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FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS
, 2007
"... The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider a ..."
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) idempotent connected semigroups VB and UB. We show how the structure of SB can be used to extract information relating to arbitrary weakly Babundant semigroups with (C).
On semidirectly closed pseudovarieties of aperiodic semigroups
 J. Pure Appl. Algebra
"... Abstract. This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B2, denoted V¤(B2). We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by B2 which leads to the main result, which states that V¤( ..."
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Abstract. This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B2, denoted V¤(B2). We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by B2 which leads to the main result, which states that V¤(B
The structure of Galois connections
 Pacific J. Math
, 1974
"... This paper deals with Galois connections between two partially ordered sets (posets) A, B. The first sections are devoted to the construction of all Galois connections between A and B. The last sections deal with properties of A ® B9 the set of mappings Γ: A—* B which "participate " in a G ..."
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Galois connection between A and B, with the pointwise partial order. Every Galois connection between two posets A, B can be uniquely extended to a Galois connection between v{A) and v(B \ the completions by cuts of A, B resp., and A ® Bis characterized as a subset of v{A) ® v(B). As an application we
IMA Journal of Mathematical Control & Information <1993) 10, 131148 The LQ controller synthesis problem
, 1993
"... The aim of this paper is to provide a new, direct, stabilizingcontrolleroriented approach to the classical LQ problem with an infinite time horizon. In our approach, the LQ problem is formulated as a parametric optimization problem of a specific type, and then analysed by the methods presented in ..."
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describing the linear feedback £ = ( # , «(<))• The pair (A, b) will be called stabilizable if the set Q = {g e "H: the semigroup generated by A — bg " is exponentially stable} (1.2) is not empty. Consider also the set r = \g 6 tf: (V«b 6 X) bH2L>(o,oo) + II£IL'(OI0O) = J V "
ABSTRACT Title of dissertation: Weakly Compressible NavierStokes Approximation of Gas Dynamics
"... This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coefficients (viscosity and thermal conductivity) are small and ..."
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This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coefficients (viscosity and thermal conductivity) are small and (2) the gas is near an absolute equilibrium — a spatially uniform, stationary state. When we consider regimes in which both the transport scales and Re vanish, we derive the weakly compressible Stokes approximation — a linear system. When we consider regimes in which the transport scales vanish while Re maintains order unity, we derive the weakly compressible NavierStokes approximation—a quadratic system. Each of these weakly compressible approximations govern both the acoustic and the incompressible modes of the gas. In the fluid dynamical setting, our derivations begin with the fully compressible NavierStokes system. We show that the structure of the weakly compressible NavierStokes system ensures that it has global weak solutions, thereby extending the Leray theory for the incompressible NavierStokes system. Indeed, we show that