Response to Rodrigues and Rosa on the twin paradox

This paper responds briefly to the criticism of Rodrigues and Rosa on my earlier analysis of the twin paradox. The main point that I have emphasized (and that the authors have not refuted, either logically or mathematically) is the error in directly identifying anabstract measure relative to a reference frame [and its transformations to all other possible reference frames in which the laws of nature are to be compared (such as temporal and spatial measures)], with aphysical extension and duration of a material body.     

On a certain type of commutators of operators

LetH be a separable infinite-dimensional Hilbert space and letC be a normal operator andG a compact operator onH. It is proved that the following four conditions are equivalent.

1. C +G is a commutatorAB-BA with self-adjointA.
2. There exists an infinite orthonormal sequencee _j inH such that |Σ _j ⁿ =1 (Ce _j, e_j)| is bounded.
3. C is not of the formC ₁ ⊕C ₂ whereC ₁ has finite dimensional domain andC ₂ satisfies inf {|(C ₂ x, x)|: ‖x‖=1}>0.
4. 0 is in the convex hull of the set of limit points of spC.

     

Some 4-quinazolinones

The acid catalyzed reaction of anthranilamide with benzoin was studied under two conditions. Condensation at 150° gave known J plus unexpected quinazolinone H. In refluxing benzene (azeolropic water removal), the reactants yielded imine III. The acid catalyzed and uncatalyzed 150° reaction of III was examined by both ir and tlc. Both benzoic acid and II were formed in each case. Triethyl ortholormate with I gave quinazolinone IV while this ester with III formed II, benzaldehyde and benzoic acid.     

The effect of including polarization functions on the geometrical parameters calculated for pyridine

Geometrical parameters for pyridine have been calculated using the 6-31G, 6-31G^*(5D), 6-31G^**(6D), and 6-31G(2 × 6D) basis sets. Comparisons are made with a microwave substitution structure and with results of other ab initio calculations reported in the literature. Particular attention is paid to the influence of polarization functions on the magnitude of the ring angle, 〈C₆N₁C₂, which is analogous to the ipso angle in monosubstituted benzene derivatives.     

Elementary particle physics from general relativity

This paper presents a qualitative comparison of opposing views of elementary matter—the Copenhagen approach in quantum mechanics and the theory of general relativity. It discusses in detail some of their main conceptual differences, when each theory is fully exploited as a theory of matter, and it indicates why each of these theories, at its presently accepted state, is incomplete without the other. But it is then argued on logical grounds that they cannot be fused, thus indicating the need for a third revolution in contemporary physics. Toward this goal, the approach discussed is one of further generalizing the theory of general relativity in a way that incorporates the inertial manifestations of matter in covariant fashion, with quantum mechanics serving as a low-energy, linear approximation. Such a theoretical extension of general relativity will be discussed, with applications in elementary particle physics, such as the appearance of mass spectra in the microdomain, as an asymptotic feature of matter, mass doublets (electron-muon and proton-heavy proton), the explanation of pair annihilation and creation from a deterministic field theory, charge quantization, and features of pions.This paper is based on a seminar given at the International Centre for Theoretical Physics, Trieste, Italy, in the summer, 1980. I thank Prof. Abdus Salam and the faculty of the Centre for their hospitality in this period.     

On Einstein's later view of the twin paradox

It is shown that Einstein abandoned his earlier view that there are material consequences, such as asymmetric aging, implied by the space-time transformations of transformations of relativity theory.     

An ab initio study of the relationship between the O?H bond length and the harmonic and anharmonic stretching force constants for planar molecules containing C?OH,N?OH,and O?OH groups

The O? H bond length and the quadratic, cubic, and quartic stretching force constants, calculated ab initio using the unscaled 4-31G basis set with full geometry optimization, are reported for 30 planar conformers of ten molecules contaning either the C? OH, N? OH, or O? OH group. The data are analyzed in terms of the general form of Clark's equation, and the power functions and exponential functions proposed by Herschbach and Laurie. In the case of the quadratic constants, significant trends are found in the values of the parameters depending on whether the O? H group is bonded to carbon, nitrogen, or oxygen, and whether it is non-hydrogen-bonded or involved in intramolecular hydrogen bond formation in four-, five-, or six-membered rings. Using data for diatomic molecules, O? H, and C? H bonds, and the C?O and C? C bonds in planar monosubstituted carbonyl compounds, the parameter d_ij in the power function equation for quadratic constants, which can be regarded as the distance of closest approach of the two nuclei, is shown to increase progressively along the series (i) diatomic molecule; (ii) similar bond in a polyatomic environment with one of the two atoms covalently bonded to a neighboring atom; (iii) as in (ii) but with the second atom hydrogen bonded; and (iv) with both atoms covalently bonded to neighboring atoms.     

A pulsar model from an oscillating black hole

The first part of this paper examines conditions in accord with Einstein's criterion of regularity on the field solutions everywhere that would correspond to the existence of a black hole star, following from solutions of his (nonvacuum) field equations. Black hole is defined here as a star whose matter is so condensed as to correspond to a complete family of spatially closed geodesics. The condition imposed is that the angular momentum of a test body in each of the closed geodesics is a constant of the motion. The second part of the paper examines the implications in the problem of the condensed star of a generalized (factorized) version of the metrical field equations, discovered earlier by the author. It is found that in general relativity stars should naturally pulsate, and in its succeeding cycles the gravitational radius of the star is attenuated by a factor exp(–0.349T), where T is the pulsation period. Conditions are discussed for the possibility that the (relatively) regular emissions of radiation from a pulsar may be dynamically rooted in a (smaller) part of the pulsation cycle when the star is out of the black hole state (less dense open geodesics)—when radiation would be emitted to the outside world—and the (greater) part of the cycle when it is in the black hole state (more dense closed geodesics)—when radiation would not be emitted.     

Maximum gradient embeddings and monotone clustering

Let (X,d _X ) be an n-point metric space. We show that there exists a distribution over non-contractive embeddings into trees f: X → T such that for every x ∈ X, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.     

Historical reflections and new positions on perceptual computing

This paper traces the historical origins of perceptual computing and credits Tong and Bonissone (IEEE Trans Syst Man Cybern 10:716–723, 1980) as being the first to originate it but under a different name. It also takes the position that interval type-2 fuzzy sets, and not type-1 fuzzy sets, should be used in perceptual computing. Finally, it proposes some testable guidelines for when a solution (e.g., perceptual computing) may be branded computing with words.