NEW ENERGY EXPRESSIONS FOR MODEL KOHN-SHAM POTENTIALS

In the Kohn-Sham density-functional theory, one has to approximate (“model”) either the exchange-correlation density functional or the ,corresponding exchange- correlation potential. If one chooses to approximate the potential, then one needs to use the van Leeuwen-Baerends line integral to assign an energy to the density coming from a given approximate potential. The problem with this approach is that when a model potential does not have a parent functional, the line integral is path- dependent and so the energy is ambiguously defined. For such potentials, existing paths are far from optimal. In this work, we introduce two new density parametriza- tions for the line-integral formula and obtain the corresponding energy expressions. We then use these expressions to explore several existing model exchange potentials. The first energy expression corresponds to a path in which the electron density is constructed by gradually filling frozen Kohn-Sham orbitals in accordance with the aufbau principle, either orbital-by-orbital or subshell-by-subshell. The second en­ ergy expression uses the Janak theorem and requires knowing the dependence of the highest-occupied molecular orbital (HOMO) energy on the HOMO’s occupation num­ ber. We also propose a new derivation of Janak’s theorem that reveals its connection to the van Leeuwen-Baerends line integral. In addition, we revisit Slater’s transition- state method and show that in the intervals between N and N —1 electrons, the total energy calculated from a typical density-functional approximation deviates from lin­ earity quadratically. We also find that the HOMO energy calculated for an (TV—1/2)- electron system becomes almost exact, which indicates that the (N —l/2)-electron potential is more accurate than the potential of the iV-electron system. This sug­ gests that the accuracy of molecular properties calculated with existing approximate exchange-correlation functionals may be improved if the corresponding Kohn-Sham potentials are constructed from electron-deficient densities

On commutativity based edge lean search

Exploring a graph through search is one of the most basic building blocks of various applications. In a setting with a huge state space, such as in testing and verification, optimizing the search may be crucial. We consider the problem of visiting all states in a graph where edges are generated by actions and the (reachable) states are not known in advance. Some of the actions may commute, i.e., they result in the same state for every order in which they are taken (this is the case when the actions are performed independently by different processes). We show how to use commutativity to achieve full coverage of the states while traversing considerably fewer edges

Electrodynamics of Media

Contains reports on two research projects.Joint Services Electronics Programs (U.S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300U.S. Air Force Cambridge Research Laboratories Contract F19628-70-C -006

On Russell's Logical Atomism

I characterize and argue against the standard interpretation of logical atomism. The argument against this reading is historical: the standard interpretation of logical atomism (1) fails to explain how the view is inspired by nineteenth-century developments in mathematics, (2) fails to explain how logic is central to logical atomism, and (3) fails to explain how logical atomism is a revolutionary and new "scientific philosophy." In short, the standard interpretation is a bad history of logical atomism. A novel interpretation of the view that repairs these difficulties is sketched in the concluding section

Fraser MacBride, On the Genealogy of Universals: The Metaphysical Origins of Analytic Philosophy

Reviewed by Landon D. C. Elkin

Computer verification for historians of philosophy

Interactive theorem provers might seem particularly impractical in the history of philosophy. Journal articles in this discipline are generally not formalized. Interactive theorem provers involve a learning curve for which the payoffs might seem minimal. In this article I argue that interactive theorem provers have already demonstrated their potential as a useful tool for historians of philosophy; I do this by highlighting examples of work where this has already been done. Further, I argue that interactive theorem provers can continue to be useful tools for historians of philosophy in the future; this claim is defended through a more conceptual analysis of what historians of philosophy do that identifies argument reconstruction as a core activity of such practitioners. It is then shown that interactive theorem provers can assist in this core practice by a description of what interactive theorem provers are and can do. If this is right, then computer verification for historians of philosophy is in the offing

Determination of cutting forces based on DMG MORI CTX300 ecoline CNC lathe drive power data

Modern machine building needs demand for machines and control systems which provide higher accuracy of machining. For this purpose, setup methods are being researched and accuracy of machines and devices is being improved. The main topic of this paper is a tool path predistortion system which is necessary for improvement of shaft turning accuracy when a steady rest cannot be used on a CNC machines. Calculation of such tool path requires one to know the cutting force during turning on a CNC lathe. The research in question allowed to determine the dependence of cutting force during turning on the power consumed by the feed drive, cutting depth, cutting velocity, and feed value. An equation for further calculation applicable to a specific lathe in the turning process was derived. This equation serves as basis for adaptive turning of shafts and other parts with the aid of a mathematical model, which must account for the cutting force. Application of this formula in a CNC controlled lathe's parametric program will provide for higher accuracy of turning without special devices. © Published under licence by IOP Publishing Ltd

The genealogy of ‘∨’

The use of the symbol ∨ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or”, vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed

Word choice in mathematical practice: a case study in polyhedra

We examine the influence of word choices on mathematical practice, i.e. in developing definitions, theorems, and proofs. As a case study, we consider Euclid's and Euler's word choices in their influential development and, in particular, their use of the term 'polyhedron'. Then, jumping to the 20th century, we look at word choices surrounding the use of the term `polyhedron' in the work of Coxeter and of Grünbaum. We also consider a recent and explicit conflict of approach between Grünbaum and Shephard on the one hand and that of Hilton and Pedersen on the other, elucidating that the conflict was engendered by disagreement over the proper conceptualization, and so also the appropriate word choices, in the study of polyhedra