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1
Content available remote When a constant subsequence implies ultimate periodicity
EN
We show a curious property of sequences given by the recurrence a0 = h1(0), an = f(n) an-1 + h1 (n) h2 (n)n, n > 0, where f, h1, h2 ϵ Z[X]. Namely, if the sequence (akn+l)n ϵ N is constant for some k ϵ N+ and l ϵ N, then either (a2n+l)n ϵ N = (0)n ϵ N and (a2n)n ϵ N is a geometric progression, or (an)n ϵ N is ultimately periodic with period dividing 2.
EN
In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.
EN
Seismic strain and b value are used to quantify seismic potential in the Zagros region (Iran). Small b values (0.69 and 0.69) are related to large seismic moment rates (9.96×1017 and 4.12×1017) in southern zones of the Zagros, indicating more frequent large earthquakes. Medium to large b values (0.72 and 0.92) are related to small seismic moment rates (2.94×1016 and 6.80×1016) in middle zones of the Zagros, indicating less frequent large earthquakes. Small b value (0.64) is related to medium seismic moment rate (1.38×1017) in middle to northern zone of the Zagros, indicating frequent large earthquakes. Large b value (0.87) is related to large seismic moment rate (2.29×1017) in northwestern zone, indicating more frequent large earthquakes. Recurrence intervals of large earthquakes (M > 6) are short in southern (10 and 14 years) and northwestern (13 years) zones, while the recurrence intervals are long in the middle (46 and 114 years) and middle to northern (25 years) zones.
EN
Seismic hazard assessment for Quetta is carried out using probabilistic seismic hazard analysis technique based on area sources and augmented by line source used for the first time in Pakistan. Seismic data has been collected and analyzed in spatial and temporal domains. Five Seismic Zones have been modeled in line with tectonics of the region with b-value of 1.14 using regression. The b-value is slightly higher, which is attributed to the fact that aftershocks were not removed as it distorted the dataset. Five fault sources are modeled, with three as reverse and two as strike-slip with 7.8 as maximum magnitude. Mach Structure is included in the tectonics for the first time. The attenuation relation used in the present study is recommended by various researchers. The expected Peak Ground Acceleration for 500-year return period is 4.79 m/s2 for rock outcrop and characterized as very high. Furthermore, variation in spectral acceleration within Quetta city is observed, for which spectral curves are developed for four different places.
5
EN
The mean return time of a discrete Markov chain to a point x is the reciprocal of the invariant probability π(x). We revisit this classical theme to investigate certain exit times for stochastic difference equations of autoregressive type. More specifically, we will discuss the asymptotics, as 0, of the first time that the n-dimensional process ...[wzór] (where ξ1, ξ2, . . . is a sequence of i.i.d. random n-vectors) leaves a given neighborhood of the fixed point of the contraction f.
PL
W artykule opisano wpływ procesu cięcia plazmą powietrzną, laserem oraz strumieniem wody na jakość powierzchni ciętej stopu aluminium 5754 o grubości 8 mm. Ocenie poddano jakość powierzchni po cięciu (odchyłkę prostopadłości, chropowatość powierzchni, kąt ukosu), szerokość szczeliny cięcia, sposób przebijania oraz zmiany strukturalne i zmiany twardości przy powierzchni cięcia.
EN
In this paper results of investigation of air plasma, laser beam and water-jet cutting processes on 5754 aluminum alloy surface quality were shown. Quality assessment of surface (perpendicular deviation, surface roughness, scarf angle), gap width after cutting, punching method and structural and hardness changes near the cutling surface were provided.
EN
Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
8
Content available remote A note on invariant sets
EN
A measurable set A is invariant with respect to a not necessarily symmetric sub-Markovian operator T on Lp (X, m) if T1A ≤ 1A, and strongly invariant if T1A = 1A. We show that these definitions accommodate many of the usual definitions of invariance, e.g., those used in Dirichlet form theory, ergodic theory or for stochastic processes. In finite measure spaces or if T∗ is sub-Markovian and recurrent, the notions of invariance and strong invariance coincide. We also show that for certain analytic semigroups of sub-Markovian operators, (strongly) invariant sets are already determined by a single operator, T1.
9
Content available remote A family of symmetric stable-like processes and its global path properties
EN
We extend the idea of the symmetric stable-like processes so that it includes the Brownian motion as well as the symmetric α-stable processes. We exhibit some sufficient conditions for their recurrence and conservativeness relying on the no-tion of Dirichlet forms. A criterion for conservativeness (Lemma 3.2) is also shown in terms of general Dirichlet forms and the associated generators.
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