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Xue Pan 《中国物理C(英文版)》2022,46(2):024104-024104-10
High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics, the temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves. 相似文献
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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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为建设适应新时代要求,突出高阶性、创新性、挑战度的一流本科课程,实现价值引领、能力培养和知识传授的教育教学目标,结合功能材料专业的特点和民族高等院校学生的学情,构建了物理化学基础课程的“四模块、三阶段、两时空、双平台”的混合式教学新模式,重塑了“价值引领模块、基础理论模块、多学科融合模块和虚拟仿真实验模块”的“四模块”内容体系。通过“四模块”嵌入下的混合式教学实践研究,结合学生的课前、课中、课后等学习成绩,多维度评价学习效果,并藉由调查问卷来分析学生对混合式教学的评价,最终研究结果表明学生的个性化自主学习能力有了显著提高、学生运用物理化学理论解决复杂问题的综合能力得到了提升,学生经过刻苦学习获得了素质提高的成就感。 相似文献
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Niamh O'Meara Mark Prendergast 《International Journal of Mathematical Education in Science & Technology》2018,49(4):501-516
Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide calling for the inclusion of double class periods on the mathematics timetable. Research from the United States suggests that the introduction of double or block periods allow for the objectives of revised curricula to be realized. The aim of this study, which is set in the school context, is first to ascertain if schools in Ireland are scheduling double periods for mathematics at both lower post-primary level (Junior Cycle) and upper post-primary level (Senior Cycle). It also seeks to determine if there is a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods and to get insights from teachers in relation to their opinions on what can be achieved through the introduction of such classes. Questionnaires were sent to 400 post-primary schools (approximately 1600 teachers) which were selected using stratified sampling techniques. It was found that 8.7% of mathematics teachers reported the provision of double periods at Junior Cycle while 55% reported that double periods were included on their timetable at Senior Cycle. The study also identified a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods. Finally, teachers felt that double periods allowed for new teaching methodologies, which were promoted by the revised curricula, to be implemented and teaching for understanding was also more feasible. In essence, it was found that double periods have an influence on the mathematical experience of post-primary students as well as the teaching approaches employed. 相似文献
10.
We derive trace formulas for a pair of self-adjoint operators and H under the assumption that is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10]. 相似文献