The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the other hand the "metric" approach leads to new elementary conditions equivalent to the uniform convexity. The initial part of the paper contains the proof that discus spaces (they seem to have a richer structure) are identical with bead spaces.
The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory, signal power, system energy and a power balance relation are other basic terms used in the paper.
Unikaryon montanum sp, n. infects the fat body, muscle, Malpighian tubules and ovaries of adult Ips typographus L. The development is haplokaryotic, with separate nuclei during the schizogony and sporogony. Sporonts have the cellular envelope with added layer of electron dense material. Two types of spores are formed: small broad-oval primary spores, 1.5 x 1.0 pm, with warty surface of spore wall, uninucleate, with isofilar polar filament in 5/6 coils and elongated-oval environmental spores, 0.8-1 x 2 pm, with warty spore wall attenuated at the anterior end, uninucleate, with spore polar filament in 8 coils. Both types have a dual polaroplast with the anterior part of a layer of confluent fine lamellae ending posteriorly in bulbous processes, and posterior part composed of coil of tubules.
Usually, an abelian $\ell $-group, even an archimedean $\ell $-group, has a relatively large infinity of distinct $a$-closures. Here, we find a reasonably large class with unique and perfectly describable $a$-closure, the class of archimedean $\ell $-groups with weak unit which are “$\mathbb Q$-convex”. ($\mathbb Q$ is the group of rationals.) Any $C(X,\mathbb Q)$ is $\mathbb Q$-convex and its unique $a$-closure is the Alexandroff algebra of functions on $X$ defined from the clopen sets; this is sometimes $C(X)$.
Understanding the genetic mechanisms of morphological evolution is one of the greatest challenges in evolutionary biology and for such studies sexually dimorphic traits in closely related species are of prime interest. In the Drosophila bipectinata species complex, which consists of four closely related species, namely D. bipectinata, D. parabipectinata, D. malerkotliana and D. pseudoananassae, the pattern of sex combs (a sexually dimorphic trait) is found to be highly diversified. The present investigation documents some unique and new sex comb phenotypes and demarcates intra- and interspecific variations in the sex comb pattern among the four species and their hybrids. There is remarkable similarity in sex comb pattern of D. bipectinata and D. parabipectinata but it differs from that of D. malerkotliana and D. pseudoananassae, which is in consistent with the phylogenetic relationships among the four species traced out by cytological, biochemical and molecular studies. The genetic basis of inheritance of sex comb patterns, its plausible implication with biogeographical distribution of species and the relationship between degree of hybridization and phylogenetic proximity have been addressed.
We investigate the problem with perturbed periodic boundary values \[ \left\rbrace \begin{array}{ll}y^{\prime \prime \prime }(x) + a_2(x) y^{\prime \prime }(x) + a_1(x) y^{\prime }(x) + a_0(x) y(x) = f(x) , y^{(i)}(T) = c y^{(i)}(0), \ i = 0, 1, 2; \ 0 < c < 1 \end{array}\right.\] with $a_2, a_1, a_0 \in C[0,T]$ for some arbitrary positive real number $T$, by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients $a_2$, $a_1$ and $a_0$ which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all physical signals and quantities (amplitude, velocity, acceleration, curvature, etc.) experience.
It is proved that a radical class $\sigma $ of lattice-ordered groups has exactly one cover if and only if it is an intersection of some $\sigma $-complement radical class and the big atom over $\sigma $.
Let k be a nonnegative integer or infinity. For a ∈ C ∪ {∞} we denote by Ek(a; f) the set of all a-points of f where an a-point of multiplicity m is counted m times if m ≤ k and k + 1 times if m > k. If Ek(a; f) = Ek(a; g) then we say that f and g share the value a with weight k. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).
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 $.