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Previously, it is difficult or even impossible to tackle some real integrals that may not be calculating by classic methods in calculus. However, this paper would summarize methods using the Residue theorem to calculate some types of these “impossible integrals”. However, before one calculates the integral using the residue theorem, one will introduce two important conclusions, one is about when the function decays faster than , which involve integral inequality and the method finding the upper bound. The second one would give reader a general conclusion of integration. At the same time, the readers have to understand the proof of the Cauchy’s Residue Theorem, and other theorems such as Cauchy’s theorem, Cauchy’s Integral formula. One should notice that the importance of branch cut and branch points, since the integrand one face could be multifunction, so one may try to turn them into single valued function. Also, the integral inequality plays a very important role in the first conclusion.

Near-infrared (NIR) spectroscopy is widely used for the classification of materials and the quantification of their properties. Today, there is a high demand for extending the use of this technique to portable applications, and eventually, the integration with consumer appliances and smartphones. To reach this goal, the overall size of the NIR sensor, its production cost, robustness, and resistance to vibrations are of particular importance. This paper describes an approach to spectral sensing in the NIR (850–1700 nm) using a handheld sensor module based on a fully integrated multipixel detector array with a footprint of around 2×2 mm2. The capabilities of the spectral sensor module were recently evaluated in two application cases: Quantification of the fat percentage in raw milk and the classification of plastic types. Fat quantification was achieved with a root mean square error (RMSE) of prediction of 0.14% and classification of plastic types was achieved with a prediction accuracy on unknown samples of 100%. The results demonstrate the feasibility of the direct NIR sensing approach used by the integrated sensor, which has potential to be used in a variety of applications.

One main challenge of realizing high-energy-density lithium-sulfur batteries is low active materials utilization, excessive use of inert components, high electrolyte intake, and mechanical instability of high-mass-loading sulfur cathodes. Herein, chunky sulfur/graphene particle electrodes were designed, where active sulfur was confined in vertically aligned nanochannels (width ∼12 nm) of chunky graphene-based particles (∼70 μm) with N, O-containing groups. The short charge transport distance and low tortuosity enabled high utilization of active materials for high-mass-loading chunky sulfur/graphene particle electrodes. The intermediate polysulfide trapping effect by capillary effect and heteroatoms-containing groups, and a mechanically robust graphene framework, helped to realize stable electrode cycling. The as-designed electrode showed high areal capacity (10.9 mAh cm

We propose and demonstrate a mode-division-multiplexed transmitter by employing a VCSEL-based 2-D matrix and a multi-plane light converter (MPLC). The triangular matrix light spots from VCSELs are designed with a 250-μ pitch in both x- and y- directions for scalable and low-loss mode multiplexing. The VCSELs are directly modulated by co-packaged BiCMOS drivers on a silicon interposer, fabricated on a wafer level. The MPLC is utilized to form seven phase masks to convert the individual Gaussian beams to multiplex Hermite-Gaussian modes, which can be coupled into a multi-mode fiber. In the demonstration, we packaged ten 10-G class VCSELs with the drivers, and the form factor of the co-packaged optics is 10-mm × 10-mm. With the fan-out evaluation board, the sub-module is characterized for short and long transmissions by multiplexing the ten directly modulated outputs from VCSELs. The testing results indicate 200-Gb/s capacity over 100-m MMF with direct detection and 28-km few-mode fiber with coherent detection.

We design an optical interface system for vertically coupling between Vertical-Cavity Surface-Emitting Lasers and 3-μm silicon waveguides. The system includes a photoresist lens and a total internal reflection mirror, which allows for passive alignment and flip-chip bonding of VCSELs. The simulated coupling loss is 0.7dB, in optimal conditions, which increases to 1 dB when 3-μm and 20-μm alignment tolerances are considered in lateral and longitudinal directions, respectively. The system is built by post-processing lens and metallic wiring on the backside of a 3-μm silicon photonic platform. After flip-chip bonding and embedding of the VCSELs, the system performance is characterized, and VCSEL-to-waveguide coupling efficiency of -7.5 dB is obtained.

Background: In clinical practice, Preoperative differentiation between hepatocellular carcinoma and intrahepatic cholangiocarcinoma is challenging but critical for treatment decisions. Objective: This study investigated the discriminatory power of the stretched-exponential model and fractional-order calculus model parameters for hepatocellular carcinoma versus intrahepatic cholangiocarcinoma in orthotopic xenograft nude mice. Methods: Prototype orthotopic xenograft models of hepatocellular carcinoma and intrahepatic cholangiocarcinoma were developed using 20 nude mice divided into two groups and separately transplanted with MHCC97H and HUCCT1 cells. Readout-segmented diffusion-weighted imaging with multiple b-values (0–2000 s/mm2) was obtained using a 3.0-T magnetic resonance imaging scanner. The apparent diffusion coefficient was calculated using the mono-exponential model. The distributed diffusion coefficient and intravoxel water molecular diffusion heterogeneity (α) were calculated using the stretched-exponential model. The diffusion coefficient (D), fractional-order derivative in space (β), and spatial parameter (μ) were calculated using the fractional-order calculus model. The liver and tumor specimens of nude mice were immunostained after euthanasia to clarify the liver cancer type. Differences in diffusion-related parameters between the groups were evaluated using Mann–Whitney U-test and univariate logistic analysis. Receiver operating characteristic curves were used to assess the diagnostic efficacy of each parameter. P Results: α, D, and β were significant discriminators between the groups. The area under the curve for these three variables was 0.890, 0.830, and 0.870, respectively, with cutoff values of 0.491, 0.435, and 0.782, respectively. Conclusion: The stretched-exponential model parameters α and the fractional-order calculus model parameters D and β showed high diagnostic efficacy in discriminating intrahepatic cholangiocarcinoma from hepatocellular carcinoma in orthotopic xenograft nude mouse models. conclusion: The stretched-exponential model parameter α and the fractional-order calculus model parameters D and β showed high diagnostic efficacy in discriminating intrahepatic cholangiocarcinoma from hepatocellular carcinoma in orthotopic xenograft nude mouse models.

The Tibetan Plateau and its surroundings have recently experienced several catastrophic glacier-related disasters. It is of great scientific and practical significance to establish ground-based early warning systems (EWS) to understand the processes and mechanisms of glacial disasters and warn against potential threats to downstream settlements and infrastructure. However, there are few sophisticated EWSs on the Tibetan Plateau. With the support of the Second Tibetan Plateau Scientific Expedition and Research Program, an EWS was developed and implemented in the Sedongpu Valley, southeastern Tibetan Plateau, where repeated river blockages have occurred due to ice/rock collapse debris flow. The EWS collected datasets of optical/thermal videos/photos, geophone waveforms, water levels, and meteorological variables in this sparsely populated zone. It has successfully warned against three ice-rock collapse-debris flow - river blockage chain events and seven small-scale ice-rock collapse-debris flow events. Meanwhile, it was found that the low-cost geophone can effectively indicate the occurrence and magnitude of ice/rock collapses by local thresholds, and water level observation is an efficient way to warn of river blockages. Our observations showed that several factors, such as the volume and location of the collapses and the percentage of ice content involved, influence the velocities of debris flows and the magnitude of river blockages. There are still two possible glaciers in the study area that are at risk of ice collapse. It is worth monitoring their dynamic changes using high-resolution satellite data and the ground-based EWS to safeguard the surrounding hydrological projects and infrastructure in this transboundary region.