Factor versus palindromic complexity of uniformly recurrent infinite words

We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1) \leq \Delta C(n) + 2, for all n \in N. For a large class of words it is a better estimate of the palindromic complexity in terms of the factor complexity then the one presented by Allouche et al. We provide several examples of infinite words for which our estimate reaches its upper bound. In particular, we derive an explicit prescription for the palindromic complexity of infinite words coding r-interval exchange transformations. If the permutation \pi connected with the transformation is given by \pi(k)=r+1-k for all k, then there is exactly one palindrome of every even length, and exactly r palindromes of every odd length.Comment: 16 pages, submitted to Theoretical Computer Scienc

Various Properties of Sturmian Words

This overview paper is devoted to Sturmian words. The first part summarizes different characterizations of Sturmian words. Besides the well known theorem of Hedlund and Morse it also includes recent results on the characterization of Sturmian words using return words or palindromes. The second part deals with substitution invariant Sturmian words, where we present our recent results. We generalize one-sided Sturmian words using the cut-and-project scheme and give a full characterization of substitution invariant Sturmian words.

Assessment of investment in heating house

Bakalářská práce posuzuje způsoby, kterými se dají snížit náklady na vytápění rodinného domu. Po výpočtu tepelné ztráty objektu jsou vybírána vhodné tepelně-izolační aplikace na snížení prostupu tepla přes fasádu, strop a okna stavby. V dalším kroku je vybírán účinnější a ekologicky šetrnější způsob vytápění. Návratnosti použitých investic vybraných opatření jsou znázorněna graficky.Bachelor thesis assesses the ways in which you can reduce the cost of heating a house. After the calculation of heat loss, there are chosen appropriate thermal-insulation applications to reduce heat transmission through the facade, roof and windows of the building. In the next step is chosen more efficient and environmentally friendly way of heating. Return on investments of selected applications, are shown graphically.

Proof of Brlek-Reutenauer conjecture

Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n) +2 - P_U(n+1) - P_u(n), where C_u and P_u are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.Comment: 9 page

Grate Boiler for Biomass and Coal Co-combustion

Tato diplomová práce řeší návrh roštového kotle na spalování dřevní štěpky nebo hnědého uhlí o tepelném výkonu 160 MW. Stechiometrie spalin je vypočtena dle zadaného složení jednotlivých paliv. Rozměry jednotlivých výhřevných ploch jsou primárně vypočteny pro spalování dřevní štěpky a následně překontrolovány pro spalování hnědého uhlí. Návrh kotle je zakončen kontrolou celkového tepelného výkonu. Návrh kotle je doplněn výkresovou dokumentací.This thesis solves a design of a grate boiler burning wood chips or brown coal with a heat output of 160 MW. Stoichiometry flue gas is calculated according to the specified composition of each fuel. The dimensions of the individual heating surfaces are primarily calculated for burning wood chips and subsequently checked for the combustion of brown coal. Design of the boiler is completed by checking the overall heat output. Boiler design is accompanied by drawing documentation.

Languages invariant under more symmetries: overlapping factors versus palindromic richness

Factor complexity $\mathcal{C}$ and palindromic complexity $\mathcal{P}$ of infinite words with language closed under reversal are known to be related by the inequality $\mathcal{P}(n) + \mathcal{P}(n+1) \leq 2 + \mathcal{C}(n+1)-\mathcal{C}(n)$ for any $n\in \mathbb{N}$\,. Word for which the equality is attained for any $n$ is usually called rich in palindromes. In this article we study words whose languages are invariant under a finite group $G$ of symmetries. For such words we prove a stronger version of the above inequality. We introduce notion of $G$-palindromic richness and give several examples of $G$-rich words, including the Thue-Morse sequence as well.Comment: 22 pages, 1 figur

Specular sets

We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets.Comment: arXiv admin note: substantial text overlap with arXiv:1405.352

Novel assay for the detection of CRP protein in rabbit leukocytes using flow cytometry

C-reactive protein (CRP) is an acute phase serum protein secreted by liver hepatocytes. Besides its presence in the serum, CRP was also found on the surface of human leukocytes. However, the binding ability of CRP to rabbit leukocytes has never been previously investigated. The objective of our study was to optimize the detection of rabbit CRP binding leukocytes in order to observe the acute phase of immune response by flow cytometry after Complete Freund´s Adjuvant (CFA) administration. Blood samples were analysed using ELISA assay and flow cytometry immediately before and 2 days after the CFA administration. Significant (P<0.01) increase in the proportion of CRP+ leukocytes (up to 10%) and in their subsets (lymphocytes up to 14% and granulocytes up to 8%) were observed in samples after CFA immunization. ELISA also revealed significantly (P<0.01) higher CRP concentration in rabbit blood plasma after CFA immunization (about 3 mg/L) compared to control samples (about 1.5 mg/L) before immunization. In conclusion, the increase in level of CRP protein during the immune response in rabbits could be measured beside the ELISA also using flow cytometry via CRP binding leukocytes. This novel assay could be therefore successfully applied in further biomedical and veterinary research

New possibilities of using DEMATEL and ERPN in the new PFMEA hybrid model

The aim of the paper is to examine the requirements of producers in post-communist countries with lower economic level. The first requirement was how to overcome the limitations of conventional PFMEA to propose measures effectively. The second requirement solved the economic effect of failure modes. The aim of the paper was to create a new hybrid PFMEA–DEMATEL–ERPN model to manage failure modes to resolve the requirements. The DEMATEL model overcame the limitations of PFMEA. DEMATEL data were used to estimate the functionality of the proposed models. Criteria such as the occurrence of defective products and the probability of their occurrence (O and RPN) were monitored. ERPN also overcame the limitations of PFMEA. Internal and external costs arise as effects of failure modes. The costs were included in the economic evaluation of the models. We validated the models in a transfer pressing process. The estimation of models’ functionality proved to be correct. The economic evaluation refined the research results and resolved the second requirement of the manufacturers. The DEMATEL and ERPN models (compared to PFMEA) proved their validity when the use of PFMEA was limited. By using DEMATEL, we registered the lowest number of defective products and the lowest costs

Interval exchanges, admissibility and branching Rauzy induction

We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular interval exchange set is a regular interval exchange set with the same number of intervals. Derivation is taken here with respect to return words. We characterize the admissible intervals using a branching version of the Rauzy induction. We also study the case of regular interval exchange transformations defined over a quadratic field and show that the set of factors of such a transformation is primitive morphic. The proof uses an extension of a result of Boshernitzan and Carroll