Physical Sciences in Lisbon

We provide a two-day tour of Lisbon, Portugal, focusing on sites of scientific and technological importance, setting them within their historical contexts. On the first day we visit the Academy of Sciences of Lisbon, the building that successively housed the College of Nobles, the Polytechnic School, and the University of Lisbon Faculty of Sciences, and then go on to the Arpad Szenes-Vieira da Silva Museum and the Astronomical Observatory of Lisbon. On the second day we visit the Industrial Institute and Museum, the Geographical Society of Lisbon, the Jesuit College of Santo Ant?o, and the Technical Institute.     

The Mathematical Basis for Physical Laws

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by these purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory.     

Bayesian Logical Data Analysis for the Physical Sciences,edited by P.C. Gregory

(1) Combined Effects of Radioactive, Chemical and Thermal Rebases to the Environment. Proceedings of a Symposium held in Stockholm, 2–5 June 1975. Vienna, 1975. International Atomic Energy Agency. London, H.M.S.O., pp. 358. £10·00.

(2) Impacts of Nuclear Releases into the Aquatic Environment. Proceedings of an International Symposium held at Ontaniemi, Finland, 30 June—4 July 1975. Vienna, 1975. International Atomic Energy Agency. London, H.M.S.O., pp. 524. £14.60.     

Bridging the Gap between Archaeology and the Physical Sciences

The collaboration between archaeologists and representatives of the physical sciences is often rendered difficult by differing training and expectations, poor mutual understanding, inconsistent terminologies, and a lack of time and willingness to bridge these gaps. In this paper some thoughts and suggestions on research design and interpretation in interdisciplinary studies are brought forth and suggestions towards a fruitful collaboration are made.     

物理概念与数学运算

在解物理题时，物理概念与数学运算有着十分密切的关系．合理运用物理概念能使数学运算简单明了，恰当的数学运算又能促进对物理概念的理解．但是，过分地强调使用数学运算方法，而忽视物理概念，有时会带来麻烦的计算，使简单的问题数学运算复杂化．下面我们看一个简单而著名的例子．     

初中物理量的非常规测量法

各省市历年物理中考实验题中,如何测物质密度、测电阻、测电功率等实验的比例很大,涉及测其他物理量的题很少.研究近一、两年的物理中考实验命题,发现有一种新的趋势即如何用非常规的方法测上述三个物理量(密度、电阻、电功率)之外的其他物理量,现归纳、列举如下.     

数学条件不等于物理条件——对两道高考试题条件的深入探讨

有一些物理问题,如果从纯数学的角度看,题中的某些条件可能是多余或重复的,但为了使试题具有考试价值,即试题既要有一定的区分度,又要让大多数学生不至于一筹莫展、毫无下手的余地,这些条件又是必须的,是试题设置所不可或缺的物理条件．下面通过两道高考试题对数学条件与物理条件的差异进行探讨．     

Physical solutions and Mathematical properties of the Lorentz-Dirac equation

The rectilinear motion of a charge obeying the Lorentz-Dirac equation and moving in an external electrostatic field is analyzed. Imposing no additional constraints, it is shown that the asymptotic motion of this charge is inertial. Energy conservation by the entire process is proved. Mathematical arguments concerning the irrelevance of runaway solutions are discussed.     

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M(x) of a research object is defined by the researcher–modeler as a space¹ (X, p(X), \(P{I^{\bar x}}\), \(Be{l^{\bar x}}\)) with plausibility\(P{I^{\bar x}}\) and believability \(Be{l^{\bar x}}\) measures, where x is an uncertain element taking values in X that models researcher—modeler’s uncertain propositions about an unknown x ∈ X, measures \(P{I^{\bar x}}\), \(Be{l^{\bar x}}\) model modalities of a researcher–modeler’s subjective judgments on the validity of each x ∈ X: the value of \(P{I^{\bar x}}(\tilde x = x)\) determines how relatively plausible, in his opinion, the equality \((\tilde x = x)\) is, while the value of \(Be{l^{\bar x}}(\tilde x = x)\) determines how the inequality \((\tilde x = x)\) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher–modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike “standard” mathematical modeling, ?enables a researcher–modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model \(M(\tilde x)\), and if the data on observations of a research object is available, then it: ?enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.     

Mathematical Methods of Subjective Modeling in Scientific Research. 2: Applications

This article considers applications of the formalism of subjective modeling proposed in [36], based on modeling of uncertainty reflecting unreliability of subjective information and fuzziness common of its content. A subjective model of probabilistic randomness is defined and studied. It is shown that a researcher–modeler (RM) defines a subjective model of a discrete probability space as a space with plausibility and believability that de facto turns out to be a subjective model of the class of subjectively equivalent probability spaces that model an arbitrary evolving stochastic object, and the same space with plausibility and believability is its subjective model. This enables us to empirically recover a subjective model of an evolving stochastic object accurately and using a finite number of event observations, while its probabilistic model cannot be empirically recovered. A similar connection is established between equivalence classes of plausibility and believability distributions and classes of subjectively equivalent absolutely continuous probability densities. For two versions of plausibility and believability measures, entropies of plausibility and believability distributions of the values of an uncertain element (UCE) \(\tilde x\)that model RM’s subjective judgments as characteristics of the information content and uncertainty of his judgments are considered. It is shown that in the first version entropies have properties that are formally similar to those of Shannon entropy but due to absence of the law of large numbers (LLN) their interpretation fundamentally differs from the interpretation of Shannon entropy. In the third version there is an analog of the LLN, and its connection to the Shannon entropy was obtained for the expected value of subjective informational content/uncertainty. A subjective model M(\(\tilde x\))=(Ω,3(Ω), P ^ζ,? (·,·;\(\tilde x\)), N ^ζ,? (·,·;\(\tilde x\)) of an uncertain fuzzy element is considered, and an optimal subjective rule of identification of its states using observation data is obtained and studied. Methods of expert-aided reconstruction of fuzzy and uncertain fuzzy element models are also considered.     

Physical Principles Underlying the Experimental Methods for Studying the Orientational Order of Liquid Crystals

The basic physical principles underlying different experimental methods frequently used for the determination of orientational order parameters of liquid crystals are reviewed. The methods that are dealt with here include the anisotropy of the diamagnetic susceptibility, birefringence, linear dichroism, Raman scattering, fluorescence depolarization, electron paramagnetic resonance (EPR), and nuclear magnetic resonance (NMR). The fundamental assertions that can be obtained by the different methods as well as their advantages, drawbacks and limitations are inspected. Typical sources of uncertainties and inaccuracies are discussed. To quantitatively evaluate the experimental data with reference to the orientational order the general tensor formalism developed by Schmiedel (Wiss. Z. KMU Leipzig, Math.-Naturwiss. R. 33 (1984) 441) was employed throughout according to which the order matrix comprises 25 real elements yet. Within this context the interplay of orientational ordering and molecular conformation is scrutinized.     

物理量串并联关系中的数学共性

从简单的物理模型中提炼出物理量串并联关系中的数学共性并加以推广、应用。使得在大学物理教学中物理量串并联的物理意义更加明显地被学生所接受。     

物理"海马"、数学"海马"与生物"海马"

在C60-TCNQ(一种有机分子名称的缩写)和纯的TCNQ有机分子薄膜中,文章作者得到了一种形似海洋中生存的动物海马的图案结构,取名为"海马"分形结构.这种"海马"图案在旋转180度时具有近似的对称性,但是不同于简单的二维反转对称.在数学中用复变函数的多项式,通过Julia对复杂空间中函数的纯粹数学映射(即z→z2 c,其中c=-0.74543 0.1130i),也能模拟出相似的"海马"图案.对于"海马"分形,文章作者提出如下的一种形成机制,即:在薄膜形成初期过程中,中性分子或团簇中存在部分荷电粒子,由于库仑排斥作用,成核和生长过程中会形成对称性破缺,最终形成"海马"状分形."海马"的有趣图案,加深了人们对自然与科学统一的认识,激发了人们对自然本源的探索激情.     

关于数学物理方法课程的若干问答

围绕教学物理方法课程教学中的若干常见、然而教材中又很少展开的问题,提出了自己的见解.