use the concept of a view in different way than we do. These approaches focus on the consistent integration of these views in order to maintain a consistent and up-to-date representation of the whole development process by superimposition of all views. While these approaches focus on the problems of view-based process definition that arise with modifiable views, we use views which usually are not modified by anyone else than the view pubhsher, so we do not face problems of consistent integration to that extent. Because we do not use different modeling formalisms for all process views (we always use dynamic task nets in all process views), we do not face the problem that two views onto the same process part model different aspects of it in a conflicting way. 

The definition of dynamics and their possible contribution to enzyme catalysis has been a matter of debate in recent years [10-13]. In a couple of recent reviews in Science, two groups of prominent researchers appear to disagree on the definition of dynamics [14, 15]. Ref [15] and several textbooks of physical chemistry prefer the definition that dynamics is any time dependent process . Any motion in a given system can be considered a dynamic process regardless of whether or not it... 

All states and all dynamical processes connecting states are of interest for chemistry, chemical engineering, and physical chemistry. Some properties can be defined for all the states (such as the thermodynamic basic quantities) others are specific for some situations, such as the surface tension. But also for properties of general definition, the techniques to use have often to be very different. It is not possible, for example, to use the same technique... 

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