We prove that a semialgebraically connected affine Nash group over a real closed field R is Nash isogenous to the semialgebraically connected component of the group H(R) of R-points of some algebraic group H defined over R. In the case when R = R this result was claimed in [5], but a mistake in the proof was recently found, and the new proof we obtained has the advantage of being valid over an ...

R. Devi, A. Selvakumar and M. Parimala, αψ-closed sets in Topological spaces (Submitted). Y. Kucuk, On some characterizations of δ-continuous multifunctions, Demonstratio Math., Vol 28(3)(1995), 587-595. P. E. Long and L. L. Herrington, The τθ topology and faintly continuous functions, Kyungpook Math. J., 22(1982), 7-14. T. Noiri and V. Popa, Almost weakly continuous multifunctions, Demon-strat...

In the present paper we obtain a closed form expression for the squared H⊥ 2 norm of a partial fraction expansion with repeated unstable poles. We also obtain a closed form expression for the squared H2 norm of a partial fraction expansion with repeated stable poles. As an application we use the H⊥ 2 result to extend the closed form solution of the discretetime linear time invariant (LTI) signa...

The degree Ramsey number of a graph G, denoted R∆(G; s), is min{∆(H) : H s → G}, where H s → G means that every s-edge-coloring of H contains a monochromatic copy of G. The closed k-blowup of a graph is obtained by replacing every vertex with a clique of size k and every edge with a complete bipartite graph where both partite sets have size k. We prove that there is a function f such that R∆(G;...

It is truly a priviledge and an honour to be invited to present this inaugural Garrett Lecture, It was also a priviledge and an honour the first time I met Professor S, D, (Denis) Garrett, which was in October 1963, when I was a graduate student at the University of California, Berkeley, under the late W, C, Snyder, Professor Garrett was the invited keynote speaker (Garrett, 1965) at the First ...

In this article the frame-theoretic account of what is archimedean for order-algebraists, and semisimple for people who study commutative rings, deepens with the introduction of J -frames: compact normal frames that are join-generated by their saturated elements. Yosida frames are examples of these. In the category of J -frames with suitable skeletal morphisms, the strongly projectable frames a...

The paper considers algebraic directed-complete partial orders with a semi-regular Scott topology, called regular domains. As is well known, the category of Scott domains and continuous maps is Cartesian closed. This is no longer true, if the domains are required to be regular. Two Cartesian closed subcategories of the regular Scott domains are exhibited: regular dI-domains with stable maps and...

The rst mathematical model of the untyped lambda calculus was discovered by DANA SCOTT in the category of algebraic lattices and Scott continuous maps. The question then arises as to which other cartesian closed categories contain a model of the calculus. In this paper we show that any compact Hausdor model of the calculus must satisfy the property that the semantic map from the calculus to the...

A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly discontinuously on G/H, such that the quotient space Γ\G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work ...

The polar moment of inertia of a closed orbit curve of a point under one-parameter closed planar motions was studied by H. R. Müller, [1]. We study the polar moment of inertia of the enveloping curve of a line under one-parameter closed homothetic motions of planar kinematics. AMS Mathematics Subject Classification (2000): 53A17, 53A04