Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

Handbook of the freshwater fishes of India : giving the characteristic peculiarities of all the species at present known, and intended as a guide to students and district officers / By R. Beavan.

[Incomplete]

Notebook concerning mathematical equations : manuscript, 1769-1774

Notes on measuring height and distance, trigonometry, spherical projection, and other mathematical equations. Probably William Winthrop (1753-1825; Harvard AB 1770).

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

(Table 1) Magnetic characteristic properties of selected samples of ODP Hole 134-831B

During Ocean Drilling Program Leg 134 (Vanuatu), geological high sensitivity magnetic tools (GHMT) developed by CEA-LETI and TOTAL were used at two drill sites. GHMT combine two sensors, a proton magnetometer for total magnetic field measurements with an operational accuracy of 0.1 nanoteslas (nT), and a highly sensitive induction tool to measure the magnetic susceptibility with an operational accuracy of a few 10**-6 SI units. Hole 829A was drilled through an accretionary prism and the downhole measurements of susceptibility correlate well with other well-log physical properties. Sharp susceptibility contrasts between chalk and volcanic silt sediment provide complementary data that help define the lithostratigraphic units. At Hole 831B magnetic susceptibility and total field measurements were performed through a 700-m reef carbonate sequence of a guyot deposited on top of an andesitic volcano. The downhole magnetic susceptibility is very low and the amplitude of peak-to-peak anomalies is less than a few 10**-5 SI units. Based on the repeatability of the measurements, the accuracy of the magnetic logging measurements was demonstrated to be excellent. Total magnetic field data at Hole 831B reveal low magnetic anomalies of 0.5 to 5 nT and the measurement of a complete repeat section indicates an accuracy of 0.1 to 0.2 nT. Due to the inclination of the earth's magnetic field in this area (~-40°) and the very low magnetic susceptibility of the carbonate, the contribution of the induced magnetization to the total field measured in the hole is negligible. Unfortunately, because the core recovery was extremely poor (<5%) no detailed comparison between the core measurements and the downhole magnetic data could be made. Most samples have a diamagnetic susceptibility and very low intensity of remanent magnetization (< 10**-4 A/m), but a few samples have a stable remanent magnetization up to 0.005 A/m. These variations of the intensity of the remanent magnetization suggest a very heterogeneous distribution of the magnetization in the carbonate sequence that could explain the magnetic field anomalies measured in these weakly magnetized rocks.

Efficient algorithms for solving systems of ordinary differential equations for ecosystems modeling /

Mode of access: Internet.

A dictionary of chemical equations.

Mode of access: Internet.

Partial differential equations.

Mode of access: Internet.