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Here we report on the fabrication of reconfigurable and solution processable nanoscale biosensors with multisensing capability, based on single-walled carbon nanotubes (SWCNTs). Distinct DNA-wrapped (hence water-soluble) CNTs were immobilized from solution onto different prepatterned electrodes on the same chip, via a low-cost dielectrophoresis (DEP) methodology. The CNTs were functionalized with specific, and different, aptamer sequences that were employed as selective recognition elements for biomarkers indicative of stress and neuro-trauma conditions. Multiplexed detection of three different biomarkers was successfully performed, and real-time detection was achieved in serum down to physiologically relevant concentrations of 50 nM, 10 nM, and 500 pM for cortisol, dehydroepiandrosterone-sulfate (DHEAS), and neuropeptide Y (NPY), respectively. Additionally, the fabricated nanoscale devices were shown to be reconfigurable and reusable via a simple cleaning procedure. The general applicability of the strategy presented, and the facile device fabrication from aqueous solution, hold great potential for the development of the next generation of low power consumption portable diagnostic assays for the simultaneous monitoring of different health parameters.

This paper mainly considers Toeplitz algebras, subnormal tuples and rigidity concerning reproducing C½z 1 ; y; z d -modules. By making use of Arveson's boundary representation theory, we find there is more rigidity in several variables than there is in single variable. We specialize our attention to reproducing C½z 1 ; y; z d -modules with U-invariant kernels by examining the spectrum and the essential spectrum of the d-tuple fM z1 ; y; M zd g; and deducing an exact sequence of C Ã -algebras associated with Toeplitz algebra. Finally, we deal with Toeplitz algebras defined on Arveson submodules and rigidity of Arveson submodules. r

On Sn , there is a naturally metric defined n th order conformal invariant operator P n . Associated with this operator is a so-called Q-curvature quantity. When two metrics are pointwise conformally related, their associated operators, together with their Q-curvatures, satisfy the natural differential equations. This paper is devoted to the question of which function can be a Q-curvature candidate. This is the so-called prescribing Q-curvature problem. Our main result is that if Q is positive, nondegenerate and the naturally defined mapping associated with Q has nonzero degree, then our problem has a solution. This is the natural generalization of prescribing Gaussian curvature on S 2 into S n .1998 Academic Press

By using the equivalent integral form for the Q-curvature equation, we generalize the wellknown non-existence results on two-dimensional Gaussian curvature equation to all dimensional Q-curvature equation. Somehow, we introduce a new approach to Q-curvature equation which is higher order and even pseudo-differential equation. As a by-product, we do classify the solutions for Q = 1 solutions on S n as well as on R n with necessary growth rate assumption.

In this paper, we study global positive C 4 solutions of the geometrically interesting equation: 2 u + u −q = 0 with q > 0 in R 3 . We will establish several existence and non-existence theorems, including the classification result for q = 7 with exactly linear growth condition.