On a Morse conjecture for analytic flows on compact surfaces

The aim of this paper is to prove a Morse conjecture; in particular it is shown that a topologically transitive analytic flow on a compact surface is metrically transitive. We also build smooth topologically transitive flows on surfaces which are not metrically transitive.     

On meromorphic solutions of f 3 + g 3 = 1

We show that meromorphic solutions f, g of f ³ + g ³ = 1 in must be constant, if and have the same zeros (counting multiplicities). Received: 12 March 2007     

Existence and convergence of positive weak solutions of −Δu=u^{\frac{n}{{n - 2}}} in bounded domains of ℝ n,n≥3

For the equation –u= in ⁿ we prove the existence of positive weak solutions with prescribed singular set. We also prove the existence of sequences of weak solutions which converge weakly but not strongly inL ^n/n–2()     

On a conjecture of Butler and Graham

Motivated by a hat guessing problem proposed by Iwasawa, Butler and Graham made the following conjecture on the existence of a certain way of marking the coordinate lines in [k] ⁿ : there exists a way to mark one point on each coordinate line in [k] ⁿ , so that every point in [k] ⁿ is marked exactly a or b times as long as the parameters (a, b, n, k) satisfies that there are nonnegative integers s and t such that s + t = k ⁿ and as + bt = nk ^n?1. In this paper we prove this conjecture for any prime number k. Moreover, we prove the conjecture for the case when a = 0 for general k.     

On k-symmetries of hyperbolic spaces

We determine all the possible pointwise k-symmetric spaces of negative constant curvature. In general, such spaces are not k-symmetric.In fact we show that, for all $n?3$, $k\ne 2$, $H^n$ is not k-symmetric, i.e., for any set of selected k-symmetries, one for each point of $H^n$, the regularity condition does not hold.     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.     

On a boundary value problem in the half-space

In this paper, we study the existence of positive solutions and sign-changing solutions for the following boundary value problem in the half-space

     

Classification of five-dimensional generalized pointwise symmetric Riemannian spaces

Riemannian symmetric spaces have the following two classes of spaces as their natural generalizations: (A) the class ofGS-spaces (generalized symmetric Riemannian spaces); (B) the class ofGPS-spaces (generalized pointwise symmetric Riemannian spaces). A result due to O. Kowalski says that the relation between the two classes is (A) (B), the inclusion being strict. In the present paper the author proves that in dimension 5 the class (A) and the class (B) must coincide. Consequently the explicit classification of five-dimensional GPS-spaces is obtained.     

Ruled surfaces of Weingarten type in Minkowski 3-space

In this paper, we study ruled Weingarten surfaces M : x (s, t) = α(s) + tβ (s) in Minkowski 3-space on which there is a nontrivial functional relation between a pair of elements of the set {K, K_II, H, H_II}, where K is the Gaussian curvature, K_II is the second Gaussian curvature, H is the mean curvature, and H_II is the second mean curvature. We also study ruled linear Weingarten surfaces in Minkowski 3-space such that the linear combination aK_II + bH + cH_II + dK is constant along each ruling for some constants a, b, c, d with a² + b² + c² ≠ 0.     

On a nonsolvable partial differential operator

This paper deals with the local nonsolvability in Schwartz distribution spaceD′ ofm-order partial differential operator whose principal symbol is them-th power of locally solvable and hypoelliptic Mizohata type operator.

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Sunto Questo lavoro tratta la nonrisolubilità locale nello spazio delle distribuzioni di SchwartzD′ degli operatori alle derivate parziali di ordinem il cui simbolo principale è lam-sima potenza dell'operatore tipo Mizohata localmente risolubile ed ipoellittico.

     

Contact and Conformal Maps in

When the action of the conformal group O(1, n+1) on may be characterized in simple differential geometric terms, even locally: a theorem of Liouville states that a C⁴ map between domains and in whose differential is a (variable) multiple of a (variable) isometry at each point of is the restriction to of a transformation x g·x, for some g in O(1,n+1). In this paper, we consider the problem of characterizing the action of a more general semisimple Lie group G on the space G/P, where P is a minimal parabolic subgroup.     

Ruled surfaces of Weingarten type in Minkowski 3-space, II

In our previous paper of the same title, we did not study the ruled surfaces of Weingarten type M : x(s, t)=α(s)+t β (s) in Minkowski 3-space with vector fields β and β′ along the base curve β such that β is nowhere null but β′ is null everywhere. We here fulfill our project by investigating this remaining case.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

On a conjecture of D. B. Hunter

We consider errors of positive quadrature formulas applied to Chebyshev polynomials. These errors play an important role in the error analysis for many function classes. Hunter conjectured that the supremum of all errors in Gaussian quadrature of Chebyshev polynomials equals the norm of the quadrature formula. We give examples, for which Hunter's conjecture does not hold. However, we prove that the conjecture is valid for all positive quadratures if the supremum is replaced by the limit superior. Considering a fixed positive quadrature formula and the sequence of all Chebyshev polynomials, we show that large errors are rare.