Description of Euler bricks using Fibonacci's identity

We show how the Fibonacci's identity is used to obtain Euler bricks. Also,we put forward the relation between Fibonacci's identity and Euler's formula, which provides the description of Euler's bricks with noninteger spatial diagonal. Finally,we establish a relation between the Euler bricks with integer and noninteger spatial diagonals.Comment: 8 page

A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces

The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation is extended to a narrow-band neighborhood of the surface. The resulting extended equation is a non-degenerate PDE and it is solved on a bulk mesh that is unaligned to the surface. An unfitted finite element method is used to discretize extended equations. Error estimates are proved for finite element solutions in the bulk domain and restricted to the surface. The analysis admits finite elements of a higher order and gives sufficient conditions for archiving the optimal convergence order in the energy norm. Several numerical examples illustrate the properties of the method.Comment: arXiv admin note: text overlap with arXiv:1301.470

Mutual Phase Locking of Very Nonidentical Spin Torque Nanooscillators via Spin Wave Interaction

In this paper the mutual phase locking theory of very nonidentical spin-torque nanooscillators, which is based on the Slavin-Tiberkevich model, considering the theory of nonlinear oscillations, is developed. Using generalized Adler equation we calculate phase-locking region of the system with spinwave coupling in the parameter plane - distance between nanocontacts and radii difference. We describe trajectories of such a system in the phase space and show the effect of a broadband synchronization. We introduce a generalization of this approach to the ensembles of spin-torque nanooscillatorsComment: 6 pages, 2 figure

The Role of Pre-Replication Complex Proteins in Drosophila Ovarian Stem Cell Maintenance and Proliferation

Cancer stem cells (CSCs) may hold the key to advances in cancer research. Like adult tissue-specific stem cells, CSCs are able to self-renew and last a lifetime. These shared characteristics can thus be used to help learn more about CSCs and how they work. More specifically, understanding the molecular mechanisms that control adult tissue-specific stem cell proliferation can lead to better regenerative therapies and a better understanding of CSCs overall. The proliferation of Drosophila ovarian germline stem cells (GSCs), as well as their ability to create differentiated daughters, relies on proper DNA replication. By investigating the regulation of stem cell division, we can advance our knowledge of the fine line between regulated versus unregulated division, and the causes behind each. One of the major components of replication control are the pre-initiation complex (PIC) proteins, which are essential for proper DNA replication. For example, Minichromosome maintenance protein 10 (MCM10) is recruited during the transition from G1 to S-phase, and aids in the recruitment of other PIC proteins to the replication fork. To investigate whether PIC proteins are essential for stem cell function, two comparisons were made. The average number of GSCs per germarium in control and mutant flies were compared. Next EdU staining was utilized to calculate the percentage of GSCs that were in S-phase. Once again, control and mutant percentages were compared to determine if MCM10 mutants affect stem cell function. We demonstrate that the loss of MCM10 results in a reduction in stem cell number and an increase S-phase length which is an indication of an altered cell cycle. Ongoing studies are investigating if stem cell loss in MCM10 mutants is due to DNA damage and to observe the effects of other pre-replication initiation complex mutant proteins. Combined, our data suggests that PIC proteins are critical for stem cell function

Val av lokalproducerade frukter och grönsaker i säsong - en väg mot hållbar konsumtion?

Båda nationellt och internationellt står säkerställning och arbete mot en hållbar konsumtion och produktion på agendan. Detta kan kopplas till alla de 17 globala hållbarhetsmålen som styr mot Agenda 2030, liksom flera av Sveriges miljömål. Rekommendationen från livsmedelsverket är konsumtion av minst 500 gram frukter och grönsaker om dagen, och ju större andel av kosten som utgörs av dessa desto bättre för miljön och klimatet och inte minst för hälsan. Denna uppsats försöker genom en omfattande litteraturstudie svara på frågan om hur konsumenternas val av lokalproducerad frukt och grönsaker i säsong kan bidra till en mer hållbar konsumtion och produktion. För att kunna svara på denna fråga var det nödvändig att ta reda på vad som menas med lokalproducerat och säsong, vilket behandlas i uppsatsens bakgrund. Flera studier visar tydligt alla fördelarna som är förknippade med ett kosthåll med rikliga mängder frukt och grönsaker. Ännu större fördelar däribland ett betydligt lägre miljö- och klimatavtryck kan uppnås av att välja lokalproducerat och säsonganpassade frukter och grönsaker som alternativ till dem som till exempel produceras i växthus, och ännu större effekt har det om man ersätter animaliska produkter med dessa. Dock sett från ett större perspektiv och hela livsmedelssektorn tagit i betraktning är effekten av konsumtion av frukter och grönsaker efter säsong och lokalproducerat ganska lågt. Andra åtgärd, särskild reduktion i konsumtion av animaliska produkter, och minskning av matsvinnet är också viktiga aspekter av en hälsosam och hållbar kostvana.Both nationally and internationally, ensuring and working towards sustainable consumption and production are on the agenda. This can be linked to all 17 global sustainability goals that steer towards Agenda 2030, as well as several of Sweden's environmental goals. The recommendation from the National Food Agency (Livsmedelsverket) is consumption of at least 500 grams of fruits and vegetables a day, and the greater proportion of the diet that consists of these, the better for the environment and the climate and not least to our health. Through an extensive literature review, this thesis tries to answer the question of how consumers' choice of locally produced fruit and vegetables in season can contribute to more sustainable consumption and production. To answer this question, it was necessary to find out what is meant by locally produced and seasonal, which is brought up in the background of this essay. Several studies clearly show the many benefits associated with a diet with rich amounts of fruits and vegetables. Even greater benefits, including a significantly lower environmental and climate footprint can be achieved by choosing locally produced and seasonal fruit and vegetables as alternatives to those produced in for example greenhouses, and it has an even greater effect if these replace animal products. However, seen from a larger perspective and the entire food sector considered, the effect of consumption of fruits and vegetables according to season and locally produced is quite low. Other measures, particularly reduction in consumption of animal products, and reduction of food waste are also important aspects of a healthy and sustainable diet

Powers of sets in free groups

We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best possible for each n>0.Comment: 3 page

ROLE OF JUDICIAL ORGANS IN PROVIDING THE STABILITY OF LAND LEGAL RELATIONS

Abstract.In the submitted article the following is analyzed: a concept of the land right taking into account the available doctrinal views in domestic science. The possibility of protection of the rights in the field of land legal relationship as by means of the state jurisdiction represented by judicial authorities, and public jurisdiction, represented by the arbitration courts is established. Separate types of land disputes proceeding from law-enforcement practice are separately analyzed.Keywords: land disputes; judicial authorities; receivership proceeding; law-enforcement practice