Defects in nine sarcomeric protein genes are known to cause hypertrophic cardiomyopathy (HCM). Mutation types and frequencies in large cohorts of consecutive and unrelated patients have not yet been determined. We, therefore, screened HCM patients for mutations in six sarcomeric genes: myosin-binding protein C3 (MYBPC3), MYH7, cardiac troponin T (TNNT2), alpha-tropomyosin (TPM1), cardiac troponin I (TNNI3), and cardiac troponin C (TNNC1). HCM was diagnosed in 108 consecutive patients by echocardiography (septum >15 mm, septal/posterior wall >1.3 mm), angiography, or based on a state after myectomy. Single-strand conformation polymorphism analysis was used for mutation screening, followed by DNA-sequencing. A total of 34 different mutations were identified in 108 patients: 18 mutations in MYBPC3 in 20 patients [intervening sequence (intron) 7 + 1G > A and Q1233X were found twice], 13 missense mutations in MYH7 in 14 patients (R807H was found twice), and one amino acid change in TPM1, TNNT2, and TNNI3, respectively. No disease-causing mutation was found in TNNC1. Cosegregation with the HCM phenotype could be demonstrated for 13 mutations (eight mutations in MYBPC3 and five mutations in MYH7). Twenty-eight of the 37 mutation carriers (76%) reported a positive family history with at least one affected first-grade relative; only eight mutations occurred sporadically (22%). MYBPC3 was the gene that most frequently caused HCM in our population. Systematic mutation screening in large samples of HCM patients leads to a genetic diagnosis in about 30% of unrelated index patients and in about 57% of patients with a positive family history.

Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the constant velocity. Simulations with the quadruple (32 digits) and variable precisions (more than 200 digits) are performed to find Stokes wave with high accuracy and study the Stokes wave approaching its limiting form with 2π/3 radians angle on the crest. A conformal map is used which maps a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. The Stokes wave is fully characterized by the complex singularities in the upper complex half-plane. These singularities are addressed by rational (Padé) interpolation of Stokes wave in the complex plane. Convergence of Padé approximation to the density of complex poles with the increase of the numerical precision and subsequent increase of the number of approximating poles reveals that the only singularities of Stokes wave are branch points connected by branch cuts. The converging densities are the jumps across the branch cuts. There is one branch cut per horizontal spatial period λ of Stokes wave. Each branch cut extends strictly vertically above the corresponding crest of Stokes wave up to complex infinity. The lower end of branch cut is the square-root branch point located at the distance v c from the real line corresponding to the fluid surface in conformal variables. The increase of the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value H max /λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave (also called by the Stokes wave of the greatest height). Here H is the wave height from the crest to the trough in physical variables. The limiting Stokes wave emerges as the singularity reaches the fluid surface. Tables of Padé approximation for Stokes waves of different heights are provided. These tables allow to recover the Stokes wave with the relative accuracy of at least 10 −26 . The tables use from several poles for near-linear Stokes wave up to about hundred poles to highly nonlinear Stokes wave with v c /λ ∼ 10 −6 .

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Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudodifferential equation, involving a periodic Hilbert transform for a strip, and solved by the Newton‐GMRES method. For strong positive vorticity, in the finite or infinite depth, overhanging profiles are found as the amplitude increases and tend to a touching wave, whose surface contacts itself at the trough line, enclosing an air bubble; numerical solutions become unphysical as the amplitude increases further and make a gap in the wave speed versus amplitude plane; another touching wave takes over and physical solutions follow along the fold in the wave speed versus amplitude plane until they ultimately tend to an extreme wave, which exhibits a corner at the crest. Touching waves connected to zero amplitude are found to approach the limiting Crapper wave as the strength of positive vorticity increases unboundedly, while touching waves connected to the extreme waves approach the rigid body rotation of a fluid disk.