SU(4) Fermi liquid state and spin filtering in a double quantum dot system

We study a symmetrical double quantum dot (DD) system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift pi/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four-lead setup we find perfectly spin-polarized transmission.     

1-D cobalt(II) spin transition compound with strong interchain interaction: [Co(pyterpy)Cl(2)].X

Cobalt(II) compounds [Co(pyterpy)Cl(2)].MeOH (1.(MeOH)) and [Co(pyterpy)Cl(2)].2H(2)O (1.(2H(2)O)) were synthesized. The compound 1.(MeOH) forms the quasi 3-D networks by making pi-pi stacking between the 1-D chains. The methanol molecules from 1.(MeOH) can be removed by heating, and substituted by absorption of water molecules. The MeOH molecules in 1.(MeOH) are removed by heating at 410 K, and they are substituted by water molecules to form 1.(2H(2)O). 1.(2H(2)O) exhibits a S = (3)/(2) (HS) left arrow over right arrow S = (1)/(2) (LS) spin transition with a thermal hysteresis. We have succeeded in constructing a guest dependent 1-D spin-crossover cobalt(II) compound.     

On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equations

As a continuation of our previous work [2] the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The idea is based on the fundamental work of [5]. Using spectral analysis in some related varieties we can prove the existence of special solutions (automorphisms) of the functional equation but spectral synthesis allows us to describe the entire space of solutions on a large class of finitely generated fields. It is spanned by the so-called exponential monomials which can be given in terms of automorphisms of \({\mathbb C}\) and differential operators. We apply the general theory to some inhomogeneous problems motivated by quadrature rules of approximate integration [8], see also [7, 9].     

The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II

We prove a general subconvex bound in the level aspect for Rankin–Selberg L-functions associated with two primitive holomorphic or Maass cusp forms over Q. We use this bound to establish the equidistribution of incomplete Galois orbits of Heegner points on Shimura curves associated with indefinite quaternion algebras over Q. Mathematics Subject Classification (2000) 11F66, 11F67, 11M41     

Covering the crosspolytope by equal balls

Summary We determine the minimal radius of <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>n=2$, $d$ or $2d$ congruent balls, which cover the $d$-dimensional crosspolytope.     

Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters.     

Hypoxia-induced transcription of dopamine D3 and D4 receptors in human neuroblastoma and astrocytoma cells

Background

The aim of this study is to examine the influence of the catechol-O-methyltranferase (COMT) gene (polymorphism Val158 Met) as a risk factor for Alzheimer's disease (AD) and mild cognitive impairment of amnesic type (MCI), and its synergistic effect with the apolipoprotein E gene (APOE). A total of 223 MCI patients, 345 AD and 253 healthy controls were analyzed. Clinical criteria and neuropsychological tests were used to establish diagnostic groups. The DNA Bank of the University of the Basque Country (UPV-EHU) (Spain) determined COMT Val158 Met and APOE genotypes using real time polymerase chain reaction (rtPCR) and polymerase chain reaction (PCR), and restriction fragment length polymorphism (RFLPs), respectively. Multinomial logistic regression models were used to determine the risk of AD and MCI.

Results

Neither COMT alleles nor genotypes were independent risk factors for AD or MCI. The high activity genotypes (GG and AG) showed a synergistic effect with APOE ε4 allele, increasing the risk of AD (OR = 5.96, 95%CI 2.74-12.94, p < 0.001 and OR = 6.71, 95%CI 3.36-13.41, p < 0.001 respectivily). In AD patients this effect was greater in women. In MCI patients such as synergistic effect was only found between AG and APOE ε4 allele (OR = 3.21 95%CI 1.56-6.63, p = 0.02) and was greater in men (OR = 5.88 95%CI 1.69-20.42, p < 0.01).

Conclusion

COMT (Val158 Met) polymorphism is not an independent risk factor for AD or MCI, but shows a synergistic effect with APOE ε4 allele that proves greater in women with AD.     

Popular distances in 3-space

Let m(n) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn^1/3 log log n m(n) n^3/5 β(n), where c> 0 is a constant and β(n) is an extremely slowly growing function, related to the inverse of the Ackermann function.