Characterization and Computation of Canonical Tight Windows for Gabor Frames

Let (\gnm)_{n,m ? \Zst}(\gnm)_{n,m\in\Zst} be a Gabor frame for \LtR\LtR for given window gg. We show that the window \ho = \SQI g\ho=\SQI g that generates the canonically associated tight Gabor frame minimizes ||g-h||\|g-h\| among all windows hh generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in each domain the canonical \ho\ho is expressed using functional calculus for Gabor frame operators. Furthermore, we derive a Wiener--Levy type theorem for rationally oversampled Gabor frames. Finally, a Newton-type method for a fast numerical calculation of \ho\ho is presented. We analyze the convergence behavior of this method and demonstrate the efficiency of the proposed algorithm by some numerical examples.     

ON THE ROLES OF COMPLEMENTARY AND ADMISSIBLE BOUNDARY CONSTRAINTS IN FOURIER SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS OF COMPLETELY COUPLED r TH ORDER PDES

A heretofore unavailable double Fourier series based approach, for obtaining non-separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions, has been presented. The method has been successfully implemented to solve a class of hitherto unsolved boundary-value problems, pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform, with arbitrarily prescribed (both symmetric and asymmetric with respect to the panel centerlines) admissible boundary conditions and subjected to general transverse loading.Existing solutions such as those due to Navier or Levy are based on the well-known method of separation of variables. Such solutions represent particular solutions whenever the method of separation of variables work, and when these particular solution functions fortuitously satisfy the boundary conditions. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form sets of measure zero.Various cases of lamination, geometry and dynamic response (forced and free vibrations) of a class of thin anisotropic laminated shells (curved panels) have been shown to follow from the above. Six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions. Navier-type solutions whenever available form special cases of the present general solution.     

Raman spectroscopy of topotecan, an inhibitor of DNA topoisomerase I

Topotecan (TPT), a water-soluble derivative of camptothecin (inhibitor of human DNA topoiomerase I), has found wide application in cancer chemotherapy. The central problem in using topotecan is the presence of lactone rings in its molecules, which undergo hydrolysis at a physiological pH yielding an inactive and even toxic form of the drug. The analysis of Raman spectra of TPT in H₂O and D₂O solutions made it possible to assign the spectral bands to the vibrations of particular molecular groups. Spectral features indicative of the opening of the lactone rings of the TPT molecules, deprotonation of the hydroxyl groups in their quinoline fragments, and of possible participation of the hydroxyl and carbonyl groups in H bonding are found. The data obtained are necessary to study the molecular mechanisms of TPT-DNA interaction and the formation of ternary complexes between TPT, DNA, and DNA topoisomerase I.     

Cosmic dust and our origins

The small solid particles in the space between the stars provide the surfaces for the production of many simple and complex molecules. Processes involving the effects of ultraviolet irradiation of the thin (hundredth micron) mantles are shown to produce a wide range of molecules and ions also seen in comets. Some of the more complex ones inferred from laboratory experiments are expected to play an important role in the origin of life. An outline of the chemical evolution of interstellar dust as observed and as studied in the laboratory is presented. Observations of comets are shown to provide substantial evidence for their being fluffy aggregates of interstellar dust as it was in the protosolar nebula, i.e. the interstellar cloud which collapsed to form the solar system. The theory that comets may have brought the progenitors of life to the earth is summarized.     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.     

Temperature and junction-type dependency of Andreev reflection in MgB2

We studied the voltage and temperature dependency of the dynamic conductance of normal metal-MgB₂ junctions obtained either with the point-contact technique (with Au and Pt tips) or by making Ag-paint spots on the surface of MgB₂ samples. The fit of the conductance curves with the generalized BTK model gives evidence of pure s-wave gap symmetry. The temperature dependency of the gap, measured in Ag-paint junctions (dirty limit), follows the standard BCS curve with 2Δ/k_BT_c=3.3. In out-of-plane, high-pressure point-contacts we obtained almost ideal Andreev reflection characteristics showing a single small s-wave gap Δ=2.6±0.2 meV (clean limit).     

A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.