We prove a new explicit inequality for the non-dimensional flow force constant, significantly improving the Benjamin and Lighthill conjecture about irrotational steady water waves. As a corollary, we prove a bound for the wave amplitude in terms of the Bernoulli constant. We show that the amplitude decays as r−2 when r→+∞, where r is the non-dimensional Bernoulli constant. We explain that the latt

We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be sup

The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we construct a solution with the following properties. The corresponding flow is unidirectional at infinity and has a solitary wave of elevation as its upper bounda

We prove that no two-dimensional Stokes and solitary waves exist when the vorticity function is negative and the Bernoulli constant is greater than a certain critical value given explicitly. In particular, we obtain an upper bound F≤2+ϵ for the Froude number of solitary waves with a negative constant vorticity, sufficiently large in absolute value.

Two-dimensional steady gravity driven water waves with vorticity are considered. Using a multidimensional bifurcation argument, we prove the existence of small-amplitude periodic steady waves with an arbitrary number of crests per period. The role of bifurcation parameters is played by the roots of the dispersion equation.

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin-Lighthill conjecture for flows with values of Berno

For the problem describing steady gravity waves with vorticity on a two-dimensional unidirectional flow of finite depth the following results are obtained. (i) Bounds are found for the free-surface profile and for Bernoulli's constant. (ii) If only one parallel shear flow exists for a given value of Bernoulli's constant, then there are no wave solutions provided the vorticity distribution is subje

Two-dimensional steady gravity waves with vorticity are considered on water of finite depth. The dispersion equation is analysed for general vorticity distributions, but under assumptions valid only for unidirectional shear flows. It is shown that for these flows (i) the general dispersion equation is equivalent to the Sturm-Liouville problem considered by Constantin & Strauss (Commun. Pure Ap

Some new interpolation inequalities are obtained in terms of maximal functions that measure smoothness. The results generalize a wide class of recent and classical inequalities and are valid for functions belonging to larger spaces (such as Triebel spaces).

We consider two main maximal operators measuring smoothness. For all possible values of the parameters, we give simple examples of bounded compactly supported functions that show quite clearly the difference between these maximal operators. Bibliography: 3 titles.

We prove a Galiardo-Nirenberg type pointwise interpolation inequality for special maximal functions which measure smoothness in the multidimensional case. It turns out that the classsical inequality follows from this one; it is also possible to use naturally BMO norms in the inequality. Bibliography: 6 titles.

To explore the psychology of voting secrecy, we conducted a field experiment to examine voter sensitivity to arrangements for ballot paper selection under the French ballot system (i.e., multiple ballot papers). Working closely with Swedish election authorities, we randomly assigned participants to vote in a fictional election under low, medium-high and high privacy conditions with a follow up pap

Aims: Transforming growth factor-beta (TGF-β) exists in three isoforms TGF-β1, -β2, and -β3. TGF-β1 has been suggested to be important for maintaining plaque stability, yet the role of TGF-β2 and -β3 in atherosclerosis remains to be investigated. This study explores the association of the three isoforms of TGF-β with plaque stability in the human atherosclerotic disease. Methods and results: TGF-β

Medical decision-making is critical and the decisions are made under uncertain, complex, and dynamic conditions. In this regard, practitioners’ experiences and perceptions may provide a bottom-up knowledge of the issues, as well as a corresponding support system that assists them in learning to make decisions in critical situations. The current study aimed to examine these experiences in the Pakis