Constructing a polynomial whose nodal set is the three-twist knot 525_2

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_2$. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other knots with six crossings. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.Comment: 19 pages, 6 figure

Externally triggered microcapsules

Disclosed are microcapsules comprising a polymer shell enclosing one or more immiscible liquid phases in which a drug or drug precursor are contained in a liquid phase. The microparticles also contain magnetic particles that can be heated by application of an external magnetic field and thus heated to a predetermined Curie temperature. Heating of the particles melts the polymer shell and releases the drug without causing heating of surrounding tissues

Process for Encapsulating Protein Crystals

A process for growing protein crystals encapsulated within membranes has been invented. This process begins with the encapsulation of a nearly saturated aqueous protein solution inside semipermeable membranes to form microcapsules. The encapsulation is effected by use of special formulations of a dissolved protein and a surfactant in an aqueous first liquid phase, which is placed into contact with a second, immiscible liquid phase that contains one or more polymers that are insoluble in the first phase. The second phase becomes formed into the semipermeable membranes that surround microglobules of the first phase, thereby forming the microcapsules. Once formed, the microcapsules are then dehydrated osmotically by exposure to a concentrated salt or polymer solution. The dehydration forms supersaturated solutions inside the microcapsules, thereby enabling nucleation and growth of protein crystals inside the microcapsules. By suitable formulation of the polymer or salt solution and of other physical and chemical parameters, one can control the rate of transport of water out of the microcapsules through the membranes and thereby create physicochemical conditions that favor the growth, within each microcapsule, of one or a few large crystals suitable for analysis by x-ray diffraction. The membrane polymer can be formulated to consist of low-molecular-weight molecules that do not interfere with the x-ray diffraction analysis of the encapsulated crystals. During dehydration, an electrostatic field can be applied to exert additional control over the rate of dehydration. This protein-crystal-encapsulation process is expected to constitute the basis of protein-growth experiments to be performed on the space shuttle and the International Space Station. As envisioned, the experiments would involve the exposure of immiscible liquids to each other in sequences of steps under microgravitational conditions. The experiments are expected to contribute to knowledge of the precise conditions under which protein crystals form. By enhancing the ability to grow crystals suitable for x-ray diffraction analysis, this knowledge can be expected to benefit not only the space program but also medicine and the pharmaceutical industry

Low-Shear Microencapsulation and Electrostatic Coating

A report presents additional information on the topic of a microencapsulation electrostatic processing system. Information in the report includes micrographs of some microcapsules, a set of diagrams that schematically depict the steps of an encapsulation process, and brief descriptions of (1) alternative versions of the present encapsulation processes, (2) advantages of the present microencapsulation processes over prior microencapsulation processes, and (3) unique and advantageous features of microcapsules produced by the present processes

Microcapsules and Methods for Making

Methods of forming multi-lamellar microcapsules having alternating layers of hydrophilic and hydrophobic immiscible liquid phases have been developed using different polymer/solvent systems. The methods use liquid-liquid diffusion and simultaneous lateral phase separation, controlled by proper timed-sequence exposures of immiscible phases and low shear mixing, to form narrow size distributions of spherical, multilamellar microcapsules. The use of special formulations of solubilized drugs, surfactants, and polymeric co-surfactants in aqueous vehicles which are dispersed in hydrocarbon solvents containing small quantities of oil, low molecular weight co-surfactants and glycerides that are aqueous insoluble enables the formation of unique microcapsules which can carry large amounts of pharmaceuticals in both aqueous and non-aqueous solvent compartments. The liquid microcapsules are quickly formed in a single step and can include a polymeric outer 'skin' which protects the microcapsules during physical manipulation or exposure to high shear forces. Water-in-oil and oil-in-water microcapsules have been formed both in 1 x g and in microgravity, which contain several types of drugs co-encapsulated within different fluid compartments inside the same microcapsule. Large, spherical multi-lamellar microcapsules have been formed including a cytotoxic drug co-encapsulated with a radiocontrast medium which has advantages for chemoembolization of vascular tumors. In certain cases, crystals of the drug form inside the microcapsules providing zero-order and first order, sustained drug release kinetics

Microcapsules and Methods for Making

This invention relates to methods for forming multi-lamellar microcapsules of both hydrophilic and hydrophobic immiscible liquid phases using several polymer/solvent systems. Liquid-Liquid diffusion and spontaneous emulsification are controlled by properly timed sequence exposures of immiscible phases in aqueous vehicles dispersed in hydrocarbon solvents containing small quantities of oil, co-surfactants, and glycerides. Water-in-oil and oil-in-water microcapsules are formed containing selected combinations of several types of drugs, co-encapsulated within fluid compartments inside the microcapsule. Commercial applications of the process and the resultant product relate to drug therapy for treating medical conditions such as cancer, circulatory conditions, and other conditions in which pharmaceuticals are advantageously targeted to specific organs, or delivered in combination with other pharmaceuticals. Small microcapsules may be delivered intravenously to diseased organs or clotted vessels. The use of multiple drugs within the same microcapsule structure provides advantages for applications such as chemoembolization treatments and may be used to deliver both chemotherapeutic drugs, against tumor cells, and an immuno-adjuvant or immunological stimulant to enhance the patient's immune response. Active forms of urokinase and other enzymes may be delivered without dilution to the local site of an embolism for dissolving the embolism. Thus, the invention has several potentially valuable commercial applications related to pharmaceutical and medical applications

Microencapsulation of anti-tumor, antibiotic and thrombolytic drugs in microgravity

Encapsulation of cytotoxic or labile drugs enables targeted delivery and sustained release kinetics that are not available with intravenous injection. A new liquid-liquid diffusion process has been developed for forming unique microcapsules that contain both aqueous and hydrocarbon soluble drugs. Microgravity experiments, on sounding rockets (1989-92) and Shuttle missions STS-52 (1992) and STS-56 (1993) using an automated Materials Dispersion Apparatus, produced multi-lamellar microcapsules containing both Cis-platinum (anti-tumor drug) and iodinated poppy seed oil (a radiocontrast medium), surrounded by a polyglyceride skin. Microcapsules formed with amoxicillin (antibiotic) or urokinase (a clot dissolving enzyme), co-encapsulated with IPO, are still intact after two years. Microcapsules were formed with the drug so concentrated that crystals formed inside. Multi-layered microspheres, with both hydrophobic drug compartments, can enable diffusion of complementary drugs from the same microcapsule, e.g. antibiotics and immuno-stimulants to treat resistant infections or multiple fibrinolytic drugs to dissolve emboli. Co-encapsulation of enough radio-contrast medium enables oncologists to monitor the delivery of anti-tumor microcapsules to target tumors using computerized tomography and radiography that would track the distribution of microcapsules after release from the intra-arterial catheter. These microcapsules could have important applications in chemotheraphy of certain liver, kidney, brain and other tumors

Are Consumers Willing to Pay More for Biodegradable Containers Than for Plastic Ones? Evidence from Hypothetical Conjoint Analysis and Nonhypothetical Experimental Auctions

This study used and compared hypothetical conjoint analysis and nonhypothetical experimental auctions to elicit floral customers’ willingness to pay for biodegradable plant containers. The results of the study show that participants were willing to pay a price premium for biodegradable containers, but the premium is not the same for different types of containers. This article also shows the mixed ordered probit model generates more accurate results when analyzing the conjoint analysis Internet survey data than the ordered probit model.biodegradable, willingness to pay, marketing, carbon footprint, waste composition, green industry, nursery crops, floriculture crops, Agribusiness, Agricultural and Food Policy, Environmental Economics and Policy, Financial Economics, Food Consumption/Nutrition/Food Safety, Marketing, Public Economics, Research and Development/Tech Change/Emerging Technologies, D12, Q13,

The effects of an integrated care intervention for the frail elderly on informal caregivers: A quasi-experimental study

__Abstract__ Background: This study explored the effects of an integrated care model aimed at the frail elderly on the perceived health, objective burden, subjective burden and quality of life of informal caregivers. Methods. A quasi-experimental design with before/after measurement (with questionnaires) and a control group was used. The analysis encompassed within and between groups analyses and regression analyses with baseline measurements, control variables (gender, age, co-residence with care receiver, income, education, having a life partner, employment and the duration of caregiving) and the intervention as independent variables. Results: The intervention significantly contributed to the reduction of subjective burden and significantly contributed to the increased likelihood that informal caregivers assumed household tasks. No effects were observed on perceived, health, time investment and quality of life. Conclusions: This study implies that integrated care models aimed at the frail elderly can benefit informal caregivers and that such interventions can be implemented without demanding additional time investments from informal caregivers. Recommendations for future interventions and research are provided. Trial registration. Current Controlled Trials. Registration date: 14/03/2013