Central Binomial Sums, Multiple Clausen Values and Zeta Values

We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\'ery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.Comment: 17 pages, LaTeX, with use of amsmath and amssymb packages, to appear in Journal of Experimental Mathematic

Cross-national variations in reported discrimination among people treated for major depression worldwide : the ASPEN/INDIGO international study

No study has so far explored differences in discrimination reported by people with major depressive disorder (MDD) across countries and cultures. To (a) compare reported discrimination across different countries, and (b) explore the relative weight of individual and contextual factors in explaining levels of reported discrimination in people with MDD. Cross-sectional multisite international survey (34 countries worldwide) of 1082 people with MDD. Experienced and anticipated discrimination were assessed by the Discrimination and Stigma Scale (DISC). Countries were classified according to their rating on the Human Development Index (HDI). Multilevel negative binomial and Poisson models were used. People living in ‘very high HDI’ countries reported higher discrimination than those in ‘medium/low HDI’ countries. Variation in reported discrimination across countries was only partially explained by individual-level variables. The contribution of country-level variables was significant for anticipated discrimination only. Contextual factors play an important role in anticipated discrimination. Country-specific interventions should be implemented to prevent discrimination towards people with MDD

ShortandEasyComputerProofsofPartitionandq-Identities [summarybyBrunoSalvy] RISCLinz,Austria October3,1994 PeterPaule

thefunctionf(k)satises theexpressionontheleft-handsidemayappearundernumerousdisguises,whichmakesitdicult sortofnormalformfollowsfromtheobservationthatinmanyidentitieswithleft-handsidePkf(k), tolocateitinsuchtables(ortoimplementtablelookupinacomputeralgebrasystem).However,a nXk=0?nk?xk?yk?x+y+z+n k?z+k k=?x+z+n?z+n n?x+y+z+n n?y+z+n n: n (2) forsomesuitableeldofcoecientsF.Thusfiscompletelydeterminedbyf(0)andarational hypergeometricterm.Inasuitablealgebraicextension,f(k)canbemadeexplicit: function,forwhichanormalformisavailable.Afunctionfsatisfyingthispropertyiscalleda f(k)=(a1)k(am)k f(k+1) (b1)k(bn)kzk f(k)2F(k); where(a)k=a(a+1)(a+k?1)denotestherisingfactorial.Thesumoff(whenf(0)=1)is AccordingtoG.E.Andrews,\Byusinghypergeometricseriesonecanreduce450ofthe577entries usuallycalledthehypergeometricserieswiththefollowingnotation mFna1;:::;am b1;:::;bnz=1Xk=0f(k): k!f(0); inGould'stableto32entries."Thusforinstance,theSaalschutzidentityisobtainedas omy),D.Zeilbergergaveanalgorithmtocomputealinearrecurrencesatisedbythedenitesum withrespecttooneoftheparameters.Thetechniqueisbasedoncreativetelescoping[11]which GivenafunctionF(n;k)hypergeometricinbothparameters,plusatechnicalcondition(holon- 3F2 z+1;?x?y?z?n1=(x+z+1)n(y+z+1)n?x;?y;?n 43(z+1)n(x+y+z+1)n: appliestoalargercontextofholonomicidentities.TocomputePkFn;kfromarst-orderrecurrence like(2)innandasecondoneink,theideaistodeterminearecurrencesatisedbyFn;kwherek doesnotappearinthecoecients.InthecaseoftheSaalschutzidentity,thisgives (3) (n+3+z)(n+1+x+y+z)3Fn+3;k+1 Intheholonomicuniverse,suchaneliminationisalwayspossible.Theaboveidentityisthen?(n+1)(n+2)(n+y+z+1)(n+x+z+1)Fn;k=0: +(n+1+x+y+z)[(n+2)(n+2+x+y+2z)(n+2+x+y+z)Fn+1;k+1?(n+1+x+y+z)2f[(x+y+z+2n+5)(2n+z+5)?2(n+2)(n+3)]Fn+2;k+1 rewritten +(n+2)(2n2+6n+2nz?x2?xz?yz+3z?y2+5)Fn+1;k] +(n+2?y)(n+2?x)Fn+2;k

Nuclear Mass Number

Quantum-mechanical optical model methods for calculating cross sections for the fragmentation of galactic cosmic ray nuclei by hydrogen targets are presented. The fragmentation cross sections are calculated with an abrasion-ablation collision formalism. Elemental and isotopic cross sections are estimated and compared with measured values for neon, sulfur, and calcium ions at incident energies between 400A MeV and 910A MeV. Good agreement between theory and experiment is obtained. Introduction The fragmentation of galactic cosmic ray (GCR) nuclei in hydrogen targets is an important physical process in several areas of space radiation physics research. In astrophysics, it is crucial to understanding cosmic ray propagation and source abundances (ref. 1) because interstellar hydrogen is the major type of material encountered by GCR nuclei traveling through the universe. In studies of spacecraft shielding for interplanetary missions (ref. 2), hydrogen has been found to be the most effective..