BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)──BASIC EQUATIONS

This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four simultaneous basic equations, i. e., equation of interest rate and amount of circulating fond, equations of purchasing and selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate, have been established. Discussions mainly on the solution and its simple applications of the equation of interest rate and amount of circulating fond are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping, and the influence of amount of circulating fond with exponential attenuation due to the decreasing of banking interest rate.Keyworks: stock market; network model; differential equation; contraction mapping; elasticity; methodology

Interval of effective time-step size for the numerical computation of nonlinear ordinary differential equations

The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.

Towards Science Unification through Number Theory

The Number Theory comes back as the heart of unified Science, in a Computing Cosmos using the bases 2;3;5;7 whose two symmetric combinations explain the main lepton mass ratios. The corresponding Holic Principle induces a symmetry between the Newton and Planck constants which confirm the Permanent Sweeping Holography Bang Cosmology, with invariant baryon density 3/10, the dark baryons being dephased matter-antimatter oscillation. This implies the DNA bi-codon mean isotopic mass, confirming to 0.1 ppm the electron-based Topological Axis, whose terminal boson is the base 2 c-observable Universe in the base 3 Cosmos. The physical parameters involve the Euler idoneal numbers and the special Fermat primes of Wieferich (bases 2) and Mirimanoff (base 3). The prime numbers and crystallographic symmetries are related to the 4-fold structure of the DNA bi-codon. The forgotten Eddington’s proton-tau symmetry is rehabilitated, renewing the supersymmetry quest. This excludes the concepts of Multiverse, Continuum, Infinity, Locality and Zero-mass Particle, leading to stringent predictions in Cosmology, Particle Physics and Biology.

How Semiotics Can Improve Our Knowledge on Computing

Several computer theorists and professionals share the concepts of ＂signifier＂ and ＂signified＂ in intuitive terms but are often unfamiliar with semiotics. There is a special digital divide between semiotics and the technology, because the semiotic notions are usually expressed through verbal expressions instead engineers use the mathematical language. In the first step, the present study suggests the formal descriptions of the signifier and the signified. In the second step, we show how these formal definitions are able to justify the hardware structure of a computer system, and even other properties of computing which are currently presented on the as-is basis. Concluding, the basic concepts of semiotics can unveil intriguing aspect of information technology

Computational uncertainty principle in nonlinear ordinary differential equations——Ⅱ.Theoretical analysis

The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the “normal” growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine.

The Efect of Si Impurity at the Al Σ5 Grain Boundary:a First Principle Computational Tensile Test Study

First principle computational tensile tests （FPCTT） are performed to the Al ∑5 grain boundaries （GBs） with and without substitution or interstitial Si impurity. The obtained stress-strain relationships and atomic configurations demonstrate that the Al ∑5 GBs with and without substitutional or interstitial Si impurity show different fracture modes. The mechanisms of the different fracture modes are analyzed based on the charge density and the density of states. The results show that the charge redistributions of the atoms in the vicinity of GBs and the covalent interactions between Si and its neighboring Al atoms determine the fracture modes.

CFD Study on Local Fluid-to-Wall Heat Transfer in Packed Beds and Field Synergy Analysis

To reach the target of smaller pressure drop and better heat transfer performance, packed beds with small tube-to-particle diameter ratio(D/dp<10) have now been considered in many areas. Fluid-to-wall heat transfer coefficient is an important factor determining the performance of this type of beds. In this work, local fluid-to-wall heat transfer characteristic in packed beds was studied by Computational Fluid Dynamics(CFD) at different Reynolds number for D/dp=1.5, 3.0 and 5.6. The results show that the fluid-to-wall heat transfer coefficient is oscillating along the bed with small tube-to-particle diameter ratio. Moreover, this phenomenon was explained by field synergy principle in detail. Two arrangement structures of particles in packed beds were recommended based on the synergy characteristic between flow and temperature fields. This study provides a new local understanding of fluid-to-wall heat transfer in packed beds with small tube-to-particle diameter ratio.