Slow two-phase flow through a sinusoidal channel

The two-phase flow through a symmetric sinusoidal channel is studied by means of a regular perturbation analysis, where the small parameter is defined as the ratio between the amplitude of variation of the channel wall and the average thickness of the non-wetting phase. Results are valid for Reynolds numbers of the same order of magnitude as that of the expansion parameter. It is thus found that the fluid-fluid interface presents a wavy shape characterized by an amplitude and a phase-shift with respect to the fixed solid-fluid interface. Instabilities of the two-phase flow can arise for large values of the viscosity, flow rate and phase thickness ratios. Results are expected to be a first step towards the understanding of the hydrodynamics of trickle bed reactors, where several flow regimes are possible.     

Dynamic Forces Produced by Swinging Bells

The swinging of bells on belfries is a classical problem in structural dynamics and has been addressed in the Central European specialized bibliography. To carry out our study, the different modalities of swinging bells have been classified in “systems” according to their most relevant characteristics in three groups: Central European, English and Spanish systems. Each group presents some singular characteristics of frequency and oscillation, unbalance and/or turning rate, which give rise to different forces variable in time on their supporting structures. We have analyzed the three systems and, compared the maximum values of the horizontal and vertical forces that appear on the structure as well as its main harmonics. Besides the parameters analyzed, the complete dynamic study of the structure, and therefore the evaluation of its dynamic amplification factor (D.A.F.), requires the knowledge of its dynamic characteristics: main frequencies and damping ratio.     

Remarks on a Paper of M. Ochiai

This note is related to a nice short paper of M. Ochiai. We prove in a very fast way that the two-parameter family of Heegaard diagrams, constructed by Ochiai, encodes the genuine three-sphere. The result is obtained, up to isotopy, by using a sequence of only three moves in this order: a Whitehead–Zieschang reduction, a band sum and a cancellation of a handle.     

Teoremi di completezza connessi con equazioni ellittiche di ordine superiore in due variabili in un campo con contorno angoloso

Polynomials solutions of the elliptic equation (1.1) are considered in a domain whose boundary has edges but no cusps. It is shown that by using such solutions it is possible to built complete systems of vectors in suitable function spaces.     

Curves on Generic Surfaces of High Degree Through a Complete Intersection in P 3

We consider general surfaces, S, of high degree containing a given complete intersection space curve, Y. We study integral curves in the subgroup of Pic(S) generated by Y and the plane section. We determine the cohomological invariants of these curves and classify the subcanonical ones. Then using these subcanonical curves we produce stable rank two vector bundles on P ³.     

Watson resummation of a class of Hausdorff-transformed power series

In this paper we study a class of Hausdorff-transformed power series whose convergence is extremely slow for large values of the argument. We perform a Watson-type resummation of these expansions, and obtain, by the use of the Pollaczek polynomials, a new representation whose convergence is much faster. We can thus propose a new algorithm for the numerical evaluation of these expansions, which include series playing a relevant role in the computation of the partition function in statistical mechanics. By the same procedure we obtain also a solution of the classical Hausdorff moment problem.     

On the two-dimensional Knapsack Problem

We address the two-dimensional Knapsack Problem (2KP), aimed at packing a maximum-profit subset of rectangles selected from a given set into another rectangle. We consider the natural relaxation of 2KP given by the one-dimensional KP with item weights equal to the rectangle areas, proving the worst-case performance of the associated upper bound, and present and compare computationally four exact algorithms based on the above relaxation, showing their effectiveness.     

The Noncommutative Bispectral Problem for Operators of Order One

We study a noncommutative version of the bispectral problem and consider the corresponding ad-conditions in the case when both operators have order one. These terms are explained in an extended abstract given below.     

Geometric topology of generalized 3-manifolds

In this paper, we describe the history and the present status of one of the main classical problems in low-dimensional geometric topology—the recognition of topological 3-manifolds in the class of all generalized 3-manifolds (i.e., ANR homology 3-manifolds). This problem naturally splits into the cell-like resolution problem for 3-manifolds by means of homology 3-manifolds and the general-position problem for topological 3-manifolds. We have also included some open problems. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 71–84, 2005.