Universal Properties of Infinite Matrices

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.

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On C*-Algebras Associated with Subshifts

International Journal of Mathematics ◽

10.1142/s0129167x97000172 ◽

1997 ◽

Vol 08 (03) ◽

pp. 357-374 ◽

Cited By ~ 37

Author(s):

Kengo Matsumoto

Keyword(s):

Symbolic Dynamics ◽

Markov Shift ◽

C Algebra ◽

C Algebras ◽

Markov Shifts ◽

Universal Properties

We construct and study C*-algebras associated with subshifts in symbolic dynamics as a generalization of Cuntz–Krieger algebras for topological Markov shifts. We prove some universal properties for the C*-algebras and give a criterion for them to be simple and purely infinite. We also present an example of a C*-algebra coming from a subshift which is not conjugate to a Markov shift.

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Fine Spectra of Tridiagonal Symmetric Matrices

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2011/161209 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Muhammed Altun

Keyword(s):

Explicit Form ◽

Resolvent Operator ◽

Sequence Spaces ◽

Symmetric Matrices ◽

Infinite Matrices ◽

Banded Matrices ◽

Lower Triangular ◽

The Resolvent Operator

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .

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Representation of doubly infinite matrices as non-commutative Laurent series

Special Matrices ◽

10.1515/spma-2017-0018 ◽

2017 ◽

Vol 5 (1) ◽

pp. 250-257 ◽

Cited By ~ 2

Author(s):

María Ivonne Arenas-Herrera ◽

Luis Verde-Star

Keyword(s):

Laurent Series ◽

Infinite Matrices ◽

General Properties ◽

Hessenberg Matrices ◽

Diagonal Representation

Abstract We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices. We show that such representation is a simple and useful tool for computation purposes and also to obtain general properties of the matrices related with inversion, similarity, commutativity, and Pincherle derivatives. The diagonal representation allows us to consider the ring of doubly infinite lower Hessenberg matrices over a ring R as a ring of Laurent series in one indeterminate, with coefficients in the ring of R-valued sequences that don’t commute with the indeterminate.

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The argument from souls to God

Religious Studies ◽

10.1017/s0034412515000232 ◽

2015 ◽

Vol 51 (3) ◽

pp. 293-305

Author(s):

RICHARD SWINBURNE

Keyword(s):

Mental Life ◽

Existence Of God ◽

Good Argument ◽

Causal Connections ◽

Universal Properties ◽

Mental Properties ◽

Mental Events ◽

Good And Evil ◽

In Virtue Of ◽

Enormous Number

AbstractHumans are pure mental substances, that is essentially souls, who have a rich mental life of sensations, thoughts, intentions, and other pure mental events, largely caused by and sometimes causing events in their brains and so in their bodies. God has reason to create humans because humans have a kind of goodness, the ability to choose between good and evil, which God himself does not have. The existence of these causal connections between mental events and brain events requires an enormous number of separate psychophysical laws. It is most improbable that there would be such laws if God had not made them. Each soul has a thisness; it is the particular soul it is quite independently of its mental properties and bodily connections. So no scientific law, concerned only with relations between substances in virtue of their universal properties, could explain why God created this soul rather than that possible soul, and connected it to this body. Yet a rational person often has to choose between equally good alternatives on non-rational grounds; and so there is nothing puzzling about God choosing to create this soul rather than that possible soul. Hence the existence of souls provides a good argument for the existence of God.

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Metal nanoparticles with sharp corners: Universal properties of plasmon resonances

EPL (Europhysics Letters) ◽

10.1209/0295-5075/101/57009 ◽

2013 ◽

Vol 101 (5) ◽

pp. 57009 ◽

Cited By ~ 15

Author(s):

B. Sturman ◽

E. Podivilov ◽

M. Gorkunov

Keyword(s):

Metal Nanoparticles ◽

Plasmon Resonances ◽

Universal Properties ◽

Sharp Corners

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Quality of Life in Persons with Intellectual Disabilities and Mental Health Problems: An Explorative Study

The Scientific World JOURNAL ◽

10.1155/2013/491918 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 21

Author(s):

Filip Morisse ◽

Eleonore Vandemaele ◽

Claudia Claes ◽

Lien Claes ◽

Stijn Vandevelde

Keyword(s):

Quality Of Life ◽

Mental Health ◽

Social Inclusion ◽

Mental Health Problems ◽

Health Problems ◽

Positive Outcomes ◽

Support Strategies ◽

Professional Network ◽

Universal Properties

The field of intellectual disability (ID) is strongly influenced by the Quality of Life paradigm (QOL). We aimed at investigating whether or not the QOL paradigm also applies to clients with ID and cooccurring mental health problems. This paper aims at stimulating a debate on this topic, by investigating whether or not QOL domains are universal. Focus groups with natural and professional network members were organized to gather qualitative data, in order to answer two questions: (1) Are the QOL dimensions conceptualized in the model of Schalock et al. applicable for persons with ID and mental health problems? (2) What are indicators relating to the above-mentioned dimensions in relation to persons with ID and mental health problems? The results offer some proof for the assumption that the QOL construct seems to have universal properties. With regard to the second question, the study revealed that the natural and professional network members are challenged to look for the most appropriate support strategies, taking specific indicators of QOL into account. When aspects of empowerment and regulation are used in an integrated manner, the application of the QOL paradigm could lead to positive outcomes concerning self-determination, interdependence, social inclusion, and emotional development.

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