Initial Conditions and the ‘Open Systems’ Argument against Laws of Nature

This article attacks ‘open systems’ arguments that because constant conjunctions are not generally observed in the real world of open systems we should be highly skeptical that universal laws exist. This work differs from other critiques of open system arguments against laws of nature by not focusing on laws themselves, but rather on the inference from open systems. We argue that open system arguments fail for two related reasons: 1) because they cannot account for the ‘systems’ central to their argument (nor the implied systems labeled ‘exogenous factors’ in relation to the system of interest) and 2) they are nomocentric, fixated on laws while ignoring initial and antecedent conditions that are able to account for systems and exogenous factors within a fundamentalist framework.     

Black swans and white eagles: on mathematics and finance

It is often objected that we cannot use mathematical methods in finance because (1) finance is dominated by unpredictable unique events (the black swans), (2) there are qualitative effects that cannot be quantified, and (3) the laws themselves of finance keep on changing. In this paper we discuss these three objections, offering arguments to reject them. We begin by reviewing the development of the physical sciences, pointing out parallels that are relevant for our discussion. Modern science has abandoned the objective of describing reality and has adopted an operational point of view that regards physical laws as tools to connect observations. Modern science is no longer deterministic, but has accepted a fundamental uncertainty in physical laws both at micro and macroscopic levels. Unpredictable pivotal events exist in the physical sciences as well in finance but this does not lead us to question the use of mathematics in the physical sciences. On the contrary, using principles of safe design, we try to understand how to avoid and contain unpredictability. Financial markets are manmade artifacts with, as actors, a large number of interacting agents. If we so wish, we can reduce the level of uncertainty present in markets: But if we try to do so describing financial markets with simple mathematical laws, we find that these laws are not stable but change over time, eventually with sudden structural breaks. This makes the use of mathematical finance difficult but not impossible. We can forecast human decision-making processes, crucial in forecasting financial markets, at the statistical level in aggregate. From an operational point of view, we have the tools to understand and describe the behavior of large number of interacting agents. At the present stage of development of our science, we need to use the mathematics of adaptive systems, changing mathematical models in function of different market states. However, reductionism to a small number of basic laws remains a fundamental objective of financial economics as it is in the physical sciences.     

高等数学课堂教学与一题多解

高等数学是理工科院校一门十分重要的公共基础课程,在自然科学、工程技术、生命科学、社会科学、经济管理等众多领域有着广泛的应用．对待作为高等数学课堂上的主体——学生,教师应当积极正面评价学生,激发学生的学习兴趣,启发学生主动思考,全面培养学生解决数学问题的能力,并在课堂教学中贯彻这一思想．课堂教学也表明：学生积极主动的应用多种思路解决一道题远比老师灌输性的介绍一道题的多种解法要更具有积极意义．     

Conserved quantities for a class of (1 + n)-dimensional linear evolution equation

A special type of (1 + n)-dimensional linear evolution equation is considered. A class of the equations generated by the Fokker-Planck equation becomes the subcase of the considered equation. Conserved vectors using the partial Lagrangian approach is derived in terms of the coefficients of the discussed equation. Derived results are used for the different models from different sciences. We also discuss the conservation laws of the heat equation on curved manifolds and in different coordinate systems. Potential systems are also obtained for some models. At last conclusion is given.     

Entropic order quantity (EnOQ) model for deteriorating items

Jaber et al. [M.Y. Jaber, R.Y. Nuwayhid, M.A. Rosen, Price-driven economic order systems from a thermodynamic point of view, Int. J. Prod. Res. 42 (24) (2004) 5167–5184] suggested that it might be possible to improve production systems performance by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). They then used these laws to modify the economic order quantity (EOQ) model to derive an equivalent entropic order quantity (EnOQ). The results suggested that larger quantities should be ordered than is suggested by the classical EOQ model.     

Massively Parallel Particle Simulations on Graphics Processing Units with CUDA

Particle methods are a powerful tool to model dynamic systems. Thereby, the system is discretized by a large number of particles, which are interacting via local, predefined particle-particle interaction laws. The resulting computational effort includes neighborhood search, computation of interaction forces and state update via time integration. Particle methods are used in a lot of different fields of applications like computer science, physics and engineering sciences. As the analyzed systems' number of particles constantly grow, performance enhancement has become an important part of present algorithm development. Besides the well-established approach of algorithm parallelization on multi-core CPUs or CPU clusters, modern graphics processing units (GPUs) present a different and trend-setting possibility for massive parallelization even on desktop computers. Among the top four supercomputers of the world, three are already using NVIDIA GPUs. In late 2006, NVIDIA introduced the first GPUs optimized for general purpose calculations. This was followed by the introduction of a new computing architecture differing from the standard graphics user-interface like OpenGL. This architecture is called Compute Unified Device Architecture (CUDA). It enables the user to program the GPU using standard C commands with few additional runtime functions. The differences in architecture between CPU and GPU result in a completely different algorithm implementation. So, a performance evaluation of different types of particle systems implemented on a GPU using CUDA and on a standard CPU is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relaxation dynamics of the fastest channel in multichannel parallel relaxation mechanism

Empirical evidence accumulated over the years shows that the time-dependent change of macroscopic properties of physical systems evolving to equilibrium exhibits a great degree of universality. We address the question of the origins of the universal relaxation laws in terms of probabilistic approach based on the multichannel parallel relaxation mechanism. We present a clear stochastic scheme uniquely leading to the whole class of experimentally observed relaxation responses. The proposed scheme results from the common assumption that only the fastest channel contributes to relaxation dynamics.     

Technological change,population dynamics,and natural resource depletion

In this paper, we integrate fertility and educational choices into a scale-invariant model of directed technological change with non-renewable natural resources, in order to reveal the interaction between population dynamics, technological change, and natural resource depletion. In line with empirical regularities, skill-biased technological change induces a decline in population growth and a transitory increase in the depletion rate of natural resources. In the long-run, the depletion rate also declines in the skill intensity. A decline in population growth is harmful for long-run productivity growth, if R&D is subject to diminishing technological opportunities. The effectiveness of economic policies aimed at sustained economic growth thus hinges on its impact on long-run population growth given the sign of intertemporal spillovers in R&D with respect to existing technological knowledge. We demonstrate that an increase in relative research productivities or an education subsidy enhances long-run growth, if R&D is subject to diminishing technological opportunities, while an increase in the teacher–student ratio is preferable in terms of positive intertemporal knowledge spillovers.     

从诺贝尔经济学奖看数学建模的价值

分为三个部分,第一部分,诺贝尔经济学奖的概述;第二部分,数学建模在经济学中的应用情况;最后一部分,展望经济科学的发展趋势.     

Structural Properties of Homomorphism Dilation Systems

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces. By introducing two natural dilation structures, namely the canonical and the universal dilation systems, they prove that every linearly minimal dilation is equiva...     

Order in binary sequences and the routes to chaos

The natural order in the space of binary sequences permits to recover the U-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as intrinsic properties of this ordered set, and independent from any consideration about dynamical systems.     

The forms of energy and their transformations : Plenary report of the 5-th All-Union Congress on theoretical and applied mechanics. Alma-Ata, May 27, 1981

The meaning of various model concepts, particularly those devised for space and time, or of chosen general reference systems of various kinds, of general or tetrad coordinate systems, and of universal and particular physical characteristic concepts having the property of covariance is expounded. Basic relations, such as force or scalar energy laws for purely mechanical phenomena or small individual volumes of matter and fields in physical processes of general form in the presence of internal and external interactions accompanied by transformation among themselves of various forms of energy, are noted.     

Merit Functions for Complementarity and Related Problems: A Survey

Merit functions have become important tools for solving various mathematical problems arising from engineering sciences and economic systems. In this paper, we are surveying basic principles and properties of merit functions and some of their applications. As a particular case we will consider the nonlinear complementarity problem (NCP) and present a collection of different merit functions. We will also introduce and study a class of smooth merit functions for the NCP.     

Strong Limit Theorems for Increments of Sums of Independent Random Variables

We derive universal strong laws for increments of sums of independent, nonidentically distributed, random variables. These results generalize universal results of the author for the i.i.d. case which include the strong law of large numbers, law of the iterated logarithm, Erdos-Renyi law, and Csorgo-Revesz laws. Bibliography: 27 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 260–285.     

On the Distinction Between Law Schemata and Causal Laws

The paper argues against the widely accepted assumption that the causal laws of (completed) physics, in contrast to those of the special sciences, are essentially strict. This claim played an important role already in debates about the anomalousness of the mental, and it currently experiences a renaissance in various discussions about mental causation, projectability of special science laws, and the nature of physical laws. By illustrating the distinction with some paradigmatic physical laws, the paper demonstrates that only law schemata are strict whereas causal laws are generally non-strict. Several potential replies to this argument are discussed and rejected as unsound.     

Gyroscopic control and stabilization

Summary In this paper, we consider the geometry of gyroscopic systems with symmetry, starting from an intrinsic Lagrangian viewpoint. We note that natural mechanical systems with exogenous forces can be transformed into gyroscopic systems, when the forces are determined by a suitable class of feedback laws. To assess the stability of relative equilibria in the resultant feedback systems, we extend the energy-momentum block-diagonalization theorem of Simo, Lewis, Posbergh, and Marsden to gyroscopic systems with symmetry. We illustrate the main ideas by a key example of two coupled rigid bodies with internal rotors. The energy-momentum method yields computationally tractable stability criteria in this and other examples.     

Expert systems in production scheduling

One area of computer-related studies that has recently been receiving considerable publicity is the development of expert systems. The more noteworthy applications of this approach to problem-solving are still in engineering and the natural sciences, but a growing number of applications to problems in business management are beginning to appear. This paper reviews recent research and discusses the applicability of an ‘expert system’ approach to problems in production scheduling.     

CED model for asset returns and fractal market hypothesis

A new general model for asset returns is studied in the framework of the Fractal Market Hypothesis (FMH). To accommodate markets with arbitrage opportunities, it concerns capital market systems in which the Conditionally Exponential Dependence (CED) property can be attached to each investor on the market. Employing the limit theorem for the CED systems, the universal characteristics for the distribution of asset returns are derived. This explains the special role of the Weibull distribution in modeling of global asset returns for market with no arbitrage and the two-power laws property of the density of global returns, evident in the empirical data. Finally, the link with two-parameter Pareto distributions is established.     

Topicality of Kantorovich's Economic Model

Proceeding from his discovery of linear programming, Leonid Kantorovich developed its applications to optimization at the macroeconomic level. The universal value of his model for all socio-political systems was recognized by leading representatives of western economic science. Though Kantorovich created his macromodel specifically for the centrally planned system, it was not accepted by the Soviet leadership. The paper considers the conditions under which that macromodel could be successfully used in the mixed economic system of Russia. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 30–46.