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The fuzzy linear programming(FLP) is the useful approach to many real world problems under uncertainty. This paper deals with a FLP whose objective value is fuzzy. And the right hand sides of convergent equality constraints are fuzzy numbers. We assume that the membership function of the objective value is piecewise linear and those of the right hand side are trapezoidal. Each of these trapezoidal functions can be algebraically replaced with three linear functions. Then the FLP problem is transformed into the Zimmermann`s symmetric model. The fuzzy solution based on the max-min rule can be obtained by solving the crisp linear programming problem derived from the symmetric model. A numerical example has illustrated our approach. The application of our approach to the inconsistent linear system can enable generate us to get define the useful and flexible inexact solutions within acceptable tolerance. Further research is required to generalize the membership function.

This paper presents a branch-and-bound algorithm for solving the concave minimization problems with upper bounded variables. The algorithm uses simplex to construct the branching and the bounding procedure. The linear convex envelope (the objective function of the subproblem) is uniquely determined on the candidate simplex which contains the subset of the local minimal points. The optimal solution of the subproblem is a local optimum of the original concave problem and used in reducing the list of active subproblems. The branching process splits the candidate simplex into two subsimplices by fixing the selected branching variable at value 0 or upper bound. Then the subsimplices are one less dimensional than the candidate. It means that the size of the subproblems gradually decreases. Further research needs to be focused on the efficient determination method of the simplex. The algorithm of this paper can be applied to solving the concave minimization problems under knapsack type constraints.

Background and Purpose: The pathogenesis of deep white matter medullary (WMM) artery infarcts remains controversial. To address this question, we analysed the stroke patterns of WMM infarcts using diffusion weighted magnetic resonance imaging (DWI) to detect embolic signals and investigate stroke subtypes according to the Trial of Org 10172 in Acute Stroke Treatment (TOAST) classifications. Methods: We identified WMM infarcts on DWI using templates to determine the subcortical vascular territories. We classified WMM infarcts into those with small artery disease (SAD), large artery disease (LAD), cardioembolism (CE), two or more aetiologies, or undetermined aetiology. Clinical course, risk factors, and cortical spotty lesions were compared. Results: Of the 1420 consecutive patients, 103 (7.3%) met the criteria for WMM infarcts. The stroke subtypes were as follows: 65 (63.1%) patients with LAD, 18 (17.5%) with SAD, 12 (11.7%) with CE, four (3.9%) with two or more aetiologies, three (2.1%) with undetermined aetiology, and one (1.0%) with other determined aetiology. LAD (87.7%) or CE (83.3%) was significantly accompanied by cortical embolic signals as compared to SAD (0%, p

Background and Purpose— Because of difficulty in distinguishing between superficial perforator (SP) and internal border-zone (IB) infarcts, some studies lumped SP and IB infarcts together as so-called subcortical white matter infarcts, which might complicate the classification of infarct type and its pathogenesis. Using diffusion-weighted MRI (DWI), we made comparative analyses of clinical and neuroradiological characteristics between IB and SP infarcts to clarify the difference in underlying pathogenesis. Methods— We selected SP and IB infarcts on DWI using templates for the identification of subcortical vascular territories. Sex, age, neurological symptoms, clinical course, risk factors, concomitant cortical spotty lesions, and degree and location of arterial occlusive disease were compared between the 2 groups. Results— Among the 720 consecutive patients, 54 and 29 patients met the criteria for SP and IB infarcts, respectively. The SP group had lower initial National Institutes of Health Stroke Scale scores (2.4±2.1 versus 4.4±3.1; P =0.001), favorable clinical outcomes ( P =0.001), and more frequent potential cardioembolic sources (14.8% versus 0%; P =0.046) than the IB group. Cortical spotty lesions were more frequently accompanied by SP than IB infarcts (72.2% versus 24.1%; P P P =0.001), and had a higher degree of stenosis or occlusion (86.2% versus 46.3%; P =0.001) compared with SP infarcts. Conclusions— Our present study suggests that embolic pathogenesis makes a greater contribution to SP infarcts than IB infarcts. This finding may explain the difference in clinical and neuroradiological characteristics between the 2 groups.

Idiopathic spinal cord herniation is a rare spinal cord disorder caused by spinal cord prolapse through a adural defect. It is a curable disease, so early detection is of particular importance. We report a 38-year-old woman with Brown-Sequard syndrome which was caused by the thoracic spinal cord herniation. Her weakness was almost completely resolved after surgical management, which emphasizes the importance of early diagnosis and surgical management in this rare disease entity.

Etched-edge profile equations of SiO2 in a double layer of fast- and slow-etching SiO2 layer have been derived using Fermat's principle of least time. Etched profiles obtained from the SEM (scanning electron microscope) micrographs for experimental samples show reasonable agreement with calculated profiles.