MOMENTUM OF AN ELECTROMAGNETIC WAVE IN TIME-VARYING DIELECTRIC MEDIA

In the context of the Abraham–Minkowski controversy, the problem of the propagation of electromagnetic waves in a linear dielectric medium with a time-varying dielectric constant is considered. It is shown that the momentum of an electromagnetic wave in the form of Minkowski is preserved with an instantaneous change in the dielectric permittivity of the medium. At the same time, the Abraham momentum is not conserved, despite the spatial homogeneity of the problem. This circumstance is interpreted as a manifestation of the Abraham force.

Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth

In a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of the agent’s terminal wealth must exceed a target and minimize the variance of the agent’s terminal wealth. The agent can revise the expected terminal wealth target dynamically to adapt to the change of the agent’s current wealth, and we consider the following three targets: (i) the agent’s current wealth multiplied by a target expected gross return rate, (ii) the risk-free payoff of the agent’s current wealth plus a premium, and (iii) a weighted average of the risk-free payoff of the agent’s current wealth and a preset aspiration level. We derive the so-called equilibrium strategy in closed form for each of the three targets and find that the agent effectively minimizes the variance of the instantaneous change of the agent’s wealth subject to a certain constraint on the expectation of the instantaneous change of the agent’s wealth.

Impact of China’s zero mark-up drug policy on drug cost of NCDs’ outpatients: an interrupted time series analysis

Background China proposed the Zero Markup Drug Policy (ZMDP), which popularized in tertiary hospitals across the country in 2017, to control drug expenditures’ rapid growth further and reduce the public’s medical burden. This study aims to evaluate the impact of ZMDP on the drug cost of chronic disease outpatients in the tertiary hospital in Chongqing. Methods We collected and described the drug-cost data for outpatients with chronic diseases in a Chongqing’s tertiary hospital from 2015 to 2019. The instantaneous and long-term changes of the outpatient volume and average drug cost after the ZMDP were evaluated using interrupted time series (ITS). We also analyzed the policy’s impact under the stratification of gender, age, and basic medical insurance types. Results A total of 350,848 outpatients were collected from January 2015 to February 2019. After the ZMDP, the outpatient volume for diabetes, hypertension, and coronary heart disease (CHD) all showed a downward trend, with a decrease of 53.04 (P = 0.012), 142.19 (P < 0.01) and 12.16 (P < 0.001) per month. Simultaneously, the average drug cost decreased by 4.44 yuan (P = 0.029), 5.87 yuan (P < 0.001) and 10.23 yuan (P = 0.036) per month, respectively. By gender, the average drug cost of diabetes in males had the most considerable instantaneous change, reducing by 51.21 yuan (P = 0.017); the decline of CHD in women is the most obvious, with an average monthly decrease of 12.51 yuan (P < 0.001). By age, the instantaneous change of CHD was the greatest for those older than 65 years old, with a decrease of 102.61 yuan (P = 0.030). CHD in 46–65 years old showed the most significant reduction, with an average monthly decline of 11.70 yuan (P < 0.01). BMIUE’s hypertension had the most considerable instantaneous change, which decreased 59.63 yuan (P = 0.010). BMIUE’s CHD showed the most apparent downward trend, with an average monthly decrease of 10.02 yuan (P = 0.010). Conclusion The ITS analysis is an effective method of health policy evaluation. The implementation of the ZMDP can reduce the drug cost for chronic disease outpatients in the tertiary hospital and their economic burden. Follow-up policies still require targeted price adjustments in the health service system to adjust the drug cost-effectively.

Motion Intent Recognition in Intelligent Lower Limb Prosthesis Using One-Dimensional Dual-Tree Complex Wavelet Transforms

Background: Most traditional intent recognition methods are to recognizing the movement of lower limb prosthesis through statistical features, which are unstable in short-term signals. The another key problem with recognition of lower limb prosthesis motion intent is to explore the instantaneous change between the two difffferent steady modes. Based on the above considerations, the one-dimensional dual-tree complex wavelet transform(1D-DTCWT) is introduced for motion intent recognition in intelligent prosthesis. Methods: 1D-DTCWT adopts two-way complex wavelet transforms with a binary tree structure as functional data analysis (FDA) method that preserves the time-frequency local analysis capabilities of wavelet transforms while maintaining translation invariance and direction selection. Therefore, the 1D-DTCWT can amplify the instantaneous change information hidden in the data while retaining the continuity of the motion behavior, so as to better recognize the motion intention. Furthermore, the feature vector composed of low-frequency wavelet coeffiffifficients decomposed by 1D-DTCWT is classifified and recognized by support vector machine (SVM), which can effffectively classify and recognize the motion intent of the unilateral lower limb amputees. Results: The data of the experiment comes from ten able-bodied subjects and one amputee subject to analyze 5 steady modes, 8 transitional modes, and 13 total motion modes adopting user-dependent and user-independent methods. The experimental results from the user-dependent methods show that the recognition rate for able-bodied subjects reached 98.91%, 98.92%, and 97.27% for the movement modes of steady modes, transitional modes, and total motion modes, respectively. The recognition rate of the amputee subject reached 100%, 91.16%, and 89.27%, respectively, for the three modes. Conclusions: The method in this paper can effffectively solve the problem of short-term signal instability reflflected by traditional statistical feature recognition of motion intent and explore the instantaneous change information of transitional modes while retaining the continuity of the motion behavior.

System analysis of basic of mechanics

Механика берет свое начало со статики. Основным понятием статики является понятие «сила». При нарушении равновесия возникает движение, которое определяется скоростью и ускорением в координатной системе пространство–время; скорость определяется как отношение мгновенного изменения координаты к соответствующему мгновенному изменению времени. В свою очередь изменение мгновенной скорости, т. е. ускорение, связано с воздействием силы за мгновенное время, и называется импульсом силы. Второй закон Ньютона как основной закон динамики сформулирован для воздействия на тело постоянной силы за короткий промежуток времени, т. е. импульса силы. Импульс силы вызывает изменение скорости движения тела; мерой сопротивления тела изменениям скорости является масса; произведением массы на скорость вводится понятие «количество движения» (импульс). Поэтому второй закон Ньютона определяет силу как отношение изменения количества движения к короткому времени действия импульса силы. Короткое время действия силы является частным случаем непрерывного ее действия во времени. В данном исследовании импульс силы понимается в обобщенном представлении как произведение силы на непрерывное время действия. По аналогии импульсу силы во времени вводится импульс силы в пространстве. С позиции системного анализа графиков сила–время, масса–скорость, сила–пространство, мощность время построены дифференциальные и интегральные законы динамики потенциально связного взаимодействия соответственно сила–время–масса– скорость, сила–пространство–работа, мощность–время–энергия. Анализ полных дифференциалов потенциалов приводит к представлениям функционального времени и пространства, которые сопряжено дополняют время и пространство взаимодействия. Время и пространство действия силы в исследуемых системах по аналогии с массой рассматриваются как меры сопротивления тела изменениям силы, т. е. как механические параметры, а не геометрические. Интегральные законы динамики построены в виде суперпозиции интегралов Римана для прямых функций и интегралов Стилтьеса для обратных. Интегралы Римана описывают современную динамику, а интегралы Стилтьеса ее дополнение до потенциальной. Mechanics starts with statics. The main concept of statics is the concept of force. When the equilibrium is disturbed, motion occurs, which is determined by the speed and acceleration in the space-time coordinate system; speed is defined as the ratio of an instantaneous change in the coordinate to the corresponding instantaneous change in time. In turn, the change in instantaneous speed, i.e. acceleration, is associated with the impact of a force in an instantaneous time, which is called the force pulse. The second law of Newton, as the basic law of dynamics, is formulated for the effect on the body of a constant force for a short period of time, i.e., the force impulse. The force pulse causes a change in the speed of the body; the measure of the body's resistance to changes in speed is the mass; the product of mass and speed is introduced the concept of the amount of movement (momentum). Therefore, Newton's second law defines force as the ratio of the change in the amount of motion to the short time of action of the force impulse. The short duration of the force is a special case of continuous time. In this study, the force impulse is understood in a generalized representation as the product of the force for a continuous time of action. By analogy with a force pulse in time, a force pulse in space is introduced. With the system chart analysis force-time, mass speed, force, space, power is the differential and integral laws of dynamics potentially Svyaznoy interaction, respectively, the power–time–weight–speed, power– space–work, power–time–energy. The analysis of complete potential differentials leads to representations of functional time and space that complement the interaction time and space. The time and space of the force action in the studied systems are considered by analogy with mass as measures of the body's resistance to changes in force, i. e. as mechanical parameters, rather than geometric ones. The integral laws of dynamics are constructed as a superposition of Riemann integrals for direct functions and stiltjes integrals for inverse functions. Riemann integrals describe modern dynamics, and stiltjes integrals describe its complement to the potential one.