Temperature and pressure dependence of the elastic property of GeS2 glass

The sound velocities in GeS₂ glass have been measured by means of ultrasonic interferometry as a function of temperature or pressure up to 1.8 kbar. The bulk modulus K_s = 117.6 kbar and shear modulus G = 60.60 kbar were obtained for GeS₂ glass at 15°C and 1 atm. The temperature derivatives of both sound velocities and elastic moduli are negative :

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.54 × 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C,

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.27× 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C and

$\text{(}\text{?K}{}_{\mathrm{s}}\text{?T}\text{)}$

_p =

$\text{?1.27 × 10}{}^{\mathrm{?2}}\text{kbar}\text{°C}$

,

$\text{(}\text{?G}\text{?T}\text{)}$

_p = ?1.23 × 10^?2 kbar/°C,

$\text{(}\text{?Y}\text{?T}\text{)}$

_p = ?2.93 × 10^?2 their pressure derivatives are positive:

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T = 4.43× 10^?2km/kbar,

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T =

$\text{0.633 × 10}{}^{\mathrm{?2}}\text{km}\text{kbar}$

and (?K_s?P0)_T=6.81,

$\text{(}\text{?G}\text{?P)}{}_{\mathrm{T}}$

= 1.03, (?Y?T_T= 3.57. The Grüneisen parameter, γ_th= 0.298, and the second Grüneisen parameter, δ_s = 3.27, have also been calculated from these data. The elastic behavior of GeS₂ glass has proved to be normal despite the structural similarity among the tetrahedrally coordinated SiO₂, GeO₂ and GeS₂ glasses.     

Centrifugal distortion effects in the microwave spectrum of methylene cyanide

The rotational spectrum of methylene cyanide has been measured up to J = 62 and a total of 82 b-type transitions have been obtained. These data have been analyzed with a semirigid rotor Hamiltonian to give accurate rotational and centrifugal distortion constants. The rotational constants are (in MHz) $\text{A}$ = 20882.7537 ≠ 0.017, $\text{B}$ = 2942.3003. ≠ 0.0031, $\text{C}$ = 2616.7225 ≠ 0.0031 The quartic centrifugal distortion constants are (in MHz)

$\text{Δ}{}_{\mathrm{J}}\text{(1.855455 ≠ 0.014) x 10}{}^{\mathrm{?3}}\text{Δ}{}_{\mathrm{JK}}\text{= (?6.79218 ≠ 0.027) x 10}{}^{\mathrm{?2}}$

$\text{Δ}{}_{\mathrm{K}}\text{(8.621628 ≠ 0.013) x 10}{}^{\mathrm{?1}}\text{δ}{}_{\mathrm{J}}\text{= (4.892607 ≠ 0.016) x 10}{}^{\mathrm{?4}}$

$\text{δ}{}_{\mathrm{K}}\text{= (6.7501 ≠ 0.29) x 10}{}^{\mathrm{?3}}$

The uncertainties are twice the standard deviations in the constants obtained from the least squares analysis, and represent approximately 95% confidence limits.     

Study of the production of a strange (S = −1) dibaryon in the interactions of K− and π+ on deuterium below 1.5GeV/c

The production of a strange dibaryonic system called H⁺₁ (M = 2.13 GeV/c², S = ?1), has been studied with a missing mass spectrometer, at the CERN Proton Synchrotron, in the reaction K^?d → π^?H⁺₁ and in the line-reversed reaction π⁺d → K⁺H⁺₁ between 0.9 and 1.4 GeV/c.The reactions

$\text{K}{}^{\mathrm{?}}\text{d}\text{→ π}{}^{\mathrm{?}}\text{X}{}^{\mathrm{+}}$

,

$\text{π}{}^{\mathrm{<mtext>d</mtext>}}\text{→}\text{K}{}^{\mathrm{+}}\text{X}{}^{\mathrm{+}}$

,have been studied in a missing mass spectrometer at CERN. The experiment (PS159) is well adapted to search for a signal in the missing mass X⁺ (B = 2, S = ?1) produced in the backward c.m.s. direction, between 2.0 and 2.3 GeV/c². The two reactions have been analysed at three different beam settings: 1.4, 1.06 and 0.92 GeV/c for reaction (1) and 1.4, 1.2 and 1.06 GeV/c for reaction (2).     

The electronic isotope shift in the A2Π-X2Σ+ bands of BeH,BeD and BeT

The 0-0, 1-1, 2-2, and 3-3 bands of the A²Π-X²Σ⁺ transition of the tritiated beryllium monohydride molecule have been observed at 5000 Å in emission using a beryllium hollow-cathode discharge in a He + T₂ mixture. The rotational analysis of these bands yields the following principal molecular constants.

$\text{A}{}^2\text{Π:}\text{B}{}_{\mathrm{e}}\text{= 4.192}\text{cm}{}^{\mathrm{?1}}\text{; r}{}_{\mathrm{e}}\text{= 1.333}\text{A}\text{?}$

$\text{X}{}^2\text{Σ:}\text{B}{}_{\mathrm{e}}\text{= 4.142}\text{cm}{}^{\mathrm{?1}}\text{; r}{}_{\mathrm{e}}\text{= 1.341}\text{A}\text{?}$

$\text{ω}{}_{\mathrm{e}}\text{′ ? ω}{}_{\mathrm{e}}\text{″ = 16.36}\text{cm}{}^{\mathrm{?1}}\text{; ω}{}_{\mathrm{e}}\text{′X}{}_{\mathrm{e}}\text{′ ? ω}{}_{\mathrm{e}}\text{″X}{}_{\mathrm{e}}\text{″ = 0.84}\text{cm}{}^{\mathrm{?1}}$

From the pure electronic energy difference (E_Π - E_Σ)_BeT = 20 037.91 ± 1.5 cm^?1 and the corresponding previously known values for BeH and BeD, the following electronic isotope shifts are derived

$\text{ΔE}{}_{\mathrm{e}}{}^{\mathrm{i}}\text{(}\text{BeH}\text{?}\text{BeT}\text{) = ?4.7 ≠ 1.5}\text{cm}{}^1\text{, ΔE}{}_{\mathrm{e}}{}^{\mathrm{i}}\text{(}\text{BeH}\text{?}\text{BeT}\text{) = ?1.8 ≠ 1.5}\text{cm}{}^1$

and related to the theoretical approach given by Bunker to the problem of the breakdown of the Born-Oppenheimer approximation.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

The centrifugal distortion constants of disulfur monoxide

The microwave spectrum of the molecular transient disulfur monoxide, S₂O, has been reexamined and the microwave measurements have been extended into the millimeterwave region. From the present data, the following ground-state rotational constants and quartic distortion constants have been obtained (MHz):

$\text{A = 41915.44,}\text{B = 5059.07,}\text{C = 4507.19}$

$\text{δ}{}_{\mathrm{J}}\text{= 1.895 X 10}{}^{\mathrm{?}}\text{, δ}{}_{\mathrm{JK}}\text{= ?3.192 X 10}{}^{\mathrm{?2}}\text{,}\text{δ}{}_{\mathrm{K}}\text{= 1.197 X 10}{}^0$

$\text{δ}{}_{\mathrm{J}}\text{= 3.453 X 10}{}^{\mathrm{?4}}\text{and δ}{}_{\mathrm{K}}\text{= 1.223 X 10}{}^{\mathrm{?2}}$

The centrifugal distortion constants obtained from the rotational spectrum are used to discuss the vibrational spectrum of disulfur monoxide.     

Fourier spectrometry: Rovibrational analysis of an infrared 1Π → 1Σ system of yttrium monoiodide

The infrared spectrum of yttrium monoiodide has been excited in an electrodeless microwave discharge and explored between 2500 and 12 000cm^?1 with a high-resolution Fourier transform spectrometer. A unique system is observed (ν₀₀ = 9905.520 cm^?1), which we attribute to a ${}^1\text{Π}\text{→}{}^1\text{Σ}$ transition and an extensive analysis is made. Rovibrational constants are obtained for both states mainly from a simultaneous multiband fitting. This procedure is applied to the whole set of 2231 observed line wavenumbers in the 1-0, 0-0, and 0–1 bands, yielding a final weighted standard deviation of 0.0038 cm^?1. Furthermore, a partial analysis of the 2-0 and 3-1 bands is performed. The following equilibrium constants are derived (cm^?1):

$\text{ω′}{}_{\mathrm{e}}\text{=192.210 ω′}{}_{\mathrm{e}}\text{x′}{}_{\mathrm{e}}\text{=0.463}$

$\text{B′}{}_{\mathrm{e}}\text{=0.0399133 α′}{}_{\mathrm{e}}\text{=0.0001150}$

$\text{ω″}{}_{\mathrm{e}}\text{=215.815 ω″}{}_{\mathrm{e}}\text{x″}{}_{\mathrm{e}}\text{=0.514}$

$\text{B″}{}_{\mathrm{e}}\text{=0.0422163 α″}{}_{\mathrm{e}}\text{=0.0001125}$

High-order constants D_v and H_v are also calculated for the various vibrational levels (v′ = 0, 1, 2, 3; v″ = 0, 1).     

High resolution Fourier spectroscopy of P2 infrared emission spectrum: Analysis of two new systems b3Πg → w3Δu and A1Πg → W1Δu

The investigation of the emission infrared spectrum of P₂ was performed with a high resolution Fourier spectrometer. Two new electronic systems were attributed to b³Π_g → w³Δ_u and A¹Π_g → W¹Δ_u transitions. The molecular parameters are obtained by a complete fitting procedure. The main equilibrium constants of the new states are (in cm^?1):

$\text{ω}{}^3\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 243228.07 ω}{}_{\mathrm{e}}\text{= 591.3 ω}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.5}$

$\text{B}{}_{\mathrm{e}}\text{= 0.256040 δ}{}_{\mathrm{e}}\text{= 0.001409 D}{}_{\mathrm{e}}\text{= 19.0 X 10}{}^{\mathrm{?8}}$

$\text{W}{}^1\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 31096.64 W}{}_{\mathrm{e}}\text{= 627.206 W}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.331}$

$\text{B}{}_{\mathrm{e}}\text{= 0.2628 δ}{}_{\mathrm{e}}\text{= 0.0014 D}{}_{\mathrm{e}}\text{= 23 X 10}{}^{\mathrm{?8}}$

     

The closure of cones in the algebra of test functions

We prove that the topological closure of the cone K of positive elements in the algebra of test functions is the same for several topologies (K?τo° = K?τ∞). Further we show that all elements of the closure of K are of the form

$\text{∑}\text{I=1}\text{∞}\text{f}{}^{\mathrm{(i)1}}\text{f}{}^{\mathrm{(i)}}\text{with f}{}^{\mathrm{<mtext>(</mtext><mtext>i</mtext><mtext>)</mtext>}}\text{?}\text{L}{}_{\mathrm{?}}$

and the sum converges. Applying these results, we give a characterization of the elements of K?^τ_o too.     

Sequential two-photon spectroscopy of some ion-pair states of IBr

Molecular constants of the first E 0⁺ ion-pair state of IBr vapor have been determined using polarization-labeling spectroscopy applied to the sequential transitions E 0⁺ ← B′ 0⁺ ← X 0⁺, while the second f 0⁺ ion-pair state is reported and characterized for the first time. A least-squares, simultaneous analysis of data for the I⁷⁹Br and I⁸¹Br isotopes gives the following constants (in cm^?1) for I⁷⁹Br:

$\text{E}\text{state}\text{: T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 39487.32(12), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{= 119.518(21), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{ξ}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.2109(12)}$

,

$\text{ω}{}_{\mathrm{<mtext>e</mtext>}}\text{y}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 2.34(22) × 10}{}^{\mathrm{?4}}\text{, B}{}_{\mathrm{<mtext>e</mtext>}}\text{= 2.9701(14) × 10}{}^{\mathrm{?2}}$

,

$\text{α}{}_{\mathrm{<mtext>e</mtext>}}\text{= 5.43(59) × 10}{}^{\mathrm{?5}}\text{,}\text{and}\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 6.8(16) × 10}{}^{\mathrm{?7}}$

.

$\text{F}\text{state}\text{: T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 45382.58(17), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{= 128.805(66), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{ξ}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.3630(69)}$

,

$\text{ω}{}_{\mathrm{<mtext>e</mtext>}}\text{y}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 9.7(22) × 10}{}^{\mathrm{?4}}\text{, B}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.0073(30) × 10}{}^{\mathrm{?2}}\text{,}\text{and}\text{α}{}_{\mathrm{<mtext>e</mtext>}}\text{= 8.52(48) × 10}{}^{\mathrm{?5}}$

. Preliminary data for the first $\text{Ω}\text{= 1}$ ion-pair state, accessed in the sequence $\text{1(}{}^3\text{P}{}_2\text{) ← A(}\text{Ω}\text{= 1) ← X 0}{}^{\mathrm{+}}$, indicate that T_e is ?30 cm^?1 higher in energy than that of the E state.     

Simultaneous diffusion of calcium and strontium in KCl single crystals

Concentration dependent diffusion coefficients for ⁴⁵Ca²⁺ and ⁸⁵Sr²⁺ in purified KCl were measured using a sectioning method. KCl was purified by an ion exchange — Cl₂?HCl process and the crystals grown under $\text{1}\text{6}$ atmosphere of HCl. The tracers were purified on small disposable ion exchange columns to remove precessor and daughter impurities prior to use in a diffusion anneal. Isothermal diffusion anneals were made in the temperature range from 451% to 669%C. At temperatures above 580%C (the lowest melting eutectic in this system) diffusion was from a vapor source: below 580%C surface depositied sources were used. The saturation diffusion coefficients. enthalpies and entropies of impurity-vacancy associations were calculated using the common ion model for simultaneous diffusion of divalent ions in alkali halides. In KCl the saturation diffusion coefficients D_S(ca) and D_s(Sr) are given by

$\text{D}{}_{\mathrm{s}}\text{(Ca) = 9.93 × 10}{}^{\mathrm{?5}}\text{exp(?0.592}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(1) and

$\text{D}{}_{\mathrm{s}}\text{(Sr) = 1.20 × 10}{}^{\mathrm{?3}}\text{exp(?0.871}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(2) for calcium and strontium, respectively. The Gibbs free energy of association of the impurity vacancy complex in KCl for calcium can be represented by

$\text{Δg(Ca) = ?-0.507 eV + (2.25 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

(3) and that for strontium by

$\text{Δg(Sr) = ?0.575 eV + (2.90 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

. (4)     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Ground-state molecular constants of bideuterated methane

A rotational analysis of the satellite bands of the β system of ZrO gives the splittings in the triplet states. For the lowest triplet state X′³Δ, these splittings are:

$\text{δF}{}_{\mathrm{1,2}}\text{= 287.9 ± 0.1 cm}{}^{\mathrm{?1}}\text{,}$

$\text{δF}{}_{\mathrm{2,3}}\text{= 337.6 ± 0.4 cm}{}^{\mathrm{?1}}\text{.}$

     

A study of the reactions π+p→ K+∑+ and K−p→π−∑+ at 10 GeV/c

For the first time, the reactions π⁺p→K⁺∑⁺ and K^?p→π^?∑⁺ have been studied in the same apparatus. This has been done at an adequately high momentum (10.1 GeV/c) to allow a check of the prediction of exchange degeneracy, that the differential cross sections should be converging at high energy. We have measured the cross section for momentum transfers t between t_min and t = ?0.3 (GeV/c)². We find that for both reactions the differential cross section shows an exponential fall, with no deviations right in to t =t_min (where some other experiments have shown a dip in the cross section). Furthermore, we find the magnitude of the differential cross sections to be closely similar at t = 0, with a ratio

$\text{R=}\text{(}\text{d}\text{σ}\text{d}\text{t)}{}_{\mathrm{t=0}}\text{(}\text{K}{}^{\mathrm{?}}\text{p}\text{→π}{}^{\mathrm{?}}\text{∑}{}^{\mathrm{+}}\text{)}\text{(}\text{d}\text{σ}\text{d}\text{t)}{}_{\mathrm{t=0}}\text{(π}{}^{\mathrm{+}}\text{p}\text{→}\text{K}{}^{\mathrm{+}}\text{∑}{}^{\mathrm{+}}$

However, the slope for the positive reaction is about 19% steeper than that for the negative reaction.     

Lie algebraic aspects of quantum statistics. parafermi statistics

We study in detail the Lie-algebraical properties of the quantization condition for spinor fields

$\text{[a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{,a}{}^{\mathrm{?}}{}_{\mathrm{j}}\text{],a}{}^{\mathrm{\pm }}{}_{\mathrm{i}}\text{= ±2δ}{}_{\mathrm{ij}}\text{a}{}^{\mathrm{\pm }}{}_{\mathrm{j}}$

.It turns out that the parafermi statistics is one particular solution of this relation: it is the minimal rank simple Lie algebra generated by the operators a^±_i entering into the above relation. We point out some other solutions.     

Microwave optical double resonance and continuous wave dye laser excitation spectroscopy of NO2: Rotational assignment of the K = 0−4 subbands of the 593 nm band

A rotational assignment of approximately 80 lines with K_a′ = 0, 1, 2, 3, and 4 has been made of the 593 nm ${}^2\text{A}{}_1\text{→}{}^2\text{B}{}_2$ band of NO₂ using cw dye laser excitation and microwave optical double-resonance spectroscopy. Rotational constants for the ²B₂ state were obtained as A = 8.52 cm^?1, B = 0.458 cm^?1, and C = 0.388 cm^?1. Spin splittings for the K_a′ = 0 excited state levels fit a simple symmetric top formula and give $\text{(?}{}_{\mathrm{bb}}\text{+ ?}{}_{\mathrm{cc}}\text{)}\text{2}\text{= ?0.0483}\text{cm}{}^{\mathrm{?1}}$. Spin splittings for K_a′ = 1 (N′ even) are irregular and are shown to change sign between N′ = 6 and 8. Assuming that the large inertial defect of 4.66 amu Ų arises solely from A, a structure for the ²B₂ state is obtained which gives $\text{r}\text{(NO) = 1.35}\text{A}\text{?}$ and an ONO angle of 105°. Alternatively, weighting the three rotational constants equally gives $\text{r = 1.29}\text{A}\text{?}$ and θ = 118°.     

The “strong Kadison inequality” of Woronowicz

In the terminology of [4] it is shown that a normalized positive map ? from a C¹-algebra $\text{A}$ into M₂ is a sum ?=ψ₁+ψ₂, where ψ₁ is completely positive and ψ₂ is completely copositive, if and only if for all a?1 in $\text{A}$ the normalized positive map

$\text{?}{}_{\mathrm{a}}\text{=?(a}{}^2\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{?(a·a)?(a}{}^2\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$

satisfies the “strong Kadison inequality” of S.L. Woronowicz ([4]). p. 178).     

The B̃2Σ−g (Πu) ← X̃2A1 system of nitrogen dioxide in neon matrices

The $\text{B}\text{?}\text{←}\text{X}\text{?}$ band system of NO₂, ${}^2\text{Σ}{}^{\mathrm{?}}{}_{\mathrm{g}}\text{(π}{}_{\mathrm{u}}\text{) ←}{}^2\text{A}{}_1$, has been measured in absorption in a neon matrix at 6 K, using ¹⁵NO₂ and N¹⁸O₂ in addition to the normal isotope. The spectrum consists essentially of a single, long progression of bands terminating on successive levels of the bending mode in the upper state. Transitions to odd- and even-v₂′ states occur with a uniform intensity distribution indicating that the rotation of the bent ground state of NO₂ about its near-prolate axis is hindered in the matrix. The observations strongly suggest that the top axis of the molecule coincides with a C₂ axis of neon crystals in the polycrystalline matrix. Relative to the vapor absorption the matrix spectrum is red shifted by about 150 cm^?1, the crystal field parameter V₂ and principal constants of the $\text{B}\text{?}$ state of ¹⁴N¹⁶O₂ in neon being

$\text{T}{}_{010}\text{14 571 cm}{}^{\mathrm{?1}}\text{: x}{}_{22}\text{, ?0.3 cm}{}^{\mathrm{?1}}\text{;}$

$\text{w}{}_2\text{460.2 cm}{}^{\mathrm{?1}}\text{: V}{}_2\text{, 80 cm}{}^{\mathrm{?1}}\text{.}$