critical 
We show that the structure of a block outside the critical hyperplanes of category O over a symmetrizable KacMoody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules.


We also prove the uniqueness of Verma embeddings outside the critical hyperplanes.


Using the matrix approach we prove that the sequence of sampling functions is always complete in the cases of critical sampling and oversampling.


An important example is the MoserTrudinger inequality where limiting Sobolev behavior for critical exponents provides significant understanding of geometric analysis for conformal deformation on a Riemannian manifold [5, 6].


On Generating Tight Gabor Frames at Critical Density


Finally, we show that microlocally away from a critical set the continuity estimate can be mproved:


Riesz property plays an important role in any waveletbased compression algorithm and is critical for the stability of any waveletbased numerical algorithms.


We establish spectral estimates at a critical energy level for hpseudodifferential operators.


We consider tight Gabor frames (h,a=1,b=1) at critical density with h of the form Z1(Zg/Zg).


At last, we discuss the series expressions of these functions and give a Boxcounting dimension estimation of "critical" fractal interpolation functions by using our smoothness results.


Bootstrap critical point for circular mean direction and its applications


On critical exponents for semilinear heat equations with nonlinear boundary conditions


The coefficient k in the equation is found to be a critical parameter.


there exists a C∞ rank1 map f: I2→R1 such that f(A) has nonempty interior for some subset A ?I2 of critical points with finite Hausdorff dimension.


Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation, the number of limit cycles depends on the different situations of separatrix cycle to be formed around O.


When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator.


The critical micelle concentration (cmc) and surface tension of the novel zwitterionic Gemini surfactant in aqueous solution at 15°C are 7.2×105 mol/L and 34.5 mN/m, respectively.


Then, from the curves, the critical micelle concentration (CMC) and the thermodynamic standard formation functions (ΔH?m, ΔG?m and ΔS?m) were obtained through thermodynamic theories.


Active sites on the surface of ITO are critical to the formation of the crystal nucleus and a uniform and compact CdS nanofilm.


Based on electromagnetic theory, a computing model of the Talbot interferometer is established with the temporal and the spatial coherence taken into account and with the turning angle of the reflectors as a critical parameter.

