Multilinear interpolation between adjoint operators

Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L^q estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak L^q estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak L^q has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).     

On the ?ojasiewicz-Simon gradient inequality

We prove a general version of the ?ojasiewicz-Simon inequality, and we show how to apply the abstract result to study energy functionals E of the form

     

Drift transforms and Green function estimates for discontinuous processes

In this paper, we consider Girsanov transforms of pure jump type for discontinuous Markov processes. We show that, under some quite natural conditions, the Green functions of the Girsanov transformed process are comparable to those of the original process. As an application of the general results, the drift transform of symmetric stable processes is studied in detail. In particular, we show that the relativistic α-stable process in a bounded C^1,1-smooth open set D can be obtained from symmetric α-stable process in D through a combination of a pure jump Girsanov transform and a Feynman-Kac transform. From this, we deduce that the Green functions for these two processes in D are comparable.     

Degrevlex Gröbner bases of generic complete intersections

In this paper, we study the Hilbert–Samuel function of a generic standard graded K-algebra

K[X₁,…,X_n]/(g₁,…,g_m)

when refined by an (ℓ)-adic filtration, ℓ being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gröbner) bases for this order; in particular, we consider an “orderly filling up” conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases.     

THEORY AND COMPUTATION OF SECONDARY BIFURCATIONS NEAR A DOUBLE EIGENVALUE

This paper deals with secondary bifurcations near a double eigenvalue of a nonlinear equation with two parameters. Utilizing symmetries (or more generally, equivariances ) and introducing two new parameters, we give some extended systems so that the double singular points, secondary bifurcation points and initial secondary branches respectively become their regular solutions. The methods in this paper not only give more general conditions of secondary bifurcation but also avoid the adjacent singularities of existing extended systems for computing the simple bifurcation points on non-trivial solution branches A numerical example is presented, showing the effectiveness of our methods.     

A numerical exploration of secondary separation in starting flow around a flat plate by the discrete vortex model

In the present work, a further numerical simulation of the starting flow around a flat plate normal to the direction of motion in a uniform fluid has been made by means of the discrete vortex method. The secondary separation occurring at rear surface of the plate is explored, and predicted approximately using Thwait's method. The calculated results show that in the early stages of the flow secondary separation does occur. The evolution of flow field, the vortex growing process and the characteristics of secondary vortices have been described. The time dependent drag coefficients, the vorticity shed from the edges and rear surface, and the separation positions are calculated as well as the distributions of velocity and pressure on the plate. In the case of flow normal to the plate, the calculated secondary vortices are weak. Their existence will change the local velocity distributions and affect pressure distributions. However, the effect on drag coefficient is negligible.     

Further study on vortex shedding flow by a circular cylinder

In the present paper the mechanism involved in vortex shedding flows is investigated in detail. In the early stage of the unsteady separated flow the interaction between secondary vortices and primary vortices is quite strong. In the later stage of the flow, corresponding to the vortex shedding the recirculating flow region on each side of the aft body goes through such a cycle: growth-contraction-growth, the secondary separation occurs periodically rather than continuously. The reduction of circulation is taken into account in three cases with different decay factors to study its influence on the prediction of main flow characteristics. Results show that to simulate vortex shedding flow it is necessary to include the reduction of circulation to bring the calculated results into good agreement with experiments. An improved discrete vortex model is suggested in which both the secondary separation and the reduction are incorporated. The processes of vortex shedding, the forces prediction and other flow characteristics are given and some discussions are made. Porject is supported by National Natural Science Foundation of China.     

射频磁控溅射法制备薄膜电池电极的计算机模拟初步

计算机模拟仿真射频磁控溅射实验制备薄膜及离于电池电极,研究了在特定实验条件下薄膜的生长过程,并分析了影响薄膜生长的部分因素。     

Improved Deep Q-Network for User-Side Battery Energy Storage Charging and Discharging Strategy in Industrial Parks

Battery energy storage technology is an important part of the industrial parks to ensure the stable power supply, and its rough charging and discharging mode is difficult to meet the application requirements of energy saving, emission reduction, cost reduction, and efficiency increase. As a classic method of deep reinforcement learning, the deep Q-network is widely used to solve the problem of user-side battery energy storage charging and discharging. In some scenarios, its performance has reached the level of human expert. However, the updating of storage priority in experience memory often lags behind updating of Q-network parameters. In response to the need for lean management of battery charging and discharging, this paper proposes an improved deep Q-network to update the priority of sequence samples and the training performance of deep neural network, which reduces the cost of charging and discharging action and energy consumption in the park. The proposed method considers factors such as real-time electricity price, battery status, and time. The energy consumption state, charging and discharging behavior, reward function, and neural network structure are designed to meet the flexible scheduling of charging and discharging strategies, and can finally realize the optimization of battery energy storage benefits. The proposed method can solve the problem of priority update lag, and improve the utilization efficiency and learning performance of the experience pool samples. The paper selects electricity price data from the United States and some regions of China for simulation experiments. Experimental results show that compared with the traditional algorithm, the proposed approach can achieve better performance in both electricity price systems, thereby greatly reducing the cost of battery energy storage and providing a stronger guarantee for the safe and stable operation of battery energy storage systems in industrial parks.     

Impaired pulmonary blood flow distribution in congestive heart failure assessed using synchrotron radiation microangiography

Synchrotron radiation microangiography is a powerful tool for assessing adverse changes in pulmonary vessel density associated with primary pulmonary hypertension (PH). Congestive heart failure (CHF) leads to a `secondary' onset of PH, yet it is unknown whether secondary PH is also associated with reduced vessel density. This study utilized synchrotron radiation to assess both pulmonary vessel density and endothelial function in a Dahl rat model of CHF with secondary PH. High salt‐fed Dahl salt‐sensitive (Dahl‐S) and salt‐resistant (Dahl‐R) rats were anesthetized and microangiography was performed to assess the pulmonary vessel density and vascular responses to (i) sodium nitroprusside (5.0 µg kg^?1 min^?1), (ii) acetylcholine (3.0 µg kg^?1 min^?1) and (iii) ET‐1_A receptor blockade, BQ‐123 (1 mg kg^?1). Dahl‐S rats developed CHF and secondary PH as evident by endothelial dysfunction, impaired vasodilatory responses to acetylcholine, enhanced vasodilatory responses to BQ‐123 and extensive pulmonary vascular remodeling. Consequently, the pulmonary vessel density was adversely reduced. Interestingly, the etiology of secondary PH manifests with structural and functional changes that are comparable with that previously reported for primary PH. One important discrepancy, however, is that ET‐1 modulation of pulmonary vessels is most striking in vessels with a diameter range of 100–200 µm in secondary PH, in contrast to a range of 200–300 µm in primary PH. Such discrepancies should be considered in future studies investigating primary and secondary forms of PH.