Investigating Stops in Alaska: Can Coleman Survive a Multifactored Balance

Globalization and centralization have resulted in prolonged transportation time between producer and consumer, and thus put more demand on the perseveration of a product for longer duration and protect it from oxidation. The presence of oxygen in packages severely foreshortens the storage life as it yield losses of nutrients and allow microbial growth, which can cause changes in smell, taste as well as discoloration. Earlier food and beverage containers were made in inorganic materials e.g. metal and glass, however lately more and more focus have been on synthetic organic materials as these show several advantages, e.g. weight. However, still today most of the commercial packaging materials, organic or inorganic, are not considered to be environmental friendly. Thus, efforts have to be made today in order to invent alternative materials that can make the society of tomorrow more sustainable. Cellulose is the most abundant biopolymer in the world, hence making it desirable to use in “green” packaging applications. Furthermore, cellulose has proven being able to form films with great gas barrier potential under specific conditions. However, cellulose based materials are sensitive to moisture with severely increased oxygen transmission with increased relative humidity as a result; hence it is desired to make cellulose less hygroscopic by chemical modification. First, nanofibrillated cellulose (NFC) with 720 mmol carboxylic groups/g fiber was produced by oxidation of dissolving pulp before homogenization. Thereafter a polymer was synthesized utilizing Initiator A as an initiator at T1 and T2. The polymer synthesized at T1 yielded a polymer with a viscosity average molecular weight of 5770 g/mol.  The polymer was then grafted on the oxidized NFC through a coupling reaction performed in Buffer C using Coupling agent A. The grafting procedure was performed in Buffer C at ambient conditions giving rise to a material composed of 33 wt% synthetic polymer and 67 wt% NFC. The coupling was conducted several times in order to investigate how the final product can be affected by varying reactant feed and dispersion method. Finally, films of NFC and NFC-g-Polymer were manufactured by vacuum filtration from a 0.05 wt% Solvent A dispersion and were evaluated with field emission scanning electron microscopy

Closed form summation of C-finite sequences

We consider sums of the form $$\sum_{j=0}^{n-1}F_1(a_1n+b_1j+c_1)F_2(a_2n+b_2j+c_2)... F_k(a_kn+b_kj+c_k),$$ in which each $\{F_i(n)\}$ is a sequence that satisfies a linear recurrence of degree $D(i)<\infty$, with constant coefficients. We assume further that the $a_i$'s and the $a_i+b_i$'s are all nonnegative integers. We prove that such a sum always has a closed form, in the sense that it evaluates to a linear combination of a finite set of monomials in the values of the sequences $\{F_i(n)\}$ with coefficients that are polynomials in $n$. We explicitly describe two different sets of monomials that will form such a linear combination, and give an algorithm for finding these closed forms, thereby completely automating the solution of this class of summation problems. We exhibit tools for determining when these explicit evaluations are unique of their type, and prove that in a number of interesting cases they are indeed unique. We also discuss some special features of the case of ``indefinite summation," in which $a_1=a_2=... = a_k = 0$

Getting the Most Out of Your Feed Management Software

Feeding software programs are a wise investment to save thousands on a farm’s largest expense