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1.
In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions. 相似文献
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Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of reaction–diffusion–convection equations coupled with ordinary differential equations, which models a combustion front moving through a porous medium with parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function. 相似文献
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Generalizing the quasi-cyclic codes of index introduced by Fan et al., we study a more general class of quasi-cyclic codes of fractional index generated by pairs of polynomials. The parity check polynomial and encoder of these codes are obtained. The asymptotic behaviours of the rates and relative distances of this class of codes are studied by using a probabilistic method. We prove that, for any positive real number such that the asymptotic GV-bound at is greater than , the relative distance of the code is convergent to , while the rate is convergent to . As a result, quasi-cyclic codes of fractional index are asymptotically good. 相似文献
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Ajay Gupta Fillip Kumar Sarkar Rajib Sarkar Ramen Jamatia Chang Yeon Lee Gajendra Gupta Amarta Kumar Pal 《应用有机金属化学》2020,34(9):e5782
Magnetically retrieval CuFe2O4@MIL-101(Cr) metal–organic framework was successfully prepared from easily available starting materials and characterized using various spectroscopic and analytical techniques such as powder X-ray diffraction, scanning electron microscopy, energy dispersive X-ray, transmission electron microscopy, elemental mapping, Fourier transform infrared spectroscopy, thermogravimetric analysis, X-ray photoelectron spectroscopy, Brunauer–Emmett–Teller, vibrating sample magnetometer, and inductively coupled plasma optical emission spectroscopy. The catalyst was then used in the synthesis of benzodiazepines containing a triazole moiety in water. The advantages of this protocol include high yields, reusability of the catalyst, and gram-scale synthesis. 相似文献
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An efficient, cost-effective and environmentally benign synthesis of novel tetracyclic bis-isoxazolopyrroloquinoline derivatives has been developed via one-pot four-component reaction of 4-amino-3-methyl-5-styrylisoxazoles, dimedone, aryl glyoxal monohydrates and 5-amino-3-methylisoxazole by employing water as a reaction medium and acetic acid (AcOH) as a green promoter. The advantages of this protocol are environmentally friendly, metal-free, less reaction time, operational simplicity, high yields, broad substrate scope and easy purification. Most significant of all, this method is green. 相似文献