Almost everywhere

Here inequalities (2.185), (2.186) are assumed to be satisfied almost everywhere in the Lebesgue sense on F, and in We assume that < 0 on F, so that the set Kg is nonempty. The equilibrium problem for a shallow shell with a solution satisfying the nonpenetration conditions (2.185), (2.186) can be formulated as follows ... 

Note that the function A w + kijaij —U3 is zero almost everywhere in >V r, and so the integral over the domain vanishes. 

The actual properties of this transformation combined with the convergence properties of molecular electron densities implies analyticity almost everywhere on the compact manifold. Consequently, this four-dimensional representation of the molecular electron density satisfies the conditions of a theorem of analytic continuation, that establishes the holographic properties of molecular electron densities represented on the compact manifold S3. 

Can be found in small amounts almost everywhere. Soft element, the lightest solid element. Common in chemistry as a hydride. Organolithi-um compounds are important synthetic building blocks. Lithium became popular as an anode metal for powerful batteries as the lithium ion is small and mobile. These energy dispensers can be very small and provide power for pacemakers, hearing aids, etc. Lithium salts are employed in lubricants and in fireworks (red color). Lithium ions act against depression. 

Water can be found, in all three aggregate states, almost everywhere in the universe as ice in the liquid phase on the satellites of the outer solar system, including Saturn s rings and in the gaseous state in the atmospheres of Venus, Mars and Jupiter and in comets (as can be shown, for example, from the IR spectra of Halley s comet). The OH radical has been known for many years as the photodissociation product of water. 

The elements of Group IV are found almost everywhere. All living things contain compounds of carbon, and most of the earth s sand, soil, and many of its rocks contain compounds of silicon. The five elements of this important group are ... 

Ascorbic acid gives less increase in loaf volume than the same weight of potassium bromate and is more expensive. However, potassium bromate is now banned throughout the EU. Ascorbic acid is now permitted almost everywhere, with some countries such as Australia, Greece, Portugal and Germany not even bothering to limit the maximum level. Ascorbic acid appears to be entirely safe. 

The conditional service density derived from a continuous demand density is continuous almost everywhere but has one exceptional point which carries a discrete probability mass The probability that the whole inventory s goes to service is the integral of the conditional demand density from s to oo. In other words, the service is s if the demand is s or above. 

As mentioned earlier (see Chapter 3), a unique exceedance does not exist when considering both sulfur and nitrogen, but for a given deposition of S and N one can always determine whether there is non-exceedance or not. The two maps on the top of Figure 4 show that the percent of ecosystem area is protected from acidifying deposition of S and N in 1990 and 2010. In 1990 less than 10% of the ecosystem area is protected in large parts of central and western Europe as well as on the Kola peninsula, Russia. Under the scenario of the 1999 multi-pollutant, multi-effect Protocol of UNECE LRTAP Convention (CDR 2010), the situation improves almost everywhere, but is still far from reaching complete protection. 

Based on the above-mentioned results, Ph. australis seems to be the best candidate for practical application. This idea is supported by the fact that it forms prolific biomass necessary for efficient biodegradation and is able to grow almost everywhere. 

Ants are a remarkably snccessfnl gronp of social insects. They are almost everywhere only Iceland, Greenland, Polynesia, and Antarctica lack ants. There are 10,000 known species of these insects. Their engineering and social coordination is amazing, particnlarly given that no one is in charge. Steven Johnson has employed the ants as a model of emergence— properties of a system not possessed by any member of that system. Johnson notes ... 

It can be seen from Fig. 23.3 that the values of the pressure along the length of the combustor are higher almost everywhere in the case of the elliptic nozzles, i.e., enhancement of supersonic combustion took place when kerosene was injected through elliptic nozzles. Figure 23.3 shows that at the aft of the combustor, a flow separation occurred for the case ER = 0 (due to overexpansion of the flow). It is also seen from Fig. 23.3 that after some induction and delay... 

Industrialisation lead to mass production with the characteristic feature of the division of the work process into smaller individual steps and the simplest hand movements, which each worker repeated incessantly. Different parts only fit together if they are made according to a standard. For example the inch is used as the unit for HPLC parts almost everywhere in the world, screws on the European continent have metric sizes and in the US the inch still common. 

Since thorium is found almost everywhere, you will be exposed to small amounts of it in the air you breathe and in the food and water you eat and drink. Scientists know, roughly, the average amounts of thorium in food and drinking water. Most people in the United States eat some thorium with their food every day. Normally, very little of the thorium in lakes, rivers, and oceans gets into the fish or seafood we eat. The amounts in the air are usually so small that they can be ignored. 

Silicon dioxide occurs almost everywhere on earth. It is one of the most important and abundant oxides on earth, constituting about 60% weight of the earth s crust as sdica itself or in combination with other metal oxides in sihcates. It commonly is found as sand in the vast ocean and river shores, their beds, deserts, rocks, and minerals. 

As it can be seen in Figure 2, the energy curves for He-Cu turn out fully repulsive, with the SCF-MI values above the SCF ones. The SCF-CP values are almost everywhere intermediate between the SCF and the SCF-MI results, showing that the CP method does not correct entirely the BSSE. The fact that for this system the SCF-MI potential decreases faster then the SCF and the CP ones at larger distances are consistent with the study of Eichenauer et al. (1987)... 

Remarkably, while the pharmaceutical industry undoubtedly is one of the highest value-added industries in modern economies, that industry is not generally the focus of gratitude or affection. On the contrary, almost everywhere on the globe the industry is viewed with suspicion and often is the butt of vocal criticism and rancor. Relative to its size, it attracts a disproportionate share of attention from public policy makers and critical illumination from the media. 

Infection with Mycobacterium tuberculosis, in short Tuberculosis or TBC, is the commonest cause of death in people with HIV infection world-wide. There are indications of a resurgence of tuberculosis almost everywhere where HIV is prevalent. HIV infection increases a person s susceptibility to and progression of infection with M. tuberculosis. In an individual infected with HIV the presence of other infections including TBC allows HIV to multiply more quickly. This may result in more rapid progression of HIV infection. 

Almost everywhere the topic of radioactivity is taught in the physics or chemistry classes of secondary schools. The question has been raised whether the common approach of teaching this topic would contribute to a better understanding of the risks of ionizing radiation and, if the answer is negative, how to explain and improve this situation How to effectively teach this topic and relate how solvents are involved is important (Eijkelhof, 1996). 

Why is the spatial distribution of charges in the interphase region between two phases of interest and importance There is, of course, the philosophical reason stemming from the search for understanding and for a coherent picture of natural phenomena Surfaces are found almost everywhere in nature, and many of them carry a charge. A substantial part of the understanding of nature is dependent upon a satisfactory model of charged interfaces. 

---