ALBERT

Notes: Abstract This paper studies algebras of functions on the unit disk generated byH ∞(D) and bounded harmonic functions. Using these algebras, we characterize compact semicommutators and commutators of Toeplitz operators with harmonic symbols on the Bergman space.

Notes: Abstract This paper is devoted to the question to obtain (algebraic and topologic) equivalence (after extension) relations between convolution type operators on unions of intervals and convolution type operators on the half-line. These operators are supposed to act between Bessel potential spaces,H s,p , which are the appropriate spaces in several applications. The present approach is based upon special properties of convenient projectors, decompositions and extension operators and the construction of certain homeomorphisms between the kernels of the projectors. The main advantage of the method is that it provides explicit operator matrix identities between the mentioned operators where the relations are constructed only by bounded invertible operators. So they are stronger than the (algebraic) Kuijper-Spitkovsky relation and the Bastos-dos Santos-Duduchava relation with respect to the transfer of properties on the prize that the relations depend on the orders of the spaces and hold only for non-critical orders:S − 1/p ∉ ℤ. For instance, (generalized) inverses of the operators are explicitly represented in terms of operator matrix factorization. Some applications are presented.

Notes: Abstract In this paper, we prove that the Hardy spaceH p (Ω), 1≤p〈∞, over a strictly pseudoconvex domain in ℂ n with smooth boundary is quasi-coherent. More precisely, we show that Toeplitz tuplesT φ with suitable symbols φ onH p (Ω) have property (βɛ). This proof is based on a well known exactness result for the tangential Cauchy-Riemann complex.

Notes: Abstract Conditions for the invertibility and explicit formulas for the inverse of the convolution operator on a finite interval are obtained making use of solutions of corona problems. Using these results, a family of classes of functions is defined for which the study of invertibility can be carried through. An example of one class of this family is presented and a smaller class, for which the calculations are simpler, is more thoroughly studied.

Notes: Abstract This paper is concerned with the applicability of maximum defect polynomial (Galerkin) spline approximation methods with graded meshes to Wiener-Hopf operators with matrix-valued piecewise continuous generating function defined on R. For this, an algebra of sequences is introduced, which contains the approximating sequences we are interested in. There is a direct relationship between the stability of the approximation method for a given operator and invertibility of the corresponding sequence in this algebra. Exploring this relationship, the methods of essentialization, localization and identification of the local algebras are used in order to derive stability criteria for the approximation sequences.

Notes: Abstract We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreîn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions areJ-self-adjoint.

Notes: Abstract Two classes of 2×2 matrix symbols involving oscillatory functions are considered, one of which consists of triangular matrices. An equivalence theorem is obtained, concerning the solution of Riemann-Hilbert problems associated with each of them. Conditions for existence of canonical generalized factorization are established, as well as boundedness conditions for the factors. Explicit formulas are derived for the factors, showing in particular that only one of the columns needs to be calculated. The results are applied to solving a corona problem.

Notes: Abstract In this note, we prove a harmonic-type maximal principle for the Schur parametrization of all contractive interpolants in the three chains completion problem (see [4]), which is analogous to the maximal principle proven in [2] in case of the Schur parametrization of all contractive intertwining liftings in the commutant lifting theorem.

Notes: Abstract It is known [KRS] that for each finitely generated Banach algebra $$\mathcal{A}$$ there exists a numberN such that for eachn〉N the matrix algebras $$M_n (\mathcal{A})$$ can be generated by three idempotents. In this paper we show that the same statement is true for direct sums $$\tilde {\cal A} = M_{n_1 } ({\cal A}) \oplus M_{n_2 } ({\cal A}) \oplus \ldots \oplus M_{n_p } ({\cal A})$$ and $$\tilde {\cal B} = M_{n_1 } ({\cal B}) \oplus M_{n_2 } ({\cal B}) \oplus \ldots \oplus M_{n_p } ({\cal B}) (n_j 〉 1)$$ , where $$\mathcal{B}$$ is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for algebras $$M_n (\mathcal{A})$$ because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra $${\tilde {\cal A}}$$ can be generated by two idempotents if and only ifn j =2 for eachj and $$\mathcal{A}$$ is singly generated. Also we give an example of a free singly generated algebra $$\mathcal{B}$$ for which $$M_2 (\mathcal{B})$$ can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde {\cal B}}\] can be generated by three idempotents for each singly generated free algebra $$\mathcal{B}$$ .

Notes: Abstract We completely classify all Toeplitz and Hankel operators which commute; namely, we prove that that a non-trivial Hankel operator and a non-trivial Toeplitz operator commute if and only if the Hankel operator has symbolzψ, where ψ is the symbol of the Toeplitz operator, and ψ is an affine function of the characteristic function of certain “anti-symmetric” sets of the unit circle.

Notes: Abstract In this note we give two other proofs of an identity of A. Borodin and A. Okounkov which expresses a Toeplitz determinant in terms of the Fredholm determinant of a product of two Hankel operators. The second of these proofs yields a generalization of the identity to the case of block Toeplitz determinants.

Notes: Abstract LetA be aC * — algebra for which all irrèducible representations are of dimensional n. Then ([F], [TT], [V]) algebraA is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle ε A . The basisX of this bundle coincides with the compact of all maximal two-sided ideals ofA. We obtain some conditions which provide that ε A is trivial and this yields thatA is isomorphic to the algebra of alln×n matrix functions continuous onX. In the case whenX=S n is a sphere we describe the set of algebraic bundles overX and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested.

Notes: Abstract In this paper we describe some classes of linear operatorsT∈L(H) (mainly Toeplitz, Wiener-Hopf and singular integral) on a Hilbert spacesH such that the spectrum σ(T, L(H)) is continuous at the pointsT from these classes. We also describe some subalgebras $$\mathcal{A}$$ of the algebras for which the spectrum σ(x, ) becomes continuous at the pointsx when σ(x, ) is restricted to the subalgebra $$\mathcal{A}$$ . In particular, we show that the spectrum σ(x, ) is continuous in Banach algebras with polynomial identities. Examples of such algebras are given.

Notes: Abstract In this paper we completely characterize compact products of three Hankel operators on the Hardy space. We obtain a necessary and sufficient condition for that $$H_{f_1 }^* H_{f_2 } H_{f_3 }^* ,H_{f_2 }^* H_{f_1 } H_{f_3 }^* $$ , and $$H_{f_1 }^* H_{f_3 } H_{f_2 }^* $$ are simultaneously compact.

Notes: Abstract A bi-infinite sequence ...,t −2,t −1,t 0,t 1,t 2,... of nonnegativep×p matrices defines a sequence of block Toeplitz matricesT n =(t ik ),n=1,2,...,, wheret ik =t k−i ,i,k=1,...,n. Under certain irreducibility assumptions, we show that the limit of the spectral radius ofT n , asn tends to infinity, is given by inf{σ(ξ)∶ξ∈[0,∞]}, where σ(ξ) is the spectral radius of Σ j∈z t j ξ j .

Notes: Abstract The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2) 〉 0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV=A+B exp(−x/C)]. The COV of the stress was higher for low volume fraction tissue (〈0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading. © 2000 Biomedical Engineering Society. PAC00: 8719Rr

Notes: Abstract It is indicated that up to the year 2030, the annual average temperatures in China will increase by 0.88 to 1.2°C, with increments in the south less than in the north. Annual average precipitation would raise slightly, but the increment could be 4% in northeastern China. The increment of annual mean runoff could rise over 6% in the northeastern area, and decrease in the other regions 1.4 to 10.5%. The increased water shortage due to climate change could achieve 160 to 5090 million m3 in some areas of China. Financial loss due to the lack of water could reach 1300 million yuan, and up to 4400 million yuan in serious drought years in the Beijing-Tianjin-Tangshan area.

Notes: Abstract The migration of vinyl chloride monomer (VCM) from unplasticizedpolyvinyl chloride (uPVC) pipes was investigated using locallymanufactured pipes. Specimens of 33 cm long were used throughoutthe research. The investigation was carried out under differentconditions of water temperature, pH and total dissolved solidsconcentration and at different durations of exposure. The VCMconcentration in the water was evaluated using the gaschromotography (GC)/head-space technique. A VCM concentration ofmore than 2.5 ppb was detected after 30 days of exposure at45 °C. The initial VCM concentration in the uPVC pipewas predicted using equations derived from Fick's first law ofdiffusion. Water tenperature did not affect the migration ofVCM, unless it was raised to high values (i.e. 45 °C).Total dissolved solids (TDS) and pH of water were found toaffect the release of VCM from uPVC pipes. Diffusion rate of VCMwas predicted as a function of pH or TDS values.

Notes: Abstract Long-term charcoal production in small private charcoal kilns (CK) in Eastern Bieszczady Mts. (SE Poland) can cause local smoke contamination of the ambient forest environment. Responses of model soil systems, contaminated or not contaminated by CK smoke, to contrasting combinations of hydrothermic regimes were compared in laboratory microcosms (respiration of soil community, decomposition rate of soil organic matter and cotton stripes, herb seeds germination were studied). The majority of the obtained data show a markedly higher level of soil biological activity in the CK versus the control series. In some cases CK and control soil systems show different patterns of reactions to the tested combinations of microclimate regime. These phenomena should at least partly be attributed to the effects of CK pollution.

Notes: Abstract Adaptation in response to anthropogenic climate change seeks to maintain viability by maximising benefits and minimising losses. It is necessary because some climatic change is now inevitable, despite the international focus on mitigation measures. Indeed, the measures agreed at Kyoto would by themselves result in only a small reduction in the climate changes to be expected over the next century. Discussion of the expected changes and possible impacts leads to the following conclusions regarding climate change scenarios in relation to impacts and adaptation: • Climate change in the foreseeable future will not be some new stable "equilibrium" climate, but rather an ongoing "transient" process; • Climate change predictions relevant to impacts on most sectors and ecosystems are still highly uncertain; • There is a need for a greater focus on developing countries and tropical regions, and on relevant key variables, including the magnitude and frequency of extreme events; • The focus should shift from single predictions, or extreme ranges of uncertainty, to risk assessment; • Thresholds critical to impacted sectors and ecosystems should be identified, and expressed as functions of climatic variables; • Planned adaptations will be necessary to cope with multiple stresses, including those due to non-climatic changes; • A major task of adaptation science is to identify the limits of adaptation, i.e., to identify "dangerous levels of greenhouse gases" beyond which adaptation becomes impractical or prohibitively expensive.

Notes: Abstract If current trends continue, human activities will drastically alter most of the planet's remaining natural ecosystems and their composite biota within a few decades. Compounding the impacts on biodiversity from deleterious management practices is climate variability and change. The Intergovernmental Panel on Climate Change (IPCC) recently concluded that there is ample evidence to suggest climate change is likely to result in significant impacts on biological diversity. These impacts are likely to be exacerbated by the secondary effects of climate change such as changes in the occurrence of wildfire, insect outbreaks and similar disturbances. Current changes in climate are very different from those of the past due to their rate and magnitude, the direct effects of increased atmospheric CO2 concentrations and because highly modified landscapes and an array of threatening processes limit the ability of terrestrial ecosystems and species to respond to changed conditions. One of the primary human adaptation option for conserving biodiversity is considered to be changes in management. The complex and overarching nature of climate change issues emphasises the need for greatly enhanced cooperation between scientists, policy makers, industry and the community to better understand key interactions and identify options for adaptation. A key challenge is to identify opportunities that facilitate sustainable development by making use of existing technologies and developing policies that enhance the resilience of climate-sensitive sectors. Measures to enhance the resilience of biodiversity must be considered in all of these activities if many ecosystem services essential to humanity are to be sustained. New institutional arrangements appear necessary at the regional and national level to ensure that policy initiatives and research directed at assessing and mitigating the vulnerability of biodiversity to climate change are complementary and undertaken strategically and cost-effectively. Policy implementation at the national level to meet responsibilities arising from the UNFCCC (e.g., the Kyoto Protocol) and the UN Convention on Biological Diversity require greater coordination and integration between economic sectors, since many primary drivers of biodiversity loss and vulnerability are influenced at this level. A case study from the Australian continent is used to illustrate several key issues and discuss a basis for reform, including recommendations for facilitating adaptation to climate variability and change.

Notes: Abstract Global climate change is likely to have a range of consequences for human health as a result of disturbance or weakening of the biosphere's natural or human-managed life support systems. The full range of potential human health impacts of global climate change is diverse and would be distributed differentially spatially and over time. Changes in the mortality toll of heatwaves and changes in the distribution of vector-borne infectious diseases may occur early. The public health consequences of sea level rise and of regional changes in agricultural productivity may not occur (or become apparent) for several decades. Vulnerability is a measure of both sensitivity to climate change and the ability to adapt in anticipation of, or in response to, its impacts. The basic modes of adaptation to climate-induced health hazards are biological, behavioural and social. Adaptation can be undertaken at the individual, community and whole-population levels. Adaptive strategies should not introduce new health hazards. Enhancement of the acknowledged public health infrastructure and intervention programmes is essential to reduce vulnerability to the health impacts of climate change. In the longer-term, fundamental improvements in the social and material conditions of life and in the reduction of inequalities within and between populations are required for sustained reduction in vulnerability to environmental health hazards.

Notes: Abstract A mechanism has been established to improve integration of international climate-related programmes. Known as the Climate Agenda it outlines a programme, that in a cost-effective way, responds to national obligations to respond to international agreements as well as their national needs for social and economic development. The paper briefly describes the Climate Agenda and the incorporation within it of studies of climate impact assessments and response strategies to reduce vulnerability. The need for increased emphasis on climate impact assessment and for the development of effective adaptation measures is emphasised following the elaboration of a Kyoto Protocol to the United Nations Framework Convention on Climate Change (UNFCCC). UNEP's efforts to identify national programmes contributing to the Climate Agenda are described. The response from developing countries has, however, been very disappointing, even from countries where we know work is ongoing through funding by GEF or US Country Studies Program and other bilateral programmes. Initial compilation of information available so far shows that many developed countries are putting a lot into the area of impact assessment of not just climate change, but also climate variability. There remain some research gaps, especially in the area of assessment of climate impacts on ecosystems, hydrological systems, etc. Considerable efforts are presently being directed at reduction of emissions of greenhouse gases and in the case of developing countries, most efforts are being directed towards completing national communications and providing baseline data for future studies. The paper refers to early activities by UNEP in cooperation with other international organizations to undertake integrated assessments of the impacts of climate change on important socio-economic sectors and the later incorporation of lessons learned into the IPCC Guidelines for Assessing Impacts of Climate Change. Later sections outline the development of a handbook on methods for climate change impact assessment and adaptation strategies as a practical approach to national assessments and the development of appropriate and cost-effective response to climate change. The initiation of a GEF-funded project to apply the methods contained in the handbook and improve the results based on national studies is also described for both developed and developing countries. Working in collaboration with a team of international experts under the coordination of the Institute of Environmental Studies at Vrije University (Amsterdam), the goal of this ongoing project is to develop a valuable methodological tool that Parties to the UNFCCC may apply to develop national climate change impact and adaptation assessments. Development of these guidelines was linked to a series of country studies in Antigua and Barbuda, Estonia, Cameroon and Pakistan funded under a UNEP/GEF project. The application of the first version of the UNEP Handbook by national study teams in these four countries is making valuable technical and practical contributions and will ensure that the next version of the Handbook will be a more useful tool for experts in developing countries undertaking similar studies in the future. The methods contained in the Handbook are also the basis for similar assessments funded under bilateral development programmes in other countries. These and similar studies elsewhere are coordinated with the UNEP programme and will eventually aim to create reliable and comparable assessments, a compatible set of tools for such purpose and the identification of realistic adaptation options for incorporation into national planning for adapting to climate change. The paper also addresses how climate impact assessment and response strategies are undertaken as part of national enabling activities carried out in co-operation with UNEP.

Notes: Abstract Many developing countries, especially in Africa, contribute only very small amounts to the world total of greenhouse gas emissions. For them, the reduction of such emissions is not a priority, and the more important issue is to find ways to reduce their vulnerability to the projected climate change which is being imposed upon them largely as a result of emissions from developed countries. This priority does not accord with the ultimate objective of the United Nations Framework Convention on Climate Change, which is to achieve stabilization of greenhouse gas emissions. This paper reports upon studies in Uganda designed to help in the development of a national adaptation strategy, and addresses the need to reconcile such a strategy with the global priority accorded to mitigation and with national economic development priorities. Some features of a national climate change adaptation strategy are identified and questions are raised about the need for an international regime to facilitate and support adaptation.

Notes: Abstract Climate change impacts on African human settlements arise from a number of climate change-related causes, notably sea level changes, impacts on water resources, extreme weather events, food security, increased health risks from vector home diseases, and temperature-related morbidity in urban environments. Some coastlines and river deltas of Africa have densely populated low-lying areas, which would be affected by a rise in sea level. Other coastal settlements will be subjected to increased coastal erosion. Recent flooding in East Africa highlighted the vulnerability of flood plain settlements and the need to develop adaptive strategies for extreme weather events management and mitigation. In the semi arid and arid zones many settlements are associated with inland drainage water sources. Increases in drought will enhance water supply related vulnerabilities. Inter-basin and international water transfers raise the need for adequate legal frameworks that ensure equity among participating nations. Similarly, water supply and irrigation reservoirs in seasonal river catchments might fail, leading to poor sanitation in urban areas as well as food shortage. Hydroelectric power generation could be restricted in drought periods, and where it is a major contributor to the energy budget, reduced power generation could lead to a multiplicity of other impacts. States are advised to develop other sources of renewable energy. Temperature changes will lead to altered distribution of disease vectors such as mosquitoes, making settlements currently free of vector borne diseases vulnerable. Rapid breeding of the housefly could create a menace associated with enteric disorders, especially in conditions of poor sanitation. The dry savannahs of Africa are projected as possible future food deficit areas. Recurrent crop failures would lead to transmigration into urban areas. Pastoralists are likely to undertake more trans-boundary migrations and probably come into conflict with settled communities. Adaptive measures will involve methods of coastal defences (where applicable), a critical review of the energy sector, both regionally and nationally, a rigorous adherence to city hygiene procedures, an informed agricultural industry that is capable of adapting to changing climate in terms of cropping strategies, and innovations in environment design to maximise human comfort at minimum energy expenditure. In the savannah and arid areas water resource management systems will be needed to optimise water resource use and interstate co-operation where such resources are shared. Climate change issues discussed here raise the need for state support for more research and education in impacts of climate change on human settlements in Africa.

Notes: Abstract The sodium arsenite method developed by Jacobs andHochheiser is one of the most widely used manualmethods for nitrogen dioxide (NO2) monitoring inambient air, particularly in developing countries. Asreported, the method gives 82% NO2 absorptionefficiency (NAE) in the concentration range from 40 to750 μg/m3, when only one impinger tube isemployed in the sampling train at a flow rate of 0.2lpm and for 24 h sampling duration. Accordingly,a uniform correction factor (0.82) is used indenominator to calculate the ultimate concentration ofNO2 in ambient air.In the present investigation, the effect oftemperature on absorption efficiency of NO2 isstudied employing four impinger tubes in series tocollect the maximum NO2 generated in the gasstream. The study conducted at 16, 26 and 36 °Ctemperatures shows maximum absorption efficiency(average) of 87.8% at 26°C in 1st impingertube. At lower and higher temperatures, it is foundconsiderably less. A suitable correction factor,therefore, must be applied to estimate actual NO2concentration in ambient air using arsenite method, intropical countries like India, where atmospherictemperature variations are large (less than 5°Cin winter and more than 45°C in summer).

Notes: Abstract The influence of thermal discharges on thephytoplankton community from a coastal zone of theGulf of Mexico was evaluated through their structureand photosynthetic behaviour focusing on responses tochanges in light and temperature. Biological andphysicochemical parameters were measured over a periodof two years in an area with permanent hot waterdischarges from a thermoelectric plant. Thetemperature in the sampling area ranged from 23.5 to36 °C with differences between the coldest andthe hottest station from 5.3 to 9.2 °C.Photosynthetically active radiation (PAR) were reducedin the discharge area water column, due to turbulence.One hundred and one different taxa were identifiedwith a strong predominance of Diatoms. The chlorophylla concentration ranged from 0.3 to 6.1 μgL-1, with highest values of thephaeophytin:chlorophyll ratio found at the hottest station.The community structure did not show significativedifferences among sampling stations with respect totemperature variations. However, in the algalassemblages influenced by thermal discharges, it waspossible to observe alterations in the photosynthesisbehaviour. Phytoplankton response to short termphotosynthesis experiments was segregated according tocomposition and origin of microalgal assemblages.Samples with larger heterogeneous composition had moreconsistent oxygen production responses. Algalcommunities exposed to hot effluent showed differentdegrees of photosynthesis rate reduction,higher light requirements (〉500 μE m2 s-1)and lower temperature (25 °C) to achieve Pmaxthan algae sampled in sites without such exposure.

Notes: Abstract Bleaching in stony-corals is the result of disruption of symbiosis between the coral hosts and photosynthetic microalgal endosymbionts (zooxanthellae). Coral bleaching events of unprecedented frequency and global extent have been reported during the last two decades. Recently, we demonstrated that bleaching of the coral Oculina patagonica in the Mediterranean Sea is caused by the bacterium Vibrio shiloi, when seawater temperature rises and allows the bacterium to become virulent. The first step in the infection process is host-specific adhesion of V. shiloi to O. patagonica via a β-galactoside receptor on the coral surface. The bacterium then penetrates into the coral tissue and produces extracellular materials which rapidly inhibit photosynthesis of zooxanthellae and bleach and lyse the algae. The inhibition of pothosynthesis is due to a low molecular weight, heat stable toxin and ammonia. Bleaching and lysis are due to a heat-labile, high molecular weight materials, probably lytic enzymes. Elevated temperature induces different virulence factors within the infectious agent of the disease, V. shiloi. Adhesion was found to be temperature-regulated. When the bacteria were grown at 16°C there was no adhesion to corals maintained at either 25°C or 16°. However, when the bacteria were grown at 25°C they adhered avidly to corals maintained at 16°C and 25°C. In addition, the production of lytic enzymes and the photosynthesis inhibitor was also found to be temperature dependent. Production of the latter toxin was ten times greater at 29°C than at 16°C, and extracellular protease was 5-fold higher in cultures grown at 29°C than at 16°C. The data presented here suggest an explanation for the correlation between elevated seawater temperatures and seasonal coral bleaching.