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Marcus Carlsson 《Expositiones Mathematicae》2021,39(1):149-157
von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”. 相似文献
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Mohammad Javad TAGHIZADEH Maryam Saleh MOHAMMADNIA Masoumeh GHALKHANI Esmail SOHOULI 《高等学校化学研究》2022,38(2):546-551
Azaperone, with anti-anxiety and anti-aggressive activities used in veterinary medicine, is a member of the butyrophenone class. It is ordinarily utilized for a wide range of indications, such as sedation, obstetrics, and anesthesia. In this research, an improved synthetic route is presented for azaperone using a phase-transfer catalyst(PTC). In general, it was synthesized as a dopamine antagonist in four steps. The bis(2-chloroethyl) amine intermediate is easily obtained after the conversion of the alcohol groups into the chloride leaving group using thionyl chloride(95% yields). The alkylation of commercially available 2-amino pyridine in the presence of PTC was then carried out, giving 1-(pyridin-2-yl) piperazine with 75% yield. 1-(Pyridin-2-yl) piperazine was finally alkylated using 4-chloro-1-(4-fluorophenyl) butan-1-one to achieve azaperone with 60% yield. The butyrophenone intermediate was obtained via the Friedel-Crafts reaction of fluorobenzene with 4-chlorobutyryl chloride in the presence of AlCl3. High efficiency, gentle reaction conditions, and fast and simple procedure are the advantages of this method. Also, the electrochemical oxidation behaviour of azaperone was investigated using cyclic and differential pulse voltammetry techniques. Cyclic voltammetric studies indicated an irreversible process for azaperone electro-oxidation with a peak potential of 0.78 V in a phosphate buffer solution(pH=7.0) vs. Ag/AgCl(saturated KCl) electrode. The value of the peak current vs. the azaperone concentration was enhanced linearly in the range of 10―70 μmol/L, and the detection limit was found to be 3.33 μmol/L. 相似文献
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《Mathematische Nachrichten》2018,291(8-9):1177-1190
We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings. 相似文献
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We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation. 相似文献
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Awatif Alqahtani Mohamed Jleli Bessem Samet 《Mathematical Methods in the Applied Sciences》2019,42(3):861-870
In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided. 相似文献
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