The series product for gaussian quantum input processes

In 1958, Richard Guy proved that the number of partitions of $n$ into odd parts greater than one equals the number of partitions of $n$ into distinct parts with no powers of 2 allowed, which is closely related to Euler's famous theorem that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We consider extensions of Guy's result, which naturally lead to a new algorithm for producing bijections between various equivalent partition ideals of order 1, as well as to two new infinite families of parity results which follow from Euler's Pentagonal Number Theorem and a well-known series-product identity of Jacobi.

Download Full-text

EXPERIMENTAL MODEL OF A COMBINED THERMAL SYSTEM FOR EFFICIENT USE OF RENEWABLE ENERGIES

INMATEH Agricultural Engineering ◽

10.35633/inmateh-60-32 ◽

2020 ◽

Vol 60 (1) ◽

pp. 287-294

Author(s):

C. Dumitrescu ◽

R. Rădoi ◽

C. Cristescu ◽

L. Dumitrescu

Keyword(s):

Renewable Energy ◽

Experimental Model ◽

Thermal Energy ◽

Renewable Energy Sources ◽

Energy Sources ◽

Thermal System ◽

Remote Areas ◽

Energy Independence ◽

Atmospheric Factors ◽

Series Product

The article presents an experimental model of a modular structure system for the production of thermal energy and the results of conducting specific tests. The experimental model uses two renewable energy sources - solar energy and energy generated by burning biomass - to provide thermal energy for an increased duration, regardless of the atmospheric factors. Properly sized, the system can be designed as a series product, in a variety of powers, to be used by heat suppliers, and also by individuals, especially the ones from remote areas, who want to ensure their thermal energy independence by using renewable energy.

Download Full-text