Abstract Square contingency tables with ordinal classifications are used in many disciplines that include but not limited to data science, engineering, and medical research. This study proposes two original asymmetry models based on non-integer scores for the analysis of square tables. The quasi-symmetry model applies sets can be assigned known ordered all categories. When we assign equally spa...

The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent strength oscillator field. most clearly appears when crucial two-body systems are unbound in three, but...

Polarization measurement has been used for many optical applications in science and technology. Herein, we adopt a reliable method to measure the polarization parameters of incident light, including principal axis, chirality ellipticity based on superposition two orthogonal vortex beams with non-integer topological charges (TCs). All three can be measured analyzed by interference pattern produc...

In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.

In this paper, the exact rate of decrease best approximations non-integer numbers by polynomials with integer coefficients is established.