In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let f(z) and g(z) be two transcendental entire functions of finite order, and α(z) a small function with respect to both f(z) and g(z). Suppose that c is a non-zero complex constant and n ≥ 7 (or n ≥ 10) is an integer. If f n (z)(f(z)−1)f(z +c) and g n (z)(g(z) − 1)g(z + c) share ''(α(z), 2)'' (or (α(z), 2)∗ ), then f(z) ≡ g(z). Our results extend and generalize some well known previous results.
Let $FG$ be a group algebra of a group $G$ over a field $F$ and ${\mathcal U}(FG)$ the unit group of $FG$. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $FA_4$ over any finite field of characteristic $3$ and the structure of the unit group of $FQ_{12}$ over any finite field of characteristic $2$, where $Q_{12}=\langle x, y; x^6=1, y^2=x^3, x^y=x^{-1} \rangle $.
As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.
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].
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
The PC is and will remain a basic instrument in the laboratory arsenal in the next few years. The key role of the IBM PC and its clones prompted us to develop a universal multifunctional I/O board (CNIMCJL) for this computer. The board will make it possible to use the IBM PC for a wide range of tasks from a simple interface for laboratory processing of data to complex IBM PC-based instruments, e.g. a stimulator, signal analyzer, chart recorder. The present article summarizes the experience gathered during the design and application of the described I/O board in more than 10 different IBM PC-based laboratory and clinical systems listed in the Appendix. An example of the application of the I/O board is presented in the conclusion of this report together with the discussion of the future role of new Application-Specific Integration Circuits (ASICs) and single chip processors in this domain.
Using sequence alignment, a conserved domain in the 3' untranslated region (UTR) of the cytoplasmic heat shock protein 90 (HSP90) of Lepidoptera was found. This region is highly variable in other insect groups. Furthermore, universal primers were designed to amplify the complete coding sequence (CDS) of HSP90 from total genomic DNA in Lepidoptera, avoiding the commonly used reverse transcription-polymerase chain reaction (RT-PCR) and 3', 5'-rapid amplification of cDNA ends (RACE) methods based on cDNA. These primers amplified a fragment of about 2.25 kb in the 11 species tested, which represent seven different families of Lepidoptera, including moths and butterflies. The results suggest that the conserved domain of 3'UTR is universal in Lepidoptera and these primers successfully amplify the complete CDS of cytoplasmic HSP90 from genomic DNA. and Peng Jun XU, Tong LI, Jin Hua XIAO, Robert W. MURPHY, Huang DA WEI.
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.