Families of weighted sum formulas for multiple zeta values

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.Comment: The conjecture at the end is reformulate

Weighted sums with two parameters of multiple zeta values and their formulas

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum formula, have been studied by many people. In this paper, we give two formulas of weighted sums with two parameters of multiple zeta values. As applications of the formulas, we find some linear combinations of multiple zeta values which can be expressed as polynomials of usual zeta values with coeffcients in the rational polynomial ring generated by the two parameters, and obtain some identities for weighted sums of multiple zeta values of small depths.Comment: 14 page

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Daily Physical Activities and Sports in Adult Survivors of Childhood Cancer and Healthy Controls: A Population-Based Questionnaire Survey

BACKGROUND: Healthy lifestyle including sufficient physical activity may mitigate or prevent adverse long-term effects of childhood cancer. We described daily physical activities and sports in childhood cancer survivors and controls, and assessed determinants of both activity patterns. METHODOLOGY/PRINCIPAL FINDINGS: The Swiss Childhood Cancer Survivor Study is a questionnaire survey including all children diagnosed with cancer 1976-2003 at age 0-15 years, registered in the Swiss Childhood Cancer Registry, who survived ≥5 years and reached adulthood (≥20 years). Controls came from the population-based Swiss Health Survey. We compared the two populations and determined risk factors for both outcomes in separate multivariable logistic regression models. The sample included 1058 survivors and 5593 controls (response rates 78% and 66%). Sufficient daily physical activities were reported by 52% (n = 521) of survivors and 37% (n = 2069) of controls (p<0.001). In contrast, 62% (n = 640) of survivors and 65% (n = 3635) of controls reported engaging in sports (p = 0.067). Risk factors for insufficient daily activities in both populations were: older age (OR for ≥35 years: 1.5, 95CI 1.2-2.0), female gender (OR 1.6, 95CI 1.3-1.9), French/Italian Speaking (OR 1.4, 95CI 1.1-1.7), and higher education (OR for university education: 2.0, 95CI 1.5-2.6). Risk factors for no sports were: being a survivor (OR 1.3, 95CI 1.1-1.6), older age (OR for ≥35 years: 1.4, 95CI 1.1-1.8), migration background (OR 1.5, 95CI 1.3-1.8), French/Italian speaking (OR 1.4, 95CI 1.2-1.7), lower education (OR for compulsory schooling only: 1.6, 95CI 1.2-2.2), being married (OR 1.7, 95CI 1.5-2.0), having children (OR 1.3, 95CI 1.4-1.9), obesity (OR 2.4, 95CI 1.7-3.3), and smoking (OR 1.7, 95CI 1.5-2.1). Type of diagnosis was only associated with sports. CONCLUSIONS/SIGNIFICANCE: Physical activity levels in survivors were lower than recommended, but comparable to controls and mainly determined by socio-demographic and cultural factors. Strategies to improve physical activity levels could be similar as for the general population

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions

Measurement of the J/ψ pair production cross-section in pp collisions at s=13 \sqrt{s}=13 TeV

The production cross-section of J/ψ pairs is measured using a data sample of pp collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 279 ±11 pb$^{−1}$. The measurement is performed for J/ψ mesons with a transverse momentum of less than 10 GeV/c in the rapidity range 2.0 < y < 4.5. The production cross-section is measured to be 15.2 ± 1.0 ± 0.9 nb. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the J/ψ pair are measured and compared to theoretical predictions.The production cross-section of $J/\psi$ pairs is measured using a data sample of $pp$ collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s} = 13 \,{\mathrm{TeV}}$, corresponding to an integrated luminosity of $279 \pm 11 \,{\mathrm{pb^{-1}}}$. The measurement is performed for $J/\psi$ mesons with a transverse momentum of less than $10 \,{\mathrm{GeV}}/c$ in the rapidity range $2.0<y<4.5$. The production cross-section is measured to be $15.2 \pm 1.0 \pm 0.9 \,{\mathrm{nb}}$. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the $J/\psi$ pair are measured and compared to theoretical predictions

Measurement of forward W→eνW\to e\nu production in pppp collisions at s=8 \sqrt{s}=8\,TeV

A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{align*} \begin{split} \sigma_{W^{+} \to e^{+}\nu_{e}}&=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb},\\ \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}&=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{split} \end{align*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{align*} \begin{split} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{split} \end{align*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{equation*} \sigma_{W^{+} \to e^{+}\nu_{e}}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb}, \end{equation*} \begin{equation*} \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{equation*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{equation*} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{equation*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for W → eν production in pp collisions is presented using data corresponding to an integrated luminosity of 2 fb$^{−1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The electrons are required to have more than 20 GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive W production cross-sections, where the W decays to eν, are measured to be ${\sigma}_{W^{+}\to {e}^{+}{\nu}_e}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\kern0.5em \mathrm{p}\mathrm{b},$ ${\sigma}_{W^{-}\to {e}^{-}{\overline{\nu}}_e}=809.0\pm 1.9\pm 18.1\pm \kern0.5em 7.0\pm \kern0.5em 9.4\,\mathrm{p}\mathrm{b},$ where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination

The Theory of Jacobi Forms over the Cayley Numbers

La presente investigación tuvo como objetivo identificar la percepción sobre la calidad de atención de enfermería que tienen los usuarios del Servicio de Quimioterapia Ambulatoria del IREN SUR. Se realizó un estudio descriptivo utilizando como técnica la entrevista y como instrumento una cédula de entrevista. Se encuestó una muestra representativa de 110 usuarios aplicando una escala de valoración de calidad previamente validada. Los resultados se muestran mediante estadística descriptiva. Se encontró que La valoración dada a los componentes de la dimensión humana fueron: alta en respeto y amabilidad (68,18%), media en información e interés (46,36%). En la dimensión técnico científica, fue alta en seguridad y continuidad (85,45%), alta en eficiencia y eficacia (81,82%) y en integralidad (73,64%). En la dimensión del entorno, fue alta en orden y limpieza (80,91%), en comodidad (54,55%) y alta en iluminación y ventilación (90,91%). El nivel de las dimensiones de la calidad fue alto en 50,91% para la dimensión humana, alta en 90,91% para la dimensión técnico científica, y alta en 95,45% para la dimensión del entorno. La calidad de la atención de la enfermera en quimioterapia ambulatoria percibida por los pacientes fue baja en 0,91% de casos, media en 17,27% y alta en 81,82%. Se concluye que los usuarios del servicio de Quimioterapia Ambulatoria del IREN SUR tienen una buena percepción de la atención de enfermería, pero requiere de mejora en algunos aspectos de la dimensión humana para lograr una mejora continua de la calidad. PALABRAS CLAVE: calidad – dimensión humana – dimensión técnico científica – dimensión del entorno – enfermería – quimioterapia ambulatoria.