Universal arcs in local tournaments

An arc $uv$ of a digraph $D$ is called universal if $uv$ and $w$ are in a common cycle for any vertex $w$ of $D$. In this paper we characterize local tournaments whose every arc is universal.     

Structures of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra

In this paper, we determine the universal central extension, derivation algebra and automorphism group of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra. Furthermore, we generalize these results to the generalized twisted N = 1 Schrödinger–Neveu–Schwarz algebra in the final section.     

On the general expression of Fredholm Integral Equations Method in elasticity

In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When numerical computations are needed for the solution, the method proves to have high precision and fast convergency.     

Homogeneous monotropic elastic rods: Normal uniform configurations and universal solutions

A number of simple solutions are obtained which are universal for an homogeneous monotropic elastic rod whose theory is based on a Cosserat-type model.

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Sommario Si ottengono alcune soluzioni semplici che sono universali per una trave omogenea monotropica la cui teoria è basata su un modello alla Cosserat.

     

Simultaneous spreading and evaporation: Recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1–2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.     

A universal differentiability set in Banach spaces with separable dual

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fréchet differentiable somewhere in S.     

Universality properties of Taylor series inside the domain of holomorphy

It is proven that the Taylor series of functions holomorphic in C_∞?{1} generically have certain universality properties on small sets outside the unit disk. Moreover, it is shown that such sets necessarily are polar sets.     

A new infinite family of minimally nonideal matrices

Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on the possible cores of minimally nonideal matrices. This paper disproves their conjecture by constructing a new infinite family of square minimally nonideal matrices. In particular, we show that there exists a minimally nonideal matrix with r ones in each row and column for any r?3.     

Sequential optimizing strategy in multi-dimensional bounded forecasting games

We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001) [10]. By studying the asymptotic behavior of its capital process, we prove a generalization of the strong law of large numbers, where the convergence rate of the sample mean vector depends on the growth rate of the quadratic variation process. The growth rate of the quadratic variation process may be slower than the number of rounds or may even be zero. We also introduce an information criterion for selecting efficient betting items. These results are then applied to multiple asset trading strategies in discrete-time and continuous-time games. In the case of a continuous-time game we present a measure of the jaggedness of a vector-valued continuous process. Our results are examined by several numerical examples.