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It is known [M4] that K?-orbits S and G?-orbits S' on a complex flag manifold are in one-to-one correspondence by the condition that S ∩ S' is nonempty and compact.
      
When the characteristic of k is 0, it is known that the invariants of d vectors, d ≥ n, are obtained from those of n vectors by polarization.
      
It is known thatT (A, D) tiles?n by some subset of?n.
      
It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ? of one variable into a function and its cosine transform in a generalized sense.
      
Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces.
      
In practical applications, $\mathcal{D}F$ is known only for a small subset of lines in $\mathbb{R}^3$.
      
These characterizations are based on the joint conditional probability distribution of arrival times given that the number of arrivals occuring up to any fixed time is known.
      
It is known that the problem for general graphs is NP-hard while it is polynomially solvable for trees.
      
It is known that the square of a ω-hyponormal operator is also ω-hyponormal.
      
When the number of change points is known, the rate of convergence of change-points estimation is derived.
      
Little is known about the expression characteristics of the various kinds of possible markers in hepatic stem cells (HSCs) and other HSC-related cells in human fetal liver in various developmental stages.
      
However, little is known about whether it is required for activation of tubular cells induced by albumin overload.
      
At present, little is known about hydrocarbon migration and pressure distribution in deep-water areas.
      
It is known that high-quality, black-shale source rocks occur in the uppermost Ordovician Wufeng Formation and in the lowermost Silurian Longmaxi Formation in South China.
      
For a wide class of systems, as is known, hyper-minimal phase is necessary and sufficient for the strict passivicability of a system.
      
The problem of the minimum committee is known to be NP-hard.
      
Consideration was given to the p-median problem for minimum in the integer formulation which is known to be NP-hard.
      
Classic problems of control law construction for a linear dynamic object that is optimal by the quadratic criterion in the determinate and stochastic cases are reduced, as is known, to solving nonlinear matrix Riccati equations.
      
It is known that the initial stages of urodele limb regeneration depend on the presence of intact nerve fibers connected to their cell bodies.
      
Apoptosis is known as a major achievement of biological evolution aimed at eliminating "genetic waste," transformed or deteriorated cells, and hence at controlling neoplastic processes.
      
 

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