A New Family of Solvable Self-Dual Lie Algebras

A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of non-reductive self-dual Lie algebras: an orthogonal direct product, a double-extension of an Abelian algebra, and a Wigner contraction. It is shown that the presented algebras cannot be obtained by these methods.Comment: LaTeX, 12 page

Tensor Network Methods for Invariant Theory

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical approach provides an alternative to the polynomial equations that describe invariants, which often contain a large number of terms with coefficients raised to high powers. This approach also enables one to use known methods from tensor network theory (such as the matrix product state factorization) when studying polynomial invariants. As our main example, we consider invariants of matrix product states. We generate a family of tensor contractions resulting in a complete set of local unitary invariants that can be used to express the R\'enyi entropies. We find that the graphical approach to representing invariants can provide structural insight into the invariants being contracted, as well as an alternative, and sometimes much simpler, means to study polynomial invariants of quantum states. In addition, many tensor network methods, such as matrix product states, contain excellent tools that can be applied in the study of invariants.Comment: 21 page

A q-analogue of convolution on the line

In this paper we study a q-analogue of the convolution product on the line in detail. A convolution product on the braided line was defined algebraically by Kempf and Majid. We adapt their definition in order to give an analytic definition for the q-convolution and we study convergence extensively. Since the braided line is commutative as an algebra, all results can be viewed both as results in classical q-analysis and in braided algebra. We define various classes of functions on which the convolution is well-defined and we show that they are algebras under the defined product. One particularly nice family of algebras, a decreasing chain depending on a parameter running through (0,1], turns out to have 1/2 as the critical parameter value above which the algebras are commutative. Morerover, the commutative algebras in this family are precisely the algebras in which each function is determined by its q-moments. We also treat the relationship between q-convolution and q-Fourier transform. Finally, in the Appendix, we show an equivalence between the existence of an analytic continuation of a function defined on a q-lattice, and the behaviour of its q-derivatives.Comment: 31 pages; many small corrections; accepted by Methods and Applications of Analysi

Developing modular product family using GeMoCURE within an SME

Companies adopt the strategy of producing variety of products to be competitive and responsive to market. Product variation is becoming an important factor in companies' ability to accurately meet customer requirements. Ever increasing consumer options mean that customers have more choices than ever before which put commercial pressures on companies to continue to diversify. This can be a particular problem within Small to Medium Enterprises (SMEs) who do not always have the level of resources to meet these requirements. As such, methods are required that provide means for companies to be able to produce a wide range of products at the lowest cost and shortest time. This paper details a new modular product design methodology that provides a focus on developing modular product families. The methodology's function is described and a case study detailed of how it was used within an SME to define the company's product portfolio and create a new Generic Product Function Structure from which a new family of product variants can be developed. The methodology lends itself to modular re-use which has the potential to support rapid development and configuration of product variants

Perhetyökansio

Ajatus opinnäytetyöhön saatiin työelämästä ja omista työelämän kiinnostuksen kohteista. Toiminnallinen opinnäytetyömme käsittelee korjaavan perhetyön kehittämistä. Opinnäytetyön produktin taustalla on työelämälähtöinen tarve kehittää työväline tukemaan perhetyötä. Produkti on suunnattu käytettäväksi kaikille korjaavan perhetyön toimijoille. Tämä opinnäytetyö toteutettiin vuosina 2012-2013. Opinnäytetyön tarkoituksena oli kehittää apuväline korjaavan perhetyön suunnitteluun ja kirjaamiseen. Perheelle annetaan kansion kautta mahdollisuus ymmärtää perhetyön tarkoitusperiä, miksi asetetaan jokin tavoite ja miten tavoite saavutetaan. Produktin avulla perhetyön piirin asiakkaille luodaan kokemus tavoitteellisesta perhetyöstä. Perheen tuen tarpeita kartoitetaan kansion eri osa-alueilla, jonka ansiosta tuki voidaan kohdentaa oikeisiin ongelmakohtiin. Perhetyökansion toteutuksessa on käytetty haastatteluja, keskusteluita eri ammattilaisten kanssa sekä käytännön testaamista. Tuotokseksi saatiin vanhoja sekä uusia menetelmiä hyödyntävä työväline, jota voidaan kehittää niissä instansseissa joissa työvälinettä tullaan käyttämään. Raportissa käydään läpi perhetyökansion osioita ja niiden taustalla olevaa teoriapohjaa. Raportissa käsitellään perhetyötä, menetelmiä ja produktin valmistamisen vaiheita.The idea of thesis is based on our work and on our intrests in work. Thesis handles development of reconstructive family work. Product of thesis is based on work life and the need to develop tools for support of family work. Product is aimed for all the workers around family work. This thesis was produced during years 2012-2013. The main purpose of our thesis was to develope a tool for planning and registering of correcting family work. Our product gives family an opportunity to understand the main reasons of family work, why is there a goal and how to achieve it. Product creates the experience of purpose for the customers around family work. The needs of support is charted with different sections of the product, which creates an opportunity to focus on family's real problems. The product was made by using interviews, practical testing and conversations with dfferent professionals around family work. Final product utilizes old and new methods, which can be recreated by workers around reconstructive family work. Report explains the sections of our product and the basic theory of these sections. Report also includes family work, methods and phases of creating the product

Lyfe-cycle effects on household expenditures: A latent-variable approach

Using data from the Spanish household budget survey, we investigate life- cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.Structural equations, multi-group analysis, life cycle effects, product expenditures