From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Large Area Crop Inventory Experiment (LACIE). Intensive test site assessment report

There are no author-identified significant results in this report

For I Know the Plans I Have for You: God Locus of Control, Spiritual Change, and Death Anxiety in Primary Brain Tumor Patients

Background/Purpose. Primary brain tumor (PBT) patients risk experiencing death anxiety given the high mortality rate of their diagnosis. In line with Terror Management Theory (TMT), many diagnosed with cancer utilize religion as a method of coping with the disease. However, previous literature on the relation between death anxiety and religion in cancer patients indicates mixed findings of either a negative relationship or no association. To the authors’ knowledge, no study has analyzed these two constructs together in PBT patients. The current study sought to address this gap by investigating the relationship between religiosity and death anxiety in an understudied population. Methods. Adult PBT patients (N = 56, Mage = 49.38, 51.8% female, 71.4% Caucasian, Mmonths since diagnosis = 55.34) completed measures of religiosity and death anxiety at their routine medical appointment at an academic medical center, including: The God Locus of Health Control Scale (GLHCS), Posttraumatic Growth Inventory (PTGI), Death and Dying Distress Scale (DADDS), and the Death Distress Scale (DDS). Descriptives and Pearson correlations were utilized. Results. The results revealed that while the GLHCS was not significantly related to either measure of death anxiety, the Spiritual Change subscale of the PTGI was positively correlated to both the DADDS (r = .56, p \u3c .001) and the DDS (r = .41, p = .01). Conclusions and Implications. Results suggest that certain proxies of religiosity may be more closely associated with death anxiety than others. Although there was no evidence in our sample that PBT patient’s God locus of control was related to death anxiety, those who reported higher levels of death anxiety endorsed greater spiritual change (i.e., I have a stronger religious faith). Considering TMT, perhaps feelings of death anxiety prompt one to strengthen their religious beliefs. Future longitudinal analyses addressing the direction and course of these relationships are warranted. Acknowledgement of Funding: The current study was funded on behalf of Virginia Commonwealth University School of Medicine. Learning Objective. Participants will learn about the relationship between religiosity and death anxiety in oncology patients. Further, participants will consider how these findings may or may not differ for PBT patients and across various measures of religiosity.https://scholarscompass.vcu.edu/gradposters/1049/thumbnail.jp

Electronic health use in the european union and the effect of multimorbidity: Cross-sectional survey

Background: Multimorbidity is becoming increasingly common and is a leading challenge currently faced by societies with aging populations. The presence of multimorbidity requires patients to coordinate, understand, and use the information obtained from different health care professionals, while simultaneously striving to distinguish the symptoms of different diseases and self-manage their sometimes conflicting health problems. Electronic health (eHealth) tools provide a means to disseminate health information and education for both patients and health professionals and hold promise for more efficient and cost-effective care processes. Objective: The aim of this study was to analyze the use of eHealth tools, taking into account the citizens' sociodemographic and clinical characteristics, and above all, the presence of multimorbidity. Methods: Cross-sectional and exploratory research was conducted using online survey data from July 2011 to August 2011. Participants included a total of 14,000 citizens from 14 European countries aged 16 to 74 years, who had used an eHealth tool in the past 3 months. The variables studied were sociodemographic variables of the participants, the questionnaire items assessing the frequency of using eHealth tools, the degree of morbidity, and the eHealth adoption gradient. Chi-square tests were conducted to examine the relationship between the sociodemographic and clinical variables of participants and the group the participants were assigned to according to their frequency of eHealth use (eHealth user group). A one-way analysis of variance (ANOVA) allowed for assessing the differences in the eHealth adoption gradient average between different groups of individuals according to their morbidity level. A two-way between-groups ANOVA was performed to explore the effects of multimorbidity and age group on the eHealth adoption gradient. Results: According to the eHealth adoption gradient, most participants (68.15%, 9541/14,000) were labeled as rare users, with the majority of them (55.1%, 508/921) being in the age range of 25 to 54 years, with upper secondary education (50.3%, 464/921), currently employed (49.3%, 454/921), and living in medium-sized cities (40.7%, 375/921). Results of the one-way ANOVA showed that the number of health problems significantly affected the use of eHealth tools (F-2,F-13996=11.584; P<.001). The two-way ANOVA demonstrated that there was a statistically significant interaction between the effects of age and number of health problems on the eHealth adoption gradient (F-4,F-11991=7.936; P<.001). Conclusions: The eHealth adoption gradient has proven to be a reliable way to measure different aspects of eHealth use. Multimorbidity is associated with a more intense use of eHealth, with younger Internet users using new technologies for health purposes more frequently than older groups with the same level of morbidity. These findings suggest the need to consider different strategies aimed at making eHealth tools more sensitive to the characteristics of older populations to reduce digital disadvantages

Diagonal extendible multilinear operators between l(p)-spaces

[EN] We study extendibility of diagonal multilinear operators from l(p) to l(p) spaces. We determine the values of and for which every diagonal -linear operator is extendible, and those for which the only extendible ones are integral. We address the same question for multilinear forms on l(p).D. Carando, V. Dimant and R. Villafane were partially supported by CONICET PIP 0624 and UBACyT 20020100100746. P. Sevilla-Peris was supported by MICINN Project MTM2011-22417. R. Villafane has a doctoral fellowship from CONICET.Carando, D.; Dimant, V.; Sevilla Peris, P.; Villafañe, R. (2014). Diagonal extendible multilinear operators between l(p)-spaces. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas (RACSAM). 108(2):541-555. https://doi.org/10.1007/s13398-013-0125-7S5415551082Alencar, R.: Multilinear mappings of nuclear and integral type. Proc. Am. Math. Soc. 94(1), 33–38 (1985)Alencar, R., Matos, M.: Some classes of multilinear mappings between Banach spaces. Pub. Dep. An. Mat. Univ. Complut. Madrid 12 (1989)Blei, R.C.: Multilinear measure theory and the Grothendieck factorization theorem. Proc. Lond. Math. Soc. 56(3), 529–546 (1988)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann. Math. (2) 32(3), 600–622 (1931)Botelho, G., Braunss, H., Junek, H., Pellegrino, D.: Holomorphy types and ideals of multilinear mappings. Studia Math. 177, 43–65 (2006)Botelho, G., Michels, C., Pellegrino, D.: Complex interpolation and summability properties of multilinear operators. Rev. Mat. Complut. 23(1), 139–161 (2010)Botelho, G., Pellegrino, D.: Two new properties of ideals of polynomials and applications. Indag. Math. (N.S.) 16157–16169 (2005)Botelho, G., Pellegrino, D.: When every multilinear mapping is multiple summing. Math. Nachr. 282(10), 1414–1422 (2009)Çalışkan, E., Pellegrino, D.: On the multilinear generalizations of the concept of absolutely summing operators. Rocky Mt. J. Math. 37, 1137–1154 (2007)Carando, D.: Extendibility of polynomials and analytic functions on $$\ell _{p}$$ . Studia Math. 145(1), 63–73 (2001)Carando, D., Dimant, V., Muro, S.: Coherent sequences of polynomial ideals on Banach spaces. Math. Nachr. 282(8), 1111–1133 (2009)Carando, D., Dimant, V., Sevilla-Peris, P.: Limit orders and multilinear forms on $$\ell _p$$ spaces. Publ. Res. Inst. Math. Sci. 42(2), 507–522 (2006)Carando, D., Dimant, V., Sevilla-Peris, P.: Multilinear Hölder $$-$$ type inequalities on Lorentz sequence spaces. Studia Math. 195(2), 127–146 (2009)Carando, D., Lassalle, S.: Extension of vector-valued integral polynomials. J. Math. Anal. Appl. 307(1), 77–85 (2005)Carando, D., Sevilla-Peris, P.: Extendibility of bilinear forms on Banach sequence spaces. Israel J. Math., arXiv:1212.0777 (to appear)Castillo, J., García, R., Jaramillo, J.A.: Extension of bilinear forms on Banach spaces. Proc. Am. Math. Soc. 129(12), 3647–3656 (2001)Carl, B.: A remark on $$p$$ -integral and $$p$$ -absolutely summing operators from $$\ell _u$$ into $$\ell _v$$ . Studia Math. 57(3), 257–262 (1976)Defant, A., Floret, K.: Tensor norms and operator ideals. North Holland, Amsterdam (1993)Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators. Cambridge University Press, Cambridge (1995)Dineen, S.: Complex analysis on infinite dimensional spaces. Springer-Verlag, London (1999)Jarchow, H., Palazuelos, C., Pérez-García, D., Villanueva, I.: Hahn–Banach extension of multilinear forms and summability. J. Math. Anal. Appl. 336(2), 1161–1177 (2007)Kirwan, P., Ryan, R.: Extendibility of homogeneous polynomials on Banach spaces. Proc. Am. Math. Soc. 126(4), 1023–1029 (1998)König, H.: Diagonal and convolution operators as elements of operator ideals. Math. Ann. 218(2), 97–106 (1975)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1977)Matos, M.: Absolutely summing holomorphic mappings. An. Acad. Bras. Ci. 68, 1–13 (1996)Maurizi, B., Queffélec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16(5), 676–692 (2010)Mujica, J.: Complex analysis in Banach spaces. North-Holland mathematics studies, vol. 120, North-Holland (1986)Pérez-García, D.: Comparing different classes of absolutely summing multilinear operators. Arch. Math. (Basel) 85(3), 258–267 (2005)García Pérez, D.: The trace class is a $$Q$$ -algebra. Ann. Acad. Sci. Fenn. Math. 31(2), 287–295 (2006)Pietsch, A.: Operator ideals. Mathematische monographien (Mathematical monographs), 16. VEB Deutscher Verlag der Wissenschaften, Berlin (1978)Pisier, G.: Counterexamples to a conjecture of Grothendieck. Acta Math. 151(3–4), 181–208 (1983)Ryan, R: Introduction to tensor products of Banach spaces. Springer monographs in mathematics, Springer-Verlag, London (2002)Villanueva, I.: Integral mappings between Banach spaces. J. Math. Anal. Appl. 279(1), 56–70 (2003