Alexei Zhurov

Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the Crocco transformation, with a first-order partial derivative taken as a new independent variable and a second-order partial derivative taken as the new dependent variable. Associated Backlund transformations are constructed for evolution equations of general form (special cases of which are Burgers, Korteweg-de

Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the von Mises transformation, with the unknown function taken as the new independent variable and an appropriate partial derivative taken as the new dependent variable. RF-pairs and associated B\"acklund transformations are constructed for evolution equations of general form (special cases of which are

To explore the relationship between the prevalence of sleep disordered breathing (SDB) and face shape morphology in a large cohort of 15-year-old children. Observational longitudinal cohort study Avon Longitudinal Study of Parents and Children (ALSPAC), South West of England. Three-dimensional surface laser scans were taken for 4784 white British children from the ALSPAC during a follow-up clinic. A total of 1724 children with sleep disordered breathing (SDB) and 1862 healthy children were identified via parents' report of sleep disordered symptoms for their children. We excluded from the original cohort all children identified as having congenital abnormalities, diagnoses associated with poor growth and children with adenoidectomy and/or tonsillectomy. Parents in the ALSPAC reported sleep disordered symptoms (snoring, mouth breathing and apnoea) for their children at 6, 18, 30, 42, 57, 69 and 81 months. Average facial shells were created for children with and without SDB in ord...

The aim of this study was to compare facial 3D analysis to DNA testing in twin zygosity determinations. Facial 3D images of 106 pairs of young adult Lithuanian twins were taken with a stereophotogrammetric device (3dMD, Atlanta, Georgia) and zygosity was determined according to similarity of facial form. Statistical pattern recognition methodology was used for classification. The results showed that in 75% to 90% of the cases, zygosity determinations were similar to DNA-based results. There were 81 different classification scenarios, including 3 groups, 3 features, 3 different scaling methods, and 3 threshold levels. It appeared that coincidence with 0.5 mm tolerance is the most suitable feature for classification. Also, leaving out scaling improves results in most cases. Scaling was expected to equalize the magnitude of differences and therefore lead to better recognition performance. Still, better classification features and a more effective scaling method or classification in dif...

Summary OBJECTIVES : The aim of this study was to characterize facial and jaw morphology of children with Class III malocclusion in early mixed dentition. This study was conducted on 7- to 8-year-old Caucasian children, 48 children with Class III malocclusion and 91 children with normal occlusion. Surface images of faces and study casts were obtained using laser scanning. Two average facial templates were constructed for the males and females in the control group. The facial images were superimposed on the corresponding average templates. Facial parameters, palatal volumes, and gingival surface areas were measured and group differences were quantified. The analysis of variance was used for statistical evaluation of the measured parameters. The results revealed shorter lower face height (P < 0.001), concave facial profile (P < 0.001), retruded maxilla (P < 0.001), protruded mandible (P < 0.001), retrusive mid-face restricted area (P < 0.001), reduced gingival surface a...

We outline generalized separation of variables as applied to nonlinear second-order partial differential equations (PDEs). In this context, we suggest a method for constructing exact solutions of nonlinear PDEs. The method involves searching for transformations that ''reduce the dimensionality'' of the equation. New families of exact solutions of 3D nonlinear elliptic and parabolic equations that govern processes of heat and

The aim of this study was to evaluate facial morphology in 25 Class III and 46 non-Class III children aged 5-6 years using three-dimensional (3D) laser imaging; 3D facial images were obtained, two average facial templates were constructed for the non-Class III male and female groups, each individual face was superimposed on the corresponding average template and group comparisons were evaluated (facial height, facial convexity, mandibular position and facial surface morphology). Differences between parameters were evaluated by using an analysis of variance and colour deviation maps. The results showed that Class III children had less mid-face prominence and a concave facial profile when compared to non-Class III children (P = 0.002 and P = 0.018). The position of the pg point in the z-axis just failed to reach statistical significance when comparing the two groups (P = 0.051). A vertical analysis showed no statistical significance between the groups, when evaluating middle (n-sn) and lower (sn-pg) facial height. Coincidence of the Class III faces to normal templates with a tolerance set as 0.5 mm was low (less than 30%). The soft tissue characteristics of a Class III face differ significantly from the non-Class III face in the mid-face region and in the facial profile. A 3D laser imaging method evaluated and identified morphological characteristics of Class III children in deciduous dentition, which could in the future become an important diagnostic tool in small children. The most important clinical advantage of this study is the non-invasiveness of the method.

A crossbite (CB) occurs in approximately 4-23 per cent of young children and may lead to mandibular and facial asymmetry. Therefore, early intervention is often necessary to create conditions for normal occlusal and facial development. The aim of this study was to assess facial asymmetry and palatal volume (pre- and post-treatment) in two groups of children, one with a unilateral CB and the other with no crossbite (NCB). Thirty children with CB (13 males, 17 females, mean age 4.9 +/- 0.98 years) and 28 children with NCB (17 males, 11 females, mean age 5.3 +/- 0.36 years) were included in the study. Those with a CB were treated with an intra-oral expansion appliance. The faces and dental casts of the children were scanned using a three-dimensional (3D) laser scanning device at baseline (T0) and after six months (T1) of treatment. Student's t-tests were used to assess differences between the two groups in facial symmetry and palatal volume over the 6 month period. The CB children had statistically significantly greater asymmetry of the face (P = 0.042), especially the lower third (P = 0.039), and a significantly smaller palatal volume (P = 0.045) than the NCB subjects at baseline. There were no statistically significant differences between the two groups at T1. Treatment of a CB in the primary dentition corrected the facial asymmetry, particularly the lower part of the face. The palatal volume of the CB children increased as a result of orthodontic intervention to similar levels exhibited by the NCB children.

This English translation of the original Russian article "Алгебраический метод интегрирования дифференциальных уравнений нелинейной механики" published in Doklady Akademii Nauk, Mekhanika, Jul 1994, Vol. 337, No. 2, pp. 196-199. A more correct translation of the title would be "An algebraic method for integrating differential equations of nonlinear mechanics".