Direct photocatalytic conversion of aldehydes to esters using supported gold nanoparticles under visible light irradiation at room temperature

Visible light can drive esteri fi cation from aldehydes and alcohols using supported gold nanoparticles (Au/Al 2 O 3 ) as photo- catalysts at ambient temperatures. The gold nanoparticles (AuNPs) absorb visible light due to the localized surface plasmon resonance (LSPR) e ff ect, and the conduction electrons of the AuNPs gain the energy of the incident light. The energetic electrons, which concentrate at the NP surface, facilitate the activation of a range of aldehyde and alcohol substrates. The photocatalytic e ffi ciencies strongly depend on the Au loading, particle sizes of the AuNPs, irradiance, and wavelength of the light irradiation. Finally, a plausible reaction mechanism was proposed, and the Au/Al 2 O 3 catalysts can be reused several times without signi fi cantly losing activity. The knowledge acquired in this study may inspire further studies in new e ffi cient recyclable photocatalysts and a wide range of organic synthesis driven by sunlight.

How Australian construction contractors responded to the economic downturn

The Global Financial Crisis (GFC) in 2008 had a significant impact on the world economy and the construction industry was no exception. This study investigates the major impacts of the 2008 GFC on the Australian construction industry and, in particular how the Australian construction contractors responded to the economic downturn. A total of 35 senior managers from the Top 100 Australian construction companies were interviewed. The findings indicate that construction companies, particularly the large ones were not affected in any significant way but are expecting some difficult financial times over the next few years and are taking actions to minimize the upcoming adverse impacts. The most common strategy adopted by Australian construction contractors is to concentrate on core business while avoiding aimless bidding. Similarly, great focus is placed on retaining human resources in order to maintain the skill set so that the company can respond quickly when market conditions improves. The research findings will provide construction contractors with insights on how to establish and sustain competitive advantages during economic slowdown and become more resilient in the future.

Coordinated Verb Pairs in Texts

This dissertation discusses the relation between lexis, grammar and textual organisation. The major premise adopted here is that grammatical structures are motivated both by semantic potential of words and by text-pragmatic demands. In other words, it is argued that grammatical structures form the interface between lexis and textual organisation, and that linguistic analysis should not concentrate on analysing grammatical structures in isolation, independent of context. From this point of view, grammatical structures are said to be 'well-formed' only in relation to the context they occur in. This study is based on a corpus of three million words of recent Finnish fiction from which all the occurrences of the coordinated verb pairs ([V ja V] -pairs]) containing one of the intransitive motion verbs 'lähteä' (to go), 'mennä' (to go), 'päästä' (to get into), 'nousta' (to get up), and 'laskea' (to go down), were extracted. This set of verbs was established using methods described in earlier work by Lagus & Airola (2001, and 2005). The quantitative analysis of the [V ja V] -pairs was used to carry out a qualitative analysis of individual texts. In analysing the texts, an analogy was made between musical and textual structure. The results show among others that individual verbs specialise in different functions when occurring in coordinated verb pairs. One aspect was that those verb pairs including the verb 'nousta' tend to function as markers of textual boundaries and thus reflect the organisation of narrative substance. The verb 'mennä' has weakened literal meanings, but strengthened modal meanings when occurring in [V ja V] -pairs, and, in many cases, the verb 'lähteä' in [V ja V] -pairs function as an aspectual marker rather than a pure verb of motion. That there is a gradient from the concrete sense of motion into more differentiated senses of a verb in [V ja V] -pairs alongside the structure-creating potential of the [V ja V] -pairs themselves suggest an ongoing grammaticalisation process of the patterns discussed.

From Iron Horse to Rauta-airot - a Semiotic View on the Domestication of Metaphors in Literary Translation

The thesis concentrates on two questions: the translation of metaphors in literary texts, and the use of semiotic models and tools in translation studies. The aim of the thesis is to present a semiotic, text based model designed to ease the translation of metaphors and to analyze translated metaphors. In the translation of metaphors I will concentrate on the central problem of metaphor translations: in addition to its denotation and connotation, a single metaphor may contain numerous culture or genre specific meanings. How can a translator ensure the translation of all meanings relevant to the text as a whole? I will approach the question from two directions. Umberto Eco's holistic text analysis model provides an opportunity to concentrate on the problematic nature of metaphor translation from the level of a text as a specific entity, while George Lakoff's and Mark Johnson's metaphor research makes it possible to approach the question from the level of individual metaphors. On the semiotic side, the model utilizes Eero Tarasti's existential semiotics supported by Algirdas Greimas' actant model and Yuri Lotman's theory of cultural semiotics. In the model introduced in the thesis, individual texts are deconstructed through Eco's model into elements. The textual roles and features of these elements are distilled further through Tarasti's model into their coexistent meaning levels. The priorization and analysis of these meaning levels provide an opportunity to consider the contents and significance of specific metaphors in relation to the needs of the text as a whole. As example texts, I will use Motörhead's hard rock classic Iron Horse/Born to Lose and its translation into Rauta-airot by Viikate. I will use the introduced model to analyze the metaphors in the source and target texts, and to consider the transfer of culture specific elements between the languages and cultural borders. In addition, I will use the analysis process to examine the validity of the model introduced in the thesis.

Milk Production Responses to Oversowing a Portion of Tropical Grass Pasture with Summer Crop Legumes on Sub-tropical Dairy Farms

Northern Australian dairy farms have a large area of tropical dryland grass pasture available for use as summer pastures. Late summer-autumn in sub-tropical Australia is traditionally a difficult period in which to produce milk because of the decline in both quality and quantity of tropical grasses (Ehrlich et al. 1994). Options to improve autumn feed on dairy farms include introducing forage crops and conservation, increasing concentrate feeding and introducing legumes. Perennial tropical legumes have not been successful at this time of year because of their inability to sustain stocking rates above one cow/ha. This experiment, conducted on farms, was designed to test if annual crop legumes could be successfully oversown into tropical grass areas using minimal till methods to measure the subsequent impact on milk production on farms. Previous experiments using annual legumes in plots at Mutdapilly Research Station had demonstrated yields up to 10 t/ha can be achieved using annual tropical legumes with protein levels as high as 20% in the whole legume plant. Animal production for a consuming world : proceedings of 9th Congress of the Asian-Australasian Association of Animal Production Societies [AAAP] and 23rd Biennial Conference of the Australian Society of Animal Production [ASAP] and 17th Annual Symposium of the University of Sydney, Dairy Research Foundation, [DRF]. 2-7 July 2000, Sydney, Australia.

Response By Dairy Cows Grazing Tropical Grass Pasture To Barley or Sorghum Grain Based Concentrates and Lucerne Hay

This study investigated the responses by dairy cows grazing Callide Rhodes grass (Chloris gayana cv. Callide) pasture to supplementation with barley or sorghum based concentrates (5 grain:1 cotton seed meal) or barley concentrate plus lucerne (Medicago sativa) hay. It was conducted in summer - autumn 1999 with 20 spring calved cows in 4 treatments in 3 consecutive periods of 4 weeks. Rain grown pastures, heavily stocked at 4.4 cows/ha, provided 22 to 35 kg green DM and 14 to 16 kg green leaf DM/cow.day in periods 1 to 3. Supplements were fed individually twice daily after milking. Cows received 6 kg concentrate/day in period 1, increased by 1 kg/day as barley, sorghum or lucerne chaff in each of periods 2 and 3. The Control treatment received 6 kg barley concentrate in all 3 periods. Milk yields by cows fed sorghum were lower than for cows fed equivalent levels of barley-based concentrate (P<0.05). Faecal starch levels (14, 18 and 17%) for cows fed sorghum concentrate were much higher (P<0.01) than those of cows fed similar levels of barley (2.1, 1.2 and 1.7%) in each period respectively. Additional supplementation as lucerne chaff did not increase milk production (P>0.05). Increased concentrate supplementation did not alleviate the problem of low protein in milk produced by freshly calved Holstein-Friesian cows grazing tropical grass pasture in summer. Animal production for a consuming world : proceedings of 9th Congress of the Asian-Australasian Association of Animal Production Societies [AAAP] and 23rd Biennial Conference of the Australian Society of Animal Production [ASAP] and 17th Annual Symposium of the University of Sydney, Dairy Research Foundation, [DRF]. 2-7 July 2000, Sydney, Australia.

Changes in Beer Labels and their Meaning : A Holistic Approach to the Semiosic Process

The purpose of this study is to find a framework for a holistic approach to, and form a conceptual toolbox for, investigating changes in signs and in their interpretation. Charles S. Peirce s theory of signs in a communicative perspective is taken as a basis for the framework. The concern directing the study is the problem of a missing framework in analysing signs of visual artefacts from a holistic perspective as well as that of the missing conceptual tools. To discover the possibility of such a holistic approach to semiosic processes and to form a conceptual toolbox the following issues are discussed: i) how the many Objects with two aspects involved in Peirce s definition of sign-action, promote multiple semiosis arising from the same sign by the same Interpretant depending on the domination of the Objects; ii) in which way can the relation of the individual and society or group be made more apparent in the construction of the self since this construction is intertwined with the process of meaning-creation and interpretation; iii) how to account for the fundamental role of emotions in semiosis, and the relation of emotions with the often neglected topic of embodiment; iv) how to take into account the dynamic, mediating and processual nature of sign-action in analysing and understanding the changes in signs and in the interpretation of signs. An interdisciplinary approach is chosen for this dissertation. Concepts that developed within social psychology, developmental psychology, neurosciences and semiotics, are discussed. The common aspect of the approaches is that they in one way or another concentrate on mediation provided by signs in explaining human activity and cognition. The holistic approach and conceptual toolbox found are employed in a case study. This consists of an analysis of beer brands including a comparison of brands from two different cultures. It becomes clear that different theories and approaches have mutual affinities and do complement each other. In addition, the affinities in different disciplines somewhat provide credence to the various views. From the combined approach described, it becomes apparent that by the semiosic process, the emerging semiotic self intertwined with the Umwelt, including emotions, can be described. Seeing the interpretation and meaning-making through semiosis allows for the analysis of groups, taking into account the embodied and emotional component. It is concluded that emotions have a crucial role in all human activity, including so-called reflective thinking, and that emotions and embodiment should be consciously taken into account in analysing signs, the interpretation, and in changes of signs and interpretations from both the social and individual level. The analysis of the beer labels expresses well the intertwined nature of the relationship between signs, individual consumers and society. Many direct influences from society on the label design are found, and also some indirect attitude changes that become apparent from magazines, company reports, etc. In addition, the analysis brings up the issues of the unifying tendency of the visual artefacts of different cultures, but also demonstrates that the visual artefacts are able to hold the local signs and meanings, and sometimes are able to represent the local meanings although the signs have changed in the unifying process.

Signifying Angels : Analyses and Interpretations of Rautavaara s Instrumental Compositions

The subject of doctoral thesis is the analysis and interpretation of instrumental pieces composed by Einojuhani Rautavaara (b. 1928) that have been given angelic titles: Archangel Michael Fighting the Antichrist from the suite Icons (1955)/Before the Icons (2006), Angels and Visitations (1978), the Double Bass Concerto Angel of Dusk (1980), Playgrounds for Angels (1981)and the Seventh Symphony Angel of Light (1994). The aim of the work is to find those musical elements common to these pieces that distinguish them from Rautavaara s other works and to determine if they could be thought of as a series. I prove that behind the common elements and titles stands the same extramusical idea the figure of an angel that the composer has described in his commentaries. The thesis is divided into three parts. Since all of the compositions possess titles that refer to the spiritual symbol of an angel, the first part offers a theoretical background to demonstrate the significant role played by angels in various religions and beliefs, and the means by which music has attempted to represent this symbol throughout history. This background traces also Rautavaara s aesthetic attitude as a spiritual composer whose output can be studied with reference to his extramusical interests including literature, psychology, painting, philosophy and myths. The second part focuses on the analysis of the instrumental compositions with angelic titles, without giving consideration to their commentaries and titles. The analyses concentrate in particular on those musical features that distinguish these pieces from Rautavaara s other compositions. In the third part these musical features are interpreted as symbols of the angel through comparison with vocal and instrumental pieces which contain references to the character of an angel, structures of mythical narration, special musical expressions, use of instruments and aspects of brightness. Finally I explore the composer s interpretative codes, drawing on Rilke s cycle of poems Ten Duino Elegies and Jung s theory of archetypes, and analyze the instrumental pieces with angelic titles in the light of the theory of musical ekphrasis.

Kirjan tie lukijalle : Kirjakauppojen vakiintuminen Suomessa 1740 - 1860

Books Paths to Readers describes the history of the origins and consolidation of modern and open book stores in Finland 1740 1860. The thesis approaches the book trade as a part of a print culture. Instead of literary studies choice to concentrate on texts and writers, book history seeks to describe the print culture of a society and how the literary activities and societies interconnect. For book historians, printed works are creations of various individuals and groups: writers, printers, editors, book sellers, censors, critics and finally, readers. They all take part in the creation, delivery and interpretation of printed works. The study reveals the ways selling and distributing books have influenced the printed works and the literary and print culture. The research period 1740 1860 covers the so-called second revolution of the book, or the modernisation of the print culture. The thesis describes the history of 60 book stores and their 96 owners. The study concentrates on three themes: firstly, how the particular book trade network became a central institution for printed works distribution, secondly what were the relations between cosmopolitan European book markets and the national cultural sphere, and thirdly how book stores functioned as cultural institutions and business enterprises. Book stores that have a varied assortment and are targeted to all readers became the main institution for book trade in Finland during 1740 1860. It happened because of three features. First, the book binders monopoly on selling bound copies in Sweden was abolished in 1740s. As a consequence entrepreneurs could concentrate solely to trade activities and offer copies from various publishers at their stores. Secondly the common business model of bartering was replaced by selling copies for cash, first in the German book trade centre Leipzig in 1770s. The change intensified book markets activities and Finnish book stores foreign connections. Thirdly, after Finland was annexed to the Russian empire in 1809, the Grand duchy s administration steered foreign book trade to book stores (because of censorship demands). Up to 1830 s book stores were available only in Helsinki and Turku. During next ten years book stores opened in six regional centres. The early entrepreneurs ran usually vertical businesses consisting of printing, publishing and distribution activities. This strategy lowered costs, eased the delivery of printed works and helped to create elaborated centres for all book activities. These book stores main clientele consisted of the Swedish speaking gentry. During late 1840s various opinion leaders called for the development of a national Finnish print culture, and also book stores. As a result, during the five years before the beginning of the Crimean war (1853 1856) book stores were opened in almost all Finnish towns: at the beginning of the war 36 book stores operated in 21 towns. The later book sellers, mainly functioning in small towns among Finnish speaking people, settled usually strictly for selling activities. Book stores received most of their revenues from selling foreign titles. Swedish, German, French and Belgian (pirate editions of popular French novels) books were widely available for the multilingual gentry. Foreign titles and copies brought in most of the revenues. Censorship inspections or unfavourable custom fees would not limit the imports. Even if the local Finnish print production steadily rose, many copies, even titles, were never delivered via book stores. Only during the 1840 s and 1850 s the most advanced publishers would concentrate on creating publishing programmes and delivering their titles via book stores. Book sellers regulated commissions were small. They got even smaller because of large amounts of unsold copies, various and usual misunderstandings of consignments and accounts or plain accidents that destroyed shipments and warehouses. Also, the cultural aim of a creating large and assortments and the tendency of short selling periods demanded professional entrepreneurship, which many small town book sellers however lacked. In the midst of troublesome business efforts, co-operation and mutual concern of the book market s entrepreneurs were the key elements of the trade, although on local level book sellers would compete, sometimes even ferociously. The difficult circumstances (new censorship decree of 1850, Crimean war) and lack of entrepreneurship, experience and customers meant that half of the book stores opened in 1845 1860 was shut in less than five years. In 1858 the few leading publishers established The Finnish Book Publishers Association. Its first task was to create new business rules and manners for the book trade. The association s activities began to professionalise the whole network, but at the same time the earlier independence of regional publishing and selling enterprises diminished greatly. The consolidation of modern and open book store network in Finland is a history of a slow and complex development without clear signs of a beginning or an end. The ideal book store model was rarely accomplished in its all features. Nevertheless, book stores became the norm of the book trade. They managed to offer larger selections, reached larger clienteles and maintained constant activity better than any other book distribution model. In essential, the book stores methods have not changed up to present times.

Improving sheep feedlot management

This paper summarise six studies undertaken by the Sheep CRC to elucidate certain aspects of confinement feeding of sheep. A review of confinement feeding highlighted the variability of growth rate and feed conversion of sheep and revealed that little is known about the use of sorghum for feeding sheep. The review indicated that the main factors responsible for variation of growth rate and feed conversion were adaptation to grain and feeding system, including the preparation and presentation of feed. The importance of social and physiological adaptation to grain feeding was confirmed. Factors identified as responsible for safe induction and uniform growth rates included prior exposure to grain as lambs, gradual introduction of grain and, when concentrate was provided ad libitum from the first day, the use of either virginiamycin, a pelleted feed, a total mixed ration or a step-wise increase of high-starch grain components. Separate feeding of hay and grain resulted in performance comparable with that of a pelleted diet and that of a total mixed ration. Sorghum-based concentrate diets resulted in growth rates and carcase weights similar to that for winter cereal grains or pellets. Steam flaking or expanding of sorghum had no significant effect on growth rates or carcase weights. These results can be used to determine the profitability of various feedlotting options.

Bysanttilaisten ja Akhaian ruhtinaskunnan väliset sotatoimet vuosina 1259-83 : Tapaustutkimus myöhäis-bysanttilaisesta sodankäynnistä

In my master thesis I analyse Byzantine warfare in the late period of the empire. I use military operations between Byzantines and crusader Principality of Achaia (1259–83) as a case study. Byzantine strategy was based (in “oriental manner”) on using ambushes, diplomacy, surprise attacks, deception etc. Open field battles that were risky in comparison with their benefits were usually avoided, but the Byzantines were sometimes forced to seek open encounter because their limited ability to keep strong armies in field for long periods of time. Foreign mercenaries had important place in Byzantine armies and they could simply change sides if their paymasters ran out of resources. The use of mercenaries with short contracts made it possible that the composition of an army was flexible but on the other hand heterogeneous – in result Byzantine armies were sometimes ineffective and prone to confusion. In open field battles Byzantines used formation that was made out from several lines placed one after another. This formation was especially suitable for cavalry battles. Byzantines might have also used other kinds of formations. The Byzantines were not considered equal to Latins in close combat. West-Europeans saw mainly horse archers and Latin mercenaries on Byzantine service as threats to themselves in battle. The legitimacy of rulers surrounding the Aegean sea was weak and in many cases political intrigues and personal relationships can have resolved the battles. Especially in sieges the loyalty of population was decisive. In sieges the Byzantines used plenty of siege machines and archers. This made fast conquests possible, but it was expensive. The Byzantines protected their frontiers by building castles. Military operations against the Principality of Achaia were mostly small scale raids following an intensive beginning. Byzantine raids were mostly made by privateers and mountaineers. This does not fit to the traditional picture that warfare belonged to the imperial professional army. It’s unlikely that military operations in war against the Principality of Achaia caused great demographic or economic catastrophe and some regions in the warzone might even have flourished. On the other hand people started to concentrate into villages which (with growing risks for trade) probably caused disturbance in economic development and in result birth rates might have decreased. Both sides of war sought to exchange their prisoners of war. These were treated according to conventional manners that were accepted by both sides. It was possible to sell prisoners, especially women and children, to slavery, but the scale of this trade does not seem to be great in military operations treated in this theses.

Arkeologia, historialliset kartat ja paikkatieto

This licentiate thesis is composed of three parts, of which the parts 2 and 3 have been published elsewhere. Part 1 deals with the research history of large-scaled historical maps in Finland. The research done in four disciplines – archaeology, history, art history and geography – is summarized. Compared to the other disciplines, archaeology is characterized by its deep engagement with the location. Because archaeology studies different aspects of the past through material culture, it is the only discipline in which the concrete remains portrayed on the maps are “dug up”. For the archaeologist, historical maps are not merely historical documents with written information and drawings in scale, but actual maps which can be connected with the physical features they were made to illustrate in the first place. This aspect of historical maps is discussed in the work by looking at the early (17th and 18th century) urban cartographic material of two Finnish towns, Savonlinna and Vehkalahti-Hamina. In both cases, the GIS-based relocating of the historical maps highlights new aspects in the early development of the towns. Part 1 ends with a section in which the contents of the entire licentiate thesis are summarized. Part 2 is a peer reviewed article published in English. This article deals with the role of historical maps converted into GIS in archaeological surveys made in Finnish post-medieval towns (16th and 17th centuries). It is based on the surveys made by the author between 2000 and 2003 and introduces a new method for the archaeological surveying of post-medieval towns with wooden houses. The role of archaeology in the sphere of urban research is discussed. The article emphasizes that the methods used in studying the development of southern European towns with stone houses cannot be adequately applied to the wooden towns of the north. Part 3 is a monograph written in Finnish. It discusses large-scaled historical maps and the methods for producing digital spatial information based on historical maps. Since the late 1990’s, archaeological research in Finland has been increasingly directed towards the historical period. As a result, historical cartography has emerged as one of the central sources of information for the archaeologist, too. The main theme of this work is the need for using historical maps as real maps which, surprisingly, has been uncommon in the historical sciences. Projecting historical maps to the very place they were made to illustrate is essential to understanding the maps. This is self-evident for the archaeologist, who is accustomed to studying the material past, but less so to researchers in other historical disciplines that concentrate on written and visual sources of information. With the help of GIS, the historical maps can be concretely linked to the places they were originally made to illustrate. In doing so, and equipped with a cartographic comprehension, new observations can be made and questions asked, which supplement and occasionally challenge the prevailing views.

Det pedagogiska självet : en narrativ studie av direktvalda svensklärarstudenters berättelser

The Pedagogical Self: a narrative study of stories by prospective subject teachers of Swedish The aim of this study is to examine how prospective subject teachers of Swedish experience themselves, their lives and their studies in university context. By answering this question I try to shed light on the pedagogical self of the students, i.e. to reach a deeper understanding of the narrative construction of their teacher identity. My material consists of stories written by one group of students and of transcribed interviews with another group of students at Nordica. All these students have entered both the teacher education programme and studies in their major subject simultaneously, through the so called direct admission. My study focuses on the students first year at the university. I define teacher identity, the pedagogical self, as the part of an individual s self-concept where he/she makes an assessment of himself/herself as a teacher(-to-be). The frame of reference of this interdisciplinary narrative study is founded on phenomenology, hermeneutics, social constructionism and dialogism. The main analysis of the stories is thematic, with the addition of linguistic and metaphorical analysis. With reference to the theories of Paul Ricoeur and Katharine Young, I regard the textual world of the stories as a world of its own. This implies that the researcher can feel free to concentrate on the texts, thus being able to leave the mental processes of the writers disregarded. The theoretician that has influenced my research the most is Max van Manen. He combines a pedagogical attitude with a phenomenological-hermeneutic philosophy. My research results imply that most of these students are drawn to studying Swedish by the clear professional orientation of the studies; their identity as teachers seems to be stronger than their identity as language teachers. The image of a teacher is relatively traditional: a teacher is seen as a self-evident authority, but at the same time as a fostering educator. The students see their studies in a larger perspective: studies as well as the future profession are only one part of life, albeit an important one. Keywords: narrativity, teacher identity

Impacts of feeding system and season on milk composition and Cheddar cheese yield in a subtropical environment

Milk obtained from cows on 2 subtropical dairy feeding systems were compared for their suitability for Cheddar cheese manufacture. Cheeses were made in a small-scale cheesemaking plant capable of making 2 blocks ( about 2 kg each) of Cheddar cheese concurrently. Its repeatability was tested over 10 separate cheesemaking days with no significant differences being found between the 2 vats in cheesemaking parameters or cheese characteristics. In the feeding trial, 16 pairs of Holstein - Friesian cows were used in 2 feeding systems (M1, rain-grown tropical grass pastures and oats; and M5, a feedlot, based on maize/barley silage and lucerne hay) over 2 seasons ( spring and autumn corresponding to early and late lactation, respectively). Total dry matter, crude protein (kg/cow. day) and metabolisable energy (MJ/cow.day) intakes were 17, 2.7, and 187 for M1 and 24, 4, 260 for M5, respectively. M5 cows produced higher milk yields and milk with higher protein and casein levels than the M1 cows, but the total solids and fat levels were similar (P > 0.05) for both M1 and M5 cows. The yield and yield efficiency of cheese produced from the 2 feeding systems were also not significantly different. The results suggest that intensive tropical pasture systems can produce milk suitable for Cheddar cheese manufacture when cows are supplemented with a high energy concentrate. Season and stage of lactation had a much greater effect than feeding system on milk and cheesemaking characteristics with autumn ( late lactation) milk having higher protein and fat contents and producing higher cheese yields.

Large deflections of simply supported beams

Large deflections of simply supported beams have been studied when the trans verse loading consists of a uniformity distributed load plus a century concentrate load under the two cases, (1) the reactions are vertical. (2) the reactions are normal to the bent beam together with frictional forces. The solutions are obtained by the use of power series expansions. This method is applicable to cases of symmetrical loading in beams.