Iterative methods for the split feasibility problem and the fixed point problem in Banach spaces

ABSTRACT

In this work, we suggest modifications of the self-adaptive method for solving the split feasibility problem and the fixed point problem of nonexpansive mappings in the framework of Banach spaces. Without the assumption on the norm of the operator, we prove that the sequences generated by our algorithms weakly and strongly converge to a solution of the problems. The numerical experiments are demonstrated to show the efficiency and the implementation of our algorithms.     

Evaluation of split/splitless operation and rapid heating of a multi-bed sorption trap used for gas chromatography analysis of large-volume air samples

The effects of split-flow operation and rapid trap heating on injection-plug widths from an electrically heated, microscale, multibed sorption trap were evaluated. The sorption trap has been designed to quantitatively collect volatile organic compounds from large-volume vapor samples and inject them into a gas chromatograph. Previous trap designs resulted in injection-plug widths of typically a second or more, and this significantly degraded chromatographic resolution, particularly for early-eluting sample components and for high-speed separations. Injection-plug widths are determined by the heating rate of the trap during sample desorption and the volumetric flow rate of carrier gas through the trap. The effects of the heating rate of the trap and carrier gas velocity through the trap on the injection-plug widths of pentane, octane, and undecane were studied. Carrier gas velocity through the trap was increased by splitting the flow coming from the trap between the column and a vent. This decreases transport time from the trap to the column, and thus decreases injection-plug widths. The heating rate for the trap was increased by increasing the applied voltage in the range from 4 to 30 V. Increasing the heating rate decreases the time required to desorb the analytes from the sorbent bed, thus decreasing injection-plug width. Injection-plug widths as small as 89, 210, and 520 ms were obtained in the split mode with very fast heating rates for n-pentane, noctane, and n-undecane, respectively. The effect of split ratio on resolving power, peak height, and peak width was also evaluated.     

On the interval completion of chordal graphs

For a given graph G=(V,E), the interval completion problem of G is to find an edge set F such that the supergraph H=(V,E∪F) of G is an interval graph and |F| is minimum. It has been shown that it is equivalent to the minimum sum cut problem, the profile minimization problem and a kind of graph searching problems. Furthermore, it has applications in computational biology, archaeology, and clone fingerprinting. In this paper, we show that it is NP-complete on split graphs and propose an efficient algorithm on primitive starlike graphs.     

Splitness of the Veronesean and the Taniguchi dual hyperovals

The Veronesean and the Taniguchi dual hyperovals are shown to be of split type, by constructing some symmetric bilinear maps in criterion for splitness. For the Veronesean dual hyperovals, such maps correspond to commutative presemifields in characteristic 2. For the Taniguchi dual hyperovals, their automorphism groups are determined and their actions on such maps are investigated.     

High strain rate behavior of graphene-epoxy nanocomposites

This work consists of the synthesis of high purity graphene nanoflakes (GNF), the manufacturing of GNF-epoxy nanocomposites and the mechanical characterization of the nanocomposite at high and quasi static strain rates, (2750/s - 1.E−5/s). GNF were synthesized by using the electric arc discharge technique. Thermogravimetry/Differential Thermal Analysis (TG/DTA) of synthesized graphene reveals high purity and high crystallinity. Raman spectra and the broad Brunauer-Emmet-Teller (BET) specific surface area indicate that the synthesized graphene has several layers. Following the solution mixing manufacturing process of GNF-epoxy nanocomposites, the influences of strain rate on the mechanical behaviors are investigated under quasi static and dynamic loadings. High strain rate uniaxial compression tests (1270–2750/s) using Split Hopkinson Pressure Bar (SHPB) and quasi static compression tests (1.E−3 and 1.E−5/s) of GNF-epoxy with two graphene contents (0.1 and 0.5 wt %) are performed at room temperature. The maximum elasticity modulus achieved by the GNF-epoxy with 0.5 wt% at the strain rate of 2350/s corresponds to a 68% increase compared to the neat epoxy. The yield strength of the material is doubled under dynamic loading conditions compared to the quasi static loading.     

Dynamically maintaining split graphs

We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after each modification the graph is repaired to become a split graph in a minimal way. In particular, if the graph is not split after the modification, the algorithm computes a minimal, or if desired even a minimum, split completion or deletion of the modified graph. The motivation for such operations is similar to the motivation for fully dynamic algorithms for particular graph classes. In our case we allow all modifications to the graph and repair, rather than allowing only the modifications that keep the graph split. Fully dynamic algorithms of the latter kind are known for split graphs [L. Ibarra, Fully dynamic algorithms for chordal graphs and split graphs, Technical Report DCS-262-IR, University of Victoria, Canada, 2000].Our results can be used to design linear time algorithms for some recognition and completion problems, where the input is supplied in an on-line fashion.     

Determination of Early Flow Stress for Ductile Specimens at High Strain Rates by Using a SHPB

In a dynamic experiment to obtain the high-rate stress–strain response of a ductile specimen, it takes a finite amount of time for the strain rate in the specimen to increase from zero to a desired level. The strain in the specimen accumulates during this strain-rate ramping time. If the desired strain rate is high, the specimen may yield before the desired rate is attained. In this case, the strain rates at yielding and early plastic flow are lower than the desired value, leading to inaccurate determination of the yield strength. Through experimentation and analysis, we examined the validity and accuracy of the flow stresses for ductile materials in a split Hopkinson pressure (SHPB) bar experiment. The upper strain-rate limit for determining the dynamic yield strength of ductile materials with a SHPB is identified.     

应用高速摄影机对泡沫铝在SHPB实验过程的变形跟踪与分析

SHPB技术虽然能方便地得出材料的动态应力应变关系,但却不能直观地揭示材料在经受冲击荷载时的变形特征,而这恰恰是泡沫金属力学性能研究的重要方面.为此,本文设计了一套SHPB-高速摄影机系统,借此系统对SHPB实验中的泡沫铝试件进行了实时的变形跟踪拍摄,然后应用图像处理软件对泡沫铝试件的动态变形进行分析并提取了位移信息,...     

Split Bregman method for the modified lot model in image denoising

In this paper a split Bregman iteration is proposed for the modified LOT model in image denoising. We first use the split Bregman method to solve the ROF model which can be seen as an approximate form of the first step of the original LOT model. Then we use a modified split Bregman method to fit the second step of the LOT model and give the convergence of the proposed split Bregman method. Several numerical examples are arranged to show the effectiveness of the proposed method.     

Branch and price for the vehicle routing problem with discrete split deliveries and time windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles’ capacity and customer time windows. Each customer can be visited by more than one vehicle since each customer’s demand, discretized in items, can be split in orders, i.e., feasible combinations of items. In this work, we model the DSDVRPTW assuming that all feasible orders are known in advance. Remarkably, service time at customer’s location depends on the delivered combination of items, which is a modeling feature rarely found in literature. We present a flow-based mixed integer program for the DSDVRPTW, we reformulate it via Dantzig-Wolfe and we apply column generation. The proposed branch-and-price algorithm largely outperforms a commercial solver, as shown by computational experiments on Solomon-based instances. A comparison in terms of complexity between constant service time vs delivery-dependent service time is presented and potential savings are discussed.