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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.

Objective: To determine the immediate and long-term therapeutic efficacies of Gufoni and head-shaking maneuvers in apogeotropic type of benign paroxysmal positional vertigo involving the horizontal semicircular canal (HC-BPPV), a randomized, prospective, sham-controlled study was conducted. Methods: In 10 nationwide dizziness clinics in Korea, 157 consecutive patients (95 women, age range: 18–89 years, mean age ± SD = 59.9 ± 13.6) with apogeotropic HC-BPPV were randomized to Gufoni (n = 52), head-shaking (n = 54), or sham maneuver (n = 51). For Gufoni maneuver, patients underwent ipsilesional side-lying and upward head-turn for migration of the debris toward the vestibule. Immediate responses were determined within 1 hour after a maximum of 2 trials of each maneuver and in the following day. The patients also had weekly follow-ups for 1 month after the initial maneuver. Results: After a maximum of 2 maneuvers on the initial visit day, Gufoni (38/52, 73.1%) and head-shaking (33/53, 62.3%) maneuvers showed better responses than the sham maneuver (17/49, 34.7%). The cumulative therapeutic effects were also better with Gufoni ( p p = 0.026) maneuvers compared with the sham maneuver. However, therapeutic efficacies did not differ between the Gufoni and head-shaking groups in terms of both immediate ( p = 0.129) and long-term ( p = 0.239) outcomes. Conclusion: Using a prospective randomized trial, we demonstrated that the Gufoni and head-shaking maneuvers are effective in treating apogeotropic HC-BPPV. Classification of evidence: This study provides Class II evidence that Gufoni and head-shaking maneuvers are effective in treating apogeotropic horizontal BPPV up to 1 month after initial treatment. Clinical trial registration: NCT00810641.

Several methods of physiotherapy have been advanced for apogeotropic type benign positional vertigo involving the horizontal semicircular canal (HC-BPV). The aim of this study was to determine the therapeutic efficacies of the proposed maneuvers in apogeotropic HC-BPV. Using a prospective randomized trial involving seven nationwide dizziness clinics in Korea, we compared the immediate efficacies of head-shaking and modified Semont maneuvers in 103 consecutive patients with apogeotropic HC-BPV. We also determined an additional therapeutic benefit of mastoid oscillation while the patients without response to both maneuvers were performing the Brandt–Daroff exercise. Successful treatment was defined as resolution of positional vertigo and nystagmus, or as transition into geotropic HC-BPV. Results showed that head shaking was more effective than the modified Semont maneuver (37.3 vs. 17.3%, P = 0.02). However, therapeutic efficacy did not differ between the maneuvers after the initial non-responders switched over to the other maneuver (23.3 vs. 25.0%, P = 0.861). Mastoid oscillation provided no additional benefit while the patients without response to both maneuvers were performing the Brandt–Daroff exercise. Most positional vertigos resolved within a week (89.4%) irrespective of the treatment modalities applied and all showed resolution within 28 days. The head-shaking maneuver described here proved more effective than the modified Semont maneuver in treating apogeotropic HC-BPV. Mastoid vibration conferred no additional benefit during the Brandt–Daroff exercise.

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

Objective: To compare clinical and radiologic characteristics of atherosclerotic middle cerebral artery (MCA) vs internal carotid artery (ICA) disease.Methods: The authors defined atherosclerotic MCA and ICA disease as >50% symptomatic stenosis or occlusion without significant ICA and MCA stenosis on MR angiography. Patients with potential cardiac sources of embolism were excluded. The authors analyzed clinical, laboratory, and neuroradiologic data of the two groups.Results: Among the 920 consecutive patients with acute ischemic strokes, 112 met the criteria for atherosclerotic MCA and 71 met the criteria for ICA disease. Clinically, the MCA group more frequently presented with lacunar syndrome (p = 0.001), whereas the ICA group more often presented with total anterior circulation infarct and had higher initial NIH Stroke Scale scores than the MCA group (all p < 0.001). Whereas deep perforator and internal border-zone infarcts were associated with MCA disease (p < 0.001 and 0.012), territorial infarcts and superficial perforator infarcts were associated with ICA disease (p < 0.001 and p = 0.009). The topographic patterns with respect to the degree of stenosis were also significantly different between the two groups.Conclusions: The clinical and radiologic stroke patterns were distinctively different between atherosclerotic MCA and ICA disease, suggesting different underlying pathogeneses.

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.