Isomorphic embeddings of l1(Г) into subspaces of C(Ω)

1982 ◽  
Vol 92 (2) ◽  
pp. 251-262 ◽  
Author(s):  
Spiros A. Argyros ◽  
Athanasios Tsarpalias
Keyword(s):  
Banach Spaces ◽  
Independent Family ◽  
Usual Basis ◽  
Analytic Problem

Introduction. The embeddability of l1(Γ), for uncountable sets Γ, into subspaces of Banach spaces of the form C(Ω) was investigated first by Hagler in (6) and subsequently by Haydon in (7), (8) and Argyros and Negrepontis in (1). An important role in the development of the above subject is played by a lemma of Rosenthal (12) that translates the functional analytic problem of finding a family {fξ: ξ Γ} of elements of C(Ω) equivalent to the usual basis of l1(Γ) into the problem of the existence of an independent family {(Aξ, Bξ,): ξ є Γ} of closed subsets.

In Search of Somatic Precursors of Spontaneous Insight

2018 ◽  
Vol 32 (3) ◽  
pp. 97-105 ◽  
Author(s):  
Wangbing Shen ◽  
Yuan Yuan ◽  
Chaoying Tang ◽  
Chunhua Shi ◽  
Chang Liu ◽  
...  
Keyword(s):  
Problem Solving ◽  
Direct Evidence ◽  
Electrodermal Activity ◽  
Cardiovascular Responses ◽  
Solution Time ◽  
Problem Solution ◽  
Insight Problem ◽  
Creative Insight ◽  
Insight Problem Solving ◽  
Analytic Problem

Abstract. A considerable number of behavioral and neuroscientific studies on insight problem solving have revealed behavioral and neural correlates of the dynamic insight process; however, somatic correlates, particularly somatic precursors of creative insight, remain undetermined. To characterize the somatic precursor of spontaneous insight, 22 healthy volunteers were recruited to solve the compound remote associate (CRA) task in which a problem can be solved by either an insight or an analytic strategy. The participants’ peripheral nervous activities, particularly electrodermal and cardiovascular responses, were continuously monitored and separately measured. The results revealed a greater skin conductance magnitude for insight trials than for non-insight trials in the 4-s time span prior to problem solutions and two marginally significant correlations between pre-solution heart rate variability (HRV) and the solution time of insight trials. Our findings provide the first direct evidence that spontaneous insight in problem solving is a somatically peculiar process that is distinct from the stepwise process of analytic problem solving and can be represented by a special somatic precursor, which is a stronger pre-solution electrodermal activity and a correlation between problem solution time and certain HRV indicators such as the root mean square successive difference (RMSSD).

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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