Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

A Table for Determining the Probability of a Stock out and Potential Lost Sales for a Gamma Distributed Demand

A table is given for determining the probability of a stock out and potential lost sales for a gamma distribution of demand. In addition to general applicability it is shown that the table enables a fundamental equation in inventory theory associated with the problem of minimizing the total cost of holding stock to be solved approximately.     

Stock Control—Experience and Usable Theory

Previous work on stock control has been mainly concerned with specific models or situations. This paper is an attempt at a more general method capable of dealing with distributed demands coupled with distributed lead times for a single stage stock system. Although primarily intended for manual operation, extensions to computer use are indicated. The criterion for determining stock investment is discussed and one based on return on capital employed is advocated.     

Free factor algebras of free linear ω-algebras

This paper concerns free linear -algebras in certain varieties and their subalgebras and factor algebras. Conditions are given ensuring that an epimorphic image of a free linear -algebra in a variety given by permutation identities of zero order is free in this variety. An example is constructed of a variety of linear algebras in which this assertion is false.Translated from Matematicheskie Zametki, Vol. 11, No. 5, pp. 537–544, May, 1972.     

Back Ordering in Inventory Control

An approach to determining the empirical relationship between time out of stock and back ordering is outlined. Using this relationship the expected lost sales in a reorder level system of inventory control are derived for continuous and block demand depletion, fixed and variable lead times. Their applicability to a generalized inventory model is discussed.     

Products of operators of multidimensional structured model of systems

The author has previously defined the concept of a general system in terms of operators and operands. An operand is a mapping defined on a subset of an m-fold Cartesian product instead of the usual set and collection of k-ary relations on it. An operator is a kind of mapping between two collections of operands. Here subsystems, extensions, and the notion of P-semiexactness is studied. In particular we derive conditions such that P-semiexactness of a composition of operators, and of one factor, implies P-semiexactness of the other factor.     

Reduced multilevel atom method for calculating cosmological recombination kinetics

A new method for solving the differential-algebraic set of equations, describing the kinetics of primary plasma recombination in the early Universe, is proposed. The method is based on the use of some properties of the initial high-dimensional set to construct a low-dimensional set which is mathematically equivalent in essentiality to the initial set. At the expense of certain complication of the algorithm for computing the coefficients describing the model atom with a small number of bound states, in comparison with conventional methods, complete agreement between the solution to the obtained low-dimensional set and corresponding components of the initial set is achieved. The described method allows construction of the algorithm for solving the recombination kinetics whose accuracy is comparable to integration of the complete multilevel set of kinetic equations and whose computational burden per model is comparable to the method used in the RECFAST code.     

In vitro selection of a novel nuclease-resistant RNA phosphodiesterase

BACKGROUND: Ribonucleotide-based enzymes (ribozymes) that cleave pathological RNAs are being developed as therapeutic agents. Chemical modification of the hammerhead ribozyme has produced nuclease-resistant catalysts that cleave targeted mRNAs in cell culture and exhibit antitumor activity in animals. Unfortunately, stabilizing modifications usually reduce the catalytic rate in vitro. An alternative to rationally designed chemical modifications of existing ribozymes is to identify novel motifs through in vitro selection of nuclease-stable sequence space. This approach is desirable because the catalysts can be optimized to function under simulated physiological conditions. RESULTS: Utilizing in vitro selection, we have identified a nuclease-stable phosphodiesterase that demonstrated optimal activity at simulated physiological conditions. The initial library of 10(14) unique molecules contained 40 randomized nucleotides with all pyrimidines in a nuclease-stabilized 2'-deoxy-2'-amino format. The selection required trans-cleaving activity and base-pairing specificity towards a resin-bound RNA substrate. Initial selective pressure was permissive, with a 30 min reaction time and 25 mM Mg(2+). Stringency of selection pressure was gradually increased until final conditions of 1 mM Mg(2+) and less than 1 min reaction times were achieved. The resulting 61-mer catalyst required the 2'-amino substitutions at selected pyrimidine positions and was stable in human serum (half-life of 16 h). CONCLUSIONS: We demonstrated that it is possible to identify completely novel, nuclease-resistant ribozymes capable of trans-cleaving target RNAs at physiologically relevant Mg(2+) concentrations. The new ribozyme motif has minimal substrate requirements, allowing for a wide range of potential RNA targets.     

MODELING CLIMATE CHANGE AND THE EFFECT ON THE NORWEGIAN SALMON FARMING INDUSTRY

Abstract Global warming is expected to affect the ecosystem in the Northeast Atlantic, and substantial changes will also affect the aquaculture industry. Farming of salmon and trout is the biggest aquaculture industry in Norway, with an export value of about 3 billion US dollars in 2007. The objective of the paper is to analyze the potential economic effect a general increase in sea temperature can have on the Norwegian salmon aquaculture industry. The assessment of the economic impact of global warming is made possible by estimating a growth function, which explicitly includes sea water temperature. The analysis compares the economic effect of a climate change on fish farming plants in the south and the north of Norway. The scenarios are based on a model with monthly seasonal variation in temperature.     

A first step towards practical single cell proteomics: a microfluidic antibody capture chip with TIRF detection

We have developed a generic platform to undertake the analysis of protein copy number from single cells. The approach described here is 'all-optical' whereby single cells are manipulated into separate analysis chambers using an optical trap; single cells are lysed by a shock wave caused by laser-induced microcavitation, and the protein released from a single cell is measured by total internal reflection microscopy as it is bound to micro-printed antibody spots within the device. The platform was tested using GFP transfected cells and the relative precision of the measurement method was determined to be 88%. Single cell measurements were also made on a breast cancer cell line to measure the relative levels of unlabelled human tumour suppressor protein p53 using a chip incorporating an antibody sandwich assay format. These results suggest that this is a viable method for measuring relative protein levels in single cells.