In this paper, we consider the classification of unital extensions of $AF$-algebras by their six-term exact sequences in $K$-theory. Using the classification theory of $C^*$-algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of $AF$-algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of $AF$-algebras by stable purely infinite simple $C^*$-algebras with nontrivial $K_1$-groups up to isomorphism.
The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given parameter λ > 0 allows to construct via conditioning any Ali-Mikhail-Haq copula with parameter μ \in [0,λ].
A universal set of equations for determining chlorophyll (Chl) a, accessory Chl b, c, and d, and total Chl have been developed for 90 % acetone, 100 % methanol, and ethanol solvents suitable for estimating Chl in extracts from natural assemblages of algae. The presence of phaeophytin (Ph) a not only interferes with estimates of Chl a but also with Chl b and c determinations. The universal algorithms can hence be misleading if used on natural collections containing large amounts of Ph. The methanol algorithms are severely affected by the presence of Ph and so are not recommended. The algorithms were tested on representative mixtures of Chls prepared from extracts of algae with known Chl composition. The limits of detection (and inherent error, ±95 % confidence limit) for all the Chl equations were less than 0.03 g m-3. The algorithms are both accurate and precise for Chl a and d but less accurate for Chl b and c. With caution the algorithms can be used to calculate a Chl profile of natural assemblages of algae. The relative error of measurements of Chls increases hyperbolically in diluted extracts. For safety reasons, efficient extraction of Chls and the convenience of being able to use polystyrene cuvettes, the algorithms for ethanol are recommended for routine assays of Chls in natural assemblages of aquatic plants.
Let $H(K)$ be the Hilbert space with reproducing kernel $K$. This paper characterizes some sufficient conditions for a sequence to be a universal interpolating sequence for $H(K)$.
Dynamic soil properties are important parameters for the design of structures subjected to various dynamic/cyclic loading such as earthquake which can be obtained by in situ and laboratory measurements. Numerous empirical and mathematical models have been proposed to predict the dynamic properties of soils, including maximum shear modulus (Gmax), normalized shear modulus (G/Gmax - γ) curve, reference shear strain (γr), minimum damping ratio (Dmin) and damping ratio (D - γ) curve. However, the majority of the existing models were proposed for specific soil types, loading characteristics, initial soil fabrics and strain ranges. This paper proposes five universal models to estimate the Gmax, γr and Dmin values, and also G/Gmax - γ and D - γ curves using a database that contains 117 tests on 5 different granular soils. The proposed models include the effect of grading characteristics, void ratio, mean effective confining pressure, consolidation stress ratio (KC) and specimen preparation method. The models are validated using experimental data from previous studies for granular soils. The results indicate that the proposed models are capable of evaluating the dynamic properties of granular soil., Meysam Bayat., and Obsahuje bibliografii
A simple renewal process is a stochastic process {Xn} taking values in {0,1} where the lengths of the runs of 1's between successive zeros are independent and identically distributed. After observing X0,X1,…Xn one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional distribution of the time to renewal.
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an h0 with probability one and whose cardinality grows at most at exponential rate h0.