Arithmetics of Uncertainty Distributions for Some Functions of Uncertain Variables with Experiential Uncertainty Distributions

Uncertainty distributions for functions of uncertain variables in uncertainty theory play a significant rote. The paper provides the arithmetics of uncertainty distributions for sum, difference, maxi- mum and minimum of uncertain variables with experiential uncertainty distributions, and shows the efficiency of these arithmetics by examples

Tropical linear algebra with the Lukasiewicz T-norm

The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Lukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-Lukasiewicz semiring.Comment: 27 page

Separating Bounded Arithmetics by Herbrand Consistency

The problem of $\Pi_1-$separating the hierarchy of bounded arithmetic has been studied in the paper. It is shown that the notion of Herbrand Consistency, in its full generality, cannot $\Pi_1-$separate the theory ${\rm I\Delta_0+\bigwedge_j\Omega_j}$ from ${\rm I\Delta_0}$; though it can $\Pi_1-$separate ${\rm I\Delta_0+Exp}$ from ${\rm I\Delta_0}$. This extends a result of L. A. Ko{\l}odziejczyk (2006), by showing the unprovability of the Herbrand Consistency of ${\rm I\Delta_0}$ in the theory ${\rm I\Delta_0+\bigwedge_j\Omega_j}$.Comment: Published by Oxford University Press. arXiv admin note: text overlap with arXiv:1005.265

Dešimtmečio po lietuviškos spaudos atgavimo aritmetikos vadovėlių panorama

In 1904 with the lifting of the ban on Lithuanian publications by Russian czar government and in 1906 with giving the permit to teach arithmetics in mother tongue at primary schools the legal publishing of Lithuanian arithmetic textbooks started. Already in 1906 even three arithmetic textbooks were published. These were two parts of  ``Arithmetic Taskbook“ by Pranas Mašiotas, the first part of  ``Collection of Arithmetic Tasks and Examples“ by Petras Bendorius and Pranas Daugirda and two parts of translated from Polish  ``Arithmetic Tasks and Examples“ by Stanislaw Thom. All the books step by step explained in the Lithuanian language four arithmetic operations up to ten, later a hundred and finally up to a thousand.In 1909 two important books were published: the second part of the textbook by Petras Bendorius and Pranas Daugirda and ``Elementary Arithmetics“ by Petras Mikolainis. The latter textbook could be distinguished for methodical instructions.In 1909–1916 Juozas Damijonaitis prepared and published two parts of  ``Arithmetic Textbook“. The book was recompiled into three parts during the period of the Republic of Lithuania (in 1918–1940). It became popular and was constantly republished.When forming of arithmetic basics was coming to end in 1916 ``The Short Science of Arithmetics“ by S. Thom (1916) appeared in the Lithuanian language, where the theory of arithmetics was presented.Santraukos nėra