A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented in [3].Partially supported by grant No. 22/2006 of the Sofia University with the National Science Fund of the Bulgarian Ministry of Education and Science

Equivalence Between K-functionals Based on Continuous Linear Transforms

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University

A characterization of weighted approximations by the Post–Widder and the Gamma operators, II

AbstractWe present a characterization of the approximation errors of the Post–Widder and the Gamma operators in Lp(0,∞),1≤p≤∞, with a weight xγ0(1+x)γ∞−γ0 with arbitrary real γ0,γ∞. Characteristics of two types are used — weighted K-functionals of the approximated function itself and the classical fixed-step moduli of smoothness taken on simple modifications of it

Impact of autonomic dysfunction on quality of life in Parkinson’s disease

The present study aims at investigating the impact of the most frequent autonomic symptoms in Parkinson’s disease (PD) on patients’ quality of life (QoL). Two hundred patients with Parkinson’s disease and autonomic symptoms were included, aged 45 to 76 years, distributed evenly by sex and Hoehn-Yahr stage of severity from I to IV. The most commonly reported symptoms, negatively influencing quality of life, were constipation (53%), urinary incontinence (41,5%), nicturia and hyperhydrosis (23% each). Ninety-eight patients (49%) graded their autonomic symptoms as mildly affecting QoL, 70 (35%) as moderate, and 32 (16%) as severe. Our results support the literature data about the frequency of autonomic disorders in PD and the distribution of symptoms affecting QoL. We found a clear tendency of increase of the frequency and intensity of dysautonomias with disease severity. This trend supports the predominant opinion that autonomic distur­bances in PD are mainly mild to moderate and become clinically significant usually in late stages. On the other hand, though mild to moderate in severity, they can appear even in the early stages of the disease. Widely uti­lized specific and generic questionnaires generally do not consider this subject, therefore the introduction of questions regarding the impact of autonomic symptoms in PD on quality of life is highly appropriate

Five-year follow-up of implants placed simultaneously with inferior alveolar nerve lateralisation or transposition

Introduction: The aim of this investigation was to evaluate the 5-year outcomes regarding presence of intraoperative and postoperative complications and the survival rate of implants placed simultaneously with lower alveolar nerve lateralization or transposition.Material and Methods: implants placement was performed on 34 patients with advanced atrophy of the posterior mandible simultaneously with lower alveolar nerve lateralization or transposition. Transposition was done only in two cases; in the rest of the cases lateralization of lower alveolar nerve was performed.Results: The survival rate at the end of the fifth year after implant placement was 100%. The mean height of residual bone at the region of implant placement was 2.76 mm. The mean marginal bone resorption for at the fifth year was 0.309 mm. In 20.6% of cases a positive BOP (bleeding on probing) was registered. 14.7% of the patients were free of symptoms of NSD (neuro-sensory dysfunction). In the rest of the patients the mean duration of NSD was 2.06 weeks. In 76.4% of patients the symptoms of NSD of nervus alveolaris inf. resolved after the second week. The maximum period of reported NSD was 6 weeks. No permanent NSD occured.Conclusion: Properly performed lateralization or transposition of the lower alveolar nerve is associated with minimal risk of permanent neuro-sensory dysfunction and providing an opportunity for placement of intraosseal implants in the posterior mandible with high survival rate

Diabetes mellitus in Parkinson`s disease patients

PURPOSE: Parkinson's disease (PD) is the second most common neurodegenerative disease affecting approximately 5 million people worldwide. Some studies have found out an association between PD and type 2 diabetes mellitus (DMT2). Their results suggest a common pathophysiologic pathway. Other authors fail to establish any link between these two diseases. The aim of the present study is to search for a potential association between DMT2 and PD.MATERIAL AND METHODS: We  investigated the medical records of 85 patients, 45 males and 40 females, aged 68.02±9.02 (range, 40-87) years and with disease duration of 4.98±..96 (range, 1-18) years. They were diagnosed as PD according to the United Kingdom Parkinson's Disease Society Brain Bank Diagnostic Criteria and hospitalized for a two-year period.RESULTS: We established a prevalence of DMT2 in PD patients of 18.8%. We discussed the potential relationships between these two disorders of great medical, social and economic impact. Insulin levels contribute to normal brain function.CONCLUSION: The history of DMT2 or the use of antidiabetic drugs might be a risk factor for PD.Scripta Scientifica Medica 2013; 45(1): 79-81.</p

Some Aspects Of The Feeling Of Happiness In Patients With Multiple Sclerosis

Happiness is an emotional state that reflects the positive feelings and satisfaction of life. We examined the subjective feeling of happiness with a questionnaire (MSQOL-54) including a self-assessment of happiness in 80 MS patients with and without accompanying diseases at an average age of 42.95 ± 10.39 years between 2002 and 2015. The results were processed statistically by correlation analysis. There were statistically significant positive correlations between both the self-assessments of the health status and the sense of happiness of MS patients, as well as between the impact on public activities and the sense of happiness of these patients. There were also statistically significant negative correlations between depression and the sense of hap-piness in MS patients as well as between health-related quality of life assessments and the feeling of happi-ness of these patients

Sexual Disturbances in Patients with Multiple sclerosis

Multiple sclerosis (MS) is a demyelinating disease of the central nervous system that is accompanied by different concomitant diseases. We have investigated the frequency of sexual disorders as an element of individual quality of life with a questionnaire (MSQOL-54) in 80 MS patients at an average age of 42.95 ± 10.39 for the period between 2002 and 2015. Forty of them had between one and seven accompanying diseases. There were problems in both group of patients concerning specific indicators of sexual function expressed to varying degrees. Sexual disturbances further aggravate the vitality not only of MS patients, but also of those with MS and concomitant diseases and require timely diagnosis and treatment

Serum cholesterol and triglycerides in Parkinson`s disease and essential tremor

The role of lipid metabolism in the pathogenesis of Parkinson`s disease is still controversial. Most authors suggest that higher The role of lipid metabolism in the pathogenesis of Parkinson`s disease is still controversial. Most authors suggest that higher serum cholesterol may be associated with a lower risk of Parkinson`s disease. Debates exist as to whether essential tremor shares similar neuropathological mechanisms as Parkinson`s disease. We investigated serum total cholesterol and triglyceride levels in a clinical setting of Parkinson`s disease versus essential tremor patients. Two hundred and sixteen Parkinson`s disease patients (126 males), aged 68.04 years, with 4.58 years disease duration and 342 essential tremor patients (118 males), aged 69.39 years, with 5.3 years disease duration were included, hospitalized during a period of 7 years in First Clinic of Neurology, University St Marina Hospital, Varna, Bulgaria. We found insignificantly higher levels of serum total cholesterol and triglyceride in essential tremor patients. Results differ statistically only on gender level with increased cholesterol in males and triglycerides in females. Our findings may indicate divergent pathophysiological mechanisms underlying Parkinson`s disease and essential tremor. Further research may elucidate the role of lipid metabolism changes in both diseases.Biomed Rev 2015; 26: 43-46.Key words: serum total cholesterol, triglycerides, Parkinson`s disease, essential tremo