Let $K$ be a nonempty closed convex subset of a real Hilbert space $H$ such that $K\pm K\subset K$, $T\: K\rightarrow H$ a $k$-strict pseudo-contraction for some $0\leq k<1$ such that $F(T)=\{x\in K\: x=Tx\}\neq \emptyset $. Consider the following iterative algorithm given by $$ \forall x_1\in K,\quad x_{n+1}=\alpha _n\gamma f(x_n)+\beta _nx_n+((1-\beta _n)I-\alpha _n A)P_KSx_n,\quad n\geq 1, $$ where $S\: K\rightarrow H$ is defined by $Sx=kx+(1-k)Tx$, $P_K$ is the metric projection of $H$ onto $K$, $A$ is a strongly positive linear bounded self-adjoint operator, $f$ is a contraction. It is proved that the sequence $\{x_n\}$ generated by the above iterative algorithm converges strongly to a fixed point of $T$, which solves a variational inequality related to the linear operator $A$. Our results improve and extend the results announced by many others.
We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called “strong P-type”. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit is the inductive limit of the strong duals, but on the other hand we show that this is indeed true if one deals with projective spectra of retractive (LB)-spaces. Finally, we apply our results to a question of Grothendieck about biduals of (LF)-spaces.
The role of the FTO gene in obesity development is well established in populations around the world. The NYD-SP18 variant has been suggested to have a similar effect on BMI, but the role of this gene in determining BMI has not yet been verified. The objective of ou r study was to confirm the association between NYD-SP18 rs6971091 SNP and BMI in the Slavic population and to analyze i) the gender-specific effects of NYD-SP18 on BMI and ii) the si multaneous effect of FTO rs17817449 and NYD-SP18 on BMI. We analyzed a sample of a large adult population based on the post-MONICA study (1,191 males and 1,368 females). Individuals were analyzed three times over 9 years. NYD-SP18 rs6971091 SNP is related to BMI in males (2000/1 GG 28.3±3.7 kg/m 2 vs. +A 27.5±3.7 kg/m 2 P<0.0005; in other examinations P<0.05 and <0.005), but not in females (all P values over 0.48 in all three examinations). Further analysis revealed the significant additive effect (but not the interaction) of FTO and NYD-SP18 SNPs on BMI in males (all P<0.01). These results suggest that association between NYD-SP18 rs6971091 SNP and BMI may be restricted to males. Furthermore, variants within NYD-SP18 and FTO genes revealed a significant additive effect on BMI values in males., J. A. Hubacek, D. Dlouha, V. Lanska, V. Adamkova., and Obsahuje bibliografii
In this paper we prove that the lateral completion of a projectable lattice ordered group is strongly projectable. Further, we deal with some properties of Specker lattice ordered groups which are related to lateral completeness and strong projectability.
A reflexive topological group $G$ is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group $G$ and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.
This paper introduces the notion of a strong retract of an algebra and then focuses on strong retracts of unary algebras. We characterize subuniverses of a unary algebra which are carriers of its strong retracts. This characterization enables us to describe the poset of strong retracts of a unary algebra under inclusion. Since this poset is not necessarily a lattice, we give a necessary and sufficient condition for the poset to be a lattice, as well as the full description of the poset.
An exchange ring $R$ is strongly separative provided that for all finitely generated projective right $R$-modules $A$ and $B$, $A\oplus A\cong A \oplus B\Rightarrow A\cong B$. We prove that an exchange ring $R$ is strongly separative if and only if for any corner $S$ of $R$, $aS+bS=S$ implies that there exist $u,v\in S$ such that $au=bv$ and $Su+Sv=S$ if and only if for any corner $S$ of $R$, $aS+bS=S$ implies that there exists a right invertible matrix $\begin{pmatrix} a&b\\ *&* \end{pmatrix} \in M_2(S)$. The dual assertions are also proved.
We study singular boundary value problems with mixed boundary conditions of the form (p(t)u ' ) ' + p(t)f(t, u, p(t)u ' ) = 0, lim t→0+ p(t)u ' (t) = 0, u(T) = 0, where [0, T] ⊂ . We assume that D ⊂ R 2 , f satisfies the Carathéodory conditions on (0, T) × D, p ∈ C[0, T] and 1/p need not be integrable on [0, T]. Here f can have time singularities at t = 0 and/or t = T and a space singularity at x = 0. Moreover, f can change its sign. Provided f is nonnegative it can have even a space singularity at y = 0. We present conditions for the existence of solutions positive on [0, T).
Let $(X,\Vert \cdot \Vert _X)$ be a real Banach space and let $E$ be an ideal of $L^0$ over a $\sigma $-finite measure space $(Ø,\Sigma ,\mu )$. Let $(X)$ be the space of all strongly $\Sigma $-measurable functions $f\: Ø\rightarrow X$ such that the scalar function ${\widetilde{f}}$, defined by ${\widetilde{f}}(ø)=\Vert f(ø)\Vert _X$ for $ø\in Ø$, belongs to $E$. The paper deals with strong topologies on $E(X)$. In particular, the strong topology $\beta (E(X), E(X)^\sim _n)$ ($E(X)^\sim _n=$ the order continuous dual of $E(X)$) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.