On a curvature flow in a band domain with unbounded boundary slopes

<p style='text-indent:20px;'>This paper is devoted to an anisotropic curvature flow of the form <inline-formula><tex-math id="M1">\begin{document}$ V = A(\mathbf{n})H + B(\mathbf{n}) $\end{document}</tex-math></inline-formula> in a band domain <inline-formula><tex-math id="M2">\begin{document}$ \Omega : = [-1,1]\times {\mathbb{R}} $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ \mathbf{n} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ V $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ H $\end{document}</tex-math></inline-formula> denote respectively the unit normal vector, normal velocity and curvature of a graphic curve <inline-formula><tex-math id="M6">\begin{document}$ \Gamma_t $\end{document}</tex-math></inline-formula>. We require that the curve <inline-formula><tex-math id="M7">\begin{document}$ \Gamma_t $\end{document}</tex-math></inline-formula> contacts <inline-formula><tex-math id="M8">\begin{document}$ \partial \Omega $\end{document}</tex-math></inline-formula> with slopes equaling to the heights of the contact points (which corresponds to a kind of Robin boundary conditions). In spite of the unboundedness of the boundary slopes, we are able to obtain the <i>uniform interior gradient estimates</i> for the solutions by using the zero number argument. Furthermore, when <inline-formula><tex-math id="M9">\begin{document}$ t\to \infty $\end{document}</tex-math></inline-formula>, we show that <inline-formula><tex-math id="M10">\begin{document}$ \Gamma_t $\end{document}</tex-math></inline-formula> converges to a traveling wave with cup-shaped profile and <i>infinite</i> boundary slopes in the <inline-formula><tex-math id="M11">\begin{document}$ C^{2,1}_{\rm{loc}} ((-1,1)\times {\mathbb{R}}) $\end{document}</tex-math></inline-formula>-topology.</p>

Evolution of the number of communicative civilizations in the Galaxy: implications on Fermi paradox

It has been recently proposed DeVito [(2019) On the meaning of Fermi's paradox. Futures, 389–414] that a minimal number of contacts with alien radio-communicative civilizations could be justified by their logarithmically slow rate of growth in the Galaxy. Here we further develop this approach to the Fermi paradox, with the purpose of expanding the ensemble of the possible styles of growth that are consistent with the hypothesis of a minimal number of contacts. Generalizing the approach in DeVito (2019), we show that a logarithmic style of growth is still found. We also find that a style of growth following a power law would be admissible, however characterized by an exponent less than one, hence describing a sublinear increase in the number of communicative civilizations, still qualitatively in agreement with DeVito (2019). No solutions are found indicating a superlinear increase in the number of communicative civilizations, following for example an exponentially diverging law, which would cause, in the long run, an unsustainable proliferation. Although largely speculative, our findings corroborate the idea that a sublinear rate of increase in the number of communicative civilizations in the Galaxy could constitute a further resolution of Fermi paradox, implying a constant and minimal – but not zero – number of contacts.

Modeling slow-processing of toxin messenger RNAs in type-I Toxin-Antitoxin systems: post-segregational killing and noise filtering

In type-I toxin-antitoxin (TA) systems, the action of growth-inhibiting toxin proteins is counteracted by the antitoxin small RNAs (sRNAs) that prevent the translation of toxin messenger RNAs (mRNAs). When a TA module is encoded on a plasmid, the short lifetime of antitoxin sRNA compared to toxin mRNAs mediates post-segregational killing (PSK) that contribute the plasmid maintenance, while some of the chromosomal encoded TA loci have been reported to contribute to persister formation in response to a specific upstream signal. Some of the well studied type-I TA systems such ashok/sokare known to have a rather complex regulatory mechanism. Transcribed full-length toxin mRNAs fold such that the ribosome binding site is not accessible and hence cannot be translated. The mRNAs are slowly processed by RNases, and the truncated mRNAs can be either translated or bound by antitoxin sRNA to be quickly degraded. We analyze the role of this extra processing by a mathematical model. We first consider the PSK scenario, and demonstrate that the extra processing compatibly ensures the high toxin expression upon complete plasmid loss, without inducing toxin expression upon acquisition of a plasmid or decrease of plasmid number to a non-zero number. We further show that the extra processing help filtering the transcription noise, avoiding random activation of toxins in transcriptionally regulated TA systems as seen in chromosomal ones. The present model highlights impacts of the slow processing reaction, offering insights on why the slow processing reactions are commonly identified in multiple type-I TA systems.

FAKTOR-FAKTOR YANG MEMPENGARUHI KEBERHASILAN REDENOMINASI MATA UANG: PENDEKATAN DATA HISTORIS DAN PERCOBAAN

Redenomination is a simplification of nominal value of currency by reducing digit (zero number) without reducing the real value of the currency. The main objective of this research was to examine whether the economic conditions at the time of redenomination may affect the success of currency redenomination. The methods used were regression analysis on historical data of 30 countries which are involved in redenominating their currencies, economic experiments with t-test, and survey of people’ perspective. Based on regression analysis, inflation will decrease and economic growth will rise higher after redenomination, if previously a country have experienced high economic growth as well. Based on experimental research, when inflation was high, redenomination could increase the selling price. Otherwise, when inflation was low, redenomination could decrease the selling price. Changes in selling price after redenomination was not affected significantly by differences in economic growth conditions. In different economic conditions, redenomination policy did not significantly affect the changes number of transactions and total value of transactions in the market. From the survey results, public did not believe government can control inflation after redenomination. Redenomination also will not affect consumption pattern

Dampak Redenominasi terhadap Kinerja Perekonomian: Pendekatan Ekonomi Eksperimental

Impact of Redenomination on Economic Perspective: An Experimental Economic ApproachThere is persistent debate between theoretical and empirical findings on the impact of redenomination on economic performance. Hence, this study aims to analyze the impacts of inflation, economic growth, reducing reducing digit (zero number), and stages of redenomination to changes in transaction prices and the number of the transactions using experimental methods. The result showed redenomination could decrease the transaction prices and transaction value. The best conditions to applied redenomination policy was directly in low inflation and high growth.Keywords: Redenomination; Inflation; Economic Growth; ExperimentAbstrakPenelitian ini dilakukan karena adanya teori dan hasil empiris yang masih menjadi perdebatan mengenaidampak kebijakan redenominasi terhadap kinerja perekonomian. Tujuan penelitian ini adalah untukmenganalisis dampak inflasi, pertumbuhan ekonomi, penghilangan jumlah angka nol, serta tahapanredenominasi terhadap perubahan harga dan jumlah transaksi menggunakan metode ekperimental.Redenominasi secara keseluruhan dapat menurunkan harga transaksi dan jumlah transaksi. Hasil analisisjuga menunjukkan bahwa kondisi yang ideal untuk melaksanakan redenominasi adalah secara langsungpada kondisi inflasi rendah dan pertumbuhan ekonomi yang tinggi.

Spectral properties of n-normal operators

For a bounded linear operator T on a complex Hilbert space and n ? N, T is said to be n-normal if T*Tn = TnT*. In this paper we show that if T is a 2-normal operator and satisfies ?(T) ? (-?(T)) ? {0}, then T is isoloid and ?(T) = ?a(T). Under the same assumption, we show that if z and w are distinct eigenvalues of T, then ker(T-z)? ker(T-w). And if non-zero number z ? C is an isolated point of ?(T), then we show that ker(T-z) is a reducing subspace for T. We show that if T is a 2-normal operator satisfying ?(T) ?(-?(T)) = 0, then Weyl?s theorem holds for T. Similarly, we show spectral properties of n-normal operators under similar assumption. Finally, we introduce (n,m)-normal operators and show some properties of this kind of operators.

IMPACT OF REDENOMINATION ON PRICE, VOLUME, AND VALUE OF TRANSACTION: AN EXPERIMENTAL ECONOMIC APPRAOCH

Redenomination is a simplification of nominal value of currency by reducing digit (zero number) without reducing the real value of the currency. This paper provide an overview of the impact of redenomination to changes in transaction prices, transaction value and number of transactions using experimental methods. The results showed that the most substantial price reduction on the elastic goods can occur in conditions of low economic growth and high inflation. Price reductions also occur in conditions of high economic growth and low inflation. Based on results, there is no change between before and after redenomination on the number of transactions. So redenomination would not change the number of transactions in elastic goods. Conditions which can change the value of the transaction is low growth and high growth in high inflation condition. Conditions of high inflation and low growth will decrease the value of the transaction while the condition of high inflation with high growth will increase the value of the transaction.

PENENTU KEBERHASILAN REDENOMINASI MATA UANG: PENDEKATAN HISTORIS DAN EKSPERIMENTAL

Redenomination is a simplification of nominal value of currency by reducing digit (zero number) without reducing the real value of the currency. The main objective of this research was to examine whether the economic conditions at the time of redenomination may affect the success of currency redenomination. The methods used were regression analysis on historical data of 30 countries which are involved in redenominating their currencies, economic experiments with t-test, and survey of people’ perspective. Based on regression analysis, inflation will decrease and economic growth will rise higher after redenomination, if previously a country have experienced high economic growth as well. Based on experimental research, when inflation was high, redenomination could increase the selling price. Otherwise, when inflation was low, redenomination could decrease the selling price. Changes in selling price after redenomination was not affected significantly by differences in economic growth conditions. In different economic conditions, redenomination policy did not significantly affect the changes number of transactions and total value of transactions in the market. From the survey results, public did not believe government can control inflation after redenomination. Redenomination also will not affect consumption pattern. Keywords: Redenomination, Inflation, Economic Growth, Experiment JEL Classification: C91, E31, E42, E58