Subtraction Menger algebras

Abstract characterizations of Menger algebras of partial $n$-place functions defined on a set $A$ and closed under the set-theoretic difference functions treatment as subsets of the Cartesian product $A^{n+1}$ are given

Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Interplay of quark and meson degrees of freedom in a near-threshold resonance

We investigate the interplay of quark and meson degrees of freedom in a physical state representing a near-threshold resonance for the case of a single continuum channel. We demonstrate that such a near-threshold resonance may possess quite peculiar properties if both quark and meson dynamics generate weakly coupled near-threshold poles in the S-matrix. In particular, the scattering t-matrix may possess zeros in this case. We also discuss possible implications for production reactions as well as studies within lattice QCD.Comment: LaTeX2e, 11 pages, minor typo corrections, to appear in Eur.Phys.J.

Whole Body MRI in Multiple Myeloma: Optimising Image Acquisition and Read Times

Objective: To identify the whole-body MRI (WB-MRI) image type(s) with the highest value for assessment of multiple myeloma, in order to optimise acquisition protocols and read times. Methods: Thirty patients with clinically-suspected MM underwent WB-MRI at 3 Tesla. Unenhanced Dixon images [fat-only (FO) and water-only (WO)], post contrast Dixon [fat-only plus contrast (FOC) and water-only plus contrast (WOC)] and diffusion weighted images (DWI) of the pelvis from all 30 patients were randomised and read by three experienced readers. For each image type, each reader identified and labelled all visible myeloma lesions. Each identified lesion was compared with a composite reference standard achieved by review of a complete imaging dataset by a further experienced consultant radiologist to determine truly positive lesions. Lesion count, true positives, sensitivity, and positive predictive value were determined. Time to read each scan set was recorded. Confidence for a diagnosis of myeloma was scored using a Likert scale. Conspicuity of focal lesions was assessed in terms of percent contrast and contrast to noise ratio (CNR). Results: Lesion count, true positives, sensitivity and confidence scores were significantly higher when compared to other image types for DWI (P<0.0001 to 0.003), followed by WOC (significant for sensitivity (P<0.0001 to 0.004), true positives (P = 0.003 to 0.049) and positive predictive value (P< 0.0001 to 0.006)). There was no statistically significant difference in these metrics between FO and FOC. Percent contrast was highest for WOC (P = 0.001 to 0.005) and contrast to noise ratio (CNR) was highest for DWI (P = 0.03 to 0.05). Reading times were fastest for DWI across all observers (P< 0.0001 to 0.014). Discussion: Observers detected more myeloma lesions on DWI images and WOC images when compared to other image types. We suggest that these image types should be read preferentially by radiologists to improve diagnostic accuracy and reporting efficiency

Quark-Mass Dependence of Elastic πK Scattering from QCD

We present a determination of the isospin-1/2 elastic πK scattering amplitudes in S and P partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the P-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the S-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a K/K*0(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies

Test of Nuclear Wave Functions for Pseudospin Symmetry

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.Comment: 11 pages, 4 figures, minor changes in text and figures to conform with PRL requirement

Bound -> free and bound -> bound multichannel emission spectra from selectively excited Rydberg states in the ZnAr and CdAr van der Waals complexes

Multichannel dispersed emission spectra recorded upon a selective excitation of Rydberg electronic energy states in the ZnAr and CdAr van der Waals (vdW) complexes are analysed as a proof-of-concept of the future experimental approach. Simulations of the emission spectra are based on ab-initio calculated interatomic potentials and transition dipole moments (TDMs). Experimental set-up that is under construction along with the experimental procedure are discussed