Probability information is regularly communicated to experts who must fuse multiple estimates support decision making. Such often verbally (e.g., “likely”) rather than with precise numeric (point) values “.75”), yet people are not taught perform arithmetic on verbal probabilities. We hypothesized that the accuracy and logical coherence of averaging multiplying probabilities will be poorer when ...

Here, we initiate a program to study relationships between finite groups and arithmetic–geometric invariants in systematic way. To do this, first introduce notion of optimal module for group the setting holomorphic mock Jacobi forms. Then, classify modules cyclic prime order, special case weight 2 index 1, where class numbers imaginary quadratic fields play an important role. Finally, exhibit c...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

The goal of the work. Development methods for performing basic arithmetic operations with interval complex numbers, which are presented in hyperbolic form, their modulus and argument. Results. paper considers method extending numbers defined form (hyperbolic numbers) to field numbers. To do this, real imaginary part a number is number. connections between representation classical CENTER-RADIUS ...

In 1969, Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. We know the answer to this question for various subsystems obtained by restricting in different ways the language of arithmetic expressions, yet, up to now we knew nothing of the original system that Tarski considered when he started all ...

Integers have many interesting properties. In this paper it will be shown that, for an arbitrary nonconstant arithmetic progression {an}TM=l of positive integers (denoted by N), either {an}TM=l contains infinitely many palindromic numbers or else 10|aw for every n GN. (This result is a generalization of the theorem concerning the existence of palindromic multiples, cf. [2].) More generally, for...