The additivity of the η-invariant. The case of a singular tangential operator

We prove the decomposition formula for the -invariant of the compatible Dirac operator on a closed manifoldM which is a sum of two submanifolds with common boundary.Research partially supported by NSF     

The energetics of naphthalene derivatives. II. The isomeric 1— and 2—naphthyl acetates

The isomeric 1- and 2-naphthyl acetates (acetoxynaphthalenes) are at the confluence of diverse concepts, techniques and classes of organic compounds. Summing the results of literature measurements of the enthalpy of formation of their solids and of our new sublimation enthalpies reported herein, we derive gas phase enthalpies of formation of ?209.9 ± 1.4 and ?213.3 ± 1.3 kJ mol^?1 respectively. This corresponds to 2-naphthyl acetate being more stable than its 1-isomer by 3.4 ± 1.9 kJ mol^?1. We also performed MP2(full)/6-31G(d) calculations on these species, resulting in enthalpies of formation of ?212.9 ± 3.9 and ?212.2 ± 3.9 kJ mol^?1 for 1- and 2-naphthyl acetate and a difference of ?0.7 kJ mol^?1 respectively in satisfactory agreement with the above experimental results.     

Large field renormalization. I. The basic step of the ℝ operation

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by , removes the main obstacle to prove the ultraviolet stability of four-dimensional gauge field theories. The proof will be completed in the second part of this paper.Research supported in part by the National Science Foundation under Grant DMS-86 02207     

The deformation texture of β-tin I. Compression texture

The compression texture of -tin, produced by compressing the sample at temperatures of 20° C, –80° Cand –180° C,was measured. Measurement was carried out by the reflection method on a Schulz diffractometer by measuring the pole f'gures of the (200)and (101)planes. The results of the measurements show the produced, texture to be considerably dependent on the temperature.     

The deformation texture of β-tin II. Rolling texture

Measurements were made of the rolling texture of -tin which is produced by rolling the sample at a temperature of 20 °C and in the temperature interval –80°C–60 °C and –180 °C–110 °C.     

The early scientific work (1976–2000) of E.K.U. Gross

I review the scientific production of Eberhard K.U. Gross (Hardy Gross) in the first 25 years of his scientific career, from his study time at the Goethe University in Frankfurt am Main to the time he moved to the Free University of Berlin, as Full Professor. In between there was a fruitful period, in which he worked at the University of California, Santa Barbara, with Walter Kohn, the “father” of Density Functional Theory (DFT). DFT has been the permanent tool of Hardy Gross research. His main achievement in the considered period is the proof of an existence theorem for the Time-Dependent Density Functional (TDDFT) and the search for application schemes in atoms, molecules and solids, starting with linear response. He made notable contributions to the application of DFT and TDDFT to superconductors, in static and dynamic cases.     

The infra-red L.M.R. spectrum of SeH in the X 2Π state

Magnetic dipole transitions between the ²Π_1/2 and ²Π_3/2 components of the ground state of SeH have been observed at about 1780 cm^-1 in a L.M.R. experiment using a CO laser. Transitions have been detected for the four most abundant natural isotopes of Se. The transition frequencies depend primarily on the magnitude of the spin-orbit coupling constant and have been analysed in conjunction with data from the E.P.R. spectrum to yield

The admixture of other electronic states by spin-orbit coupling has been investigated to third order in perturbation theory and found to produce significant effects.     

The interpretation of the C metric. The charged case whene 2 ≤m 2

The charged C metric involves three parametersm, e andA representing mass, charge and acceleration respectively. Using a method developed in a previous paper, we show that whene ² m ² the metric may be interpreted in terms of two Reissner-Nordström particles, each of massm and with charges +e and –e, in accelerated motion and connected by a spring. The method depends on the fact that for certain regions of the coordinate space the charged C metric may be transformed into the Weyl form for a static axisymmetric system. In this form the horizons of the C metric become line sources. One of the regions leads to a Weyl metric with two line sources, one of finite length which corresponds to the outer horizon of a Reissner-Nordström particle and the other semi-infinite corresponding to a horizon associated with uniform accelerated motion. A further coordinate transformation leads to a metric valid for a larger region of space-time in which there are two charged particles in accelerated motion. WhenAm is small, the electromagnetic invariants approximate to those for the Born field for two accelerated charges in special relativity.     

Theory of Ordered Spaces¶II. The Local Differential Structure

In this paper we investigate the conditions under which the ordered spaces defined in [1] are locally diffeomorphic to ℝ ^N . In Sect.~1 we give an introduction and an overview of the results. In Sect. 2 we show that the axioms of [1] do not suffice to make light rays locally homeomorphic to ℝ. We introduce this structure via the new connectedness axiom 2.13, and work out some of its immediate consequences. In Sect. 3 we give the (somewhat involved) construction of timelike curves in a D-set, which are basic to everything that follows. They are used in Sect. 4 to prove (i) a nested interval theorem for ordered spaces; (ii) the contractibility of order intervals in D-sets; and (iii) that order intervals in D-sets are star-shaped. The notion of D-countability (meaning that a D-set has a countable base in the subspace topology) is introduced in Sect. 5. The Urysohn lemma shows that a D-countable ordered space is locally metrizable. If this space is also locally compact, then it has finite topological dimension N; these results are established in Sect. 6. The local differential structure now follows from known results: the embedding of such spaces in ℝ^{2 n +1}, and the result that an open star-shaped region in ℝ ⁿ is diffeomorphic to ℝ ⁿ . In conclusion, we exhibit these inclusions in Fig. 3, and suggest the possibility that Wigner's position on the “Unreasonable effectiveness of mathematics in the natural sciences” may be open to reasonable doubt. The axioms of [1] are given in the Appendix. Received: 26 November 1997 / Accepted: 10 February 1999     

The deformation texture ofβ-Sn III. Derivation of texture from elements of plastic deformation

The theoretical derivation of compression and rolling textures in -tin has been carried out for a different part in the deformation by slip and twinning for two different sets of slip systems given in the literature. The textures derived theoretically were compared with the compression and rolling textures measured in -tin in [6] and [7]. The dependence of the texture produced on the temperature of deformation is explained.     

Translation of J. D. van der Waals' “The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density”

Van der Waals justifies the choice of minimization of the (Helmholtz) free energy as the criterion of equilibrium in a liquid-gas system (Sections 1–4). If density is a function of heighth then the local free energy density differs from that of a homogeneous fluid by a term proportional to (d ² /dh ²); the extra term arises from the energy not from the entropy (Section 5). He uses this result to show how varies withh (Section 6), how this variation leads to a stable minimum free energy (Section 7), and to calculate the capillary energy or surface tension (Section 9). Near the critical point varies as ( _k -)^3/2, where _k is the critical temperature (Section 11). The paper closes with short discussions of the thickness of the surface layer (Section 12), of the difficulty of assuming that varies discontinuously with height (Section 14), and of the possible effect of derivatives of higher order than (d ² /dh ²) on the free energy and surface tension (Section 15).Originally published (in Dutch) inVerhandel. Konink. Akad. Weten. Amsterdam (Sect. 1), Vol. 1, No. 8 (1893).     

Fourier Transform Vibrational Spectra of Magnesium Hydrogenphosphate Trihydrate. I. The O-H Stretching Region∗

Abstract

The Fourier transform (FT) infrared and Raman spectra of newberyite, MgHPH₄ - 3H₂O are studied in the region where the stretching vibrations of the water molecules (protiated and deuterated) and the O-H/O-D stretches of the hydrogenphosphate anions are expected to appear. The O-H stretching vibrations give rise to a complex feature known as the A,B,C trio. Since neither of the maxima found below 3000 cm^?1 represents a true band arising from a given fundamental, it is pointless to correlate their frequencies with the observed O…O distances. In the water stretching region, the two bands with highest frequencies undoubtedly correspond to the anti symmetric and symmetric stretch of one type of the water molecules. The stretching vibrations of one of the remaining two types of H₂O molecules are clearly uncoupled and the O-H oscillator involved in the weaker hydrogen bond is responsible for a band at 3376 cm^?1 whereas the rest of the water stretchings are apparently overlapped yielding the complex band below 3320 cm^?1. Thus the situation is again complicated and the correlations between the frequencies and the O_w…O distances are inappropriate. The two bands at highest frequencies (3522 and 3483 cm^?1 at RT) exhibit a positive temperature coefficient.

     

The 1/N F expansion of the γ and β functions in Q.E.D.

The Callan-Symanzik- and-functions are calculated analytically for Q.E.D. in the limit of a large number of leptons (N _F) up to terms of order 1/N _F inclusive. We give closed analytic expressions for the coefficients of these terms in their series expansion in powers ofK N _F/. We have been able to sum these series and to obtain some striking results.     

Spectroscopic analysis of a laser-induced NaCl–water plasma. The influence of self-absorption

A spectroscopic study of the plasma plume created by a laser beam on the surface of NaCl aqueous solution is presented. Optical emission spectra are recorded and temporally analyzed; electron number density is determined from the Stark broadening of the NI nitrogen line, and temperature is obtained from relative intensity of OI oxygen lines. The intensity of an atomic line from sodium was used to quantitate its molar percentage in the Oceanic and Mediterranean sea, and calibration curves have been constructed for concentrations ranging up to 1.5%.     

Thermal diffusion in binary mixtures containing molecular gases. III. The temperature dependence of αT

A recent expression for the thermal diffusion factor α_T for binary atom-molecule mixtures, which includes a full range of inelastic collisional contributions [McCourt, F. R. W., 2003, Molec. Phys., 101, 2181] has been utilized to calculate its temperature dependence for equimolar N₂-He, Ne, Ar mixtures and for an equimolar CO₂-Ar mixture. Accurate classical trajectory values for the effective cross-sections entering into the expression for α_T, obtained for the most reliable potential energy surfaces available, have been employed in the calculations. Good agreement has been attained with experiment for all four binary mixtures, including the decrease of α_T with increase in temperature observed for CO₂-Ar mixtures, heretofore considered to be anomalous.     

Chinese Journal of Spectroscopy Laboratory,Vol.19,Index in The Alphabetic Order of The Primary Author Surname and Name

BBAOYu- Min　FUGe- Yan　QIJian- Ping(包玉敏　付戈妍　齐建平 ) (4 - 473 )……………………………………………………………BIL i　 YAN GYa- L ing　 LUOKang- Bi　 LIUMou- Sheng(毕　莉　杨亚玲　罗康碧　刘谋盛 ) (2 - 2 2 9)………………………………CCAIJi- Jie(蔡继杰 ) (4 - 5 3 9)……………………………………………………………………………………………………………………CAIWen- L ian　 HEH ong　LIUJia- Ming(蔡文联　何　红　刘佳铭 ) (5 - 616)…………………………………………………………CH …     

Experimental investigation on finite-amplitude standingwaves:Ⅰ. The properties of second harmonic

I.IntroductionInrecentyears,theresearchworkonnonlinearacousticshasbeendcvelopedrapid1ybe-causethehigh-intensitysoundismoreandmoreimportantincontcmporarytechnology.Aerodynamicnoiseemittedbyrockctorjetengines,noisetestofairframcs,u1trasonicpro-cessing,andothcrs,a1linvo1vefinitc-amplitudesoundwavesand,mostlystandingwaves.Athcoryofonc-dimensiona1finitc-amp1itudestandingwavesinlosslessmediahasbeenproposedbyMAAonthebasisofthcfundamenta1principlesofhydrodynamics['l,inwhichformulasofstcadywavcformsa…