Plasmas are believed to be possibly the most abundant form of ordinary matter in the Universe, supporting a variety of the wave phenomena, while a dusty plasma is of interest as a non-Hamiltonian ...system of interacting particles. In this Letter, symbolic computation on an observationally/experimentally-supported (2+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation is done, for certain dust-acoustic, electron-acoustic, positron-acoustic, magneto-acoustic, dust-magneto-acoustic, ion-acoustic, dust-ion-acoustic and/or quantum-dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. Auto-Bäcklund transformation and families of the solitonic solutions are obtained, for the electrostatic wave potential, perturbation of the magnitude of the magnetic field, fluctuation of electron or ion density, or radial-direction component of the velocity of ions or dust particles, relying on such plasma coefficient functions as the nonlinearity, dispersion, dusty-fluid-viscosity/Burgers-dissipation, geometric-effect and diffraction/transverse-perturbation coefficients. Shock structures presented in this Letter are very close to the experimental results previously reported. Future plasma observations/experiments might verify some other effects offered by our analytic results with respect to those plasma coefficient functions.
Optical fiber communication system is one of the core supporting systems of the modern internet age, and studies on the ultrashort optical pulses are at the forefront of fiber optics, modern optics ...and optical engineering. Hereby, symbolic computation on the recently-proposed generalized higher-order variable-coefficient Hirota equation is performed, for certain ultrashort optical pulses propagating in a nonlinear inhomogeneous fiber. For the complex envelope function associated with the optical-pulse electric field in the fiber, an auto-Bäcklund transformation is worked out, along with a family of the analytic solutions. Both our Bäcklund transformation and analytic solutions depend on the optical-fiber variable coefficients which represent the effects of the first-order dispersion, second-order dispersion, third-order dispersion, Kerr nonlinearity, time delaying, phase modulation and gain/loss. Relevant constraints among those coefficients are also presented. We expect that the work could be of some use for the fiber-optics investigations.
Current studies on the liquids and lattices attract people’s attention. In this Letter, for certain interfacial waves in a two-layer liquid or elastic waves in a lattice, we investigate a ...(3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system via building a set of the similarity reductions. In respect of the amplitude or elevation of the relevant wave, our similarity reductions are from that system to a known ordinary differential equation, while dependent on the coefficients in that system.
Nowadays, marine scientists are making use of the Kadomtsev-Petviashvili (KP)-category equations in their investigations from the Straits of Georgia and Gibraltar to the Adriatic Sea, North Sea and ...South China Sea. In fluid mechanics and other fields, the (3+1)-dimensional B-type KP equations have attracted a good size of recent research. For a generalized (3+1)-dimensional variable-coefficient B-type KP equation for the nonlinear waves in fluid mechanics, with symbolic computation, we obtain a variable-coefficient-dependent auto-Bäcklund transformation, along with two variable-coefficient-dependent families of the shock-wave-type solutions.
•We study a generalized (3+1)-dimensional variable-coefficient BKP equation for the nonlinear waves in fluid mechanics.•With symbolic computation, we obtain a variable-coefficient-dependent auto-Bäcklund transformation.•With symbolic computation, we obtain two variable-coefficient-dependent families of the shock-wave-type solutions.
Pre-gestational diabetes mellitus (PGDM) has been known to be a risk factor for congenital heart defects (CHDs) for decades. However, the associations between maternal PGDM and gestational diabetes ...mellitus (GDM) and the risk of specific types of CHDs and congenital anomalies (CAs) in other systems remain under debate. We aimed to investigate type-specific CAs in offspring of women with diabetes and to examine the extent to which types of maternal diabetes are associated with increased risk of CAs in offspring.
We searched PubMed and Embase from database inception to 15 October 2021 for population-based studies reporting on type-specific CAs in offspring born to women with PGDM (combined type 1 and 2) or GDM, with no limitation on language. Reviewers extracted data for relevant outcomes and performed random effects meta-analyses, subgroup analyses, and multivariable meta-regression. Risk of bias appraisal was performed using the Cochrane Risk of Bias Tool. This study was registered in PROSPERO (CRD42021229217). Primary outcomes were overall CAs and CHDs. Secondary outcomes were type-specific CAs. Overall, 59 population-based studies published from 1990 to 2021 with 80,437,056 participants met the inclusion criteria. Of the participants, 2,407,862 (3.0%) women had PGDM and 2,353,205 (2.9%) women had GDM. The meta-analyses showed increased risks of overall CAs/CHDs in offspring born to women with PGDM (for overall CAs, relative risk RR = 1.99, 95% CI 1.82 to 2.17, P < 0.001; for CHDs, RR = 3.46, 95% CI 2.77 to 4.32, P < 0.001) or GDM (for overall CAs, RR = 1.18, 95% CI 1.13 to 1.23, P < 0.001; for CHDs, RR = 1.50, 95% CI 1.38 to 1.64, P < 0.001). The results of the meta-regression analyses showed significant differences in RRs of CAs/CHDs in PGDM versus GDM (all P < 0.001). Of the 23 CA categories, excluding CHD-related categories, in offspring, maternal PGDM was associated with a significantly increased risk of CAs in 21 categories; the corresponding RRs ranged from 1.57 (for hypospadias, 95% CI 1.22 to 2.02) to 18.18 (for holoprosencephaly, 95% CI 4.03 to 82.06). Maternal GDM was associated with a small but significant increase in the risk of CAs in 9 categories; the corresponding RRs ranged from 1.14 (for limb reduction, 95% CI 1.06 to 1.23) to 5.70 (for heterotaxia, 95% CI 1.09 to 29.92). The main limitation of our analysis is that some high significant heterogeneity still persisted in both subgroup and sensitivity analyses.
In this study, we observed an increased rate of CAs in offspring of women with diabetes and noted the differences for PGDM versus GDM. The RRs of overall CAs and CHDs in offspring of women with PGDM were higher than those in offspring of women with GDM. Screening for diabetes in pregnant women may enable better glycemic control, and may enable identification of offspring at risk for CAs.
Results Phys. 51, 106624 (2023) and 50, 106566 (2023) have recently made some outstanding contributions to the studies of certain Korteweg-de Vries (KdV)-type systems. Inspired by those ...contributions, around a noncharacteristic movable singular manifold, this Letter works out two sets of the auto-Bäcklund transformations for an enlarged three-coupled KdV system, along with some solitons. All of our results rely on the coefficients in that system.
Cosmic plasmas are considered as the most abundant form of ordinary matter in the Universe while observations of the cosmic dust in different regions provide an insight into the Universe's recycling ...processes. For different types of the cosmic dusty plasmas, we hereby, with the symbolic computation and observational/experimental supports, study a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation, which can describe the electron-acoustic, dust-acoustic, positron-acoustic, dust-magneto-acoustic, ion-acoustic, magneto-acoustic, ion, quantum-dust-ion-acoustic or dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. With respect to the fluctuation of the electron or ion density, or perturbation of the magnitude of the magnetic field, or electrostatic wave potential, or radial-direction component of the velocity of ions or dust particles, a set of the auto-Bäcklund transformations, several soliton families and a set of the similarity reductions are symbolically computed out, depending on the variable coefficients which represent the dispersion, nonlinearity, geometric effect, Burgers/dusty-fluid-viscosity dissipation and diffraction/transverse perturbation. Variable-coefficient constraints on the soliton solutions are presented. Our analytic results are in agreement with those dusty-plasma-experimentally reported. Future dusty-plasma experiments and observations might justify some other effects hereby offered.
These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves ...in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal velocity, this paper avails of symbolic computation to obtain (A) an auto-Bäcklund transformation with some solitons; (B) a group of the scaling transformations and (C) a group of the hetero-Bäcklund transformations, to a known linear partial differential equation, from that system. Results rely on the coefficients in that system
General methods for the preparation of geminal bis(boronates) are of great interest due to their widespread applications in organic synthesis. While the terminal gem‐diboron compounds are readily ...accessible, the construction of the sterically encumbered, internal analogues has remained a prominent challenge. Herein, we report a formal umpolung strategy to access these valuable building blocks. The readily available 1,1‐diborylalkanes were first converted into the corresponding α‐halogenated derivatives, which then serve as electrophilic components, undergoing a formal substitution with a diverse array of nucleophiles to form a series of C−C, C−O, C−S, and C−N bonds. This protocol features good tolerance to steric hindrance and a wide variety of functional groups and heterocycles. Notably, this strategy can also be extended to the synthesis of diaryl and terminal gem‐diboron compounds, therefore providing a general approach to various types of geminal bis(boronates).
A general method for accessing sterically encumbered geminal bis(boronates) was developed based on a formal umpolung strategy. The polarity inversion of the readily available 1,1‐diborylalkanes allows their corresponding α‐halogenated derivatives to undergo a formal substitution with a wide variety of nucleophiles to form C−C, C−O, C−S, and C−N bonds, featuring excellent tolerance to steric hindrance and functional groups.
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