On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Low correlation sequences over AM-PSK and QAM alphabets

A construction for a family of sequences over the 8-ary AM-PSK constellation that has maximum nontrivial correlation magnitude bounded as theta(max) less than or similar to root N is presented here. The famfly is asymptotically optimal with respect to the Welch bound on maximum magnitude of correlation. The 8-ary AM-PSK constellation is a subset of the 16-QAM constellation. We also construct two families of sequences over 16-QAM with theta(max) less than or similar to root 2 root N. These families are constructed by interleaving sets of sequences. A construction for a famBy of low-correlation sequences over QAM alphabet of size 2(2m) is presented with maximum nontrivial normalized correlation parameter bounded above by less than or similar to a root N, where N is the period of the sequences in the family and where a ranges from 1.61 in the case of 16-QAM modulation to 2.76 for large m. When used in a CDMA setting, the family will permit each user to modulate the code sequence with 2m bits of data. Interestingly, the construction permits users on the reverse link of the CDMA channel to communicate using varying data rates by switching between sequence famflies; associated to different values of the parameter m. Other features of the sequence families are improved Euclidean distance between different data symbols in comparison with PSK signaling and compatibility of the QAM sequence families with sequences belonging to the large quaternary sequence families {S(p)}.

Regeneration ecology and woody species diversity in the remnant natural forest at Wondo Genet, Ethiopia – Potential for landscape restoration

Regeneration ecology, diversity of native woody species and its potential for landscape restoration was studied in the remnant natural forest at the College of Forestry and Natural Resources at Wondo Genet, Ethiopia. The type of forest is Afromontane rainforest , with many valuable tree species like Aningeria adolfi-friederici, and it is an important provider of ecological, social and economical services for the population that lives in this area. The study contains two parts, natural regeneration studies (at the natural forest) and interviews with farmers in the nearby village of the remnant patch. The objective of the first part was to investigate the floristic composition, densitiy and regeneration profiles of native woody species in the forest, paying special attention to woody species that are considered the most relevant (socio-economic). The second part provided information on woody species preferred by the farmers and on multiple uses of the adjacent natural forest, it also provided information and analysed perceptions on forest degradation. Systematic plot sampling was used in the forest inventory. Twenty square plots of 20 x 20 m were assessed, with 38 identified woody species (the total number of species was 45), representing 26 families. Of these species 61% were trees, 13% shrubs, 11% lianas and 16% species that could have both life forms. An analysis of natural regeneration of five important tree species in the natural forest showed that Aningeria adolfi-friederici had the best regeneration results. An analysis of population structure (as determined by height classes) of two commercially important woody species in the forest, Aningeria adolfi-friederici and Podocarpus falcatus, showed a marked difference: Aningeria had a typical “reversed J” frequency distribution, while Podocarpus showed very low values in all height classes. Multi dimensional scaling (MDS) was used to map the sample plots according to their similarity in species composition, using the Sørensen quantitative index, coupled with indicator species analysis .Three groups were identified with respective indicator species: Group 1 – Adhatoda schimperiana, Group 2 – Olea hochstetteri , Group 3 – Acacia senegal and Aningeria adolfi-friederici. Thirty questionnaire interviews were conducted with farmers in the village of Gotu Onoma that use the nearby remant forest patch. Their tree preferences were exotic species such as Eucalyptus globulus for construction and fuelwood and Grevillea robusta for shade and fertility. Considering forest land degradation farmers were aware of the problem and suggested that the governmental institutions address the problem by planting more Eucalyptus globulus. The natural forest seemed to have moderate levels of disturbance and it was still floristically diverse. However, the low rate of natural regeneration of Podocarpus falcatus suggested that this species is threatened and must be a priority in conservation actions. Plantations and agroforestry seem to be possible solutions for rehabilitation of the surrounding degraded lands, thereby decreasing the existent pressure in the remnant natural forest.

Transposable elements in a marginal plant population

Background
How new forms arise in nature has engaged evolutionary biologists since Darwin's seminal treatise on the origin of species. Transposable elements (TEs) may be among the most important internal sources for intraspecific variability. Thus, we aimed to explore the temporal dynamics of several TEs in individual genotypes from a small, marginal population of Aegilops speltoides. A diploid cross-pollinated grass species, it is a wild relative of the various wheat species known for their large genome sizes contributed by an extraordinary number of TEs, particularly long terminal repeat (LTR) retrotransposons. The population is characterized by high heteromorphy and possesses a wide spectrum of chromosomal abnormalities including supernumerary chromosomes, heterozygosity for translocations, and variability in the chromosomal position or number of 45S and 5S ribosomal DNA (rDNA) sites. We propose that variability on the morphological and chromosomal levels may be linked to variability at the molecular level and particularly in TE proliferation.

Results
Significant temporal fluctuation in the copy number of TEs was detected when processes that take place in small, marginal populations were simulated. It is known that under critical external conditions, outcrossing plants very often transit to self-pollination. Thus, three morphologically different genotypes with chromosomal aberrations were taken from a wild population of Ae. speltoides, and the dynamics of the TE complex traced through three rounds of selfing. It was discovered that: (i) various families of TEs vary tremendously in copy number between individuals from the same population and the selfed progenies; (ii) the fluctuations in copy number are TE-family specific; (iii) there is a great difference in TE copy number expansion or contraction between gametophytes and sporophytes; and (iv) a small percentage of TEs that increase in copy number can actually insert at novel locations and could serve as a bona fide mutagen.

Conclusions
We hypothesize that TE dynamics could promote or intensify morphological and karyotypical changes, some of which may be potentially important for the process of microevolution, and allow species with plastic genomes to survive as new forms or even species in times of rapid climatic change.

A building-up process in open-framework metal carboxylates that involves a progressive increase in dimensionality

Extensive research work has been carried out in the last few years on the synthesis and characterization of several families of open-framework materials, including aluminosilicates,[1] phosphates,[2] and carboxylates.[3] These studies have shown the occurrence of a variety of three dimensional (3D) architectures containing channels and other features.

Generalized Burgers equations and Euler–Painlevé transcendents. III

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1of exact single hump solutions, similar to those found for the nonplanar Burgers equations in Paper II. Thus the parametric value β=βn seems to bifurcate the families of solutions, which remain bounded at η=±∞. Other GBE’s considered here are also found to be reducible to Euler–Painlevé equations.

Eteva Järvenpään perhepalvelukeskuksen lyhytaikaishoidon suunnittelun kehittäminen

Objectives. The thesis objective was to analyze how person-centred planning is applied to develop short term care in interaction between the disabled children, their families and the workers of the family service centre of Eteva Järvenpää. The thesis contributes to developing the methods of person-centred planning. I applied theoretical frameworks of activity theory and developmental work research, family-based work framework and disability phenomenon. The research questions were: What development needs did the families of disabled children have for the services? How were viewpoints of disabled children, their families and Eteva workers noticed in person-centred planning in the interaction between the disabled children, their families and Eteva workers? What disturbances and development challenges emerged during the person-centred planning? Methods. I first analysed the local history of the disability sector and the short term care to analyse challenges arising from the local history. The actural research material consisted of interviews with four families, two person-centred planning discussions and two discussions where the person-centred planning was reflected by the families.I used interaction voice analysis as defined by the activity theory and developmental work research. From the recorded interviews and discussions I analysed scripts, disturbances, innovation attempts and innovations. From the discussions I analysed also the interaction types (cooperation, coordination and communication). Results and conclusions. As problems, the families considered the scarce resources and the inflexibility of services. The challenges of developing the short term care were how to transfer information from short term care to home, how to develop activities for the children and how to take into account the individual needs of the children in the short term care. Both from the local history analysis and from the family interviews arised the conflict between caring and fulfilling the individual needs. In person-centred planning, the voice of the child was either interpreted by other family members or guided by family members or workers. I modelled the progress of person-centred planning in a two-dimensional coordination. Person-centred planning should be deepened in cooperation between the child, the family and the workers in everyday situations at home and during the short term care. The challenge is to expand person-centred planning to become cross-organizational cooperation connecting the actors of the child s service network in everyday life. Avainsanat Nyckelord - Keywords short term care, activity theory and developmental work research, person-centred planning, disability

Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations

We apply the method of multiple scales (MMS) to a well-known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the timescale of typical cutting tool oscillations. The MMS up to second order, recently developed for such systems, is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than the first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy in that plotted solutions of moderate amplitudes are visually near-indistinguishable. The advantages of the present analysis are that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space; lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS; the strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly; and though certain parameters are treated as small (or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation.

Elämän ja entisyyden maisemat : Kolgujev nenetsien arjessa, muistelussa ja kerronnassa

The dissertation discusses the conceptions of place and landscape amongst Nenets living on the island of Kolguyev or being of Kolguyev descent. The conceptions are examined through the everyday life of the community, oral recollections and narration that unfold meanings related to the island. The research material has been collected in ethnographic fieldwork in 2000 2005. The duration of individual fieldworks varies from two weeks to three months and their total duration is nearly six months. The fieldwork has been conducted both on the island and in the city of Nar yan-Mar. The main methods have been participant observation and recorded and unrecorded informal interviews. In addition to the field work data, archive materials, travel accounts, and other historical texts by outsiders about Kolguyev or the Nenets living in the European side of Russia have been used as a research material. The analysis is based on the idea of the place as a meeting point of the physical features, experiences in them and collective narration about them. The concept sense of place is used to describe the interaction of these three. Lived space manifests individual s or collective sense of place. The places form different kinds of networks of meanings which are called landscapes. Hot spots are places where different meanings accumulate. Furthermore, the material is analysed using the concepts of Tale World and Story Realm by Katherine Young. The Tale World is a realm created during the Story Realm, i.e. the event of narrations. The Tale Worlds are true as such but become evaluated in the Story Realm. The Tale Worlds are seen to arise both from the physical features of a place and from oral tradition, but at the same time these worlds give meanings to the place. The Tale Worlds are one of the central ingredients for the sense of place. One of the most central hot spots in Kolguyev is the arok harbour, where most of the themes of the pre-Soviet Tale Worlds are placed: trade and interaction with the Russians, rituals of the popular religion and arrival of the first Nenets to the island. arok is also part of the landscape of the coast where the meetings of Nenets and the other(s) are generally connected. Furthermore, arok is connected to the network of amans graves but also more generally to the landscape of collective sacred and sacrificial places. Another hot spot is the population centre of Bugrino which unfolds through the evaluations of the Tale Worlds. It also is the centre of the everyday life of the community studied. The Tale Worlds of the radiant past fastens on the population centre which is described through the negative models within the genre of litany. Sacred places, that represent the possibility to meet the Otherworld or mark places were encounters with the Otherworld have taken place, generate many kinds of landscapes in the island. They fasten on the graves of the amans, sirtya tradition, and to collective sacred places with their associations. The networks are not closed systems but are given meanings and new associations continuously in narration and recollection. They form multi-level and significant landscapes which reflect the fastening of the Kolguyev Nenets in the tundra of the island. In the research material the holy places and the popular religiousness are emphasised which is one of the most significant research results. It can be seen to reflect collective resistance and the questioning of the atheistic propaganda of the Soviet years. The narration and the recollection often refer also to the discourse of the anti-religious propaganda or use its strategies. The centrality of the holy places is also based on the tenacity of the religious Tale Worlds and sense of place and to the collective significance of the religion in general.

Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Code Generation Paradigms On Optical Orthogonal And Other Codes In a Fiber Optic CDMA Lan

Code Division Multiple Access (CDMA) techniques, by far, had been applied to LAN problems by many investigators, An analytical study of well known algorithms for generation of Orthogonal codes used in FO-CDMA systems like those for prime, quasi-Prime, Optical Orthogonal and Matrix codes has been presented, Algorithms for OOCs like Greedy/Modified Greedy/Accelerated Greedy algorithms are implemented. Many speed-up enhancements. for these algorithms are suggested. A novel Synthetic Algorithm based on Difference Sets (SADS) is also proposed. Investigations are made to vectorise/parallelise SADS to implement the source code on parallel machines. A new matrix for code families of OOCs with different seed code-words but having the same (n,w,lambda) set is formulated.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

For a family/sequence of Space-Time Block Codes (STBCs) C1, C2,⋯, with increasing number of transmit antennas Ni, with rates Ri complex symbols per channel use (cspcu), i = 1,2,⋯, the asymptotic normalized rate is defined as limi→∞ Ri/Ni. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least maximum-likelihood (ML) decoding complexity among all known codes for any number of transmit antennas N>;1 and rates R>;1 cspcu. For a large set of (R,N) pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes (R=N) are asymptotically-optimal and fast-decodable, and for N>;5 have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper: (i) Construction of a new class of asymptotically-good, full-diversity multigroup ML decodable codes, that not only includes STBCs for a larger set of antennas, but also either matches in rate or contains as a proper subset all other high-rate or asymptotically-good, delay-optimal, multigroup ML decodable codes available in the literature. (ii) Construction of a new class of fast-group-decodable codes (codes that combine the low ML decoding complexity properties of multigroup ML decodable codes and fast-decodable codes) for all even number of transmit antennas and rates 1 <; R ≤ 5/4.- - (iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations.