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For simple dynamical systems, knowing the trajectory is often sufficient, but most dynamical systems are too complicated to be understood in terms of individual trajectories.
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For and simple
For better or worse we cannot regard `` imitation '' in the arts in the simple mode of classical rationalism or detached realism.
For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.
For Lamprias had said that the first articulate sound made is " alpha ", because it is very plain and simple — the air coming off the mouth does not require any motion of the tongue — and therefore this is the first sound that children make.
For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must decrease
For a simple model, with two alleles:
For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope.
For example, eliminating dependence on the electrical grid is relatively simple but growing all necessary food is a more demanding and time-consuming proposition.
For a Gaussian response system ( or a simple RC roll off ), the rise time is approximated by:
For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:
For example, the rules of the Hebrew calendar depend on the seven-day week cycle ( a very simple calendar ), so the week is one of the cycles of the Hebrew calendar.
For example, industrial farming could not have been invented before simple farming, and metallurgy could not have developed without previous non-smelting processes involving metals ( such as simple ground collection or mining ).
For example, simple hydrogen gas combined with simple oxygen gas can produce a more complex substance, such as water.
For example, endosperm cell walls in the seeds of cereal grasses, nasturtium, and other species, are rich in glucans and other polysaccharides that are readily digested by enzymes during seed germination to form simple sugars that nourish the growing embryo.
For I am not as simple as I may seem.
For example, the Cyrillic letter Р is usually written as R in the Latin script, although in many cases it is not as simple as a one-for-one equivalence.
For about a decade, every student taking the 6. 004 class at MIT was part of a team — each team had one semester to design and build a simple 8 bit CPU out of 7400 series integrated circuits.
For effective utilization and handling it is desired that a data model is relatively simple and intuitive.
For the simple electric dipole given above, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges.
For low-frequency radiation ( radio waves to visible light ) the best-understood effects are those due to radiation power alone, acting through the effect of simple heating when the radiation is absorbed by the cell.
* A simple explanation of Euler's Conjecture at Maths Is Good For You!
For example, just by applying a simple rule that constrains each queen to a single column ( or row ), though still considered brute force, it is possible to reduce the number of possibilities to just 16, 777, 216 ( that is, 8 < sup > 8 </ sup >) possible combinations.
For and dynamical
For continuous dynamical systems, the map τ is understood to be a finite time evolution map and the construction is more complicated.
For a dynamical system to be classified as chaotic, it must have the following properties:
For the position of the dynamical image plane, it decreases with increasing dielectric function and is typically on the order of 0. 2 Å.
For a dynamical system with evolution equation in an n – dimensional phase space, the spectrum of Lyapunov exponents
For example, ordinary differential equations and symplectic geometry are generally viewed as purely mathematical disciplines, whereas dynamical systems and Hamiltonian mechanics belong to mathematical physics.
For discrete-time dynamical systems the orbits are sequences, for real dynamical systems the orbits are curves and for holomorphic dynamical systems the orbits are Riemann surfaces.
For discrete time dynamical system:
For a more mathematical discussion, see the articles on nonlinearity, dynamical systems, bifurcation theory, and chaos theory.
For a general dynamical system, the step response is defined as follows:
For a constrained Newtonian dynamical system the constraints described by the equations () are usually implemented by some mechanical framework.
For example, it requires a fixed choice of the topology and dimensionality of the spacetime, while any consistent quantum theory of gravity should include topology change as a dynamical process.
For example, if one is interested in dynamics on networks or the robustness of a network to node / link removal, often the dynamical importance of a node is the most relevant centrality measure.
For since reason itself is not an appearance and is not subject at all to any conditions of sensibility, no temporal sequence takes place in it even as to its causality, and thus the dynamical law of nature, which determines the temporal sequence according to rules, cannot be applied to it.
: For a series of innovative works “ New quantum number – color and establishment of dynamical regularities in the quark structure of elementary particles and atomic nuclei ” published during 1965 – 1977.
For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice.
For example, Gary Glatzmaier and collaborator Paul Roberts of UCLA have made a numerical model of the electromagnetic, fluid dynamical processes of Earth's interior.
For discrete dynamical systems, consider the system
For and systems
For example, the term is used to describe systems such as verlan and louchébem, which retain French syntax and apply transformations only to individual words ( and often only to a certain subset of words, such as nouns, or semantic content words ).
For example, autopilot systems that are prolific today were started to help bomber planes fly steadily enough to hit precision targets from high altitudes.
* For tramway systems: see List of town tramway systems in Belarus
For a time, the combined company retained the Burroughs processors as the A and V systems lines.
For example, an information systems specialist will view computing somewhat differently from a software engineer.
For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.
For instance, NASA has extremely rigorous software testing procedures for many operating systems and communication functions.
For example, programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use of programming language and complex systems.
For example, kinship and leadership function both as symbolic systems and as social institutions.
For very large systems, the relative total energies can be compared using molecular mechanics.
For π-electron systems, this was the Hückel method proposed by Erich Hückel, and for all valence electron systems, the extended Hückel method proposed by Roald Hoffmann.
For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.
For some distributed parameter systems the vectors may be infinite-dimensional ( typically functions ).
For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.
For example, there is a hard disk, from which most operating systems run and on which most store their files.
For instance, on newer MS Windows computers, the older FAT-type file systems of MS-DOS and old versions of Windows are supported, in addition to the NTFS file system that is the normal file system for recent versions of Windows.
For continuous, frequent or prolonged intravenous chemotherapy administration, various systems may be surgically inserted into the vasculature to maintain access.
For example, Burris has reviewed sociological publications and used the theories of Weber and Bourdieu to describe academic caste systems.
For this reason it is not hard to port games between these systems.
For embedded systems, the highest performance levels are often not needed or desired due to the power consumption requirements.
For a while hybrid cable / electric systems operated, for example in Chicago where electric cars had to be pulled by grip cars through the loop area, due to the lack of trolley wires there.
For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by
0.246 seconds.