Compositions Research Papers - Academia.edu (original) (raw)
A composition of a positive integer n is a finite sequence of positive integers a1, a2,. .. , a k such that a1 + a2 + • • • + a k = n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more at position i, if... more
A composition of a positive integer n is a finite sequence of positive integers a1, a2,. .. , a k such that a1 + a2 + • • • + a k = n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more at position i, if ai+1 ≥ ai + d. We study the average position, initial height and end height of the first ascent of size d or more in compositions of n as n → ∞.
Green tea is manufactured from the leaves of the plant Camellia Sinesisand belonging to the family Theaceae and is used most popularly as beverage all over the world. The major components of Green tea which are responsible for the... more
Green tea is manufactured from the leaves of the plant Camellia Sinesisand belonging to the family Theaceae and is used most popularly as beverage all over the world. The major components of Green tea which are responsible for the potentialpharmacokinetic properties, Antioxidant and other Health benefits are Polyphenols. The major polyphenols in Green tea are Flavonoids. The Flavonoids present in Green tea is Catechins these are mainly four type, Epicatechin (EC), Epigallocatechin (EGC), Epicatechin gallate(ECG) and Epigallocatechin gallate (EGCG). The most significant active component is Epigallocatechin gallate (EGCG).Human studies found that long term consumption of Green tea catechins could be beneficial against, Cardiovascular activity, as Antioxidant, Antibacterial activity, Anticancer properties, Dental caries and Diabetic properties etc. Further research that conforms to international standardsshould be performed to monitor the pharmacological and clinical effects of green tea and to elucidate its mechanismsof action.
We consider compositions of n, i.e., sequences of positive integers (or parts) (σi)ki=1 where σ1 +σ2 + · · ·+σk = n. We define a maximum to be any part which is not less than any other part. The variable of interest is the size of the... more
We consider compositions of n, i.e., sequences of positive integers (or parts) (σi)ki=1 where σ1 +σ2 + · · ·+σk = n. We define a maximum to be any part which is not less than any other part. The variable of interest is the size of the descent immediately following the first and the last maximum. Using generating functions and Mellin transforms, we obtain asymptotic expressions for the average size of these descents. Finally, we show with the use of a simple bijection between the compositions of n for n> 1, that on average the descent after the last maximum is greater than the descent after the first.
In this paper we study different restrictions imposed over the set of permutations of size n, Sn , and for specific classes of restrictions study the cycle structure of corresponding permutations. More specifically, we prove that for any... more
In this paper we study different restrictions imposed over the set of permutations of size n, Sn , and for specific classes of restrictions study the cycle structure of corresponding permutations. More specifically, we prove that for any fixed positive integer k, the number of k-cycles of a uniformly chosen permutation π ∈ Sn with the restriction " π(i) ≥ i − 1 for i ∈ {2, ..., n} " has a Normal asymptotic distribution. We further prove that this result translates into CLTs regarding multiplicities of fixed-size parts of a uniformly selected composition of n.
The manual analyzes the known methods of selecting asphalt concrete compositions, identifies their specific features, differences and shortcomings, and justifies the need for further development in the direction of functional design of... more
The manual analyzes the known methods of selecting asphalt concrete compositions, identifies their specific features, differences and shortcomings, and justifies the need for further development in the direction of functional design of optimal compositions for specific operating conditions of the arranged coatings. In the light of modern ideas about the structure of asphalt concrete, the influence of its composition and properties on the durability of road surfaces is shown. Various types of asphalt concrete are considered, indicating the optimal field of their application in the construction of road surfaces, as well as a number of innovations in the field of technology and compositions of asphalt concrete mixtures. The results of studies of the operational properties of asphalt concrete, taking into account the stress-strain state and temperature-time conditions of loading of coatings, are presented. The combined effect of the structural and rheological properties of asphalt concrete and external factors on the durability of road surfaces is shown. ООО «RASTOM» (http://www.rastom.ru), тел. +7 495 641 75 90.
The present work was undertaken to study the physicochemical characteristics, fatty acid, phenolic and tocopherol compositions as well as the antioxidant activities of red pepper seed oils extracted using different methods (soxhlet,... more
The present work was undertaken to study the physicochemical characteristics, fatty acid, phenolic and tocopherol compositions as well as the antioxidant activities of red pepper seed oils extracted using different methods (soxhlet, cold-pressing, supercritical-CO 2 and microwave-assisted extraction process). The results showed that the red pepper seeds were (on a dry-weight basis): ash 3.05%, water 6.63%, oil 18.39%, protein 28.33%, and total carbohydrate 43.60%. In addition, the results revealed that the predominant fatty acids were linoleic, palmitic and oleic acids. The highest and lowest contents of linoleic acid (76.54%) were found in microwaveassisted (76.54%) and soxhlet (73.65%) extracted pepper seed oils, respectively. < Gamma >-tocopherol was the main tocopherol at 278.65 mg/100 g seed oil, followed by < alpha >-tocopherol and < delta >-tocopherol. Nevertheless, high content in total tocopherols was found in microwave extracted red pepper seed oils. The lowest and highest values of oxidative stability were 1.25 and 11.26 h for soxhlet and microwave-assisted extracted seed oils, respectively. Overall, the high antioxidant activities of microwave-assisted extracted seed oil suggest that it could be economically used as valuable natural products for industrial, cosmetic, and pharmaceutical utilizations.
<p>The former are plotted consecutively and show early and late mineralizing tooth pairs of individuals (highlighted with a tie-line) if applicable. Three individuals (14, 8/1, 39/2) plot clearly outside the ±2 SD local signal for... more
<p>The former are plotted consecutively and show early and late mineralizing tooth pairs of individuals (highlighted with a tie-line) if applicable. Three individuals (14, 8/1, 39/2) plot clearly outside the ±2 SD local signal for Basta (shaded box: 0.70821±0.00008). Given the reported <sup>87</sup>Sr/<sup>86</sup>Sr variation between ∼0.7053 and 0.7094 in modern food webs in the region <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065649#pone.0065649-Shewan1" target="_blank">[22]</a>, the observed overall variability for Basta is very small. In case of B39/2, only the first molar shows a non-local signature, which indicates that by the time of mineralization of the 2<sup>nd</sup> premolar (∼year 6), this individual had already moved to Basta. B5060/1 M1 is only marginally below the local Sr-isotope range, which is interpreted not to be significant, also because the Sr-isotope signal of its PM2 is consistent with Basta (even identifying B5060/1 as a non-local would not change any of the conclusions herein).</p
We investigate the probability that a random composition (ordered partition) of the positive integer n has no parts occurring exactly j times, where j belongs to a specified finiteforbidden set'A of multiplicities. This probability... more
We investigate the probability that a random composition (ordered partition) of the positive integer n has no parts occurring exactly j times, where j belongs to a specified finiteforbidden set'A of multiplicities. This probability is also studied in the related case of samples Γ=(Γ1, Γ2,…, Γn) of independent, identically distributed random variables with a geometric distribution. Résumé. Nous examinons la probabilité qu'une composition faite au hasard (une partition ordonnée) du nombre entier positif n n'a pas de partie qui arrivent ...