ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Risk management for scuba diving operators on Australia's Great Barrier Reef

Australia's Great Barrier Reef is one of the world's most popular scuba diving destinations. Unfortunately, a series of recent diving injuries and deaths has tarnished the region's safety record. In particular, media attention surrounding the disappearance of American divers Thomas and Eileen Lonergan has focused attention on dive operators' legal responsibilities and the consequences of failing to discharge their duty of care to customers. This paper briefly examines the relevant Australian law for recreational diving operations, and reviews risk management strategies that may reduce or prevent the occurrence of future problems. (C) 2000 Elsevier Science Ltd. All rights reserved.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Ladder operators for integrable one-dimensional lattice models

A generalised ladder operator is used to construct the conserved operators for any one-dimensional lattice model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.

Cyclic Guanosine Monophosphate Signaling Cascade Mediates Pigment Aggregation in Freshwater Shrimp Chromatophores

The cell signaling cascades that mediate pigment movements in crustacean chromatophores are not yet well established, although Ca(2+) and cyclic nucleotide second messengers are involved. Here, we examine the participation of cyclic guanosine monophosphate (cGMP) in pigment aggregation triggered by red pigment concentrating hormone (RPCH) in the red ovarian chromatophores of freshwater shrimp. In Ca(2+)-containing (5.5 mmol l(-1)) saline, 10 mu mol l(-1) dibutyryl cGMP alone produced complete pigment aggregation with the same time course (approximate to 20 min) and peak velocity (approximate to 17 mu m/min) as 10(-8) mol l(-1) RPCH; however, in Ca(2+)-free saline (9 X 10(-11) mol l(-1) Ca(2+)), db-cGMP was without effect. The soluble guanylyl cyclase (GC-S) activators sodium nitroprusside (SNP, 0.5 mu mol l(-1)) and 3-morpholinosydnonimine (SIN-1, 100 mu mol l(-1)) induced moderate aggregation by themselves (approximate to 35%-40%) but did not affect RPCH-triggered aggregation. The GC-S inhibitors zinc protoporphyrin IX (ZnPP-XI, 30 mu mol l(-1)) and 6-anilino-5,8-quinolinedione (LY83583, 10 mu mol l(-1)) partially inhibited RPCH-triggered aggregation by approximate to 35%. Escherichia coli heat-stable enterotoxin (STa, 1 mu mol l(-1)), a membrane-receptor guanylyl cyclase stimulator, did not induce or affect RPCH-triggered aggregation. We propose that the binding of RPCH to an unknown membrane-receptor type activates a Ca(2+)-dependent signaling cascade coupled via cytosolic guanylyl cyclase and cGMP to protein kinase G-phosphorylated proteins that regulate aggregation-associated, cytoskeletal molecular motor activity. This is a further example of a cGMP signaling cascade mediating the effect of a crustacean X-organ neurosecretory peptide.

On the loss of regularity for a class of weakly hyperbolic operators

In this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators. (C) 2009 Elsevier Inc. All rights reserved.

Prion protein ablation increases cellular aggregation and embolization contributing to mechanisms of metastasis

Cellular Prion Protein (PrP(C)) is a cell surface protein highly expressed in the nervous system, and to a lesser extent in other tissues. PrP(C) binds to the extracellular matrix laminin and vitronectin, to mediate cell adhesion and differentiation. Herein, we investigate how PrP(C) expression modulates the aggressiveness of transformed cells. Mesenchymal embryonic cells (MEC) from wildtype (Prnp(+/+)) and PrP(C)-null (Prnp(0/0)) mice were immortalized and transformed by co-expression of ras and myc. These cells presented similar growth rates and tumor formation in vivo. When injected in the tail vein, PrnP(0/0)raS/myc cells exhibited increased lung colonization compared with Prnp(+/+)ras/myc cells. Additionally, Prnp(0/0)ras/myc cells form more aggregates with blood components than Prnp(+/+)ras/myc cells, facilitating the arrest of Prnp(0/0)ras/myc cells in the lung vasculature. Integrin alpha(v)beta(3) is more expressed and activated in MEC and in transformed Prnp(0/0) cells than in the respective Prnp(+/+) cells. The blocking of integrin alpha(v)beta(3) by RGD peptide reduces lung colonization in transformed Prnp(0/0) cells to similar levels of those presented by transformed Prnp(+/+) cells. Our data indicate that PrP(C) negatively modulates the expression and activation of integrin alpha(v)beta(3) resulting in a more aggressive phenotype. These results indicate that PrP(C) may have main implications in modulating metastasis formation. (C) 2009 UICC

Anisotropic Reversible Aggregation of Latex Nanoparticles Suspended in a Lyotropic Nematic Liquid Crystal: Effect of Gradients of Biaxial Order

We studied the anisotropic aggregation of spherical latex particles dispersed in a lyotropic liquid crystal presenting three nematic phases; calamitic, biaxial, and discotic. We observed that in the nematic calamitic phase aggregates of latex particles are formed, which become larger and anisotropic in the vicinity of the transition to the discotic phase, due to a coalescence process. Such aggregates are weakly anisotropic and up to 50 mu m long and tend to align parallel to the director field. At the transition to the discotic phase, the aggregates dissociated and re-formed when the system was brought back to the calamitic phase. This shows that the aggregation is due to attractive and repulsive forces generated by the particular structure of the nematic phase. The surface-induced positional order was investigated by surface force apparatus experiments with the lyotropic system confined between mica surfaces, revealing the existence of a presmectic wetting layer around the surfaces and oscillating forces of increasing amplitude as the confinement thickness was decreased. We discuss the possible mechanisms responsible for the reversible aggregation of latex particles, and we propose that capillary condensation of the N(C) phase, induced by the confinement between the particles, could reduce or remove the gradient of order parameter, driving the transition of aggregates from solidlike to liquidlike and gaslike.

A tick salivary protein targets cathepsin G and chymase and inhibits host inflammation and platelet aggregation

Platelet aggregation and acute inflammation are key processes in vertebrate defense to a skin injury. Recent studies uncovered the mediation of 2 serine proteases, cathepsin G and chymase, in both mechanisms. Working with a mouse model of acute inflammation, we revealed that an exogenous salivary protein of Ixodes ricinus, the vector of Lyme disease pathogens in Europe, extensively inhibits edema formation and influx of neutrophils in the inflamed tissue. We named this tick salivary gland secreted effector as I ricinus serpin-2 (IRS-2), and we show that it primarily inhibits cathepsin G and chymase, while in higher molar excess, it affects thrombin activity as well. The inhibitory specificity was explained using the crystal structure, determined at a resolution of 1.8 angstrom. Moreover, we disclosed the ability of IRS-2 to inhibit cathepsin G-induced and thrombin-induced platelet aggregation. For the first time, an ectoparasite protein is shown to exhibit such pharmacological effects and target specificity. The stringent specificity and biological activities of IRS-2 combined with the knowledge of its structure can be the basis for the development of future pharmaceutical applications. (Blood. 2011;117(2):736-744)