On exponential stability of nonlinear Volterra difference equations in phase spaces

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.     

Common Core State Standards in the Middle Grades: What's New in the Geometry Domain and How Can Teachers Support Student Learning?

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6–8) mathematics curriculum. The methodology employed allows for comparisons of content across multiple standards documents. We report on some dramatic changes with regards to the geometry content taught in the middle grades. We found 52% of the middle grades geometry CCSSM learning expectations will be new to the respective grade level at which they are taught in at least six of the eight states analyzed in this study (57% in grade 6, 50% in grade 7, and 50% in grade 8). We also highlight three areas that represent “new” geometry content at the middle grades based on our analysis of CCSSM and pre‐CCSSM state standards.     

Different Directions of Switching of Chromium Oxide Thin Films

We have investigated the switching behavior of as-deposited CrO _x and post-annealed CrO _y films by use of a variety of electrodes (top electrode Ag, Ti; bottom electrode Pt, fluorine tin oxide (FTO)). Resistance switching is highly dependent on electrode material and post-annealing treatment. Among Pt devices, I–V hysteresis was observed for the Ag/CrO _x /Pt device only; no resistance switching was observed for Ag/CrO _y /Pt, Ti/CrO _x /Pt, and Ti/CrO _y /Pt devices. Among FTO devices, I–V hysteresis was observed for the Ag/CrO _x /FTO device whereas I–V hysteresis with the opposite switching direction was observed for Ag/CrO _y /FTO, Ti/CrO _x /FTO, and Ti/CrO _y /FTO devices. The direction of switching depends not only on electrode material but also on post-annealing treatment, which affects the density of grain boundaries. Thus, the density of grain boundaries determines the type of charge carrier involved in the switching process. For as-deposited CrO _x films with a high density of grain boundaries Ag filament paths mediated by electrochemical redox reaction were observed, irrespective of bottom electrode material (Pt or FTO). Post-annealed CrO _y films with a low density of grain boundaries suppressed electrochemical redox reaction in the Ag/CrO _y /Pt device but promoted short-range movement of O^2? ions through the bottom interface, resulting in resistance switching in the Ag/CrO _y /FTO device. Electrochemical redox reaction-controlled resistance switching occurred solely in oxides with a high density of grain boundaries or dislocations.     

Exploitation of Diversity in Cooperative Spectrum Sharing with the Four-way Relaying AF Transmission

This paper investigates a cooperative spectrum sharing model where both the primary and secondary systems are two-way relaying-based systems. This model is also known as four-way relaying-based cooperative spectrum sharing. In the scenario of multiple relays, we propose a transmission scheme that enables a degradation-free primary system, exploitation of spatial diversity without using any interference constraint at the primary receivers. In this scheme, both of the primary and secondary systems employ the two-way amplify-and-forward (AF) relaying-based transmission (TW-AF-RT) within two timeslots and with the help of \(M\) relays \(R_1,\ldots ,R_M\) . The system operates in three modes: simultaneous sharing (SimS) mode, primary-single-access (PSA) mode, and secondary-single-access (SSA) mode. The SimS mode is a four-way AF relaying-based transmission, and it is prioritized when at least one relay node satisfies that both systems are not in outage. In this mode, the pulse-amplitude-modulation (PAM) signal is employed to present the information messages of the sources. As a result, the best relay selection method, which is based on the max–min rule, is still applicable for the exploitation of spatial diversity in this mode. Only the primary system accesses the spectrum in the PSA mode while only the secondary system does this in the SSA mode. In both the PSA and SSA modes, complex signals are used to present the information messages of the related sources instead of PAM signals. These modes are used when the SimS mode is not available. The analysis and simulation results are conducted to validate the advantages of the proposed scheme.     

High Performance Three‐Dimensional Chemical Sensor Platform Using Reduced Graphene Oxide Formed on High Aspect‐Ratio Micro‐Pillars

The sensing performance of chemical sensors can be achieved not only by modification or hybridization of sensing materials but also through new design in device geometry. The performance of a chemical sensing device can be enhenced from a simple three‐dimensional (3D) chemiresistor‐based gas sensor platform with an increased surface area by forming networked, self‐assembled reduced graphene oxide (R‐GO) nanosheets on 3D SU8 micro‐pillar arrays. The 3D R‐GO sensor is highly responsive to low concentration of ammonia (NH₃) and nitrogen dioxide (NO₂) diluted in dry air at room temperature. Compared to the two‐dimensional planar R‐GO sensor structure, as the result of the increase in sensing area and interaction cross‐section of R‐GO on the same device area, the 3D R‐GO gas sensors show improved sensing performance with faster response (about 2%/s exposure), higher sensitivity, and even a possibly lower limit of detection towards NH₃ at room temperature.     

A flexible synthesis of C-6 and N-1 analogues of a 4-amino-1,3-dihydroimidazo[4,5-c]pyridin-2-one core

A flexible route which enables access to derivatives of 4-amino-1,3-dihydroimidazo[4,5-c]pyridin-2-ones is described. Issues of selectivity, reaction safety, and low yields in original routes are overcome with the key improvements to the route, including a Negishi cross-coupling and use of a carbamate as a protecting group and intrinsic carbonyl source. The new route enables variation of C-6 and N-1 substituents.     

Conformational searching using a population-based incremental learning algorithm

A new population-based incremental learning algorithm for conformational searching of molecules is presented. This algorithm is particularly effective at determining, by relatively small number of energy minimizations, global energy minima of large flexible molecules. The algorithm is also able to find a large set of low energy conformations of more rigid small molecules. The performance of the algorithm is relation to other algorithm is examined via the test molecules: C(18) H(38) , C(39)H(80) , cycloheptadecane and a set of five drug-like molecules.     

Benzophenone absorption and diffusion in poly(dimethylsiloxane) and its role in graft photo-polymerization for surface modification

Following the great success of traditional microfluidic devices across many disciplines, a new class of microfluidic systems emerged in recent years, which features finely tuned, localized surface modifications within the microstructures in order to keep up with the demand for devices of ever increasing complexity (lab on chip, assay on chip, etc.). Graft photopolymerization has become a powerful tool for such localized surface modifications particularly in combination with poly(dimethylsiloxane) (PDMS) devices, as it is compatible with many functional monomers and allows for high spatial resolution. However, application within enclosed PDMS microstructures and in particular well-controlled surface-directed polymerization remains challenging. Detailed understanding of the interaction between photoinitiator, benzophenone (BP), and polymer matrix is needed. We have developed a visualization technique, which allows for observation of reacted BP in situ within the PDMS matrix. We present a detailed study on solvent-driven BP diffusion providing results essential to successful surface treatment. We also identified and investigated photoinitiator inhibition by oxygen and provide appropriate mitigation strategies.     

Development of interdigitated arrays coated with functional polyaniline/MWCNT for electrochemical biodetection: application for human papilloma virus

In this study, polyaniline-multiwalled carbon nanotube film (PANi-MWCNT) has been polymerized on interdigitated platinum electrode arrays (IDA), fabricated by MEMS technology for the detection of human papillomavirus (HPV) infection, using immobilized peptide aptamers as affinity capture reagent. Label-free, electrochemical detection of the specific immune reaction between antigen peptide aptamer HPV-16-L1 (with a molecular weight of 1825 Da), the most common genotype in cytological normal women worldwide, and its specific antibody of HPV-16 (which is much bigger with molecular weight of ca. 150 kDa) on multifunctional PANi-MWCNT based arrays was reported. The most significant advantage of this technique consists of reagentless and multiple detection of antigen-antibody complex formation on well conducting IDA interface of PANi-MWCNT, without intermediate steps or any labeling reagents, as normally required in the previous works.