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In this research, the minimal and maximal operators defined by q- difference expression are given in the Hilbert space Lq² (0, ∞). The existence problem of a q−1-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined. [ABSTRACT FROM AUTHOR]

In this paper, all normal extensions of the minimal operator associated with the singular degenerate linear differential expressions for first order in the Hilbert space of vector-functions are investigated in terms of boundary values. As well, it analyses the spectrum parts of any normal extension. [ABSTRACT FROM AUTHOR]

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Copyright of Southern Clinics of Istanbul Eurasia is the property of KARE Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The association of rheumatoid arthritis (RA) and immune thrombocytopenic purpura (ITP) has been reported rarely. Methotrexate, which is used for RA treatment, causes thrombocytopenia. Therefore, in medical practice, physicians avoid using methotrexate for RA in patients who have both RA and ITP. Here, we report an RA case that also had ITP, which did not decrease in platelet count after methotrexate therapy. A 50-year-old woman was diagnosed with diabetes mellitus in 1990, RA in 1995, and ITP in 2000. She had received hydroxychloroquine for more than 5 years. She was treated with prednisolone 16 mg/daily between 2006 and 2007, but she discontinued this therapy because of weight gain. Laboratory findings were not remarkable, except for thrombocytopenia. We started methotrexate therapy 10 mg per week for treatment of RA, and hydroxychloroquine therapy was stopped due to nonresponse. The methotrexate dose was increased up to 15 mg/week. Her complete blood cell count was monitored frequently. We did not observe any decrease in platelet count, while active arthritis symptoms of the patient were relieved. This case shows that methotrexate may be used in patients diagnosed with RA that is associated with ITP under strict monitoring. [ABSTRACT FROM AUTHOR]