On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the “embeddings of Banach spaces” point of view.     

Polynomials with graphs of maximum length

In this paper we find the pairs of functionsg, G (g<G) such that the maximum length of the graph of polynomials of given degree contained betweeng andG is attained on one of the two snakes generated by the functionsg andG. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 61–69, January, 1999.     

关于算子连续映射

在算子开集理论中给出了算子拓扑空间的概念，并在该空间中讨论了算子连续映射，得到了算子连续映射的等价刻划。     

High gravity batch and continuous processes for beer production: Evaluation of fermentation performance and beer quality

This study deals with two innovative brewing processes, high gravity batch and complete continuous beer fermentation systems. The results show a significant influence of the variables such as concentration and temperature on the yield factor of the substrate into ethanol and consequently on the productivity of the high gravity batch process. The technological feasibility of continuous production of beer based on yeast immobilization on cheap alternative carriers was also demonstrated. The influence of process parameters on fermentation performance and quality of the obtained beers was studied by sensorial analysis. No significant difference in the degree of acceptance between the obtained products and some traditional market brands was found. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

On representation and regularity of continuous parameter multivalued martingales

In this paper we study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the cadlag modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in convergence in the Hausdorff metric respectively.

     

Prediction of Continuous Time Processes by C[0,1]‐Valued Autoregressive Process

In order to predict a continuous time process on an entire‐time interval, we introduce the C_[0,1]‐valued autoregressive process of first order. We show, under mild regularity conditions the convergence almost sure of the predictor. We propose an estimator of the dimension of the projecting space of observations and illustrate the results by a numerical example. This revised version was published online in June 2006 with corrections to the Cover Date.     

Strong convergence theorems for nonexpansive semi-groups in Banach spaces

Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established.Results presented in the paper not only extend and improve the corresponding results of Shioji- Takahashi,Suzuki,Xu and Aleyner-Reich,but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.     

STABILITY IN DIFFERENTIAL EQUATIONS WITH CONTINUOUS AND PIECEWISE CONSTANT ARGUMENTS

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