For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best $L_p$-approximation with an unbounded number of finite poles are considered.
This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference system.
An analytical formula for the time transformation TDB-TDT valid over a few thousand years around J2000 has been computed with an accuracy at the 1 ns level. This computation was carried out by integrating the differential equation derived from a general metric.
The transformation TDB-TDT is independent of the PPN parameters, γ and β, and of the 3 most commonly-used coordinate systems (standard, isotropic, Painlevé), at least at the 1 ns level.
The analytical theories ELP2000 and VSOP82 developped at the Bureau des Longitudes were used for the motions pf the solar systém bodies, Furthermore, the numerical procedures described by Hellings and Davis to calculate this transformation yield different results to our own procedure. These differences are due to the long-period terms of the planetary theories which are averaged out
in the numerical procedures. These terms are generated by resonances in the Solar System.
This study aims at developing an artificial intelligence-based (ANN based) analytical method to analyze earthquake performances of the reinforced concrete (RC) buildings. In the scope of the present study, 66 real RC buildings with four to ten storeys were subject to performance analysis according to 19 parameters considered effective on the performance of RC buildings. In addition, the level of performance of these buildings in case of an earthquake was determined on the basis of the 4-grade performance levels specified in Turkish Earthquake Code-2007 (TEC-2007). Thus, an output performance data group was created for the analyzed buildings, in accordance with the input data. Thanks to the ANN-based fast evaluation algorithm mentioned above and developed within the scope of the proposed project study, it will be possible to make an economic and rapid evaluation of four to ten-storey RC buildings in Turkey with great accuracy (about 80%). Detection of post-earthquake performances of RC buildings in the scope of the present study will facilitate reaching important results in terms of buildings, which will be beneficial for Civil Engineers of Turkey and similar countries.
We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.
We are interested in algorithms for constructing surfaces Γ of possibly small measure that separate a given domain Ω into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians, p → 1, under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients.
Let $S$ be a non-empty subset of positive integers. A partition of a positive integer $n$ into $S$ is a finite nondecreasing sequence of positive integers $a_1, a_2, \dots , a_r$ in $S$ with repetitions allowed such that $\sum ^r_{i=1} a_i = n$. Here we apply Pólya’s enumeration theorem to find the number $¶(n;S)$ of partitions of $n$ into $S$, and the number ${\mathrm DP}(n;S)$ of distinct partitions of $n$ into $S$. We also present recursive formulas for computing $¶(n;S)$ and ${\mathrm DP}(n;S)$.
We introduce and study some new subclasses of starlike, convex and close-to-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.
An approach to indexical beliefs is presented and defended in the paper. The account is inspired by David Kaplan’s representationalist analysis of de re belief reports. I argue that imposing additional constraints on the Kaplanian notion of representation results in an elegant theory of indexical beliefs. The theory is committed to representations of limited accessibility but is not committed to relativized proposition, special de se contents or propositions of limited accessibility.
Analytical solutions describing the 1D substance transport in streams have many limitations and factors, which determine their accuracy. One of the very important factors is the presence of the transient storage (dead zones), that deform the concentration distribution of the transported substance. For better adaptation to such real conditions, a simple 1D approximation method is presented in this paper. The proposed approximate method is based on the asymmetric probability distribution (Gumbel’s distribution) and was verified on three streams in southern Slovakia. Tracer experiments on these streams confirmed the presence of dead zones to various extents, depending mainly on the vegetation extent in each stream. Statistical evaluation confirms that the proposed method approximates the measured concentrations significantly better than methods based upon the Gaussian distribution. The results achieved by this novel method are also comparable with the solution of the 1D advection-diffusion equation (ADE), whereas the proposed method is faster and easier to apply and thus suitable for iterative (inverse) tasks.