1,541,619 research outputs found

    Integers in number systems with positive and negative quadratic Pisot base

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    We consider numeration systems with base β\beta and β-\beta, for quadratic Pisot numbers β\beta and focus on comparing the combinatorial structure of the sets Zβ\Z_\beta and Zβ\Z_{-\beta} of numbers with integer expansion in base β\beta, resp. β-\beta. Our main result is the comparison of languages of infinite words uβu_\beta and uβu_{-\beta} coding the ordering of distances between consecutive β\beta- and (β)(-\beta)-integers. It turns out that for a class of roots β\beta of x2mxmx^2-mx-m, the languages coincide, while for other quadratic Pisot numbers the language of uβu_\beta can be identified only with the language of a morphic image of uβu_{-\beta}. We also study the group structure of (β)(-\beta)-integers.Comment: 19 pages, 5 figure

    Number representation using generalized (β)(-\beta)-transformation

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    We study non-standard number systems with negative base β-\beta. Instead of the Ito-Sadahiro definition, based on the transformation TβT_{-\beta} of the interval [ββ+1,1β+1)\big[-\frac{\beta}{\beta+1},\frac{1}{\beta+1}\big) into itself, we suggest a generalization using an interval [l,l+1)[l,l+1) with l(1,0]l\in(-1,0]. Such generalization may eliminate certain disadvantages of the Ito-Sadahiro system. We focus on the description of admissible digit strings and their periodicity.Comment: 22 page

    A Study on Financial Deficit and Declining Birthrate — From the Viewpoint of “Children as a Social Security Revenue Source” —-

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    While social security systems in the developed countries including Japan are taking pay-as-you-go system based on the cooperation between generations, the fertility number as a tax base of social security is decreasing and the low fertility tendency is common in the developed countries. And if each generation behaves with considering life-cycle and chooses the fertility level rationally, it is considered that there is a possibility that the existence of coverage for social security by fiscal deficit may affect the fertility to some extent. Hence, in this paper, if regarding children as a tax base of social security, we consider the following analysis; 1) from a macro viewpoint, by constructing a dynamic overlapping generation model, how the coverage for social security by fiscal deficit affects on fertility, 2) from a micro viewpoint, in case that there is no relationship between social security transfer and fertility of each household, how the fertility number in the whole economy affects. As a result, to 1), we get an implication that there is a possibility fiscal deficit may affect negatively on fertility from the time series analysis with using 17 countries panel data. Moreover, to 2), from a micro viewpoint, by simplified Nash equilibrium game, in case that there is no relationship between social security benefit and fertility number, there is a negative impact as compared to a social optimal fertility level. In this paper, it is shown that, if children are regarded as a tax base, in order to avoid the negative relationship, it is necessary to consider the following policies; 1) the coverage for social security by fiscal deficit should be set to zero, 2) and a system such that the payment schedule is depending on the number of household children should be introduced, considering the balance of benefit and burden.Finacial deficit: endogenous fertility: child investment: social security system

    The Role of Social Security in Household Decisions: Var Estimates of Saving and Fertility Behaviour in Germany

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    Estimating saving and fertility simultaneously by the VAR method, we find that social security cover has a positive effect on household saving, and a negative effect on fertility. In Germany, as in other countries where the hypothesis was tested, social security is thus good for growth. A possible explanation for this unconventional finding is that compulsory saving in the form of pension contributions tends to displace intra-family transfers, rather than asset formation. However, the negative effect of social security on fertility tends to erode the system’s own contributory base, because it reduces the number of future contributors. That is one of the reasons why, in Germany as elsewhere, pay-as-you-go pension systems tend to be financially unstable. To some extent, this is counteracted by child-related benefits, which tend to encourage fertility, but the effect appears to be weak.

    Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems

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    In this paper we study the expansions of real numbers in positive and negative real base as introduced by R\'enyi, and Ito & Sadahiro, respectively. In particular, we compare the sets Zβ+\mathbb{Z}_\beta^+ and Zβ\mathbb{Z}_{-\beta} of nonnegative β\beta-integers and (β)(-\beta)-integers. We describe all bases (±β)(\pm\beta) for which Zβ+\mathbb{Z}_\beta^+ and Zβ\mathbb{Z}_{-\beta} can be coded by infinite words which are fixed points of conjugated morphisms, and consequently have the same language. Moreover, we prove that this happens precisely for β\beta with another interesting property, namely that any integer linear combination of non-negative powers of the base β-\beta with coefficients in {0,1,,β}\{0,1,\dots,\lfloor\beta\rfloor\} is a (β)(-\beta)-integer, although the corresponding sequence of digits is forbidden as a (β)(-\beta)-integer.Comment: 22p

    Pilot Contamination Mitigation Techniques in Massive MIMO Systems: A Precoding Approach

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    A massive MIMO system comprises of base stations with a very large number of antennas serving a considerably smaller number of users and providing substantial gains in spectral and energy efficiency in comparison to conventional MIMO systems. However, these benefits are limited by pilot contamination which is caused by the use of training sequences for channel estimation. This negative effect has given rise to various research works on schemes to mitigate pilot contamination and among them are precoding techniques. This thesis reviews some of the precoding techniques that mitigate pilot contamination and studies the effect of pilot contamination on the performance of massive MIMO systems through simulations. It was found that pilot contamination leads to a severe degradation of the network performance. Furthermore, as the number of antennas at the base station increases, the effect of pilot contamination is more prominent on the probability of outage and the bit error rate but this is not the case for the average sum capacity. With the average sum capacity, the effect diminishes very gradually as the antenna array at the base station grows. However, overall, the presence of pilot contamination further lowers the network performance as the number of antennas at the base station increases.fi=Opinnäytetyö kokotekstinä PDF-muodossa.|en=Thesis fulltext in PDF format.|sv=Lärdomsprov tillgängligt som fulltext i PDF-format

    Analysis of the booster DC to DC converter with feedback

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    The field effect power transistors are used in many applications in electromechanical systems. Control of the field effect power transistors requires isolated 5V control signals and isolated 12V DC sources. The first problem is resolved by using optical pairs: light emitting diodes with phototransistors. The second problem can be resolved by using impulse voltage sources. The primary coil of a transformer is connected to the battery by a transistor switch. In the first period of operation of this voltage source, the energy is stored in the magnetic field of transformer’s inductance. In the second period, the energy is delivered to the output voltage source. Energy is delivered from the secondary transformer’s coil to the output capacitor through a diode. As a rule, one separate voltage source has a small power, that is why one impulse voltage source can have the necessary number of isolated output voltage sources, i.e., 3, 6, 9, 12, etc So, we can design an impulse DC to DC voltage source with multiple isolated output voltage sources. By changing the charge time of the inductor, we can control the output voltage by using negative feedback proportional to the output voltage and / or a current. In the report, different variants of impulse voltage sources are considered, with analog base elements and on the base of microprocessors. Analyses operation of these impulse voltage sources enable us to determine the period (frequency) of internal operation with ordered maximum transformer efficiency values. The concept of controlled impulse voltage sources is very important because these sources are very simple. They are reliable and have high level of electrical isolation
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