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    Coherent `ab' and `c' transport theory of high-TcT_{c} cuprates

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    We propose a microscopic theory of the `cc'-axis and in-plane transport of copper oxides based on the bipolaron theory and the Boltzmann kinetics. The fundamental relationship between the anisotropy and the spin susceptibility is derived, ρc(T,x)/ρab(T,x)x/Tχs(T,x)\rho_{c}(T,x)/\rho_{ab}(T,x)\sim x/\sqrt{T}\chi_{s}(T,x). The temperature (T)(T) and doping (x)(x) dependence of the in-plane, ρab\rho_{ab} and out-of-plane, ρc\rho_{c} resistivity and the spin susceptibility, χs\chi_{s} are found in a remarkable agreement with the experimental data in underdoped, optimally and overdoped La2xSrxCuO4La_{2-x}Sr_{x}CuO_{4} for the entire temperature regime from TcT_{c} up to 800K800K. The normal state gap is explained and its doping and temperature dependence is clarified.Comment: 12 pages, Latex, 3 figures available upon reques

    The composition of R. Cohen's elements and the third periodic elements in stable homotopy groups of spheres

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    In this paper, we study the cohomology of the Morava stabilizer algebra S(3)S(3). As an application, we show that for p7p \geq 7, if s≢0,±1modps\not \equiv 0, \pm 1 \,\, mod \,p , n≢1mod3n\not \equiv 1 \,\, mod\, 3, n>1n>1, then ζnγs\zeta_n\gamma_s is a nontrivial product in π(S)\pi_*(S) by Adams-Novikov spectral sequence, where ζn\zeta_n is created by R. Cohen \cite{Co}, γs\gamma_s is a third periodic homotopy elements

    Linear orthogonality preservers of Hilbert CC^*-modules over general CC^*-algebras

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    As a partial generalisation of the Uhlhorn theorem to Hilbert CC^*-modules, we show in this article that the module structure and the orthogonality structure of a Hilbert CC^*-module determine its Hilbert CC^*-module structure. In fact, we have a more general result as follows. Let AA be a CC^*-algebra, EE and FF be Hilbert AA-modules, and IEI_E be the ideal of AA generated by {x,yA:x,yE}\{\langle x,y\rangle_A: x,y\in E\}. If Φ:EF\Phi : E\to F is an AA-module map, not assumed to be bounded but satisfying Φ(x),Φ(y)A = 0wheneverx,yA = 0, \langle \Phi(x),\Phi(y)\rangle_A\ =\ 0\quad\text{whenever}\quad\langle x,y\rangle_A\ =\ 0, then there exists a unique central positive multiplier uM(IE)u\in M(I_E) such that Φ(x),Φ(y)A = ux,yA(x,yE). \langle \Phi(x), \Phi(y)\rangle_A\ =\ u \langle x, y\rangle_A\qquad (x,y\in E). As a consequence, Φ\Phi is automatically bounded, the induced map Φ0:EΦ(E)\Phi_0: E\to \overline{\Phi(E)} is adjointable, and Eu1/2\overline{Eu^{1/2}} is isomorphic to Φ(E)\overline{\Phi(E)} as Hilbert AA-modules. If, in addition, Φ\Phi is bijective, then EE is isomorphic to FF.Comment: 15 page

    When is |C(X x Y)| = |C(X)||C(Y)|?

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    Sufficient conditions on the Tychonoff spaces X and Y are found that imply that the equation in the title holds. Sufficient conditions on the Tychonoff space X are found that ensure that the equation holds for every Tychonoff space Y . A series of examples (some using rather sophisticated cardinal arithmetic) are given that witness that these results cannot be generalized much
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