scholarly journals Exponential Codimension Growth of PI Algebras: An Exact Estimate

1999 ◽  
Vol 142 (2) ◽  
pp. 221-243 ◽  
Author(s):  
A Giambruno ◽  
M Zaicev
Keyword(s):  
Exact Estimate

On an Exact Estimate for a Local Theorem

1959 ◽  
Vol 4 (2) ◽  
pp. 215-218 ◽  
Author(s):  
S. Kh. Sirazhdinov
Keyword(s):  
Exact Estimate ◽  
Local Theorem

An exact estimate of the second derivative in Lp

1991 ◽  
Vol 49 (5) ◽  
pp. 443-445
Author(s):  
N. Ainulloev
Keyword(s):  
Exact Estimate ◽  
Second Derivative

scholarly journals Integral operators, bispectrality and growth of Fourier algebras

2020 ◽  
Vol 2020 (766) ◽  
pp. 151-194 ◽  
Author(s):  
W. Riley Casper ◽  
Milen T. Yakimov
Keyword(s):  
Differential Operator ◽  
Integral Kernel ◽  
Exact Estimate ◽  
Airy Functions ◽  
Direct Computation ◽  
Infinite Dimensional ◽  
First Order ◽  
Rank 2 ◽  
Commuting Differential Operator ◽  
Algorithmic Procedure

AbstractIn the mid 1980s it was conjectured that every bispectral meromorphic function {\psi(x,y)} gives rise to an integral operator {K_{\psi}(x,y)} which possesses a commuting differential operator. This has been verified by a direct computation for several families of functions {\psi(x,y)} where the commuting differential operator is of order {\leq 6}. We prove a general version of this conjecture for all self-adjoint bispectral functions of rank 1 and all self-adjoint bispectral Darboux transformations of the rank 2 Bessel and Airy functions. The method is based on a theorem giving an exact estimate of the second- and first-order terms of the growth of the Fourier algebra of each such bispectral function. From it we obtain a sharp upper bound on the order of the commuting differential operator for the integral kernel {K_{\psi}(x,y)} leading to a fast algorithmic procedure for constructing the differential operator; unlike the previous examples its order is arbitrarily high. We prove that the above classes of bispectral functions are parametrized by infinite-dimensional Grassmannians which are the Lagrangian loci of the Wilson adelic Grassmannian and its analogs in rank 2.

scholarly journals The Impact of Variant Allele Frequency in EGFR Mutated NSCLC Patients on Targeted Therapy

2021 ◽  
Vol 11 ◽  
Author(s):  
Alex Friedlaender ◽  
Petros Tsantoulis ◽  
Mathieu Chevallier ◽  
Claudio De Vito ◽  
Alfredo Addeo
Keyword(s):  
Targeted Therapy ◽  
Allele Frequency ◽  
Kinase Inhibitors ◽  
Survival Rates ◽  
Allelic Frequency ◽  
Exact Estimate ◽  
Egfr Mutations ◽  
Tumor Evolution ◽  
Cancer Evolution ◽  
The Impact

EGFR mutations represent the most common currently targetable oncogenic driver in non-small cell lung cancer. There has been tremendous progress in targeting this alteration over the course of the last decade, and third generation tyrosine kinase inhibitors offer previously unseen survival rates among these patients. Nonetheless, a better understanding is still needed, as roughly a third of patients do not respond to targeted therapy and there is an important heterogeneity among responders. Allelic frequency, or the variant EGFR allele frequency, corresponds to the fraction of sequencing reads harboring the mutation. The allelic fraction is influenced by the proportion of tumor cells in the sample, the presence of copy number alterations but also, most importantly, by the proportion of cells within the tumor that carry the mutation. Mutations that occur early in tumor evolution, often called clonal or truncal, have a higher allelic frequency than late, subclonal mutations, and are more often drivers of cancer evolution and attractive therapeutic targets. Most, but not all, EGFR mutations are clonal. Although an exact estimate of clonal proportion is hard to derive computationally, the allelic frequency is readily available to clinicians and could be a useful surrogate. We hypothesized that tumors with low allelic frequency of the EGFR mutation will respond less favorably to targeted treatment.

scholarly journals On the nonsymmetric approximation of continuous functions in the integral metric

2020 ◽  
Vol 27 (2) ◽  
pp. 7
Author(s):  
V.F. Babenko ◽  
O.V. Polyakov
Keyword(s):  
Best Approximation ◽  
Continuous Functions ◽  
Exact Estimate ◽  
Approximation Of Continuous Functions

In the paper, an exact estimate of the best nonsymmetric approximation in the integral metric by the constants of continuous functions that belong to the classes $H^\omega[a,b]$ is proved. Taking into account Babenko's theorem on the connection of nonsymmetric approximation with the usual best approximation in the integral metric and the best one-sided approximations, from the proved result we obtain the exact estimate for the usual best approximation obtained by N.P. Korneichuk, and the exact estimate for the best one-sided approximation obtained by V.G. Doronin and A.A. Ligun.

scholarly journals How Metacognitive Awareness Relates to Overconfidence in Interval Judgments

2018 ◽  
Author(s):  
Darci Klein ◽  
Arielle Cunningham ◽  
Erin Michelle Buchanan
Keyword(s):  
Everyday Life ◽  
Exact Estimate ◽  
Metacognitive Awareness ◽  
General Knowledge ◽  
Lower Range ◽  
Factors Influencing ◽  
Potential Factors ◽  
Metacognitive Awareness Inventory

Making judgments is an important part of everyday life, and overconfidence in these judgments can lead to serious consequences. Two potential factors influencing overconfidence are metacognitive awareness, or the awareness of one’s own learning, and the hard-easy effect, which states that overconfidence is more prevalent in difficult tasks while underconfidence is more prevalent in easy tasks. Overall, we hypothesized that participants’ metacognitive awareness would significantly relate to their overconfidence levels. Specific hypotheses were that those participants who display higher levels of metacognitive awareness will have lower levels of overconfidence, that harder questions will elicit higher levels of overconfidence and easy questions will elicit underconfidence (congruent with the hard-easy effect), and that the lower range and upper range will on average be equal, with the exact estimate as the midpoint. Participants (N = 49) completed a questionnaire containing a set of hard and easy general knowledge questions followed by the Metacognitive Awareness Inventory. The correlation between metacognitive awareness and confidence was negative for hard questions and positive for easy questions. Furthermore, the ranges for easy questions were smaller, resulting in more overconfidence, and the ranges for the hard questions were larger, resulting in underconfidence, thus, showing the opposite of our expected hypotheses.

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