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In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different ...
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.
Weak bases and weak acids are generally weak electrolytes. In an aqueous solution there will be some CH 3 COOH and some CH 3 COO − and H +. A strong electrolyte is a solute that exists in solution completely or nearly completely as ions. Again, the strength of an electrolyte is defined as the percentage of solute that is ions, rather than ...
Aqueous solutions or molten bases dissociate in ions and conduct electricity. Reactions with indicators: bases turn red litmus paper blue, phenolphthalein pink, keep bromothymol blue in its natural colour of blue, and turn methyl orange-yellow. The pH of a basic solution at standard conditions is greater than seven. Bases are bitter. [5]
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...
The stability of solutions in holds as follows: a locally uniform limit of a sequence of solutions (or subsolutions, or supersolutions) is a solution (or subsolution, or supersolution). More generally, the notions of viscosity sub- and supersolution are also conserved by half-relaxed limits.
A weak base is a base that, upon dissolution in water, does not dissociate completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base.
Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem. Therefore, the solution to the primal is an upper bound to the solution of the dual, and the solution of the dual is a lower bound to the solution of the primal. [1] This fact is called weak duality.