Stabilized two-dimensional vector solitons

In this Letter, we introduce the concept of stabilized vector solitons as nonlinear waves constructed by the addition of mutually incoherent fractions of Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We analyze the stability of these new kinds of structures and describe their behavior and formation in Manakov-like interactions. Potential applications of our results in Bose-Einstein condensation and nonlinear optics are also discussed.     

A Characterization of Subspaces of Weakly Compactly Generated Banach Spaces

It is proved that a Banach space X is a subspace of a weaklycompactly generated Banach space if and only if, for every >0,X can be covered by a countable collection of bounded closedconvex symmetric sets where the weak^* closure in X^** of eachof them lies within the distance from X. A new short functional-analyticproof of the known result that a continuous image of an Eberleincompact is Eberlein is given as a corollary.     

A note on weakly Lindelöf determined Banach spaces

We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a “full” projectional generator. Some other results pertaining to this class of Banach spaces are given.     

Effectiveness of Photodynamic Therapy in Elimination of HPV‐16 and HPV‐18 Associated with CIN I in Mexican Women

This study aimed to determine the effectiveness of photodynamic therapy (PDT), using δ‐aminolevulinic acid (5‐ALA), in the elimination of premalignant cervical lesions in Mexican patients with human papillomavirus (HPV) infection and/or cervical intraepithelial neoplasia (CIN). Thirty women diagnosed with CIN I and/or positive for HPV participated in the study. Topical 6% 5‐ALA in gel form was applied to the uterine cervix; after 4 h, the lesion area was irradiated with a light dose of 200 J cm^?2 at 635 nm. This procedure was performed three times at 48‐h intervals. Clinical follow‐up was performed at 3, 6, and 12 months after the initial PDT administration, by colposcopy, cervical cytology, histopathological analysis, polymerase chain reaction, and hybrid capture. Of HPV‐infected patients without evidence of CIN I, 80% cleared the infection, while HPV associated with CIN I was eliminated in 83% of patients (P < 0.05). At 12 months, CIN I had regressed in 57% of patients, although this response was not statistically significant. PDT using 6% 5‐ALA is concluded to be effective in eliminating HPV infection associated or not with CIN I.     

Boundedness of biorthogonal systems in Banach spaces

We prove that every Banach space that admits a Markushevich basis also admits a bounded Markushevich basis.     

Dido's problem in the plane for domains with fixed diameter

We find the connected compact domains in the closed half-plane, with fixed area and diameter, which minimize the relative perimeter.This work has been partially supported by the DGICYT (Spain) Grant no. PB 91-0324.