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The first one is a conjecture of Ian Hughes which states that iff1, ..., fn are primary invariants of a finite linear groupG, then the least common multiple of the degrees of thefi is a multiple of the exponent ofG.
      
This paper studies intersection theory on the compactified moduli space ${\mbox{$\cal M$}} (n,d)$ of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface $\Sigma$ of genus $g \geq 2$ where n and d may have common factors.
      
For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory.
      
For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory.
      
More generally, these results apply both to Gabor frames and to systems of Gabor molecules, whose elements share only a common envelope of concentration in the time-frequency plane.
      
The model with three common biophoric sites such as center of triazole ring for A, center of phenyl ring for B, and charge heteroatom for C.
      
The CoMFA model developed using most common structure based alignment and tripos standard field demonstrated high predictive ability (q2 = 0.573, r2 = 0.711).
      
The 3D QSAR studies using Apex 3D expert system led to the identification of the pharmacophore in terms of common biophoric sites and secondary sites for interacting with PPARγ receptors.
      
Pancreatic cancer is not only common, but also extremely difficult to treat, for which it has been called "the challenge of the twenty-first century".
      
The fact that the pKi values for both butyrylcholinesterase and acetylcholinesterase inhibitions are linearly correlated with each other suggests that both enzyme inhibitions proceed via a common mechanism.
      
Ameltolide shares with phenytoin and carbamazepine a common mode of action involving interaction with central voltage-dependent sodium channels.
      
Evaluation of the efficacy of 99mTc-labeled ascorbic acid on common cold-cough drugs in rats
      
Multiple-drug therapy is common in current clinical practice.
      
The present data show that vitamin C might be more effective for the treatment of common cold when coadministered with PPA compared to with CPR, with APAP, or alone.
      
LetYi=M(Xi)+ei, whereM(x)=E(Y|X=0) is an unknown real function onB(? R), {(Xi, Yi)} is a stationary andm(n)-dependent sample from (X, Y), the residuals {ei} are independent of {Xi} and have unknown common densityf(x).
      
As application, the results are used to study the existence and uniqueness problems of common solutions for a class of systems of nonlinear integral equations.
      
In this paper, the geometrical meaning of two basic optimality conditions for a class of common cases in nonsmooth programming is exposed.
      
Approximate common divisors of polynomials and degree reduction for rational curves
      
This paper deals with how to perturb a given set of polynomials so as to include a common linear factor.
      
The results showed that the catalyst had higher catalytic performance than common hydrogenation catalysts.
      
 

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