In this paper we shall consider ordinary graphs, that is, graphs without loops and multiple edges . Given a graph L, ex(n , L) will denote the maximum number of edges a graph G" of order n can have without containing any L . Determining ex(n,L), or at least finding good bounds on it will be called TURÁN TYPE EXTREMAL PROBLEM. Assume that a graph G" has E > ex(n , L) edges. Then it must contain ...

Although curcumin is considered to have various therapeutic effects, its use as a functional food or supplement restricted owing low water solubility and bioavailability. To increase the of in water, polyvinylpyrrolidone (PVP) vinylpyrrolidone-vinyl acetate copolymers with pyrrolidone skeleton was noted be promising. In particular, bi-component formulations curcumin/PVP prepared through spray d...

Bubble nucleation in weakly supersaturated solutions of carbon dioxide—such as champagne, sparkling wines and carbonated beers—is well understood. Bubbles grow and detach from nucleation sites: gas pockets trapped within hollow cellulose fibres. This mechanism appears not to be active in stout beers that are supersaturated solutions of nitrogen and carbon dioxide. In their canned forms these be...

The maintenance of protein solubility is a fundamental aspect of cellular homeostasis because protein aggregation is associated with a wide variety of human diseases. Numerous proteins unrelated in sequence and structure, however, can misfold and aggregate, and widespread aggregation can occur in living systems under stress or aging. A crucial question in this context is why only certain protei...

Chemical kinetic data, complemented with scanning electron-microscope observations of the crystalline phase, show that seed crystals of hydroxyapatite have the ability to induce the growth of calcium oxalate monohydrate crystals epitaxially from a metastable supersaturated solution of calcium oxalate. The rate of growth of calcium oxalate crystals is dependent on the surface area of the seed ma...

A bulk O2 budget for Lake Hoare, Antarctica, is presented. Five years of seasonal data show the lake to be persistently supersaturated with O2. Oxygen is carried into the lake in glacial meltstreams and is left behind when this water is removed as ice by ablation and sublimation. A diffusive loss of O2 from the lake through the summer moat is suggested. Measured values of the total O2 in the...

A new technique is described to study the condensation of supersaturated vapors on nanoparticles under well-defined conditions of vapor supersaturation, temperature, and carrier gas pressure. The method is applied to the condensation of supersaturated trifluoroethanol (TFE) vapor on Mg nanoparticles. The nanoparticles can be activated to act as condensation nuclei at supersaturations significan...

A population of cool dwarfs with extreme rotational velocities (vsin i ∼ > 100 km/sec) is present in young open clusters. ROSAT observations have shown that these very fast rotators exhibit a level of X-ray activity a factor of 3–5 below the saturated level which is usually observed (both in X-rays and other magnetic activity indicators) for ‘normally’ fast rotators. This phenomenon has been de...

The self-assembly of the protein shell ("capsid") of a virus appears to obey the law of mass action (LMA) despite the fact that viral assembly is a nonequilibrium process. In this paper we examine a model for capsid assembly, the "assembly line model," that can be analyzed analytically. We show that, in this model, efficient viral assembly from a supersaturated solution is characterized by a sh...

A method for the direct assessment of the dissolved CO2 concentration in supersaturated water is presented that is based on changes to the physical chemistry of soda lime due to uptake of CO2. The approach is an adaptation of a standard method used for the quantifi cation of soil respiration, and was found to agree with pCO2 measurements made using infrared gas analysis. In this method, the sod...