Rankin-Selberg periods for spherical principal series

By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic representations. By the multiplicity-one theorems due to Sun-Zhu and Chen-Sun such invariant forms are unique up to scalar multiples and can therefore be related to invariant forms on equivalent principal series representations. We construct meromorphic families of such invariant forms for spherical principal series representations of ${\rm GL}(n,\mathbb{R})$ and conjecture that their special values at the spherical vectors agree in absolute value with the archimedean local L-factors of the corresponding L-functions. We verify this conjecture in several cases. This work can be viewed as the first of two steps in a technique due to Bernstein-Reznikov for estimating L-functions using their period integral expressions.Comment: 25 pages. v3 replaces the previous versions which have a gap in Lemma 4.1 due to the non-co-compactness of the lattic

Effect of overmolding process on the integrity of electronic circuits

Traditional injection molding processes have been widely used in the plastic processing industry. It is the major processing technique for converting thermoplastic polymers into complicated 3D parts with the aid of heat and pressure. Next generation of electronic circuits used in different application areas such as automotive, home appliances and medical devices will embed various electronic functionalities in plastic products. In this study, over-molding injection molding (OVM) of electronic components will be examined to insert novel performance in polymer materials. This low-cost manufacturing process offers potential benefits such as, reduction in processing time, higher freedom of design and less energy used when compared to the conventional injection molding method. This paper aims to evaluate the performance of this process and propose a series of alternative solutions to optimize the adhesion between and integration of electronics and engineering plastics. A number of methods are used to optimize the process so that the electronic circuits are not damaged during the over-molding, moreover to test the reliability of the system in order to control the continuity of connections between the electronic circuit foils and the electronic components after the OVM process. Correspondingly, we have performed specific tests for this purpose varying in some conditions: the type of injected plastic used, over-molding parameters (temperature, pressure and injection time), electronic circuit design, type of assembled electronic components, type of foils used and the effect of using underfill material below the electronic component. From these tests, first conclusions were made. We have also studied adhesion between the foil and the over-molding material. In this case, various types of engineering plastics have been tested; polypropylene (PP), 30% weight percentage glass,fiber filled polypropylene (GF-PP), Polyamide-6 (PA6) and 50% weight percentage glass fiber filled polyamide-6 (GF-PA6). It was proved that throughout the wide range of tested materials, (PA6) over-molded samples showed a better adhesion on the copper-polyimide foils than the rest. These plastics were over-molded on two types of polyimide (PP/Copper (Cu) tracks foils with and without an adhesive layer between PI and Cu. It was obviously clear that the foils with on adhesive layer between PI and Cu had more delamination in the Cu tracks than the foils without an adhesive layer. Furthermore, it was shown that the presence of an underfill material has on effect on the system as the foils that had an underfill material below their components successfully had a better connection than the folis without an underfill material. Finally, experiments were executed using the two probe method as an electrical measurement and microscope investigation as the visual inspection

Statistical regularities across trials bias attentional selection

Previous studies have shown that attentional selection can be biased toward locations that are likely to contain a target and away from locations that are likely to contain a distractor. It is assumed that through statistical learning, participants are able to extract the regularities in the display, which in turn biases attentional selection. The present study employed the additional singleton task to examine the ability of participants to extract regularities that occurred across trials. In four experiments, we found that participants were capable of picking up statistical regularities concerning target positions across trials both in the absence and presence of distracting information. It is concluded that through statistical learning, participants are able to extract intertrial statistical associations regarding subsequent target location, which in turn biases attentional selection. We argue here that the weights within the spatial priority map can be dynamically adapted from trial to trial such that the selection of a target at a particular location increases the weights of the upcoming target location within the spatial priority map, giving rise to a more efficient target selection

Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice

We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening $J_e$, the system scales exponentially, either with or without a magnetic field $h$: the order parameter, the five critical fields that separate the $J_e$-$h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on $J_e$. We calculate the temperature dependence of the specific heat, which can be directly compared with future experiments.Comment: 7 pages, 6 figure

Facile fabrication of stretchable Ag nanowire/polyurethane electrodes using high intensity pulsed light

Silver nanowires (AgNWs) have emerged as a promising nanomaterial for next generation stretchable electronics. However, until now, the fabrication of AgNW-based components has been hampered by complex and time-consuming steps. Here, we introduce a facile, fast, and one-step methodology for the fabrication of highly conductive and stretchable AgNW/polyurethane (PU) composite electrodes based on a high-intensity pulsed light (HIPL) technique. HIPL simultaneously improved wire-wire junction conductivity and wire-substrate adhesion at room temperature and in air within 50 mu s, omitting the complex transfer-curing-implanting process. Owing to the localized deformation of PU at interfaces with AgNWs, embedding of the nanowires was rapidly carried out without substantial substrate damage. The resulting electrode retained a low sheet resistance (high electrical conductivity) of <10 Omega/sq even under 100% strain, or after 1,000 continuous stretching-relaxation cycles, with a peak strain of 60%. The fabricated electrode has found immediate application as a sensor for motion detection. Furthermore, based on our electrode, a light emitting diode (LED) driven by integrated stretchable AgNW conductors has been fabricated. In conclusion, our present fabrication approach is fast, simple, scalable, and cost-efficient, making it a good candidate for a future roll-to-roll process

Flexible microsystems using over-molding technology

Today’s world is full of intelligent electronics and with the development of flexible printed electronics technologies, different integration approaches are of high demand. The combination of electronics with polymer is a new technology platform as it integrates multiple functionalities into plastic products. This work shows preliminary results in the integration of electronic components (e.g. NFC chips and LEDs) using over-molding technology. A significant degree of freedom in product design is obtained resulting in a low-cost fabrication of flexible smart objects. The integration is achieved by using adhesion between flexible circuits and injection molded plastics. In order to check the adhesion performance between the flexible circuit and polymer injected, the polyimide foils with patterned copper cladding were over-molded with different engineering plastics into the form of peel test specimens. The technology was shown by the realization of a demonstrator, in which LEDs are wirelessly powered using an NFC antenna and a chip. The NFC antenna is executed in the copper layer and the LEDs and NFC chip are soldered on the foil. The antenna and NFC chip can harvest the energy from (e.g. a smartphone) in order to power the LEDs. This is a simple example of wireless energy transfer that could be used to power circuits and readout sensor values using NFC without the need of having an integrated battery