Rapidly Convergent Algorithms for Nonsmooth Optimization.

Let F be a mapping from real n -dimensional Euclidean space into itself. Most practical algorithms for finding a zero of F are of the form \[ x k + 1 = x k − B k − 1 F x k , {x_{k + 1}} = {x_k} - B_k^{ - 1}F{x_k}, \] where { B k } \{ {B_k}\} is a sequence of nonsingular matrices. The main result of this paper is a characterization theorem for the superlinear convergence to a zero of F of sequences of the above form. This result is then used to give a unified treatment of the results on the superlinear convergence of the Davidon-Fletcher-Powell method obtained by Powell for the case in which exact line searches are used, and by Broyden, Dennis, and Moré for the case without line searches. As a by-product, several results on the asymptotic behavior of the sequence { B k } \{ {B_k}\} are obtained. An interesting aspect of these results is that superlinear convergence is obtained without any consistency conditions; i.e., without requiring that the sequence { B k } \{ {B_k}\} converge to the Jacobian matrix of F at the zero. In fact, a modification of an example due to Powell shows that most of the known quasi-Newton methods are not, in general, consistent. Finally, it is pointed out that the above-mentioned characterization theorem applies to other single and double rank quasi-Newton methods, and that the results of this paper can be used to obtain their superlinear convergence.

Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of ∂ 1 , …, ∂ n with ∂ i=d/dx i for 1≤i ≤ n. As in the single variable case, Lax equations can be constructed using such pseudodifferential operators, whose solutions can be provided by Baker functions. We extend the usual notion of tau functions to the case of pseudodifferential operators of several variables so that each Baker function can be expressed in terms of the corresponding tau function.

Preparation and properties of ZnMoO4 anode materials with polymer network gel method

Compared with conventional reservoirs, shale reservoirs are more difficult to develop due to their characteristics of self-generation and self-storage and tightness. Based on the experience accumulated in production practice, the technical method of improving shale oil development through shut-in is put forward. The literature research on shale reservoirs shows that there is a lack of microscopic study on imbibition, the essence of oil–water exchange is not clear enough, and there is a lack of the systematic summary and induction of theoretical knowledge. This article starts from the background of shut-in stimulation of Gulong shale oil, conducts literature research on the related knowledge of shut-in of shale oil from three aspects: characterization of fracture network, shut-in mechanism, and oil and water distribution state, and summarizes the law of shut-in of shale oil in a microscopic aspect. On this basis, a dual-porosity numerical simulation model is established according to the geological and fluid characteristics of the Gulong shale oil reservoir. Through the simulation of a numerical simulation model, the water saturation and pressure maps of the matrix and lamellation-fracture system in the process of shut-in were obtained. It was found that the matrix system basically did not participate in the oil–water exchange in the process of shut-in, so in the subsequent characteristic curve analysis, only the lamellation-fracture system was mapped and analyzed. The water saturation and pressure curves of different distances of the main fracture at different times were made, and it was found that the water saturation and pressure in the main fracture and near fracture areas were higher, and the change was more obvious than that in the far. Thus, the pressure drop curves of the near fracture were used to analyze the flow stage of the fluid. The single variable method is used to analyze the influencing factors from two aspects: the fracture density and permeability of the stimulated zone. The results will give a better understanding of the oil and water distribution during shut-in and guide the duration of shut-in in shale oil reservoirs.

Single crystal germanium, which is a typical infrared optical crystal used for aerospace and astronomy applications due to their excellent mechanical, optical, and chemical property is difficult to obtain super smooth surface in ultra-precision turning and easy to cause tool wear owing to its inherent brittleness and hardness. In the processing process of single crystal germanium optical elements, good surface roughness is beneficial to improve the diffraction efficiency of single crystal germanium, while small cutting force can effectively lower the diamond tool wear caused by high hardness of germanium. In this paper, the single variable method is used to study the influence of the main factors in the single point diamond turning process on the surface roughness and cutting force of single crystal germanium, including spindle speed back cutting depth and feed. The experimental results are used to guide the machining process of the single crystal germanium diffraction surface, and the appropriate process parameters are selected to perform ultra-precision turning on the single crystal germanium with a very small cutting force to obtain a sub-nanometer ultra-smooth surface to improve the diffraction efficiency and reducing tool wear.

A new method for analyzing the problem of the thermal-hydrodynamic instability of OTSG (Once-Through Steam Generator) of movable nuclear power devices is presented in this paper. The method is based on multivariable frequency domain theory and is more efficient for analyzing the instability of OTSG with coupling interactions and complicated boundary conditions than the usually used single variable method. A mathematical model for the system is derived from the fundamental equations by using perturbation, Laplace-transform and the nodalization techniques. The stable boundary and parametric effects on the stability of the system are evaluated with a computer code. Numerical examples are given and the predictions of the model are in good agreement with the experimental results.

Three-dimensional transient heat conduction analysis by boundary knot method

A trust-region algorithm combining line search filter method with Lagrange merit function for nonlinear constrained optimization

In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function f and a convex (possibly non-smooth and extended-valued) function φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document}. Instead of controlling a step size by a line search procedure, we update the regularization parameter in a suitable way, based on the success of the previous iteration. The global convergence of the sequence of iterations and its superlinear convergence rate under a local Hölderian error bound assumption are shown. Notably, these convergence results are obtained without requiring a global Lipschitz property for ∇f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ abla f $$\\end{document}, which, to the best of the authors’ knowledge, is a novel contribution for proximal Newton methods. To highlight the efficiency of our approach, we provide numerical comparisons with an IRPNM using a line search globalization and a modern FISTA-type method.

A multivariate version of Rosenblum’s Fejér-Riesz theorem on outer factorization of trigonometric polynomials with operator coefficients is considered. Due to a simplification of the proof of the single variable case, new necessary and sufficient conditions for the multivariable outer factorization problem are formulated and proved.

Single case studies of neurological patients has a long and storied history (Zillmer & Spiers, 2001). First used as a teaching tool (Haas, 2001), the method of thoroughly exploring the cognitive and motor functions of a unique individual patient has led to extraordinary advances in our understanding of structure-function relationships in the human brain. Single cases have led to important advances in many fields, including pioneering work on language (Broca, 1861; see also Ryalls & Lecours, 1996) and visual perception (Poppelreuter, 1917/1990; see also Humphreys & Riddoch, 1996) to more recent work on memory systems (Scoville & Milner, 1957; Milner & Penfield, 1955-1956; see Milner, 2005 for a recent review) where one patient (HM) has arguably done more to advance that field than any other single case study in history. Prior to the advent of x-rays and eventually computerised axial tomography (CT scans), the method of studying single cases was the only way to determine the location of a patient's pathology. The advent of CT scans in the 1970's obviated, to some degree, the need for detailed neuropsychological testing, at least as it was needed to determine the location of pathology (Banich, 2004; Lezak, et al., 2004; Kolb & Wishaw, 2009). A few decades later and the advent of functional MRI (fMRI) provides an even more powerful tool for examining the nature of structure-function relationships in humans and in non-human primates (Ogawa et al., 1992; Ford et al., 2009). Indeed, the rapid rise of fMRI studies (Fox, 1997; Raichle, 1994) has outstripped the pace of single case studies in the past few decades (Figure 1). By 2005 the proportion of neuroimaging abstracts accepted for presentation at the Cognitive Neuroscience Society meeting was around 35% compared to only 15% for patient studies (which included group and single case methods; Chatterjee, 20051). There are a range of reasons behind the rise of functional neuroimaging studies including the ease and relatively low cost with which these studies can be carried out (Chatterjee, 2005). Although per hour imaging costs seem high to most, the cost of patient research is undoubtedly far higher both in time committed and real costs related to screening and following patients over longer periods of time (Chatterjee, 2005). In addition, each method

Thermomechanical modeling of dissimilar-material interfaces in composite structures

Combining with static information of injection wells and using effective thickness, number of layers greater than 1 meter and ratio of 3 to 4 connected thickness greater than 1 meter as evaluation index, this paper use cluster analysis method to category injection wells of west and east blocks in north first and second row of Sazhong development area in Daqing oilfield. Then, with evaluation of accumulated increased oil per unit thickness, using single dependent variable two-factor variance analysis method to optimize injection rate and injection concentration of injection well groups which have been classified into different types.

To study in simulation and in theory the accuracy and precision of dynamic T1 measurements obtained using the previously published single-reference variable flip angle (SR-VFA) technique, with a focus on the effects of dynamic changes in T2 * on the calculation. Monte Carlo simulations were performed over 1000 noisy iterations for the VFA method, the SR-VFA method, and a proposed method, SR-VFA with a T2 * correction (SR-VFA-T2 *). Dynamic T1 estimates were calculated analytically for each method, with signals modeled by the steady-state spoiled gradient echo equation. The mean and standard deviation of these estimates were calculated and compared to truth, while varying repetition time (TR), baseline and dynamic T1 , echo time (TE), baseline and dynamic T2 *, flip angles, and the number of averages on baseline scans. Additionally, the variance of T1 in the SR-VFA and SR-VFA-T2 * methods was derived analytically based on the theory of propagation of errors. This equation was used to produce an inverse-variance weighted linear combination to improve T1 mapping precision in the SR-VFA-T2 * method. Flip angle sensitivity of dynamic T1 precision in the SR-VFA and SR-VFA-T2 * methods was also performed. Substantial bias can be produced by the SR-VFA method when the ratio of the T2 * decay of the dynamic signal versus that of the baseline signals deviates from 1, with a 0.01 deviation leading to approximately a 1% bias in cases of high SNR and TR ≫ T1 . This bias can be corrected by estimating the baseline and dynamic T2 * values in this ratio via multiecho measurements. The bias and precision of the SR-VFA-T2 * method, when normalized to scan time, is found to rival and sometimes improve upon the two flip angle VFA method when an inverse variance weighted linear combination is applied across its multiecho T1 maps. The analytic variance equation presented is found to be accurate within 1% relative to the Monte Carlo simulations over a broad parameter space. Flip angle ranges that maximize SR-VFA and SR-VFA-T2 *T1 precision over a broad parameter space are given, and each is defined relative to TR and T1 . Multiecho SR-VFA-T2 * T1 mapping is found in simulation and theory to be a promising alternative to the VFA method that maintains speed of the SR-VFA method with accuracy and precision similar to the VFA method.

The expansion of science has resulted in an increased information flow and in an exponentially growing number of connections between knowledge in different research fields. In this study, we used methods of scientometric analysis to obtain a conceptual network that forms the structure of active scientific research fields in anesthesia. We extracted from the Web of Science (Institute for Scientific Information) all original articles (n = 3275) including their references (n = 79,972) that appeared in 2003 in all 23 journals listed in the Institute for Scientific Information Journal Citation Reports under the subject heading "Anesthesiology." After identification of highly cited references (> or = 5), pairs of co-cited references were created and grouped into uniformly structured clusters of documents using a single linkage and variable level clustering method. In addition, for each such cluster of documents, we identified corresponding front papers published in 2003, each of which co-cited at least two documents of the cluster core. Active anesthetic research fields were then named by examining the titles of the documents in both the established clusters and in their corresponding front papers. These research fields were sorted according to the proportion of recent documents in their cluster core (immediacy index) and were further analyzed. Forty-six current anesthetic research fields were identified. The research field named "ProSeal laryngeal mask airway" showed the highest immediacy index (100%) whereas the research fields "Experimental models of neuropathic pain" and "Volatile anesthetic-induced cardioprotection" exhibited the highest level of co-citation strength (level 9). The research field with the largest cluster core, containing 12 homogeneous papers, was "Postoperative nausea and vomiting." The journal Anesthesia & Analgesia published most front papers while Anesthesiology published most of the fundamental documents used as references in the front papers. Using co-citation analysis, we identified distinct homogenous clusters of highly cited documents representing 46 active current anesthetic research fields and determined multiple nets of knowledge among them.