Spectrum of Linear Difference Operators and the Solvability of Nonlinear Discrete Problems

Let T∈ℕ with T>5. Let 𝕋:={1,…,T}. We study the Fučik spectrum Σ of the discrete problem Δ2u(t-1)+λu+(t)-μu-(t)=0, t∈𝕋, u(0)=u(T+1)=0, where u+(t)=max⁡{u(t),0}, u-(t)=max⁡{-u(t),0}. We give an expression of Σ via the matching-extension method. We also use such discrete spectrum theory to study nonlinear boundary value problems of difference equations at resonance

Design of Unsigned Approximate Hybrid Dividers based on Restoring Array and Logarithmic Dividers

Approximate computer arithmetic has been extensively studied due to its advantages to further reduce power consumption and increase performance at reduced accuracy. Although a number of approximate adders and multipliers have been studied, only a few approximate dividers have been proposed. A logarithmic divider (LD) has low complexity and accuracy, while an exact array divider (EXD) has a high complexity. Therefore, in this paper, an approximate hybrid divider (AXHD) is proposed. It takes advantage of both LD and EXD to achieve a tradeoff between hardware performance and accuracy. Exact restoring divider cells are used to generate the most significant bits (MSBs) of the quotient for attaining a high accuracy while the other quotient digits are generated by using a LD as an approximate scheme to improve figures of merit such as power consumption, area and delay. To further save hardware resources, a so-called eliminated approximate hybrid divider (E-AXHD) based on AXHD is also proposed. In this improved design, a reduced width divider is used to replace the EXD in AXHD. Specifically, for a 16-by-8 design, n=(n + 1) array division is used to replace the n=8 array division (n < 8). The proposed AXHD and E-AXHD are evaluated and analyzed using error and hardware metrics. The proposed designs are also compared with EXD, LD and previous approximate dividers. The results show that the proposed designs outperform previous approximate dividers by considering both energy and error. The proposed hybrid dividers are of particular interest for error tolerant applications such as image processing and machine learning

Enzyme Biosensors for Point-of-Care Testing

Biosensors are devices that integrate a variety of technologies, containing biology, electronics, chemistry, physics, medicine, informatics, and correlated technology. Biosensors act as transducer with a biorecognition element and transform a biochemical reaction on the transducer surface directly into a measurable signal. The biosensors have the advantages of rapid analysis, low cost, and high precision, which are widely used in many fields, such as medical care, disease diagnosis, food detection, environmental monitoring, and fermentation industry. The enzyme biosensors show excellent application value owing to the development of fixed technology and the characteristics of specific identification, which can be combined with point-of-care testing (POCT) technology. POCT technology is attracting more and more attention as a very effective method of clinic detection. We outline the recent advances of biosensors in this chapter, focusing on the principle and classification of enzyme biosensor, immobilization method of biorecognition layers, and fabrication of amperometric biosensors, as well as the applications of POCT. A summary of glucose biosensor development and integrated setups is included. The latest applications of enzyme biosensors in diagnostic applications focusing on POCT of biomarkers in real samples were described

Ethyne Reducing Metal-Organic Frameworks to Control Fabrications of Core/shell Nanoparticles as Catalysts

An approach using cobalt metal-organic frameworks (Co-MOF) as precursors is established for the fabrication of cobalt nanoparticles in porous carbon shells (core/shell Co@C). Chemical vapor deposition of ethyne is used for controlling the reduction of cobalt nanoclusters in the MOF and the spontaneous formation of the porous carbon shells. The metallic cobalt cores formed are up to 4 - 6 nm with the crystal phase varying between hexagonally-close-packed (hcp) and face-centre-packed (fcc). The porous carbon shells change from amorphous to graphene with the ethyne deposition temperature increasing from 400 to 600 oC. The core/shell Co@C nanoparticles exhibit high catalytic activity in selectively converting syngas (CTY: 254.1 - 312.1 μmolCO·gCo-1·s-1) into hydrocarbons (4.0 - 5.2 gHC·g-cat-1·h-1) at 260 oC. As well as the crystal size and phase, the coordination numbers of the cobalt to oxygen and to other cobalt atoms on the surface of the cobalt nanoparticles, and the permeability of the porous carbon shell have been related to the catalytic performance in FTS reactions

Confinement of carbon dots localizing to the ultrathin layered double hydroxides toward simultaneous triple-mode bioimaging and photothermal therapy

It is a great challenge to develop multifunctional nanocarriers for cancer diagnosis and therapy. Herein, versatile CDs/ICG-uLDHs nanovehicles for triple-modal fluorescence/photoacoustic/two-photon bioimaging and effective photothermal therapy were prepared via a facile self-assembly of red emission carbon dots (CDs), indocyanine green (ICG) with the ultrathin layered double hydroxides (uLDHs). Due to the J-aggregates of ICG constructed in the self-assembly process, CDs/ICG-uLDHs was able to stabilize the photothermal agent ICG and enhanced its photothermal efficiency. Furthermore, the unique confinement effect of uLDHs has extended the fluorescence lifetime of CDs in favor of bioimaging. Considering the excellent in vitro and in vivo phototherapeutics and multimodal imaging effects, this work provides a promising platform for the construction of multifunctional theranostic nanocarrier system for the cancer treatment