For arbitrary fixed consider the restriction of functions and on the interval and let Then for.
Restriction of functions from a reductive p-adic group G to its compact subgroups defines an operator on the Hochschild and cyclic homology of the Hecke algebra of G.
(1.2) We will look for solutions for problem (1.1) inside the set X = { u ∈ C ( I ˜ ) : u ∈ C 2 ( I − ∘ ∪ I + ∘ ) and L [ u ] ∈ W 2, 1 ( I ) }. (Notice that there is an abuse of notation here, in order to simplify our notation. Of course, the regularity conditions in each subinterval of Ĩ are understood to be referred to the correspondent restrictions of function u).
The Sobolev space (mathbf{H}^{mathbf{s}}(mathbf{0},mathbf{T})) represents the set of restrictions of functions from (mathbf{H}^{mathbf{s}}(mathbb{R})) to ([mathbf{0},mathbf{T}]). Let (phiinmathbf{H}^{mathbf{1}/mathbf{4}}(mathbf{0},mathbf{T})) and (psiinmathbf{H}^{mathbf{3}/mathbf{4}}(mathbf{0},mathbf{T})) with (psi(0)=0) be two functions extended by zero beyond T, that is, for all (s>T) and (s<0).
Their median (observed minimum to maximum range) AUSCAN scores for pain, stiffness and function were 8 (0-20), 1 (0-4), and 10 (0-36) respectively, suggesting moderate restriction of hand function.
To see the problem, let L be the function from each sentence of English to its intuitive truth condition, and let L* be the restriction of that function to sentences that aren't very long.
Now denote by (u_{1} (t)) the restriction of the function (upsilon (t )) to (mathbb{R}_ ).
Put (2.2). with,, and let be the restriction of a function to.
These may lead to a decline in intra-thorax pressure and restriction of diaphragm function.
