Existence of Eigenvalues for Anisotropic and Fractional Anisotropic Problems via Ljusternik-Schnirelmann Theory

In this work, our interest lies in proving the existence of critical values of the following Rayleigh-type quotients $$Q_{\mathbf p}(u) = \frac{\|\nabla u\|_{\mathbf p}}{\|u\|_{\mathbf p}},\quad\text{and}\quad Q_{\mathbf s,\mathbf p}(u) = \frac{[u]_{\mathbf s,\mathbf p}}{\|u\|_{\mathbf p}},$$ where $\mathbf p = (p_1,\dots,p_n)$, $\mathbf s=(s_1,\dots,s_n)$ and $$\|\nabla u\|_{\mathbf p} = \sum_{i=1}^n \|u_{x_i}\|_{p_i}$$ is an anisotropic Sobolev norm, $[u]_{\mathbf s,\mathbf p}$ is a fractional version of the same anisotropic norm, and $\|u\|_{\mathbf p}$ is an anisotropic Lebesgue norm. Using the Ljusternik-Schnirelmann theory, we prove the existence of a sequence of critical values and we also find an associated Euler-Lagrange equation for critical points. Additionally, we analyze the connection between the fractional critical values and its local counterparts.Comment: 18 pages, submitte

Parametrization of the octupole degrees of freedom

A simple parametrization for the octupole collective variables is proposed and the symmetries of the wave functions are discussed in terms of the solutions corresponding to the vibrational limit. [PACS: 21.60Ev, 21.60.Fw, 21.10.Re]Comment: 14 page

Alpha decay and proton-neutron correlations

We study the influence of proton-neutron (p-n) correlations on alpha-decay width. It is shown from the analysis of alpha Q values that the p-n correlations increase the penetration of the alpha particle through the Coulomb barrier in the treatment following Gamow's formalism, and enlarges the total alpha-decay width significantly. In particular, the isoscalar p-n interactions play an essential role in enlarging the alpha-decay width. The so-called "alpha-condensate" in Z > 84 isotopes are related to the strong p-n correlations.Comment: 5 pages, 6 figures, accepted for publication in Phys. Rev. C (R.C.

Tumor talk and child-well being: perceptions of \u27good\u27 and \u27bad\u27 news among parents of children with advanced cancer

CONTEXT: Little is known about how parents of children with advanced cancer classify news they receive about their child\u27s medical condition. OBJECTIVE: To develop concepts of "good news" and "bad news" in discussions of advanced childhood cancer from parent perspectives. METHODS: Parents of children with advanced cancer cared for at three children\u27s hospitals were asked to share details of conversations in the preceding 3 months that contained "good news" or "bad news" related to their child\u27s medical condition. We used mixed methods to evaluate parent responses to both open-ended and fixed response items. RESULTS: Of 104 enrolled parents, 86 (83%) completed the survey. Six (7%) parents reported discussing neither good nor bad news, 18 (21%) reported only bad news, 15 (17%) reported only good news, and 46 (54%) reported both good and bad news (1 missing response). Seventy-six parents (88%) answered free response items. Descriptions of both good and bad news discussions consisted predominantly of "tumor talk" or cancer control. Additional treatment options featured prominently, particularly in discussions of bad news (42%). Child well-being, an important good news theme, encompassed treatment tolerance, symptom reduction, and quality of life. CONCLUSION: A majority of parents of children with advanced cancer report discussing both good and bad news in the preceding 3 months. While news related primarily to cancer control, parents also describe good news discussions related to their child\u27s well-being. Understanding how parents of children with advanced cancer classify and describe the news they receive may enhance efforts to promote family-centered communication

Feasibility of conducting a palliative care randomized controlled trial in children with advanced cancer: assessment of the PediQUEST study

ediatric palliative care randomized controlled trials (PPC-RCTs) are uncommon

An Algebraic Pairing Model with Sp(4) Symmetry and its Deformation

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0^+ ground states, they also have a large effect on the energies of excited states, including especially excited 0^+ states. In this article we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp_{(q)}(4) to different realizations of u_{(q)}(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0^{+} states of even-even and odd-odd nuclei in the 1d_{3/2}, 1f_{7/2}, and 1f_{5/2}2p_{1/2}2p_{3/2}1g_{9/2} shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Sp_{q}(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with non-linear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0^{+} energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking, and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher-order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.Comment: 19 pages, 5 figures minor changes; improvements to achieve a better and clearer presentation of our messages and idea

Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States

We present the study of weakly bound, neutron-rich nuclei using the nuclear shell model employing the complex Berggren ensemble representing the bound single-particle states, unbound Gamow states, and the non-resonant continuum. In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body finite depth (Woods-Saxon) potential and a residual two-body interaction. We discuss the basic ingredients of the Gamow Shell Model. The formalism is illustrated by calculations involving {\it several} valence neutrons outside the double-magic core: $^{6-10}$He and $^{18-22}$O.Comment: 19 pages, 20 encapsulated PostScript figure

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page

Diversities, affinities and diasporas: a southern lens and methodology for understanding multilingualisms

We frame multilingualisms through a growing interest in a linguistics and sociology of the ‘south’ and acknowledge earlier contributions of linguists in Africa, the Américas and Asia who have engaged with human mobility, linguistic contact and consequential ecologies that alter over time and space. Recently, conversations of multilingualism have drifted in two directions. Southern conversations have become intertwined with ‘decolonial theory’, and with ‘southern’ theory, thinking and epistemologies. In these, ‘southern’ is regarded as a metaphor for marginality, coloniality and entanglements of the geopolitical north and south. Northern debates that receive traction appear to focus on recent ‘re-awakenings’ in Europe and North America that mis-remember southern experiences of linguistic diversity. We provide a contextual backdrop for articles in this issue that illustrate intelligences of multilingualisms and the linguistic citizenship of southern people. In these, southern multilingualisms are revealed as phenomena, rather than as a phenomenon defined usually in English. The intention is to suggest a third direction of mutual advantage in rethinking the social imaginary in relation to communality, entanglements and interconnectivities of both South and North