Isotrivially fibred isles in the moduli space of surfaces of general type

We complement Catanese's results on isotrivially fibred surfaces by completely describing the components containing an isotrivial surface with monodromy group . We also give an example for deformation equivalent isotrivial surfaces with different monodromy group.

     

On the worst case of a minimal spanning tree algorithm for euclidean space

This paper concerns the worst case running time of the minimal spanning tree algorithm presented by Bentley and Friedman. For a set ofN points ink-dimensional Euclidean space the worst case performance of the algorithm is shown to beΘ(N ² logN), fork≧2 andΘ(N ²), fork=1.     

Natural maps on the iterated jet prolongation of a fibred manifold

Summary Using an analytic procedure by the first author [5, 6], we first determine all natural transformations of the second iterated jet prolongation J¹J¹Y of a fibred manifold YX into itself depending on a linear connection on the base manifold X. We obtain two 3-parameter families and we interpret them geometrically. Our results clarify the distinguished role of the involution on J¹ J¹ Y depending on introduced by the second author [11]. Then we discuss the role of our transformations in the theory of the natural operators transforming a connection on a fibred manifold YX and a linear connection on X into a connection on the first jet prolongation J¹YX of Y. In the final remark we determine all natural transformations of the second sesquiholonomic and holomonic jet prolongations of Y into themselves. Our attention to second order jet spaces is due to the role they play in fundamental geometric and physical theories (cf. curvature of connections and lagrangian theories).     

On the extremals of a functional in space

We study the problem on the existence of extremals with given boundary conditions for the functional I(l) = ∫ ₀ ¹ (px′ ² + qy′ ² + rz′ ²)^1/2 dt under various assumptions about the functions p, q, r ∈ C ¹(R ³).     

On Pareto optimality conditions in the case of two-dimension non-convex utility space

The paper suggests a new — to the best of the author’s knowledge — characterization of Pareto-optimal decisions for the case of two-dimensional utility space which is not supposed to be convex. The main idea is to use the angle distances between the bisector of the first quadrant and points of utility space. A necessary and sufficient condition for Pareto optimality in the form of an equation is derived. The first-order necessary condition for optimality in the form of a pair of equations is also obtained.     

On the scale of a uniform space

Inventiones mathematicae -     

On the Trotter-Kato theorem in a variable space

In this paper, the proof of a Trotter-Kato type theorem in a variable Banach space is given and some special cases and examples are considered.     

On the Jordan form in a unitary space

A method is given, which determines an orthonormal part of a basis with reto which a given transformation is in Jordan canonical form.     

On the weight-spectrum of a compact space

The weight-spectrumSp(w, X) of a spaceX is the set of weights of all infinite closed subspaces ofX. We prove that ifκ>ω is regular andX is compactT ₂ withω(X)≥κ then some λ withκ≤λ≤2^<κ is inSp(ω, X). Under CH this implies that the weight spectrum of a compact space can not omitω ₁, and thus solves problem 22 of [M]. Also, it is consistent with 2^ω=c being anything it can be that every countable closed setT of cardinals less thanc withω ∈ T satisfiesSp(w, X)=T for some separable compact LOTSX. This shows the independence from ZFC of a conjecture made in [AT]. Research supported by OTKA grant no. 1908.     

On one boundary value problem for a nonlinear heat equation in the case of two space variables

The article addresses a boundary value problem with degeneration for a nonlinear heat equation in the case of two space variables. Solving this problem makes it possible to study heat conduction in a neighborhood of a closed cylindrical surface. The theorem of the existence and uniqueness of an analytic solution to the problem is proved.     

Invariant subspaces in higher order jet prolongations of a fibred manifold

We present a generalization of the concept of semiholonomic jets within the framework of higher order prolongations of a fibred manifold. In this respect, a compilation of our 2-fibred manifold approach with the methods of natural operators theory is used.     

On the coincidence of the canonical embeddings of a metric space into a Banach space

Recall the two classical canonical isometric embeddings of a finite metric space X into a Banach space. That is, the Hausdorff–Kuratowsky embedding x → ρ(x, ⋅) into the space of continuous functions on X with the max-norm, and the Kantorovich–Rubinshtein embedding x → δ _x (where δ _x , is the δ-measure concentrated at x) with the transportation norm. We prove that these embeddings are not equivalent if |X| > 4. Bibliography: 2 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 360, 2008, pp. 153–161.     

On the Chebyshev nets in a hypersurface of a Weyl space

In [1], Zlatanov introduced the Chebyshev vector fields of the first and second kind and the geodesic vector fields for an n-dimensional net in the Weyl spaceW _n . After having defined, in [2], the Chebyshev and geodesic curvatures of the lines of an arbitrary net,the b-nets and the c-nets, Tsareva and Zlatanov studied, among other things, some properties of the Chebyshev nets. In this paper, we consider an n-dimensional net in the hypersurfaceW _n of the Weyl SpaceW _n+1 and study some properties of the Chebyshev vector fields of the first and second kind and the geodesic vector fields of this net. Finally, two theorems concerning the b-nets and c-nets inW _n are obtained.     

On the Ricci curvature of a hypersurface in a space form

We give an estimate for the Ricci curvature of a complete hypersurface M in a hyperbolic space H and in a sphere S under the same condition. As its application, we give the condition for unboundedness of a complete hypersurface M.