Search

A $q$-analogue of $r$-Whitney numbers of the second kind, denoted by $W_{m,r}[n,k]_q$, is defined by means of a triangular recurrence relation. In this paper, several fundamental properties for the $q$-analogue are established including other forms of recurrence relations, explicit formulas and generating functions. Moreover, a kind of Hankel transform for $W_{m,r}[n,k]_q$ is obtained., Comment: The paper is composed of 13 pages

The recently proposed Fluctuating Two-Ray (FTR) model is gaining momentum as a reference fading model in scenarios where two dominant specular waves are present. Despite the numerous research works devoted to the performance analysis under FTR fading, little attention has been paid to effectively understanding the interplay between the fading model parameters and the fading severity. According to a new scale defined in this work, which measures the hyper-Rayleigh character of a fading channel in terms of the Amount of Fading, the outage probability and the average capacity, we see that the FTR fading model exhibits a full hyper-Rayleigh behavior. However, the Two-Wave with Diffuse Power fading model from which the former is derived has only strong hyper-Rayleigh behavior, which constitutes an interesting new insight. We also identify that the random fluctuations in the dominant specular waves are ultimately responsible for the full hyper-Rayleigh behavior of this class of fading channels., Comment: This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accesible

For a given planar convex compact set $K$, consider a bisection $\{A,B\}$ of $K$ (i.e., $A\cup B=K$ and whose common boundary $A\cap B$ is an injective continuous curve connecting two boundary points of $K$) minimizing the corresponding maximum diameter (or maximum width) of the regions among all such bisections of $K$. In this note we study some properties of these minimizing bisections and we provide analogous to the isodiametric (Bieberbach, 1915), the isominwidth (P\'al, 1921), the reverse isodiametric (Behrend, 1937), and the reverse isominwidth (Gonz\'alez Merino \& Schymura, 2018) inequalities., Comment: 18 pages, 5 figures

An off-line ion source station has been commissioned at the IGISOL (Ion Guide Isotope Separator On-Line) facility. It offers the infrastructure needed to produce stable ion beams from three off-line ion sources in parallel with the radioactive ion beams produced from the IGISOL target chamber. This has resulted in improved feasibility for new experiments by offering reference ions for Penning-trap mass measurements, laser spectroscopy and atom trap experiments., Comment: 3 pages, 1 figure, submitted to Nuclear Instruments and Methods

The MORA (Matter's Origin from the RadioActivity of trapped and oriented ions) project aims at measuring with unprecedented precision the D correlation in the nuclear beta decay of trapped and oriented ions. The D correlation offers the possibility to search for new CP-violating interactions, complementary to searches done at the LHC and with Electric Dipole Moments. Technically, MORA uses an innovative in-trap orientation method which combines the high trapping efficiency of a transparent Paul trap with laser orientation techniques. The trapping, detection, and laser setups are under development, for first tests at the Accelerator laboratory, JYFL, in the coming years., Comment: 16 pages, 6 figures, proceedings of the TCP 2018 conference, to appear in Hyp. Int

Isomeric yield ratios for the odd-$A$ isotopes of $^{119-127}$Cd and $^{119-127}$In from 25-MeV proton-induced fission on natural uranium have been measured at the JYFLTRAP double Penning trap, by employing the Phase-Imaging Ion-Cyclotron-Resonance technique. With the significantly improved mass resolution of this novel method isomeric states separated by 140 keV from the ground state, and with half-lives of the order of 500 ms, could be resolved. This opens the door for obtaining new information on low-lying isomers, of importance for nuclear structure, fission and astrophysics. In the present work the experimental isomeric yield ratios are used for the estimation of the root-mean-square angular momentum ($J_\mathrm{rms}$) of the primary fragments. The results show a dependency on the number of unpaired protons and neutrons, where the odd-$Z$ In isotopes carry larger angular momenta. The deduced values of $J_\mathrm{rms}$ display a linear relationship when compared with the electric quadrupole moments of the fission products., Comment: 10 pages, 4 captioned figures

Orthogonal frequency division multiplexing (OFDM) signals with rectangularly windowed pulses exhibit low spectral confinement. Two approaches usually referred to as pulse-shaping and active interference cancellation (AIC) are classically employed to reduce the out-of-band emission (OOBE) without affecting the receiver. This paper proposes a spectral shaping method that generalizes and unifies these two strategies. To this end, the OFDM carriers are shaped with novel pulses, referred to as generalized pulses, that consist of the ones used in conventional OFDM systems plus a series of cancellation terms aimed at reducing the OOBE of the former. Hence, each generalized pulse embeds all the terms required to reduce its spectrum in the desired bands. This leads to a data-independent optimization problem that notably simplifies the implementation complexity and allows the analytical calculation of the resulting power spectral density (PSD), which in most methods found in the literature can only be estimated by means of simulations. As an example of its performance, the proposed technique allows complying with the stringent PSD mask imposed by the EN 50561-1 with a data carrier loss lower than 4%. By contrasts, 28% of the data carriers have to be nulled when pulse-shaping is employed in this scenario.

We report the first detection of the second-forbidden, non-unique, $2^+\rightarrow 0^+$, ground-state transition in the $\beta$ decay of $^{20}$F. A low-energy, mass-separated $^{20}\rm{F}^+$ beam produced at the IGISOL facility in Jyv\"askyl\"a, Finland, was implanted in a thin carbon foil and the $\beta$ spectrum measured using a magnetic transporter and a plastic-scintillator detector. The $\beta$-decay branching ratio inferred from the measurement is $b_{\beta} = [ 0.41\pm 0.08\textrm{(stat)}\pm 0.07\textrm{(sys)}] \times 10^{-5}$ corresponding to $\log ft = 10.89(11)$, making this one of the strongest second-forbidden, non-unique $\beta$ transitions ever measured. The experimental result is supported by shell-model calculations and has significant implications for the final evolution of stars that develop degenerate oxygen-neon cores. Using the new experimental data, we argue that the astrophysical electron-capture rate on $^{20}$Ne is now known to within better than 25% at the relevant temperatures and densities., Comment: 13 pages, 16 figures, 4 tables

Background: $\beta$-delayed multiple neutron emission has been observed for some nuclei with A$\leq$100, with $^{100}$Rb being the heaviest $\beta$2n emitter measured to date. So far, only 25 P$_{2n}$ values have been determined for the $\sim$300 nuclei that may decay in this way. Accordingly, it is of interest to measure P$_{2n}$ values for the other possible multiple neutron emitters throughout the chart of the nuclides. It is of particular interest to make such measurement for nuclei with A$>$100 to test the predictions of theoretical models and simulation tools for the decays of heavy nuclei in the region of very neutron-rich nuclei. In addition, the decay properties of these nuclei are fundamental for the understanding of astrophysical nucleosynthesis processes such as the $r$-process, and safety inputs for nuclear reactors. Purpose: To determine for the first time the two neutron branching ratio, P$_{2n}$ value, for $^{136}$Sb through a direct neutron measurement, and to provide precise P$_{1n}$ values for $^{136}$Sb and $^{136}$Te. Method: Pure beams were provided by the JYFLTRAP at the IGISOL facility of the University of Jyv\"askyl\"a, Finland. The purified ions were implanted into a moving tape at the end of the beam line. The detection setup consisted of a plastic scintillator placed right behind the implantation point, and the BELEN detector, based on neutron counters embedded in a polyethylene matrix. The analysis was based on the study of the $\beta$- and neutron- growth-and-decay curves and the $\beta$-one-neutron and $\beta$-two-neutron time correlations. Results: The P$_{2n}$ value of $^{136}$Sb was found to be 0.14(3)\% and the measured P$_{1n}$ values for $^{136}$Sb and $^{136}$Te were found to be 32.2(15)\% and 1.47(6)\%, respectively. The measured P$_{2n}$ value is a factor 44 smaller than predicted by the FRDM+QRPA model used for $r$-process calculations., Comment: 11 pages, 10 figures

In this paper we study the bisections of a centrally symmetric planar convex body which minimize the maximum relative diameter functional. We give necessary and sufficient conditions for being a minimizing bisection, as well as analyzing the behavior of the so-called standard bisection., Comment: 16 pages, 14 figures

The rare-earth peak in the $r$-process abundance pattern depends sensitively on both the astrophysical conditions and subtle changes in nuclear structure in the region. This work takes an important step elucidating the nuclear structure and reducing the uncertainties in $r$-process calculations via precise atomic mass measurements at the JYFLTRAP double Penning trap. $^{158}$Nd, $^{160}$Pm, $^{162}$Sm, and $^{164-166}$Gd have been measured for the first time and the precisions for $^{156}$Nd, $^{158}$Pm, $^{162,163}$Eu, $^{163}$Gd, and $^{164}$Tb have been improved considerably. Nuclear structure has been probed via two-neutron separation energies $S_{2n}$ and neutron pairing energy metrics $D_n$. The data do not support the existence of a subshell closure at $N=100$. Neutron pairing has been found to be weaker than predicted by theoretical mass models. The impact on the calculated $r$-process abundances has been studied. Substantial changes resulting in a smoother abundance distribution and a better agreement with the solar $r$-process abundances are observed., Comment: 8 pages, 4 figures, accepted for publication in Physical Review Letters

We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated algebras, mainly the nilpotency and solvability in the case of Leibniz algebras.

Masses of $^{52}$Co, $^{52}$Co$^m$, $^{52}$Fe, $^{52}$Fe$^m$, and $^{52}$Mn have been measured with the JYFLTRAP double Penning trap mass spectrometer. Of these, $^{52}$Co and $^{52}$Co$^m$ have been experimentally determined for the first time and found to be more bound than predicted by extrapolations. The isobaric multiplet mass equation for the $T=2$ quintet at $A=52$ has been studied employing the new mass values. No significant breakdown (beyond the $3\sigma$ level) of the quadratic form of the IMME was observed ($\chi^2/n=2.4$). The cubic coefficient was 6.0(32) keV ($\chi^2/n=1.1$). The excitation energies for the isomer and the $T=2$ isobaric analogue state in $^{52}$Co have been determined to be 374(13) keV and 2922(13) keV, respectively. The $Q$ value for the proton decay from the $19/2^-$ isomer in $^{53}$Co has been determined with an unprecedented precision, $Q_{p} = 1558.8(17)$ keV. The proton separation energies of $^{52}$Co and $^{53}$Ni relevant for the astrophysical rapid proton capture process have been experimentally determined for the first time. \end{abstract}, Comment: 12 pages, 13 figures, submitted to Phys. Rev. C (26.9.2016)

The two interferometers of the Laser Interferometry Gravitaional-wave Observatory (LIGO) recently detected gravitational waves from the mergers of binary black hole systems. Accurate calibration of the output of these detectors was crucial for the observation of these events, and the extraction of parameters of the sources. The principal tools used to calibrate the responses of the second-generation (Advanced) LIGO detectors to gravitational waves are systems based on radiation pressure and referred to as Photon Calibrators. These systems, which were completely redesigned for Advanced LIGO, include several significant upgrades that enable them to meet the calibration requirements of second-generation gravitational wave detectors in the new era of gravitational-wave astronomy. We report on the design, implementation, and operation of these Advanced LIGO Photon Calibrators that are currently providing fiducial displacements on the order of $10^{-18}$ m/$\sqrt{\textrm{Hz}}$ with accuracy and precision of better than 1 %., Comment: 14 pages, 19 figures

The mass of $^{31}$Cl has been measured with the JYFLTRAP double Penning trap mass spectrometer at the Ion-Guide Isotope Separator On-Line (IGISOL) facility. The determined mass-excess value, -7034.7(34) keV, is 15 times more precise than in the Atomic Mass Evaluation 2012. The quadratic form of the isobaric multiplet mass equation for the T=3/2 quartet at A=31 fails ($\chi^2_n$=11.6) and a non-zero cubic term, d=-3.5(11) keV, is obtained when the new mass value is adopted. $^{31}$Cl has been found to be less proton-bound with a proton separation energy of $S_p$=265(4) keV. Energies for the excited states in $^{31}$Cl and the photodisintegration rate on $^{31}$Cl have been determined with significantly improved precision using the new $S_p$ value. The improved photodisintegration rate helps to constrain astrophysical conditions where $^{30}$S can act as a waiting point in the rapid proton capture process in type I x-ray bursts., Comment: 6 pages, 4 figures, submitted to Phys. Rev. C Rapid Comm

In this work we study the maximum relative diameter functional $d_M$ in the class of multi-rotationally symmetric planar convex bodies. A given set $C$ of this class is $k$-rotationally symmetric for $k\in\{k_1,\ldots,k_n\}\subset\nn$, and so it is natural to consider the standard $k_i$-partition $P_{k_i}$ associated to $C$ (which is a minimizing $k_i$-partition for $d_M$ when $k_i\geq3$) and the corresponding value $d_M(P_{k_i})$. We establish the relation among these values, characterizing the particular sets for which all these values coincide., Comment: 16 pages, 9 figures

In this work we study subdivisions of $k$-rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called $k$-partitions, consisting of $k$ curves meeting in an interior vertex, we prove that the so-called \emph{standard $k$-partition} (given by $k$ equiangular inradius segments) is minimizing for any $k\in\mathbb{N}$, $k\geq 3$. For general subdivisions, we show that the previous result only holds for $k\leq 6$. We also study the optimal set for this problem, obtaining that for each $k\in\mathbb{N}$, $k\geq 3$, it consists of the intersection of the unit circle with the corresponding regular $k$-gon of certain area. Finally, we also discuss the problem for planar convex sets and large values of $k$, and conjecture the optimal $k$-subdivision in this case.

In this work we study the fencing problem consisting of finnding a trisection of a 3-rotationally symmetric planar convex body which minimizes the maximum relative diameter. We prove that an optimal solution is given by the so-called standard trisection. We also determine the optimal set giving the minimum value for this functional and study the corresponding universal lower bound., Comment: Preliminary version, 20 pages, 15 figures