An Elementary Product Identity in Polynomial Dynamics

2001 ◽  
Vol 108 (9) ◽  
pp. 860-864
Author(s):  
Robert L. Benedetto
Keyword(s):  
Product Identity ◽  
Polynomial Dynamics

scholarly journals Profile of Volatile Compounds of On-Farm Fermented and Dried Cocoa Beans Inoculated with Saccharomyces cerevisiae KY794742 and Pichia kudriavzevii KY794725

Molecules ◽  
2021 ◽  
Vol 26 (2) ◽  
pp. 344
Author(s):  
Gilson Celso Albuquerque Chagas Junior ◽  
Nelson Rosa Ferreira ◽  
Eloisa Helena de Aguiar Andrade ◽  
Lidiane Diniz do Nascimento ◽  
Francilia Campos de Siqueira ◽  
...  
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Volatile Compounds ◽  
Multivariate Analyses ◽  
High Capacity ◽  
Starter Cultures ◽  
Cocoa Beans ◽  
Pichia Kudriavzevii ◽  
Fermentative Capacity ◽  
Product Identity ◽  
On Farm

This study aimed to identify the volatile compounds in the fermented and dried cocoa beans conducted with three distinct inoculants of yeast species due to their high fermentative capacity: Saccharomyces cerevisiae, Pichia kudriavzevii, the mixture in equal proportions 1:1 of both species, and a control fermentation (with no inoculum application). Three starter cultures of yeasts, previously isolated and identified in cocoa fermentation in the municipality of Tomé-Açu, Pará state, Brazil. The seeds with pulp were removed manually and placed in wooden boxes for the fermentation process that lasted from 6 to 7 days. On the last day of fermentation, the almonds were packaged properly and placed to dry (36 °C), followed by preparation for the analysis of volatile compounds by GC-MS technique. In addition to the control fermentation, a high capacity for the formation of desirable compounds in chocolate by the inoculants with P. kudriavzevii was observed, which was confirmed through multivariate analyses, classifying these almonds with the highest content of aldehydes, esters, ketones and alcohols and low concentration of off-flavours. We conclude that the addition of mixed culture starter can be an excellent alternative for cocoa producers, suggesting obtaining cocoa beans with desirable characteristics for chocolate production, as well as creating a product identity for the producing region.

scholarly journals Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product

2022 ◽  
Vol Volume 44 - Special... ◽  
Author(s):  
Liuquan Wang
Keyword(s):  
Analogous Result ◽  
Triple Product ◽  
Combinatorial Proof ◽  
Jacobi’S Triple Product Identity ◽  
Product Identity ◽  
Pentagonal Number Theorem ◽  
Nonnegative Coefficients ◽  
Jacobi's Triple Product Identity

Andrews and Merca investigated a truncated version of Euler's pentagonal number theorem and showed that the coefficients of the truncated series are nonnegative. They also considered the truncated series arising from Jacobi's triple product identity, and they conjectured that its coefficients are nonnegative. This conjecture was posed by Guo and Zeng independently and confirmed by Mao and Yee using different approaches. In this paper, we provide a new combinatorial proof of their nonnegativity result related to Euler's pentagonal number theorem. Meanwhile, we find an analogous result for a truncated series arising from Jacobi's triple product identity in a different manner.

scholarly journals Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy

10.37236/1796 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
James A. Sellers ◽  
Andrew V. Sills ◽  
Gary L. Mullen
Keyword(s):  
Famous Theorem ◽  
Partition Identities ◽  
Product Identity ◽  
Powers Of 2 ◽  
Pentagonal Number Theorem ◽  
Series Product

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.

scholarly journals Peningkatan Omset Usaha Keripik Nanas Khas Pekanbaru Melalui Pembaharuan Desain Packaging Dan Pengembangan Pemasaran Produk

2021 ◽  
Vol 5 (1) ◽  
pp. 63-68
Author(s):  
Wan laura Hardilawati ◽  
Arista Tri Astuti ◽  
Alex Candra ◽  
Kintan Syafwa Prastika ◽  
Muhammad Abrar Al-azhar
Keyword(s):  
Community Service ◽  
Packaging Design ◽  
Product Identity ◽  
New Business ◽  
Increase Productivity ◽  
Product Marketing ◽  
The City

This research aims to outline the results of research on the increasing turnover of the typical pineapple chips business of pekanbaru through packaging design renewal and product marketing development.This pineapple chips business has excellent potential, so it needs to get special attention from various parties such as from government, private and college as has been done by many universities through community service activities.This research focuses on packaging, design and marketing of pineapple chips products of Ibu's new business located on the outskirts of the city, precisely on Rimbo Panjang street, Pekanbaru.Through this devotional activity, pineapple chip manufacturers can increase knowledge on how to attract consumers by changing packaging to be safer along with a more attractive design display that can become a product identity and market products through e-commerce to increase productivity and sales.

Sign in / Sign up

Export Citation Format

Share Document