An approximate solution of one class of singular integro-differential equations

AbstractThe problem of definition of mechanical field in a homogeneous plate supported by finite inhomogeneous inclusion is considered. The contact between the plate and inclusion is realized by a thin glue layer. The problem is reduced to the boundary value problem for singular integro-differential equations. Asymptotic analysis is carried out. Using the method of orthogonal polynomials, the problem is reduced to the solution of an infinite system of linear algebraic equations. The obtained system is investigated for regularity

The investigation of singular integro-differential equations relating to adhesive contact problems of the theory of viscoelasticity.

Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/14498The exact and approximate solutions of singular integro-differential equations relating to the problems of interaction of an elastic thin finite or infinite non-homogeneous patch with a plate are considered, provided that the materials of plate and patch possess the creep property. Using the method of orthogonal polynomials the problem is reduced to the infinite system of Volterra integral equations, and using the method of integral transformations this problem is reduced to the different boundary value problems of the theory of analytic functions. An asymptotic analysis is also performed

Exact solutions of some singular integro-differential equations related to adhesive contact problems of elasticity theory.

Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/14498The problem of constructing an exact solution of singular integro-differential equations related to problems of adhesive interaction between elastic thin semi-infinite homogeneous patch and elastic plate is investigated. For the patch loaded with horizontal forces the usual model of the uniaxial stress state is valid. Using the methods of the theory of analytic functions and integral transformation, the singular integro-differential equation is reduced to the Riemann boundary value problem of the theory of analytic functions. The exact solution of this problem and asymptotic estimates of tangential contact stresses are obtained

The adhesive contact problem for a piecewise-homogeneous orthotropic plate with an elastic patch.

El copyright pertenece a los autores.A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedge-shaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. Using methods of the theory of analytic functions, the problem is reduced to the system of singular integro-differential equations (SIDE) with fixed singularity. Under tension-compression of patch using an integral transformation a Riemann problem is obtained, the solution of which is presented in explicit form. The tangential contact stresses along the contact line are determined and their asymptotic behavior in the neighborhood of singular points is established

Evaluation of Behavioral Factors for Periodontal Inflammatory Diseases in the Georgian Students Population and Correlations with Parents' Social Status

Objective: This study examined the relationship between behavioral factors, parents’ social status and inflammatory periodontal diseases among the Georgian students’ population. Methods: The study was based on the results of the examination of 400 medical students aged 18 to 35 (mean age 20.94+1.98) in Tbilisi universities. Students were selected random. The study was conducted according to a questionnaire developed by us, which includes the probable predictors of the periodontium - socio-biological characteristics, hygienic habits, harmful habits, type of diet, and parents’ social status. We used the Greene-Vermllion Hygiene Index to determine oral hygiene status. Statistical Analysis: Categorical variables are expressed by frequencies and percentag. Categorical variables were compared using Fisher's exact test. Correlation analysis between variables was performed by Spearman's correlation analysis. A p-value <0.05 was considered statistically significant. Statistical analyses were performed using SPSS for Windows, version 23. European Scientific Journal, ESJ ISSN: 1857-7881 (Print) e - ISSN 1857-7431 June 2021 Special Edition: Actual Problems of Medicine and Dentistry www.eujournal.org 22 Results : Among students who had inflammatory periodontal disease, had a high incidence of predominantly food carbohydrates, frequent consumption of sweet and spicy foods, fast foods and synthetic beverages, diet, smoking. Bad or very bad oral hygiene. It identifies the role of social factors in the manifestation of the disease. The hygiene index correlates with the periodontal index r=0.312, p=0.009. Conclusion: In Georgian population the inflammatory periodontal diseases have a incredibly high unsatisfactory hygenic status. The incidence of individuals is high, who undergo professional cleaning once or more rarely a year, and who use a circular movement, when brushing their teeth. Also who intake carbohydrates and fast and spicy foods, sweets, using of synthetic liquids and who smoke. A relation among inflammatory periodontal diseases, socio- economic status, and correlation of parents’ social status to oral care habits have been identified. Awareness of the need for dental services, the development of oral care habits, healthy diet, the prevention of manageable risk factors, hygiene, and professional cleaning of teeth is recommended for the prevention of periodontal inflammatory diseases

The effects of hibernation on the contractile and biochemical properties of skeletal muscles in the thirteen-lined ground squirrel, Ictidomys tridecemlineatus

Hibernation is a crucial strategy of winter survival used by many mammals. During hibernation, thirteen-lined ground squirrels, Ictidomys tridecemlineatus, cycle through a series of torpor bouts, each lasting more than a week, during which the animals are largely immobile. Previous hibernation studies have demonstrated that such natural models of skeletal muscle disuse cause limited or no change in either skeletal muscle size or contractile performance. However, work loop analysis of skeletal muscle, which provides a realistic assessment of in vivo power output, has not previously been undertaken in mammals that undergo prolonged torpor during hibernation. In the present study, our aim was to assess the effects of 3 months of hibernation on contractile performance (using the work loop technique) and several biochemical properties that may affect performance. There was no significant difference in soleus muscle power output-cycle frequency curves between winter (torpid) and summer (active) animals. Total antioxidant capacity of gastrocnemius muscle was 156% higher in torpid than in summer animals, suggesting one potential mechanism for maintenance of acute muscle performance. Soleus muscle fatigue resistance was significantly lower in torpid than in summer animals. Gastrocnemius muscle glycogen content was unchanged. However, state 3 and state 4 mitochondrial respiration rates were significantly suppressed, by 59% and 44%, respectively, in mixed hindlimb skeletal muscle from torpid animals compared with summer controls. These findings in hindlimb skeletal muscles suggest that, although maximal contractile power output is maintained in torpor, there is both suppression of ATP production capacity and reduced fatigue resistance

Erratum to: Voluntary resistance wheel exercise from mid-life prevents sarcopenia and increases markers of mitochondrial function and autophagy in muscles of old male and female C57BL/6J mice

Gadd45α (A), Runx1 (B), Chrnd (C), Chrng (D), Musk (E), and Myog (F) mRNA in the quadriceps muscles of 15-month SED, 23-month SED, and 23-month RWE mice, of both sexes. Gene expression in the quadriceps muscles was normalized to the geometric mean of Hprt and Ppia expression values. Data were analyzed by ANOVA, using age and sex, and sex and activity as variables. Data are mean ± SEM. Asterisk (*) denotes significance at *P < 0.05; **P < 0.01; ***P < 0.001. For each age group, N = 5–9 mice/group. Y-axes represent arbitrary units

Striking Denervation of Neuromuscular Junctions without Lumbar Motoneuron Loss in Geriatric Mouse Muscle

Reasons for the progressive age-related loss of skeletal muscle mass and function, namely sarcopenia, are complex. Few studies describe sarcopenia in mice, although this species is the mammalian model of choice for genetic intervention and development of pharmaceutical interventions for muscle degeneration. One factor, important to sarcopenia-associated neuromuscular change, is myofibre denervation. Here we describe the morphology of the neuromuscular compartment in young (3 month) compared to geriatric (29 month) old female C57Bl/6J mice. There was no significant difference in the size or number of motoneuron cell bodies at the lumbar level (L1–L5) of the spinal cord at 3 and 29 months. However, in geriatric mice, there was a striking increase (by ∼2.5 fold) in the percentage of fully denervated neuromuscular junctions (NMJs) and associated deterioration of Schwann cells in fast extensor digitorum longus (EDL), but not in slow soleus muscles. There were also distinct changes in myofibre composition of lower limb muscles (tibialis anterior (TA) and soleus) with a shift at 29 months to a faster phenotype in fast TA muscle and to a slower phenotype in slow soleus muscle. Overall, we demonstrate complex changes at the NMJ and muscle levels in geriatric mice that occur despite the maintenance of motoneuron cell bodies in the spinal cord. The challenge is to identify which components of the neuromuscular system are primarily responsible for the marked changes within the NMJ and muscle, in order to selectively target future interventions to reduce sarcopenia

Transcriptional regulation of the IGF signaling pathway by amino acids and insulin-like growth factors during myogenesis in Atlantic salmon

The insulin-like growth factor signalling pathway is an important regulator of skeletal muscle growth. We examined the mRNA expression of components of the insulin-like growth factor (IGF) signalling pathway as well as Fibroblast Growth Factor 2 (FGF2) during maturation of myotubes in primary cell cultures isolated from fast myotomal muscle of Atlantic salmon (Salmo salar). The transcriptional regulation of IGFs and IGFBP expression by amino acids and insulin-like growth factors was also investigated. Proliferation of cells was 15% d(-1) at days 2 and 3 of the culture, increasing to 66% d(-1) at day 6. Three clusters of elevated gene expression were observed during the maturation of the culture associated with mono-nucleic cells (IGFBP5.1 and 5.2, IGFBP-6, IGFBP-rP1, IGFBP-2.2 and IGF-II), the initial proliferation phase (IGF-I, IGFBP-4, FGF2 and IGF-IRb) and terminal differentiation and myotube production (IGF2R, IGF-IRa). In cells starved of amino acids and serum for 72 h, IGF-I mRNA decreased 10-fold which was reversed by amino acid replacement. Addition of IGF-I and amino acids to starved cells resulted in an 18-fold increase in IGF-I mRNA indicating synergistic effects and the activation of additional pathway(s) leading to IGF-I production via a positive feedback mechanism. IGF-II, IGFBP-5.1 and IGFBP-5.2 expression was unchanged in starved cells, but increased with amino acid replacement. Synergistic increases in expression of IGFBP5.2 and IGFBP-4, but not IGFBP5.1 were observed with addition of IGF-I, IGF-II or insulin and amino acids to the medium. IGF-I and IGF-II directly stimulated IGFBP-6 expression, but not when amino acids were present. These findings indicate that amino acids alone are sufficient to stimulate myogenesis in myoblasts and that IGF-I production is controlled by both endocrine and paracrine pathways. A model depicting the transcriptional regulation of the IGF pathway in Atlantic salmon muscle following feeding is proposed.Publisher PDFPeer reviewe