Math. Meth. Appl. Sci.
 1997
DOI: 10.1002/(sici)1099-1476(19970710)20:10<855::aid-mma887>3.0.co;2-5
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On the Finiteness of the Number of Determining Elements for von Karman Evolution Equations

Igor Čhuešhov
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Cited by 17 publications

(10 citation statements)
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“…For characterization of a set of determining functionals it is convenient to use the following concept of completeness defect which has been suggested in CHUESHOV [37,38] in the case of pairs of embedded Banach spaces. To consider a certain class of quasi-stable systems (see Section 3.4 below), we introduce this notion in the case of a single space equipped with an additional seminorm.…”
Section: Main Conceptsmentioning
confidence: 99%
“…is said to be the completeness defect of a set L of linear functionals on V with respect to X (see CHUESHOV [37,38]). …”
Section: Definition 333mentioning
confidence: 99%
See 1 more Smart Citation
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…For characterization of a set of determining functionals it is convenient to use the following concept of completeness defect which has been suggested in CHUESHOV [37,38] in the case of pairs of embedded Banach spaces. To consider a certain class of quasi-stable systems (see Section 3.4 below), we introduce this notion in the case of a single space equipped with an additional seminorm.…”
Section: Main Conceptsmentioning
confidence: 99%
“…is said to be the completeness defect of a set L of linear functionals on V with respect to X (see CHUESHOV [37,38]). …”
Section: Definition 333mentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…To characterize a set of asymptotically determining functionals, it is convenient to use the notion of the completeness defect suggested in [15,16] for the case of two embedded Banach spaces. See also [27] for the case of one space endowed with additional seminorm.…”
Section: Global Attractorsmentioning
confidence: 99%
“…is said to be a completeness defect of the set of linear functionals L on V with respect to X [15,16]).…”
Section: Global Attractorsmentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…We can also prove the Lipschitz property in H provided one of two solutions belongs to W 2 . Proposition 1.4 Let U 1 (t) and U 2 (t) be two strong solutions to (1)- (5).…”
Section: Proposition 12 Let the Hypotheses Of Proposition 11 Be In Fo...mentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
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