Representer Theorems in Banach Spaces: Minimum Norm Interpolation, Regularized Learning and Semi-Discrete Inverse Problems

Learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation (MNI) problem, a regularized learning problem or, in general, a semi discrete inverse problem (SDIP), in either Hilbert spaces or Banach spaces. The goal of this paper is to systematically study solutions of these problems in Banach spaces. We aim at obtaining explicit representer theorems for their solutions, on which convenient solution methods can then be developed. For the MNI problem, the explicit representer theorems enable us to express the infimum in terms of the norm of the linear combination of the interpolation functionals. For the purpose of developing efficient computational algorithms, we establish the fixed-point equation formulation of solutions of these problems. We reveal that unlike in a Hilbert space, in general, solutions of these problems in a Banach space may not be able to be reduced to truly finite dimensional problems (with certain infinite dimensional components hidden). We demonstrate how this obstacle can be removed, reducing the original problem to a truly finite dimensional one, in the special case when the Banach space is ℓ1(N)

A Novel Structure of High Efficiency Rotary Compressor

In recent years, various frequency compressors are developed rapidly and successfully in household air conditioner area. However, it is difficult to make advance progress on compressor performance, noise and reliability. The innovation of structure and technique are indispensable impetus to make a breakthrough. This paper presents a novel structure of high efficiency rotary compressor, which focuses on the connection mode between roller and vane of a compressor. On the one hand, the leakage gap between roller wall and vane tip is eliminated, which upgrades the capacity of compressor. On the other hand, through changing movement type of compressor parts, the mechanical state is meliorated and frictional loss is decreased. Several analysis are studied to validate the rationality of the above amelioration, which include strength and deformation simulation, frictional loss and leakage loss calculation. By comparison with conventional compressor, the performance of the novel compressor is improved obviously. In the end, the results of reliability and durability experiments reveal that they satisfy the national standard

The Finite Element Analysis of the Deflection of the Crankshaft of Rotary Compressor

The deflection of the crankshaft which transfers the power of motor to the pump of the compressor directly affects the vibration, noises and wear problems in the rotary compressor, therefore, with the requirement of higher reliability, it is important to obtain it exactly in compressor design. Various forces that the crankshaft suffers were calculated by theoretical analysis in the operation process of the compressor. And based on the finite element method (FEM), the deflection of the crankshaft was obtained by simulation in the rotary compressor. And then the measurements were performed concerning the orbit of the top dead centre of the crankshaft with non-contacting displacement sensors in the compressor. In comparison with the tests, the validity of the calculation method was verified. It was found that the results of calculation were good agreement with the tests’. In addition, several factors which affect the deflection of the crankshaft were analyzed with the FEM, and the influences of flange height, shaft diameter, mechanical air gap in the motor, rotor weight on the deflection were found distinctly, which as a primary theoretical basis is provided for the compressor design

CFD Analysis and Experiment Study of the Rotary Two-Stage Inverter Compressor with Vapor Injection

The offset angle of the upper and lower part of the crankshaft will affect the resistance of inspiration of high stage cylinder in the rotary two-stage inverter compressor with vapor injection, and then affect the performance. this paper presents the performance of the rotary two-stage inverter compressor with vapor injection in the bias angle of the crankshaft is calculated and compared with the experimental. The simulation results are in agreement with the experimental results. Under the operation of close vapor injection and open vapor injection, the performance of compressor can be improved 1% and 3% separately by optimize the bial angle of crankshaft.

Study of Novel Rotary Cylinder Compressor

A positive displacement rotary compressor is introduced:RCC(Rotary Cylinder Compressor). For implementing suction and exhaust process, the compressor\u27s cylinder and shaft revolve around their own axes while the piston reciprocates relative to the cylinder and shaft. Compared with rotary piston compressor, the RCC has the advantages of high volumetric efficiency and small torque ripple

Interactive Causal Correlation Space Reshape for Multi-Label Classification

Most existing multi-label classification models focus on distance metrics and feature spare strategies to extract specific features of labels. Those models use the cosine similarity to construct the label correlation matrix to constraint solution space, and then mine the latent semantic information of the label space. However, the label correlation matrix is usually directly added to the model, which ignores the interactive causality of the correlation between the labels. Considering the label-specific features based on the distance method merely may have the problem of distance measurement failure in the high-dimensional space, while based on the sparse weight matrix method may cause the problem that parameter is dependent on manual selection. Eventually, this leads to poor classifier performance. In addition, it is considered that logical labels cannot describe the importance of different labels and cannot fully express semantic information. Based on these, we propose an Interactive Causal Correlation Space Reshape for Multi-Label Classification (CCSRMC) algorithm. Firstly, the algorithm constructs the label propagation matrix using characteristic that similar instances can be linearly represented by each other. Secondly, label co-occurrence matrix is constructed by combining the conditional probability test method, which is based on the label propagation reshaping the label space to rich label semantics. Then the label co-occurrence matrix combines with the label correlation matrix to construct the label interactive causal correlation matrix to perform multi-label classification learning on the obtained numerical label matrix. Finally, the algorithm in this paper is compared with multiple advanced algorithms on multiple benchmark multi-label datasets. The results show that considering the interactive causal label correlation can reduce the redundant information in the model and improve the performance of the multi-label classifier

Mining frequent sequences using itemset-based extension

In this paper, we systematically explore an itemset-based extension approach for generating candidate sequence which contributes to a better and more straightforward search space traversal performance than traditional item-based extension approach. Based on this candidate generation approach, we present FINDER, a novel algorithm for discovering the set of all frequent sequences. FINDER is composed oftwo separated steps. In the first step, all frequent itemsets are discovered and we can get great benefit from existing efficient itemset mining algorithms. In the second step, all frequent sequcnces with at least two frequent itemsets are detected by combining depth-first search and item set-based extension candidate generation together. A vertical bitmap data representation is adopted for rapidly support counting reason. Several pruning strategies are used to reduce the search space and minimize cost of computation. An extensive set ofexperiments demonstrate the effectiveness and the linear scalability of proposed algorithm