Atypical Representations of Uq(sl(N))U_{q}(sl(N)) at Roots of Unity

We show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of ${\cal U}_{\displaystyle{q}}(sl(N))$ when $q$ is root of unity. The explicit construction of atypical representation is presented in details for $N=3$.Comment: 18 pages, Tex-file and 2 figures. Uuencoded, compressed and tared archive of plain tex file and postscript figure file. Upon uudecoding, uncompressing and taring, tex the file atypique.te

Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur

A Jordanian quantum two-photon/Schrodinger algebra

A non-standard quantum deformation of the two-photon algebra $h_6$ is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock-Bargmann realizations that provide a direct formalism for the definition of deformed states of light. Finally, the isomorphism between $h_6$ and the (1+1) Schr\"odinger algebra is used to introduce a new (non-standard) Hopf algebra deformation of this latter symmetry algebra.Comment: 12 pages, LaTeX, misprints correcte

Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure

Tensor Operators for Uh(sl(2))

Tensor operators for the Jordanian quantum algebra Uh(sl(2)) are considered. Some explicit examples of them, which are obtained in the boson or fermion realization, are given and their properties are studied. It is also shown that the Wigner-Eckart's theorem can be extended to Uh(sl(2)).Comment: 11pages, LaTeX, to be published in J. Phys.

Boson representations, non-standard quantum algebras and contractions

A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of $sl(2,\R)$ which directly provides its infinite and finite dimensional irreducible representations. Tensor product decompositions are worked out for some examples. Relations between contraction methods and boson realizations are also explored in several contexts. So, a class of two-boson representations for the non-standard deformation of $sl(2,\R)$ is introduced and contracted to the non-standard quantum (1+1) Poincar\'e representations. Likewise, a quantum extended Hopf $sl(2,\R)$ algebra is constructed and the Jordanian $q$-oscillator algebra representations are obtained from it by means of another contraction procedure.Comment: 21 pages, LaTeX; two new references adde

First Observation of the Hadronic Transition Υ(4S)→ηhb(1P)and New Measurement of the hb(1P) and ηb(1S) Parameters

Using a sample of 771.6×106 ΥΥ(4S) decays collected by the Belle experiment at the KEKB e+e− collider, we observe, for the first time, the transition Υ(4S)→ηhb(1P) with the branching fraction B[Υ(4S)→ηhb(1P)]=(2.18±0.11±0.18)×10−3 and we measure the hb(1P) mass Mhb(1P)=(9899.3±0.4±1.0)  MeV/c2, corresponding to the hyperfine (HF) splitting ΔMHF(1P)=(0.6±0.4±1.0)  MeV/c2. Using the transition hb(1P)→γηb(1S), we measure the ηb(1S) mass Mηb(1S)=(9400.7±1.7±1.6)  MeV/c2, corresponding to ΔMHF(1S)=(59.6±1.7±1.6)  MeV/c2, the ηb(1S) width Γηb(1S)=(8+6−5±5)  MeV/c2and the branching fraction B[hb(1P)→γηb(1S)]=(56±8±4)%

Design Guidelines for a Global and Self-Managed LEO Satellites-Based Sensor Network

科研費報告書収録論文(課題番号:17500030/研究代表者:加藤寧/インターネットと高親和性を有する次世代低軌道衛星ネットワークに関する基盤研究

Apolipoprotein E Genotypes in Alzheimer's Disease in Central Algerian Population

Background: Alzheimer's disease (AD) is a progressive and fatal neurodegenerative disorder associated with cognitive decline and is the most common form of dementia in the elderly. Early-onset familial AD accounts for less than 1% of AD cases and develops before the age of 65 years because of mutations in either the APP gene or genes encoding presenilin 1 (PSEN1) or presenilin 2 (PSEN2). The majority of sporadic AD cases are referred to as late-onset AD (LOAD) because they occur late in life (>65 years). Apolipoprotein E (APOE) polymorphic alleles are the major genetic risk factor for AD. The human APOE gene exists as three polymorphic alleles, ε2, ε3, and ε4, with a worldwide frequency of 8%, 78%, and 13%, respectively, with ε4 reaching frequencies of 40% in AD patients. The purpose of this preliminary study was to determine ApoE genotype status since no previous association studies between LOAD and ApoE gene were available for the Central Algerian population. Methods: The cohort of our study was composed of 47 AD patients recruited from the Neurology Department of Frantz Fanon Hospital of Blida. Forty-seven controls with no type of dementia were also included in the study. All samples were genotyped for the ApoE Polymorphisms by PCR-RFLP method. Statistical studies can use the Fisher exact test or Chi-2 using the GraphPad Prism 7.0 software. Results: The results show that the genotype ɛ3/ɛ3 is most common in both groups followed by the heterozygous genotype ɛ3/ɛ4 which showed an increased frequency in patients compared to controls (27.66% vs. 12.77%, OR=3.66, IC=0.89-7.9, p=0,11). Although rare, all other possible genotypes have been observed in our cohort, namely ɛ2/ɛ2, ɛ2/ɛ3, ɛ2/ɛ4 and ɛ4/ɛ4. The ɛ2/ɛ4 genotype was observed only in AD patients, while the ɛ2/ɛ2 genotype was observed only in controls. As expected, the homozygous genotype ɛ4/ɛ4 was more frequent in AD patients, compared to controls (6.38% vs. 2.13%, respectively OR=2.64, IC=0.36-37.33; p=0,33). At the allelic level, ɛ4 allele was significantly associated with AD compared to controls (21,28% vs. 4,26% ; OR= 2.75, 95% CI= 1.109-6.35; p = 0.02, respectively), while the ɛ2 allele seems to be protective (4,26% vs. 9,57%, OR = 0.49 ; 95% CI=0.14-1.66 ; p=0,38, respectively), but without statistical significance. In population-based studies, the ApoEɛ4-AD association was weaker among African Americans (ε4/ε4, OR 5.7) and Hispanics (ε4/ε4, OR 2.2) and was stronger in the Japanese population (ε4/ε4, OR 33.1) compared with Caucasian cases (ε4/ε4, OR 12.5). The results obtained in our preliminary study indicate that the ApoEɛ4-AD association in the Central Algerian population is similar to that observed in the Mediterranean populations. Conclusion: We have presented, for the first time in the North Central Algerian population, the association of the ɛ4 allele with AD, which could be of great use in the diagnosis but also the follow-up of patients with this disease