Optimization of a one dimensional hypertelescope for a direct imaging in astronomy

We describe an application of nonlinear optimization in interferometric optical astronomy. The aim is to find the relative positions of the output pupils and the modulus of the beams through each pupil of a linear array of telescopes in order to design an instrument capable of imaging exoplanets. The problem is modelized under the form of a semi-infinite nonlinear minimization problem. The model problem is transformed by a simple discretization into a minimization problem with a finite number of constraints, then it is solved by using a minimization solver. Numerical experiments are reported.     

Quantitative immunofluorescent assay of full-length,recombinant CD4 in solution and mapping of its epitopes

A specific, rapid, and sensitive method for the detection of CD4 in solution was developed using pairs of fluorescently stained monoclonal antibodies which do not cross-compete. The assay is quantitated by flow cytometry using Simply Cellular microbeads (SC beads) as the primary support for the first anti-CD4 mAb. This method uses the standard conditions for anti-CD4 monoclonal antibody binding, washing, detection, and quantitation by flow cytometry of the CD4 antigen either bound to the SC beads or expressed on the cell surface. The monoclonal antibody used (Leu 3a PE) is the standard reference used to evaluate the CD4 concentration. This method differs from ELISA techniques, which need an antigen standard curve and thus can be influenced by the quality and source of the antigen. This type of assay is also a procedure which enables determination of the level of oligomerization of the bound antigen. It can be used for any antigen to which monoclonal antibodies recognizing at least two distinct epitopes are available. The use of soluble or full-length CD4 derivatives as potential therapeutic agents against AIDS, would benefit from a precise quantitation of the CD4 molecules which still have their proper tertiary structure.     

Synthesis and biological evaluation of a novel 99mTc‐cyclopentadienyltricarbonyl technetium complex as a new potential brain perfusion imaging agent

A new cytectrene prototype of general formula RCpTc(CO)₃ (R = C₆H₅NHCO, Cp = cyclopentadienyl moiety) has been synthesized from N‐phenylferrocenecarboxamide 2 , characterized and evaluated as a potential brain perfusion imaging agent. An improved procedure has been developed to obtain both the ligand 2 , characterized by its solid‐state structure (orthorhombic, Pccn, a = 10.4443(2) Å, b = 26.1467(6) Å, c = 9.9977(3) Å), and the corresponding metallic Tc‐ and Re‐complexes in good yield. These latter complexes possessed similar HPLC retention times, thereby indicating identity of their molecular structures. The Tc‐complex ^99m Tc‐2 is lipophilic enough to cross the blood‐brain barrier. This complex exhibits good brain uptake (1.41% injected dose per gram tissue at 5 min) combined with a fairly good retention of radioactivity in brain (0.48% injected dose per gram tissue after 1 h). Then, the distribution of the activity at 5 min post‐injection in various rat brain regions showed a higher accumulation in the hippocampus area. The new ^99mTc‐cyclopentadienyltricarbonyl technetium complex reported here showed promising biological results, making it an interesting base for the development of a new generation of cytectrene as brain perfusion imaging agent. Copyright © 2011 John Wiley & Sons, Ltd.     

Chebyshev approximation of the null function by an affine combination of complex exponential functions

We describe the theoretical solution of an approximation problem that uses a finite weighted sum of complex exponential functions. The problem arises in an optimization model for the design of a telescope array occurring within optical interferometry for direct imaging in astronomy. The problem is to find the optimal weights and the optimal positions of a regularly spaced array of aligned telescopes, so that the resulting interference function approximates the zero function on a given interval. The solution is given by means of Chebyshev polynomials.     

Contractibility of the Efficient Set in Strictly Quasiconcave Vector Maximization

In this paper, we investigate the contractibility of the efficient frontier in a vector maximization problem defined by a continuous vector-valued strictly quasiconcave function and a convex compact set D in ^p . It is shown that the efficient frontier is contractible if one of the components of g is strongly quasiconcave on X. This work extends a result by Sun (see Ref. 1), which confirms the connectedness of the efficient frontier.     

Equidistribution of Rational Matrices in their Conjugacy Classes

Let G be a connected simply connected almost -simple algebraic group with non-compact and a cocompact congruence subgroup. For any homogeneous manifold of finite volume, and a , we show that the Hecke orbit T _a (x ₀ H) is equidistributed on as , provided H is a non-compact commutative reductive subgroup of G. As a corollary, we generalize the equidistribution result of Hecke points ([COU], [EO1]) to homogeneous spaces G/H. As a concrete application, we describe the equidistribution result in the rational matrices with a given characteristic polynomial. The second author partially supported by DMS 0333397. Received: May 2005 Revision: March 2006 Accepted: June 2006     

Spectroscopic and electrochemical studies of new copper(II) and nickel(II) N2S2 tetradentate complexes of potential interest to nuclear medicine

The coupling of radionuclides such as copper (67Cu and 64Cu) to antibodies by bifunctional chelating agents (or BCA) requires extremely high stability to avoid in vivo release of metal. Six copper(II) and five nickel(II) complexes with N2S2 tetradentate ligands were synthesised for potential medical applications, and stability studies were conducted. I.r and u.v.-vis. spectra provided structural data on the geometry of the complexes. The redox potentials obtained from cyclic voltammetry allowed us to estimate the stability constants of each complex and then select the more suitable ligand for future applications in radioimmunotherapy.     

New Synthetic Analogs of Retinoids: Synthesis of Aromatic Analogs of 9‐Methylidene‐ and 13‐Demethyl‐9‐methylidene‐retinol, ‐retinal,and Ethyl 13‐Demethyl‐9‐methylideneretinoate

Aromatic analogs of 9‐methylidene and 13‐demethyl‐9‐methylideneretinol, ‐retinal, and ethyl 13‐demethyl‐9‐methylideneretinoate were synthesized via a new β‐methylidene‐aldehyde synthon.