On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Long-term results of obstetric brachial plexus surgery

Background: Brachial plexus birth palsy (BPBP) most often occurs as a result of foetal-maternal disproportion. The C5 and C6 nerve roots of the brachial plexus are most frequently affected. In contrast, roots from the C7 to Th1 that result in total injury together with C5 and C6 injury, are affected in fewer than half of the patients. BPBP was first described by Smellie in 1764. Erb published his classical description of the injury in 1874 and his name became linked with the paralysis that is associated with upper root injury. Since then, early results of brachial plexus surgery have been reasonably well documented. However, from a clinical point of view not all primary results are maintained and there is also a need for later follow-up results. In addition most of the studies that are published emanate from highly specialized clinics and no nation wide epidemiological reports are available. One of the plexus injuries is the avulsion type, in which the nerve root or roots are ruptured at the neural cord. It has been speculated whether this might cause injury to the whole neural system or whether shoulder asymmetry and upper limb inequality results in postural deformities of the spine. Alternatively, avulsion could manifest as other signs and symptoms of the whole musculoskeletal system. In addition, there is no available information covering activities of daily living after obstetric brachial plexus surgery. Patients and methods: This was a population-based cross-sectional study on all patients who had undergone brachial plexus surgery with at least 5 years of follow-up. An incidence of 3.05/1000 for BPBP was obtained from the registers for this study period. A total of 1706 BPBP patients needing hospital treatment out of 1 717 057 newborns were registered in Finland between 1971 and 1997 inclusive. Of these BPBP patients, 124 (7.3%) underwent brachial plexus surgery at a mean age of 2.8 months (range: 0.4―13.2 months). Surgery was most often performed by direct neuroraphy after neuroma resection (53%). Depending on the phase of the study, 105 to 112 patients (85-90%) participated in a clinical and radiological follow-up assessment. The mean follow up time exceeded 13 years (range: 5.0―31.5 years). Functional status of the upper extremity was evaluated using Mallet, Gilbert and Raimondi scales. Isometric strength of the upper limb, sensation of the hand and stereognosis were evaluated for both the affected and unaffected sides then the differences and their ratios were calculated and recorded. In addition to the upper extremity, assessment of the spine and lower extremities were performed. Activities of daily living (ADL), participation in normal physical activities, and the use of physiotherapy and occupational therapy were recorded in a questionnaire. Results: The unaffected limb functioned as the dominant hand in all, except four patients. The mean length of the affected upper limb was 6 cm (range: 1-13.5 cm) shorter in 106 (95%) patients. Shoulder function was recorded as a mean Mallet score of 3 (range: 2―4) which was moderate. Both elbow function and hand function were good. The mean Gilbert elbow scale value was 3 (range: -1―5) and the mean Raimondi hand scale was 4 (range:1―5). One-third of the patients experienced pain in the affected limb including all those patients (n=9) who had clavicular non-union resulting from surgery. A total of 61 patients (57%) had an active shoulder external rotation of less than 0° and an active elbow extension deficiency was noted in 82 patients (77%) giving a mean of 26° (range: 5°―80°). In all, expect two patients, shoulder external rotation strength at a mean ratio 35% (range: 0―83%) and in all patients elbow flexion strength at a mean ratio of 41% (range: 0―79%) were impaired compared to the unaffected side. According to radiographs, incongruence of the glenohumeral joint was noted in 15 (16%) patients, whereas incongruence of the radiohumeral joint was found in 20 (21%) patients. Fine sensation was normal for 34/49 (69%) patients with C5-6 injury, for 15/31 (48%) with C5-7 and for only 8/25 (32%) of patients with total injury. Loss of protective sensation or absent sensation was noted in some palmar areas of the hand for 12/105 patients (11%). Normal stereognosis was recorded for 88/105 patients (84%). No significant inequalities in leg length were found and the incidence of structural scoliosis (1.7%) did not differ from that of the reference population. Nearly half of the patients (43%) had asynchronous motion of the upper limbs during gait, which was associated with impaired upper limb function. Data obtained from the completed questionnaires indicated that two thirds (63%) of the patients were satisfied with the functional outcome of the affected hand although one third of all patients needed help with ADL. Only a few patients were unable to participate in physical activities such as: bicycling, cross-country skiing or swimming. However, 71% of the patients reported problems related to the affected upper limb, such as muscle weakness and/or joint stiffness during the aforementioned activities. Incongruity of the radiohumeral joints, extent of the injury, avulsion type injury, age less than three months of age at the time of plexus surgery and inexperience of the surgeon was related to poor results as determined by multivariate analyses. Conclusions: Most of the patients had persistent sequelae, especially of shoulder function. Almost all measurements for the total injury group were poorer compared with those of the C5-6 type injury group. Most of the patients had asymmetry of the shoulder region and a shorter affected upper limb, which is a probable reason for having an abnormal gait. However, BPBP did not have an effect on normal growth of the lower extremities or the spine. Although, participation in physical activities was similar to that of the normal population, two-thirds of the patients reported problems. One-third of the patients needed help with ADL. During the period covered by this study, 7.3% BPBP of patients that needed hospital treatment had a brachial plexus operation, which amounts to fewer than 10 operations per year in Finland. It seems that better results of obstetric plexus surgery and more careful follow-up including opportunities for late reconstructive procedures will be expected, if the treatment is solely concentrated on by a few specialised teams.

Performing immobility / protesting immobility: The risks & rewards of public space protest performances

Though there is much interest in mobilities and performing mobilities as a characteristic of modern, urban, social life today, this is not always matched by attention to immobilities, as the flipside of mobility in modern life. In this paper, I investigate public space performances designed to draw attention to precisely this counterpoint to current discourses of mobilities – performances about the socially produced immobilities many people with disabilities find a more fundamental feature of day-to-day life, the fight for mobility, and the freedom found when accommodations for alternative mobilities are made available. Although public policy is increasingly aligned with a social model of disability, which sees disability as socially constructed through systems, institutions and infrastructure deliberately designed to exclude specific bodies – stairs, curbs, queues and so forth – and although governments in the US, UK, and to a lesser degree Australia, New Zealand and other Commonwealth nations aim to address these inequalities, the experience of immobility is still every-present for many people. This often comes not just from pain, or from impairment, or event from lack of accommodations for alternative mobilities, but from fellow social performers’ antipathy to, appropriation of, or destruction of accommodations designed to facilitate access for a range of different bodies in public space, and thus the public sphere. The archetypal instance of this tension between the mobile, and those needing accommodations to allow mobility, is, of course, the antipathy many able bodied people feel towards the provision of disabled parking spaces. A cursory search online shows thousands of accounts of antagonism, vitriol, and even violence prompted by disputes which began when a disabled person asked an able person to exit a designated disabled parking space. For many, it seems, expecting them to pass by such parks so others can experience the mobility they take for granted is too much. In this paper, I examine a number of protest performances in public space in which activist present actions – for example, placing wheelchairs in every regular parking space in a precinct – to give bystanders, passersby and spectators, as well as antagonistic fellow social performers, a sense of what socially produced immobility feels like. I examine responses to such protest performances, and what they say about the potential social, political and ethical impacts of such protests, in terms of their potential to produce new attitudes to mobility, alternative mobility, and access to alternative modes of mobility.

Context-dependency of a complex fruit-frugivore mutualism: temporal variation in crop size and neighborhood effects

The quantity of fruit consumed by dispersers is highly variable among individuals within plant populations. The outcome Of Such selection operated by firugivores has been examined mostly with respect to changing spatial contexts. The influence of varying temporal contexts on frugivore choice, and their possible demographic and evolutionary consequences is poorly understood. We examined if temporal variation in fruit availability across a hierarchy of nested temporal levels (interannual, intraseasonal, 120 h, 24 h) altered frugivore choice for a complex seed dispersal system in dry tropical forests of southern India. The interactions between Phyllanthus emblica and its primary disperser (ruminants) was mediated by another frugivore (a primate),which made large quantities of fruit available on the ground to ruminants. The direction and strength of crop size and neighborhood effects on this interaction varied with changing temporal contexts.Fruit availability was higher in the first of the two study years, and at the start of the season in both years. Fruit persistence on trees,determined by primate foraging, was influenced by crop size andconspecific neighborhood densities only in the high fruit availability year. Fruit removal by ruminants was influenced by crop size in both years and neighborhood densities only in the high availability year. In both years, these effects were stronger at the start of the season.Intraseasonal reduction in fruit availability diminished inequalities in fruit removal by ruminants and the influence of crop size and fruiting neighborhoods. All trees were not equally attractive to frugivores in a P. emblica population at all points of time. Temporal asymmetry in frugivore-mediated selection could reduce potential for co-evolution between firugivores and plants by diluting selective pressures. Inter-dependencies; formed between disparate animal consumers can add additional levels of complexity to plant-frugivore mutualistic networks and have potential reproductive consequences for specific individuals within populations.

Contesting Forests and Power : Dispute, Violence and Negotiations

"Contesting Forests and Power; Dispute, Violence and Negotiations in Central Java" is an ethnographic analysis of an ongoing forest land dispute and its negotiations in an upland forest village in the district of Wonosobo, Central Java. Rather than focusing only on the village site, this ethnography of global connections explores the inequalities of power in different negotiation arenas and how these power relations have had an effect on the dispute and efforts made to settle it. Today, national and transnational connections have an effect on how land disputes develop. This study argues that different cosmological and cultural orientations influence how the dispute and its negotiations have evolved. It draws its theoretical framework from legal and political anthropology by looking at the position of law in society, exploring state formation processes and issues of power. The dispute over state forest land is about a struggle over sovereignty which involves violence on the parts of different parties who maintain that they have a legitimate right to the state forest land. This anthropological study argues that this dispute and its negotiations reflect the plurality of laws in Java and Indonesia in a complex way. It shows that this dispute over forests and land in Java has deep historical roots that were revealed as the conflict emerged. Understanding land disputes in Java is important because of the enormous potential for conflicts over land and other natural resources throughout Indonesia. After the fall of President Suharto in 1998, disputes over access to state forest land emerged as a problem all over upland Java. As the New Order came to an end, forest cover on state forest lands in the Wonosobo district was largely destroyed. Disputes over access to land and forests took another turn after the decentralization effort in 1999, suggesting that decentralization does not necessarily contribute to the protection of forests. The dispute examined here is not unique, but, rather, this study attempts to shed light on forest-related conflicts all around upland Indonesia and on the ways in which differential power relations are reflected in these conflicts and the negotiation processes meant to resolve them.

Yhteinen verkosto? : Tutkimus nuorten syrjäytymistä ehkäisevistä poikkihallinnollisista ryhmistä

Since the 1990s, European policy strategies have stressed the mutual responsibility and joint action of all societal branches in preventing social problems. Network policy is an integral part of the new governance that generates a new kind of dependency between the state and civil society in formulating and adhering to policy goals. Using empirical group interview data collected in Helsinki, the capital of Finland, this case study explores local multi-agency groups and their efforts to prevent the exclusion of children and young people. These groups consist mainly of professionals from the social office, youth clubs and schools. The study shows that these multi-agency groups serve as forums for professional negotiation where the intervention dilemma of liberal society can be addressed: the question of when it is justified and necessary for an authority or network to intervene in the life of children and their families, and how this is to be done. An element of tension in multi-agency prevention is introduced by the fact that its objectives and means are anchored both in the old tradition of the welfare state and in communitarian rhetoric. Thus multi-agency groups mend deficiencies in wellbeing and normalcy while at the same time try to co-ordinate the creation of the new community, which will hopefully reduce the burden on the public sector. Some of the professionals interviewed were keen to see new and even forceful interventions to guide the youth or to compel parents to assume their responsibilities. In group discussions, this approach often met resistance. The deeper the social problems that the professionals worked with, the more solidarity they showed for the families or the young people in need. Nothing seems to assure professionals and to legitimise their professional position better than advocating the under-privileged against the uncertainties of life and the structural inequalities of society. The groups that grappled with the clear, specific needs of certain children and families were the most capable of co-operation. This requires the approval of different powers and the expertise of distinct professions as well as a forum to negotiate case-specific actions in professional confidentiality. The ideals of primary prevention for everyone and value discussions alone fail to inspire sufficient multiagency co-operation. The ideal of a network seems to give word and shape to those societal goals that are difficult or even impossible to reach, but are nevertheless yearned for: mutual understanding of the good life, close social relationships, mutual trust and active agency for all citizens. Individualisation, the multiplicity of life styles and the possibility to choose have come true in such a way that the very idea of a mutual and binding network can be attained only momentarily and between restricted participants. In conclusion, uniting professional networks that negotiate intervention dilemmas with citizen networks based on changing compassions and feelings of moral superiority seems impossible. Rather, one should encourage openness to scrutiny among tangential or contradicting groups, networks and communities. Key words: network policy, prevention of exclusion, multi-agency groups, young people

Social Networks and Everyday Practices in Russia

My doctoral dissertation in sociology and Russian studies, Social Networks and Everyday Practices in Russia, employs a "micro" or "grassroots" perspective on the transition. The study is a collection of articles detailing social networks in five different contexts. The first article examines Russian birthdays from a network perspective. The second takes a look at health care to see whether networks have become obsolete in a sector that is still overwhelmingly public, but increasingly being monetarised. The third article investigates neighbourhood relations. The fourth details relationships at work, particularly from the vantage point of internal migration. The fifth explores housing and the role of networks and money both in the Soviet and post-Soviet era. The study is based on qualitative social network and interview data gathered among three groups, teachers, doctors and factory workers, in St. Petersburg during 1993-2000. Methodologically it builds on a qualitative social network approach. The study adds a critical element to the discussion on networks in post-socialism. A considerable consensus exists that social networks were vital in state socialist societies and were used to bypass various difficulties caused by endemic shortages and bureaucratic rigidities, but a more debated issue has been their role in post-socialism. Some scholars have argued that the importance of networks has been dramatically reduced in the new market economy, whereas others have stressed their continuing importance. If a common denominator in both has been a focus on networks in relation to the past, a more overlooked aspect has been the question of inequality. To what extent is access to networks unequally distributed? What are the limits and consequences of networks, for those who have access, those outside networks or society at large? My study provides some evidence about inequalities. It shows that some groups are privileged over others, for instance, middle-class people in informal access to health care. Moreover, analysing the formation of networks sheds additional light on inequalities, as it highlights the importance of migration as a mechanism of inequality, for example. The five articles focus on how networks are actually used in everyday life. The article on health care, for instance, shows that personal connections are still important and popular in post-Soviet Russia, despite the growing importance of money and the emergence of "fee for service" medicine. Fifteen of twenty teachers were involved in informal medical exchange during a two-week study period, so that they used their networks to bypass the formal market mechanisms or official procedures. Medicines were obtained through personal connections because some were unavailable at local pharmacies or because these connections could provide medicines for a cheaper price or even for free. The article on neighbours shows that "mutual help" was the central feature of neighbouring, so that the exchange of goods, services and information covered almost half the contacts with neighbours reported. Neighbours did not provide merely small-scale help but were often exchange partners because they possessed important professional qualities, had access to workplace resources, or knew somebody useful. The article on the Russian work collective details workplace-related relationships in a tractor factory and shows that interaction with and assistance from one's co-workers remains important. The most interesting finding was that co-workers were even more important to those who had migrated to the city than to those who were born there, which is explained by the specifics of Soviet migration. As a result, the workplace heavily influenced or absorbed contexts for the worker migrants to establish relationships whereas many meeting-places commonly available in Western countries were largely absent or at least did not function as trusted public meeting places to initiate relationships. More results are to be found from my dissertation: Anna-Maria Salmi: Social Networks and Everyday Practices in Russia, Kikimora Publications, 2006, see www.kikimora-publications.com.

Rethinking Media Pluralism : A Critique of Theories and Policy Discourses

This study examines different ways in which the concept of media pluralism has been theorized and used in contemporary media policy debates. Access to a broad range of different political views and cultural expressions is often regarded as a self-evident value in both theoretical and political debates on media and democracy. Opinions on the meaning and nature of media pluralism as a theoretical, political or empirical concept, however, are many, and it can easily be adjusted to different political purposes. The study aims to analyse the ambiguities surrounding the concept of media pluralism in two ways: by deconstructing its normative roots from the perspective of democratic theory, and by examining its different uses, definitions and underlying rationalities in current European media policy debates. The first part of the study examines the values and assumptions behind the notion of media pluralism in the context of different theories of democracy and the public sphere. The second part then analyses and assesses the deployment of the concept in contemporary European policy debates on media ownership and public service media. Finally, the study critically evaluates various attempts to create empirical indicators for measuring media pluralism and discusses their normative implications and underlying rationalities. The analysis of contemporary policy debates indicates that the notion of media pluralism has been too readily reduced to an empty catchphrase or conflated with consumer choice and market competition. In this narrow technocratic logic, pluralism is often unreflectively associated with quantitative data in a way that leaves unexamined key questions about social and political values, democracy, and citizenship. The basic argument advanced in the study is that media pluralism needs to be rescued from its depoliticized uses and re-imagined more broadly as a normative value that refers to the distribution of communicative power in the public sphere. Instead of something that could simply be measured through the number of media outlets available, the study argues that media pluralism should be understood in terms of its ability to challenge inequalities in communicative power and create a more democratic public sphere.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.

Tyttöjen kesken : Monikulttuurisuus ja sukupuolten tasa-arvo nuorisotyössä.

Among Girls Youth Work, Multiculturalism and Gender Equality Finland s increasingly multicultural society concerns younger generations in a very particular manner. Starting already in pre-school kindergartens, children from different cultural backgrounds share their everyday existence. The focus of this study is Finland s increasingly multicultural society that has challenged youth work professionals in particular and made them rethink questions related to content, basic values and goals of youth work. These reconsiderations include the following essential questions: which of these pedagogic principles are defined as Finnish, and under what kinds of circumstances would the youth workers be ready to negotiate about them. These questions, which are related to multiculturalism, are then linked to the girls position, status and gender equality. The research examines how gender equality is articulated in relation to multiculturalism and vice versa, in what contexts youth work-related questions are negoatiated in, and how these negotiations then relate to gender issues. The present study combines theoretical concepts and debates from both post-colonial and youth research, and has benefited greatly from previous research which has examined the everyday lives of young people with multicultural backgrounds and conceptualised the different meanings of age, ethnicity, culture and gender. Neither multiculturalism nor gender equality is, however, taken as a given concept in this study; rather the research focuses on how youth workers understand and define these concepts and how they are used. The emphasis has been on monitoring the varying consequences of different understandings and definitions in terms of everyday work and practices. The goal of this study has been to find typical ways of conceptualising multiculturalism, gender equality and the role of girls in the context of youth work. The focus of the research is not just the youth workers different views but also the notions of the girls themselves. These are then further analysed by examining the ways the girls negotiate their agency. Examples of how the girls agency is defined and the different forms of agency that are offered to the girls within the context of leisure time activities and youth work have been sought. The kind of agency the girls then assume is also examined. The data in this research is comprised of interviews with young people with multicultural backgrounds (n=39), youth workers (n=42) and of ethnographic fieldwork (2003 2005). The fieldwork concentrated on following different types of youth work activities that were targeted at girls with migrant backgrounds. These were organized both by selected municipalities and NGOs. The research shows that various questions related to multicultural issues have enhanced the visibility of gender equality in the field of youth work. The identification of gender-based inequality is especially closely linked to the position of girls from migrant backgrounds. These girls are a source of particular worry and the aim of the many activity groups for migrant girls is to educate them so that they can become equal Finnish citizens . The youth work itself is seen as gender-neutral and equality based. Equality in this context is defined as a purely quantitative concept, and the solution to any possible inequalities is thus the exact same treatment for everyone . The girls themselves seem mainly confused by the role that is offered to them. They would need a voice and the possibility to have an impact on the planning of youth work activities. They want to have their views heard. The role of the victim assigned to them is very confining and makes it difficult to act. At the same time the research shows how gender-sensitive youth work is seen to mean youth work with girls. Gender-sensitive work with boys is not really done or is done very little, even if many of the interviewees are of the opinion that the true materialization of gender equality would require boys to be taken into account too. The principle of gender equality should be shared by the entire youth work profession. Keywords Youth work, equality, multiculturalism, gender sensitivity, agency, girls, young people, sexuality

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Distributed nonlinear optimization algorithms for general network problems

There are a number of large networks which occur in many problems dealing with the flow of power, communication signals, water, gas, transportable goods, etc. Both design and planning of these networks involve optimization problems. The first part of this paper introduces the common characteristics of a nonlinear network (the network may be linear, the objective function may be non linear, or both may be nonlinear). The second part develops a mathematical model trying to put together some important constraints based on the abstraction for a general network. The third part deals with solution procedures; it converts the network to a matrix based system of equations, gives the characteristics of the matrix and suggests two solution procedures, one of them being a new one. The fourth part handles spatially distributed networks and evolves a number of decomposition techniques so that we can solve the problem with the help of a distributed computer system. Algorithms for parallel processors and spatially distributed systems have been described.There are a number of common features that pertain to networks. A network consists of a set of nodes and arcs. In addition at every node, there is a possibility of an input (like power, water, message, goods etc) or an output or none. Normally, the network equations describe the flows amoungst nodes through the arcs. These network equations couple variables associated with nodes. Invariably, variables pertaining to arcs are constants; the result required will be flows through the arcs. To solve the normal base problem, we are given input flows at nodes, output flows at nodes and certain physical constraints on other variables at nodes and we should find out the flows through the network (variables at nodes will be referred to as across variables).The optimization problem involves in selecting inputs at nodes so as to optimise an objective function; the objective may be a cost function based on the inputs to be minimised or a loss function or an efficiency function. The above mathematical model can be solved using Lagrange Multiplier technique since the equalities are strong compared to inequalities. The Lagrange multiplier technique divides the solution procedure into two stages per iteration. Stage one calculates the problem variables % and stage two the multipliers lambda. It is shown that the Jacobian matrix used in stage one (for solving a nonlinear system of necessary conditions) occurs in the stage two also.A second solution procedure has also been imbedded into the first one. This is called total residue approach. It changes the equality constraints so that we can get faster convergence of the iterations.Both solution procedures are found to coverge in 3 to 7 iterations for a sample network.The availability of distributed computer systems — both LAN and WAN — suggest the need for algorithms to solve the optimization problems. Two types of algorithms have been proposed — one based on the physics of the network and the other on the property of the Jacobian matrix. Three algorithms have been deviced, one of them for the local area case. These algorithms are called as regional distributed algorithm, hierarchical regional distributed algorithm (both using the physics properties of the network), and locally distributed algorithm (a multiprocessor based approach with a local area network configuration). The approach used was to define an algorithm that is faster and uses minimum communications. These algorithms are found to converge at the same rate as the non distributed (unitary) case.

Karnaugh map synthesis of multigate threshold networks

It has been shown in an earlier paper that I-realizability of a unate function F of up to six variables corresponds to ' compactness ' of the plot of F on a Karnaugh map. Here, an algorithm has been presented to synthesize on a Karnaugh map a non-threahold function of up to Bix variables with the minimum number of threshold gates connected in cascade. Incompletely specified functions can also be treated. No resort to inequalities is made and no pre-processing (such as positivizing and ordering) of the given switching function is required.

A homotopy approach for stabilizing single-input systems with control structure constraints

A linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized. Some examples of feedback realizations which impose constraints on the gain vector are: static output feedback, constant gain feedback for several operating points of a system, and two-controller feedback. We consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them. Each of these problems is cast into a problem of solving a system of equalities and inequalities. In this formulation, the coefficients of the quadratic and linear factors of the closed-loop characteristic polynomial are the variables. To solve the system of equalities and inequalities, a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework. Our method is illustrated with an example for each class of control structure constraint.