Logic Gates Based on Magnetic Nanoparticles Functionalized with a Bioelectrocatalytic System

Magneto‐controlled OR, AND and INHIB logic gates were designed using cobalt ferrite magnetic nanoparticles (CoFe₂O₄, saturated magnetization ca. 70 emu g^?1, 17±2 nm diameter) functionalized with microperoxidase‐11. Tunable magnetic field generated by three external permanent magnets (NdFeB) upon moving them below the electrochemical cell resulted in translocation of the biofunctionalized magnetic nanoparticles between conductive and nonconductive domains of a solid plate. This resulted in electrochemically readable output signals with the Boolean logic controlled by the magnetic input signals. The current corresponding to the reversible redox process of the heme measured at ?0.4 V (vs. SCE) was considered as “1” output signal, while a small background current obtained from the conducting interface in the absence of the magnetic nanoparticles was considered as “0” output signal. Addition of H₂O₂ to the solution resulted in the generation of a cathodic catalytic current when the microperoxidase‐11‐functionalized magnetic nanoparticles are associated with the conductive domain of the support. This resulted in the amplification of “1” output signal and the increased difference between “1” and “0” signals generated by the cell, thus reducing the possibility of errors in the Boolean logic operations.     

Decision Effects,the Hahn–Jordan Decomposition for States,and Their Connection to Ludwig’s Axiomatic Approach to Quantum Mechanics

We begin with a quantum logic carrying a large collection of states. We then form a dual pair of Banach spaces—base normed and order unit normed—containing the states and the logic, respectively. A Galois connection on the face lattices of the states and the dual positive order unit interval is introduced. The elements of the logic are connected to a dense subset of the extreme points of this order interval in the order unit space using a generalized form of the Hahn–Jordan decomposition theorem. Decision effects are defined and identified with the elements of the original logic. Finally, an important axiom of Ludwig is introduced which ties together all the lattices of Galois closed faces of states, Galois closed order intervals of the positive order unit interval, decision effects, and the original quantum logic. The emphasis here is on the consequences of functional analytic assumptions. The paper concludes with a simple example where Ludwig’s axiom does not hold and we see parts of the theory dissolve. PACS: 02.30.Sa, 03.65.Ta.     

Ortho and Causal Closure as a Closure Operations in the Causal Logic

We investigate two different closure operations (ortho and causal closure) generated by a causal structure. In the case of orthogonal sets bounded in time two closure operations coincide and a lattice of double orthoclosed sets in this case is orthomodular.     

Representation Systems and Quantum Structures

Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation systems, we show that these quantum structures can be obtained by expressing conditions on the existence of particular points of view, of particular ways to observe a system. PACS: 02.70.Wz, 03.67.Lx.     

The algebraic and geometric classification of Zinbiel algebras

This paper is devoted to the complete algebraic and geometric classification of complex 5-dimensional Zinbiel algebras. In particular, we proved that the variety of complex 5-dimensional Zinbiel algebras has dimension 24, it is defined by 16 irreducible components and it has 11 rigid algebras.     

A new class of generalized almost perfect nonlinear power function

As a generalization of almost perfect nonlinear functions, generalized almost perfect nonlinear (GAPN) functions defined over finite fields of odd characteristic have also important applications in cryptography and finite geometry. In this paper, we mainly focus on GAPN power functions, and a new class of such function (up to EA equivalence) is obtained. Furthermore, using our method, almost all the known GAPN power functions can be confirmed in a simple way.     

Bases of Riemann–Roch spaces from Kummer extensions and algebraic geometry codes

We construct explicit bases of Riemann–Roch spaces from Kummer extensions and algebraic geometry codes with good parameters. This correspondence is a generalization of a work of Maharaj, Matthews, and Pirsic.     

Robust stability of Switched Boolean Networks with function perturbation

In genetic regulatory networks, gene mutations are one of natural phenomena, which attract much attention by biological researchers. In modeling gene networks using switched Boolean networks (SBNs), gene mutations can be described by function perturbations, which is a meaningful issue in analyzing function perturbation of SBNs. This paper studies robust stability of SBNs with function perturbation. With the help of semi-tensor product (STP) of matrices, one equivalent algebraic form of SBNs is established. By constructing two state sets, a criterion for global stability of SBNs under arbitrary switching signals is proposed. In order to relax the conditions of global stability, pointwise stabilizability and consistent stabilizability of SBNs are further considered. Based on state reachable sets, several criteria are established for the proposed kinds of stability. Finally, the obtained results are verified by two examples and lac operon in the Escherichia coli, respectively.     

Motivic invariants of symmetric powers of curves

We study the structure of various invariants of the symmetric powers of a smooth projective curve in terms of that of the Jacobian of the curve. We generalise the results of Macdonald and Collino to various invariants including the Weil-cohomology theory, the higher Chow groups, the additive higher Chow groups and the rational K-groups.     

A Kekulé structure basis for phenylenes

By means of Kekulé structures and, in particular, their count K, many properties of benzenoid molecules can be rationalized. The analogous properties of non-benzenoid polycyclic conjugated molecules require the consideration of some, but not all, Kekulé structures, whose number is the precisely defined and long time known ‘algebraic structure count’ ASC. In the general case it is not known how to construct a Kekulé structure basis for non-benzenoid molecules, consisting of ASC Kekulé structures, ASC≤K. We now offer a solution of this problem for phenylenes and point out some applications.