An effective method of investigation of positive maps on the set of positive definite operators

Let $\text{A}$₁ be the algebra of linear operators on the n-dimensional Hilbert space $\text{H}$₁, and let $\text{A}$₂ be the algebra of linear operators of the m-dimensional Hilbert space $\text{H}$₂. Let $\text{L}$($\text{A}$₁, $\text{A}$₂) denote the complex space of linear maps from $\text{A}$₁ to $\text{A}$₂. By a positive map we mean an element of the space $\text{L}$($\text{A}$₁, $\text{A}$₂) (superoperator with respect to $\text{H}$₁) which maps positive definite operators in $\text{A}$₁ into positive definite operators in $\text{A}$₂. The aim of this paper is to present an effective method which allows to verify whether a given superoperator Λ∈$\text{L}$($\text{A}$₁, $\text{A}$₂) is a positive map. Besides that necessary and sufficient conditions for the positive definiteness of even-degree forms in many variables are given.     

Complete N=4 structure of low-energy effective action in N=4 super-Yang–Mills theories

Using the $\text{N}\text{=2}$ superfield approach, we construct full $\text{N}\text{=4}$ supersymmetric low-energy effective actions for $\text{N}\text{=4}$ SYM models, with both $\text{N}\text{=2}$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on $\text{N}\text{=2}$ superfield strengths W and W̄ to the full on-shell $\text{N}\text{=4}$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form $\text{ln}\text{W}\text{ln}\text{W}\text{̄}$ can be $\text{N}\text{=4}$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the $\text{N}\text{=4}$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in $\text{N}\text{=4}$ SYM models.     

Mössbauer effect studies of excited states of 155Gd

Mössbauer effect studies of the 60.0, 86.5 and 105.3 keV transitions of ¹⁵⁵Gd, yield the following nuclear parameters: $\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(60}\text{keV level}\text{) = 194 ± 15}\text{ps}$, $\text{g(87)}\text{g(0)}\text{= 1.235 ± 0.008}$, $\text{g(105)}\text{g(0)}\text{= 2.01 ± 0.05 or ?0.55 ± 0.05}$; $\text{Q(87)}\text{Q(0)}\text{= +0.087 ± 0.006}$ and $\text{Q(105)}\text{Q(0)}\text{= 1.00 ± 0.03}$ or $\text{Q(87)}\text{Q(0)}\text{= ?0.083 ± 0.008}$ and $\text{Q(105)}\text{Q(0)}\text{= = 1.16 ± 0.03}$. Theoretical considerations favour the first set of values of $\text{Q(87)}\text{Q(0)}$ and $\text{Q(105)}\text{Q(0)}$.     

Intrinsic and rotational excitations in 175Lu

The γ-ray cascades following the ¹⁷⁶Yb(p, 2n)¹⁷⁵Lu reaction are studied with Ge(Li) detectors and interpreted within the level scheme of ¹⁷⁵Lu. According to this interpretation the $\text{1}\text{2}$⁺[411], $\text{1}\text{2}$^?[541], $\text{5}\text{2}$⁺[402], $\text{7}\text{2}$⁺[404] and $\text{9}\text{2}$^?[514] rotat $\text{15}\text{2}$⁺, $\text{21}\text{2}$^?, $\text{13}\text{2}$⁺, $\text{19}\text{2}$⁺ and $\text{19}\text{2}$^? members, respectively. Fu band head is determined to be 626.6 keV. The data for the rotational bands are discussed within the particle-rotor model and compared with the available information on the corresponding bands in the adjacent Lu isotopes.     

The energy spectra and electromagnetic transitions of odd-a titanium isotopes

The isotopes ^{55, 47, 49, 51}Ti are studied in the framework of the deformed configuration mixing shell model. The calculated spectra and electromagnetic properties agree well with the observed ones. The calculations suggest the existence of an excited $\text{K =}\text{1}\text{2}$ band of states in ^{45, 47, 49}Ti and a $\text{K =}\text{7}\text{2}$ band in ⁵¹Ti. In ⁴⁹Ti this excited $\text{K =}\text{1}\text{2}$ band is more deformed than the “ground state band”. On the basis of the overall agreement between the calculated and experimental spectra and decay properties we suggest the spin assignments $\text{J =}\text{5}\text{2}$, $\text{7}\text{2}$, $\text{9}\text{2}$, $\text{5}\text{2}$ and $\text{7}\text{2}$ to the states in ⁴⁷Ti observed at 2.168, 2.97, 2.408, 2.835 and 3.223 MeV, respectively.     

Signatures of excited leptons in pp̄ collisions

We argue that the coupling strength of excited leptons to Z⁰ and W^± could be large. If excited leptons $\text{l}$¹ decay mainly radiatively they will produce a clean $\text{l}$⁺$\text{l}$^?γ signature in pp? → Z⁰ → $\text{l}$¹$\text{l}$ → $\text{l}$⁺$\text{l}$^?γ . For $\text{m}{}_{\mathrm{<mtext>l</mtext>}}{}^1\text{?40}$ GeV the photon always follows the less energetic lepton and this system has a fairly small invariant mass. The ratio of $\text{l}$⁺$\text{l}$^?γ final states to $\text{l}$⁺$\text{l}$^? final states, with the photon-lepton angle less than 90°, could be as high as 25%, an order of magnitude larger than expected from bremsstrahlung.     

The rotational bands 12+[411]and 12−[541]in 175Lu

In a study of the γ-radiation emitted in the reaction ¹⁷⁶Yb(p, 2n) excited states of the nucleus ¹⁷⁵Lu up to spin I = $\text{13}\text{2}$ have been investigated. The main results concern the rotational bands $\text{1}\text{2}$⁺ [411]and $\text{1}\text{2}$^? [541]with the corresponding band heads found at 626.60 and 370.88 keV, respectively. The half-life of the $\text{1}\text{2}$⁺[411] level has been determined to be $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 10.7±0.5}\text{ns}$. Furthermore, the band heads $\text{3}\text{2}$^?[532]and $\text{3}\text{2}{}^{\mathrm{+}}$[411]are proposed at energies of 999.0 and 1150.8 keV, respectively. Experimental E1 transition probabilities between both $\text{K =}\text{1}\text{2}$ bands are compared with calculations including the Coriolis and pairing effects, as well as theoretically deduced quadrupole deformation parameters.     

Hyperfine structure of CW dye laser populated high lying levels of 45Sc by atomic-beam magnetic-resonance

Using a cw dye laser the 3d²4s⁴F_{$\text{5}\text{2}$, $\text{7}\text{2}$} metastable levels of ⁴⁵Sc were populated by optical pumping. The second order corrected hyperfine constants are: $\text{A(}\text{5}\text{2}\text{) = 154.035 (2) MHHz}$, $\text{B(}\text{5}\text{2}\text{) = -6.45(4) MHz}$, $\text{A(}\text{7}\text{2}\text{) = 250.012(2) MHz}$, $\text{(}\text{7}\text{2}\text{) = -9.07(4) MHz}$.     

νμp and νμn charged-current interactions unfolded from high energy νμ interactions in neon

We have developed a method to separate $\text{ν}$n and $\text{ν}$p interactions from antineutrino-neon interactions by using the final state electric charge. We present the distributions of the scaling variables x and y for $\text{ν}$n and $\text{ν}$p interactions separately , along with the $\text{ν}$n and $\text{ν}$p cross section ratios as a function of x and y. We obtain a total $\text{ν}$n to $\text{ν}$p cross section ratio of 0.45± 0.08. Our results are consistent with the predictions of the simple quark parton model.     

AES,photoemission and work function study of the deposition of Cs on (100) and (111)B GaAs epitaxial layers

Work function, photoemission and AES measurements have been made on (100) and (111)B epitaxial GaAs layers as a function of caesium coverage. It has been shown that the photoemission maximum and work function minimum occur at a coverage of $\text{2}\text{3}$ of a monolayer. The reduction of the work function takes place in distinct stages with changes in the rate of fall occurring at $\text{1}\text{8}$ and $\text{1}\text{2}$ of a monolayer for the (111)B face and $\text{1}\text{8}$, $\text{1}\text{4}$, $\text{1}\text{3}$ and $\text{1}\text{2}$ of a monolayer for the (100) face. This indicates the presence of specific adsorption sites which have not been observed in previous work on these faces.     

A mathematical interpretation of Dirac's formalism part b: generalized eigenfunctions in trajectory spaces

Starting with a Hilbert space $\text{L}{}_2\text{(}\text{R}\text{,μ)}$ we introduce the dense subspace $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ where $\text{R}$ is a positive self-adjoint Hilbert–Schmidt operator on $\text{L}$₂(R,μ). For the space $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ a measure-theoretical Sobolev lemma is proved. The results for the spaces of type $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ are applied to nuclear analyticity spaces $\text{S}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}\text{=}\text{?}\text{t>0}\text{e}{}^{\mathrm{<mtext>-t</mtext><mtext>A</mtext>}}\text{(X)}$, where e^?t$\text{A}$ is a Hilbert–Schmidt operator on the Hilbert space X for each t>0. We solve the so-called generalized eigenvalue problem for a general self-adjoint operator $\text{P}$ in X.     

Resonance structure of 32S + n from transmission and differential elastic scattering experiments

Neutron transmission experiments were performed on ³²S between 0.18 MeV and 19 MeV and differential elastic scattering experiments up to 2 MeV. The resonance parameters, including spin and parity, were determined up to 1.7 MeV. The distribution of neutron strength was determined for s_{$\text{1}\text{2}$}, P_{$\text{1}\text{2}$}, P_{$\text{3}\text{2}$}, d_{$\text{3}\text{2}$}, d_{$\text{5}\text{2}$} and f-wave levels, and is compared to recent model calculations. The isotopic purity of some possible $\text{T =}\text{3}\text{2}$ isobaric analog states was deduced from their neutron widths.     

The S-wave QQqq states in the adiabatic approximation

The static potential energy for an S-wave $\text{Q}\text{Q}\text{q}\text{q}$ system is discussed in an adiabatic (Born-Oppenheimer) approximation. Both spherical bag and arbitrary bag are considered. We concentrate on those $\text{Q}\text{Q}\text{q}\text{q}$ states in which both ($\text{Q}\text{Q}$) and ($\text{q}\text{q}$) are colour singlets. Their energy level, wave function, and possible experimental observation are studied.     

Chaotic behaviour and limit cycle behaviour of anharmonic systems with periodic external perturbations

The chaotic behaviour and limit cycle behviaiour of the dynamical system $\text{x}\text{?}\text{+ α}\text{x}\text{?}\text{+}\text{d}\text{V(x)}\text{d}\text{x}\text{= ?}\text{cos}\text{(Ωt)}$ is investigated for various potentials V and parameters values α, $\text{?}$ and $\text{Ω}$.     

The electronic structures of cis-polyacetylene

The electronic structures of two possible forms of the so-called $\text{cis}$-skeletal polyacetylene ($\text{cis}$-polyacetylene) are investigated on the basis of the tight-binding LCAO-SCF-MO method under the CNDO/2 version. The analyses of the total energies per unit cell, the π bond orders and the interatomic interaction energies as to the both forms predict the $\text{cis}$-transoid backbone for the $\text{cis}$-polyacetylene. The examination of the patterns of particular molecular orbitals of the hypothetical $\text{cis}$-polymer with equal C-C bond lengths also supports the $\text{cis}$-transoid form.     

Comparison of pp and pp interactions at s = 53 GeV

Results are presented from the first p$\text{p}$ colliding beam runs at the CERN ISR, using the UA5 streamer chamber detector. p$\text{p}$ interactions at $\text{s}\text{= 53}\text{GeV}$ are compared with pp data taken in the same experiment. The results are in good agreement with extrapolations of low-energy p$\text{p}$ data.     

The p-approximations and inverse problems of expansion and contraction of n-fermion operators

The orthogonal projectors from the space $\text{L}$(n) of n-fermion operators onto its sub-spaces $\text{L}$_p(n) consisting of p-reducible elements of $\text{L}$(n>), as well as those from $\text{L}$(n) onto $\text{L}$_p(n)?$\text{L}$_p?1(n) are constructed. Using the above projectors the inverse problems of contraction and expansion are solved.