Split (3)

train · 1M rows

text stringlengths 8 5.77M
--- abstract: 'In this paper, we study the equidistribution of certain families of special subvarieties in general mixed Shimura varieties. We introduce the notion of bounded sequences of special subvarieties, and we prove that the André-Oort conjecture holds for such sequences. The proof follows the equidistribution approach used by Clozel, Ullmo, and Yafaev in the pure case. We then propose the notion of test invariant of a special subvariety, which is adapted from the lower bound formula of degrees of special subvarieties in the pure case studied by Ullmo and Yafaev, and we show that sequences of special subvarieties with bounded test invariants are bounded, hence the André-Oort conjecture holds in this case.' address: \| Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, and School of Mathematical Sciences, University of Science and Technology of China\ No. 96 Jinzhai Road, Hefei, Anhui Province, 230026, P. R. China author: - Ke Chen title: \| bounded equidistribution of special subvarieties\ in mixed Shimura varieties --- Introduction to the main results ================================ In this paper, we study the equidistribution of certain families of special subvarieties in a general mixed Shimura variety, and the André-Oort conjecture for these varieties, as a generalization of some results in [@clozel; @ullmo] and in [@ullmo; @yafaev]. The theory of mixed Shimura varieties, including their canonical models and toroidal compactifications, is developed in [@pink; @thesis]. They serve as moduli spaces of mixed Hodge structures, and often arise as boundary components in the toroidal compactifications of pure Shimura varieties. Among mixed Shimura varieties there are Kuga varieties, cf. [@chen; @kuga], which are certain “universal” abelian schemes over Shimura varieties, and in general, a mixed Shimura variety can be realized as a torus bundle over a Kuga variety (namely a torsor whose structure group is a torus). Similar to the pure case, we have the notion of special subvarieties in mixed Shimura varieties. Y. André and F. Oort conjectured that the Zariski closure of a sequence of special subvarieties in a given pure Shimura variety remains a finite union of special subvarieties, cf. [@andre; @note] and [@oort; @conjecture]. R. Pink has proposed a generalization of this conjecture for mixed Shimura varieties by combining it with the Manin-Mumford conjecture and the Mordell-Lang conjecture for abelian varieties, a principal case of which is the following Let $M$ be a mixed Shimura variety, and let $(M_n)_n$ be a sequence of special subvarieties. Then the Zariski closure of $\bigcup_nM_n$ is a finite union of special subvarieties. Remarkable progress has been made for the André-Oort conjecture in the pure case, including the ergodic-Galois approach, cf. [@clozel; @ullmo], [@klingler; @yafaev], [@ullmo; @yafaev], [@yafaev; @bordeaux], the $p$-adic approach cf. [@moonen; @compositio], [@yafaev; @compositio], and the model-theoretic approach, cf. [@pila; @annals], [@scanlon; @bourbaki]. For the case of mixed Shimura varieties, Pila’s work in [@pila; @annals] has already included products of universal families of elliptic curves over modular curves as well as some torus bundles on them, and Scanlon has also considered in [@scanlon; @inventiones] some cases in the universal families of abelian varieties over the Siegel modular variety. Recently, Z. Gao has proved the conjecture for mixed Shimura varieties fibred over Siegel modular varieties. The strategy of Klingler-Ullmo-Yafaev is summarized in [@yafaev; @bordeaux]. It assumes the GRH (Generalized Riemann Hypothesis) for CM fields, and does not involve model-theoretic tools. The main ingredients of the strategy in the pure case can be expressed as the following “ergodic-Galois alternative”: - equidistribution of special subvarieties with bounded Galois orbits (using ergodic theory), cf. [@clozel; @ullmo] and [@ullmo; @yafaev]; - for a sequence of special subvarieties $(M_n)$ of unbounded Galois orbits, one can construct a new sequence of special subvarieties $(M_n')$ such that $\bigcup_nM_n$ has the same Zariski closure as $\bigcup_nM_n'$, and that $\dim M_n<\dim M_n'$ for $n$ large enough. Note that both ingredients involve estimations that rely on the GRH for CM fields. In this paper, we study the equidistribution part of the ergodic-Galois alternative for mixed Shimura varieties. Our main result is the following: Let $M$ be a mixed Shimura variety of the form $M_K({\mathbf{P}},Y)$ with $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{P}},Y)$ and $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$ a [[compact open subgroup]{}]{}of ${\mathbf{P}}({{\hat{\mathbb{Q}}}})$, and let $\pi:M{\rightarrow}S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ be the fibration over the pure Shimura variety $S$. Let $M_n$ be a sequence of special subvarieties in $M$. Write $E$ for the field of definition of $M$. Assume that the test invariants of $(M_n)$ are bounded, i.e. $$\tau_M(M_n)\leq C,\ \forall n$$ for some constant $C\in{\mathbb{R}}_{>0}$. Then the Zariski closure of $\bigcup_n M_n$ is a finite union of special subvarieties. Here the notion of test invariants is an analogue of the degree of Galois orbits against the automorphic line bundle in the pure case. The main theorem is deduced from a theorem of bounded equidistribution in certain spaces associated to mixed Shimura varieties, cf.\[equidistribution of TW-special subspaces\], \[bounded equidistribution\], \[bounded André-Oort\] and a characterization of special subvarieties with bounded Galois orbits using test invariants, cf. \[pure special subvarieties of bounded Galois orbits\], \[special subvarieties of bounded test invariants\]. We briefly explain the main idea of the paper. A mixed Shimura datum in the sense of [@pink; @thesis] is of the form $({\mathbf{P}},{\mathbf{U}},Y)$ with ${\mathbf{P}}$ a connected linear ${\mathbb{Q}}$-group, with a Levi decomposition ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}$, ${\mathbf{U}}$ a normal unipotent ${\mathbb{Q}}$-subgroup of ${\mathbf{P}}$ central in ${\mathbf{W}}$, and $Y$ a complex manifold homogeneous under ${\mathbf{U}}({\mathbb{C}}){\mathbf{P}}({\mathbb{R}})$ subject to some algebraic constraints. The notion of special subvarieties in mixed Shimura varieties is defined in a similar way as in the pure case. We often express it as an extension $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ with $({\mathbf{G}},X)$ some pure Shimura datum, and ${\mathbf{W}}$ the unipotent radical of ${\mathbf{P}}$, in which ${\mathbf{U}}$ is central. When ${\mathbf{U}}$ is trivial, we get Kuga data and Kuga varieties, cf. [@chen; @kuga]. Parallel to the pure case studied in [@clozel; @ullmo] and [@ullmo; @yafaev], we first consider the André-Oort conjecture for sequences of ${{{(\mathbf{T},w)}}}$-special subvarieties in a mixed Shimura variety $M$ defined by $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$. Here ${\mathbf{T}}$ is a ${\mathbb{Q}}$-torus in ${\mathbf{G}}$ and $w$ an element of ${\mathbf{W}}({\mathbb{Q}})$. Using the language of [@chen; @kuga] 2.10 etc, in a Kuga variety $M=\Gamma_{\mathbf{V}}\rtimes\Gamma_{\mathbf{G}}{\backslash}Y^+$ defined by $({\mathbf{P}},Y)={\mathbf{V}}\rtimes({\mathbf{G}},X)$, ${{{(\mathbf{T},w)}}}$-special subvarieties are defined by subdata of the form ${\mathbf{V}}'\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$, and they are obtained from diagrams of the form $$\xymatrix{ M'\ar[r]^\subset & M_{S'}\ar[r]^\subset \ar[d]^\pi & M \ar[d]^\pi\\ & S'\ar[r]^\subset & S}$$ where - $S=\Gamma_{\mathbf{G}}{\backslash}X^+$ is a pure Shimura variety and $\pi:M{\rightarrow}S$ is an abelian $S$-scheme defined by the natural projection $({\mathbf{P}},Y){\rightarrow}({\mathbf{G}},X)$; - $S'$ is a (pure) special subvariety of $S$ defined by $({\mathbf{G}}',X')$ with ${\mathbf{T}}$ equal to the connected center of ${\mathbf{G}}'$, - $M_{S'}$ is the abelian $S'$-scheme pulled-back from $M{\rightarrow}S$, and ${\mathbf{V}}'$ is a subrepresentation in ${\mathbf{V}}$ of ${\mathbf{G}}'$, corresponding to an abelian subscheme $A'$ of $M_{S'}{\rightarrow}S'$; - $M'$ is a translation of $A'$ by a torsion section of $M_{S'}{\rightarrow}S'$ given by $w$. In particular, this notion is more restrictive than ${\mathbf{T}}$-special subvarieties studied in [@chen; @kuga] as we specify $w$. The case in general mixed Shimura varieties is similar. We show that certain spaces of probability measures on $M$ associated to ${{{(\mathbf{T},w)}}}$-special subvarieties are compact for the weak topology, from which we deduce the equidistribution of the supports of such measures, as well as the André-Oort conjecture for such sequences of ${{{(\mathbf{T},w)}}}$-special subvarieties. We formulate the notion of $B$-bounded sequences of special subvarieties, which means special subvarieties that are ${{{(\mathbf{T},w)}}}$-special with ${{{(\mathbf{T},w)}}}$ coming from some prescribed finite set $B$ of pairs ${{{(\mathbf{T},w)}}}$ as above. The main result of [@ullmo; @yafaev] shows that in the pure case a sequence with bounded Galois orbits is $B$-bounded for some $B$, where sequences with bounded Galois orbits are sequences of special subvarieties whose Galois orbits are of bounded degree against the automorphic line bundle. In the mixed case, we propose the notion of test invariants for special subvarieties, and we prove a similar characterization of bounded sequences using test invariants. The paper is organized as follows: In Section 1, we recall the basic notions of mixed Shimura data, their subdata, mixed Shimura varieties, their special subvarieties, as well as their connected components. We emphasize the fibration of a mixed Shimura variety over a pure Shimura variety, whose fibers are torus bundles over abelian varieties. We also include some results about irreducible subdata and a few reductions for the André-Oort conjecture. Section 2 and 3 are concerned with ergodic-theoretic results in the equidistribution of special subvarieties. In Section 2, we introduce some measure-theoretic objects, such as lattice (sub)spaces, S-(sub)spaces, and canonical probability measures associated to special subvarieties in mixed Shimura varieties. The lattice (sub)spaces are similar to the cases treated in [@clozel; @ullmo] and [@chen; @kuga]. For a Kuga variety, the associated S-space is the variety itself; for a general mixed Shimura variety, the S-space is a subspace of the variety, which is a torsor over the corresponding Kuga variety by some compact tori. In particular, they support canonically defined probability measures and they are Zariski dense in the ambient mixed Shimura varieties. We also introduce the notion of a $B$-bounded sequence of special subvarieties, where $B$ is a finite set of pairs of the form $({\mathbf{T}},w)$ as is explained above. In Section 3, we prove the equidistribution of bounded sequences of special lattice subspaces and special S-spaces. The proof is reduced to the case when the bound $B$ consists of a single element ${{{(\mathbf{T},w)}}}$, and the arguments are completely parallel to the pure ${\mathbf{T}}$-special case in [@clozel; @ullmo] and [@ullmo; @yafaev]. The equidistribution of $B$-bounded S-subspaces implies the André-Oort conjecture for a $B$-bounded sequence of special subvarieties in a mixed Shimura variety. In the remaining sections we investigate the relation between bounded sequences and lower bounds of degrees of Galois orbits. In Section 4, we give a lower bound of the degrees of Galois orbits of a pure special subvariety $M'$ in a given mixed Shimura variety $M$ against the pull-back of the automorphic line bundle. The estimation is essentially reduced to the case studied in [@ullmo; @yafaev]. If the pure special subvariety under consideration is ${{{(\mathbf{T},w)}}}$-special, then the lower bound relies on the GRH for the splitting field $F_{\mathbf{T}}$ of ${\mathbf{T}}$, and it involves the discriminant of $F_{\mathbf{T}}$ and the position of $w$ relative to the level structure of the ambient mixed Shimura variety. We show that the study of the André-Oort conjecture can be reduced to ambient mixed Shimura data that are embedded in a “good product”, in which the splitting fields $F_{\mathbf{T}}$ of irreducible ${{{(\mathbf{T},w)}}}$-special subdata are CM fields. In this latter setting we estimate the contribution of unipotent translation in the lower bound. In Section 5, we consider a general special subvariety which is not pure. We did not prove an explicit lower bound formula in this case, instead we introduce the notion of test invariant as a substitute, and we show that a sequence with bounded test invariants is $B$-bounded for some finite $B$. We also show that in this case the Galois orbits are essentially minorated by the test invariants. The results in this section are formulated for ambient mixed Shimura embedded in “good products” as in Section 4. Recently we have been informed by GAO Ziyang on the work [@gao; @mixed] where he has proved the André-Oort conjecture for mixed Shimura varieties whose pure parts are subvarieties of Siegel modular varieties assuming the GRH for CM fields. His approach is model-theoretic, generalizing the works of [@pila; @annals] etc. He has obtained independently some results related to the Galois orbits of special points. Our treatment works for special subvarieties of higher dimension, but relies on the GRH. We hope that the results presented are still useful as a step towards the ergodic-Galois alternative for mixed Shimura varieties. Acknowledgement {#acknowledgement .unnumbered} --------------- The author thanks Prof.Emmanuel Ullmo heartily for suggesting to him the equidistribution approach towards the André-Oort conjecture for mixed Shimura varieties, without whose guidance this work would not have been possible. He thanks Mr. GAO Ziyang for discussion on mixed Shimura varieties and his work [@gao; @mixed]. He also thanks Mr. Cyril Démarche and Mr. LIANG Yongqi for discussion on strong approximation of semi-simple groups. Finally, he thanks the anonymous referee sincerely for a very careful reading of the manuscript and many useful suggestions. The author is partially supported by the following grants: National Key Basic Research Program of China, No. 2013CB834202, Chinese Universities Scientific Fund Project WK0010000029, and National Natural Science Foundation of China, Grant No. 11301495. Notations and conventions {#notations and conventions .unnumbered} ========================= Over a base ring $k$, a linear $k$-group ${\mathbf{H}}$ is a smooth affine algebraic $k$-group scheme, and ${\mathbf{T}}_{\mathbf{H}}$ is the connected center of ${\mathbf{H}}$, namely the neutral component of the center of ${\mathbf{H}}$. For ${\mathbf{V}}$ a free $k$-module of finite type, we have the general linear $k$-group ${{\mathbf{GL}}}_{\mathbf{V}}$, and we also view ${\mathbf{V}}$ as a vectorial $k$-group, i.e. isomorphic to ${\mathbb{G}}_{\mathrm{a}}^r$ with $r$ the rank of ${\mathbf{V}}$. We write ${\mathbb{S}}$ for the Deligne torus ${\mathrm{Res}}_{{\mathbb{C}}/{\mathbb{R}}}{{\mathbb{G}_\mathrm{m}}}_{\mathbb{C}}$. The ring of finite adeles is denoted by ${{\hat{\mathbb{Q}}}}$. ${\mathbf{i}}$ is a fixed square root of -1 in ${\mathbb{C}}$. For a real or complex analytic space (not necessarily smooth), its analytic topology is the one locally deduced from the archimedean metric on ${\mathbb{R}}^n$ or ${\mathbb{C}}^m$. A linear ${\mathbb{Q}}$-group is compact if its set of ${\mathbb{R}}$-points form a compact Lie group. For ${\mathbf{P}}$ a linear ${\mathbb{Q}}$-group with maximal reductive quotient ${\mathbf{P}}{{\twoheadrightarrow}}{\mathbf{G}}$, we write ${\mathbf{P}}({\mathbb{R}})^+$ resp. ${\mathbf{P}}({\mathbb{R}})_+$ for the preimage of ${\mathbf{G}}({\mathbb{R}})^+$ resp. of ${\mathbf{G}}({\mathbb{R}})_+$, in the sense of [@deligne; @pspm]. ${\mathbf{P}}({\mathbb{R}})^+$ is just the neutral component of the Lie group ${\mathbf{P}}({\mathbb{R}})$ because the fiber ${\mathbf{W}}({\mathbb{R}})$ of the projection ${\mathbf{P}}({\mathbb{R}}){\rightarrow}{\mathbf{G}}({\mathbb{R}})$, namely the unipotent radical of ${\mathbf{P}}({\mathbb{R}})$, is a connected Lie group. For ${\mathbf{H}}$ a linear ${\mathbb{Q}}$-group and $L$ a number field, we write ${\mathbf{H}}^L$ for the ${\mathbb{Q}}$-group ${\mathrm{Res}}_{L/{\mathbb{Q}}}{\mathbf{H}}_L$. For ${\mathbf{H}}$ a linear ${\mathbb{Q}}$-group, we write ${\mathfrak{X}}({\mathbf{H}})$ for the set of ${\mathbb{R}}$-group homomorphisms ${\mathbb{S}}{\rightarrow}{\mathbf{H}}_{\mathbb{R}}$, and ${\mathfrak{Y}}({\mathbf{H}})$ for the set of ${\mathbb{C}}$-group homomorphisms ${\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{H}}_{\mathbb{C}}$. We have the natural action of ${\mathbf{H}}({\mathbb{R}})$ on ${\mathfrak{X}}({\mathbf{H}})$ by conjugation, and similarly the action of ${\mathbf{H}}({\mathbb{C}})$ on ${\mathfrak{Y}}({\mathbf{H}})$. In particular, we have an inclusion ${\mathfrak{X}}({\mathbf{H}}){\hookrightarrow}{\mathfrak{Y}}({\mathbf{H}})$, equivariant [[with respect to]{}]{}the inclusion ${\mathbf{H}}({\mathbb{R}}){\hookrightarrow}{\mathbf{H}}({\mathbb{C}})$. Preliminaries on mixed Shimura varieties {#Preliminaries on mixed Shimura varieties} ======================================== We start with the definition of mixed Shimura data, which is “essentially” the same as [@pink; @thesis]2.1, cf. [@chen; @kuga]2.1 : \[mixed Shimura data\] (1) A mixed Shimura datum is a triple $({\mathbf{P}},{\mathbf{U}},Y)$ consisting of - a connected linear ${\mathbb{Q}}$-group ${\mathbf{P}}$, with a Levi decomposition ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}$; - a unipotent normal ${\mathbb{Q}}$-subgroup ${\mathbf{U}}$ (necessarily contained in ${\mathbf{W}}$); - a ${\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$-orbit $Y\subset{\mathfrak{Y}}({\mathbf{P}})$; such that by putting $\pi_{\mathbf{U}}:{\mathbf{P}}{\rightarrow}{\mathbf{P}}/{\mathbf{U}}$ and $\pi_{\mathbf{W}}:{\mathbf{P}}{\rightarrow}{\mathbf{P}}/{\mathbf{W}}={\mathbf{G}}$ for the quotient maps, the following properties hold for any $y\in Y$: 1. the composition $\pi_{\mathbf{U}}\circ y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}{\rightarrow}({\mathbf{P}}/{\mathbf{U}})_{\mathbb{C}}$ is defined over ${\mathbb{R}}$; 2. the composition $\pi_{\mathbf{W}}\circ y\circ w:{\mathbb{G}}_{{\mathrm{m}}{\mathbb{R}}}{\hookrightarrow}{\mathbb{S}}{\rightarrow}{\mathbf{G}}_{\mathbb{R}}$ is a central cocharacter of ${\mathbf{G}}_{\mathbb{R}}$, where $w:{\mathbb{G}}_{{\mathrm{m}}{\mathbb{R}}}{\rightarrow}{\mathbb{S}}$ is induced by ${\mathbb{R}}^\times{\hookrightarrow}{\mathbb{C}}^\times$; 3. the composition ${\mathrm{Ad}}_{\mathbf{P}}\circ y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}{\rightarrow}{{\mathbf{GL}}}_{{\mathfrak{p}},{\mathbb{C}}}$ induces on ${\mathfrak{p}}={\mathrm{Lie}}{\mathbf{P}}$ a rational mixed Hodge structure of type $\{(-1,-1),(-1,0),(0,-1),(-1,1),(0,0),(1,-1)\}$, with rational weight filtration $W_{-2}={\mathrm{Lie}}{\mathbf{U}}$, $W_{-1}={\mathrm{Lie}}{\mathbf{W}}$, and $W_0={\mathrm{Lie}}{\mathbf{P}}$; 4. the conjugation by $y({\mathbf{i}})$ induces on ${\mathbf{G}}^{\mathrm{ad}}_{\mathbb{R}}$ a Cartan involution, and ${\mathbf{G}}^{\mathrm{ad}}$ admits no compact ${\mathbb{Q}}$-factors; 5. it is also required that the center of ${\mathbf{G}}$ acts on ${\mathbf{W}}$ through some ${\mathbb{Q}}$-torus isogeneous to the product of a compact ${\mathbb{Q}}$-torus with a split ${\mathbb{Q}}$-torus. $Y$ is actually a complex manifold on which ${\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$ acts transitively preserving the complex structure. \(2) A pure Shimura datum (in the sense of Deligne [@deligne; @pspm]) is the same as a mixed Shimura datum $({\mathbf{G}},X)$ where the unipotent radical ${\mathbf{W}}$ is trivial. A Kuga datum (cf.[@chen; @kuga]) is just a mixed Shimura datum $({\mathbf{P}},Y)$ with ${\mathbf{U}}=1$. (3) For $S$ a subset of $Y$, the Mumford-Tate group of $S$, written as ${\mathrm{MT}}(S)$, is the smallest ${\mathbb{Q}}$-subgroup ${\mathbf{P}}'$ of ${\mathbf{P}}$ such that $y({\mathbb{S}}_{\mathbb{C}})\subset{\mathbf{P}}'_{\mathbb{C}}$ for all $y\in{\mathbb{S}}$. A mixed Shimura datum $({\mathbf{P}},{\mathbf{U}},Y)$ is irreducible if ${\mathbf{P}}$ equals ${\mathrm{MT}}(Y)$. \[Deligne vs. Pink\] In the original definition [@pink; @thesis]2.1, the space $Y$ is not a subset of ${\mathfrak{Y}}({\mathbf{P}})$; Pink uses a complex manifold $Y$ homogeneous under the Lie group ${\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$, together with a ${\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$-equivariant map $h:Y{\rightarrow}{\mathfrak{Y}}({\mathbf{P}})$ of finite fibers, such that the Hodge-theoretic conditions (i)-(iv) in \[mixed Shimura data\] hold for points in $h(Y)$. One can show, cf. [@pink; @thesis]2.12, that the connected components of the space $Y$ in the sense of Pink are the same as the connected components of the space $Y$ in the sense of \[mixed Shimura data\]. The main results of this paper focus on connected mixed Shimura varieties, and we prefer to use the simpler definition given above. \[morphisms of mixed Shimura data\] A morphism between mixed Shimura data is of the form $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$ where $f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ is a ${\mathbb{Q}}$-group homomorphism sending ${\mathbf{U}}$ into ${\mathbf{U}}'$, and the push-forward $f_:{\mathfrak{Y}}({\mathbf{P}}){\rightarrow}{\mathfrak{Y}}({\mathbf{P}}'),\ h\mapsto f\circ h$ sends $Y$ into $Y'$, such that $f_:Y{\rightarrow}Y'$ is equivariant [[with respect to]{}]{}$f:{\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}}){\rightarrow}{\mathbf{P}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})$; one can show that $f_:Y{\rightarrow}Y'$ is a smooth map between complex manifolds, cf.[@pink; @thesis]2.3 and 2.4. We further single out the following cases: \(1) $({\mathbf{P}},{\mathbf{U}},Y)$ is said to be a mixed Shimura subdatum of $({\mathbf{P}}',{\mathbf{U}}',Y')$ if $f$ and $f_$ are both injective. \(2) For ${\mathbf{N}}\subset{\mathbf{P}}$ a normal ${\mathbb{Q}}$-subgroup, the quotient* of $({\mathbf{P}},{\mathbf{U}},Y)$ by ${\mathbf{N}}$ is the mixed Shimura datum $({\mathbf{P}}',{\mathbf{U}}',Y')$ where ${\mathbf{P}}'$ is the quotient ${\mathbb{Q}}$-group ${\mathbf{P}}/{\mathbf{N}}$, ${\mathbf{U}}'$ is the image of ${\mathbf{U}}$ in ${\mathbf{P}}'$, and $Y'$ is the ${\mathbf{P}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})$-orbit of the composition $\pi_{\mathbf{N}}\circ y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}'_{\mathbb{C}}$ for any $y\in Y$, where $\pi_{\mathbf{N}}:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'={\mathbf{P}}/{\mathbf{N}}$ is the natural projection, cf.[@pink; @thesis 2.9]. We thus write $({\mathbf{P}}',{\mathbf{U}}',Y')=({\mathbf{P}}/{\mathbf{N}},{\mathbf{U}}/({\mathbf{U}}\cap{\mathbf{N}}),Y/{\mathbf{N}})$ with $Y/{\mathbf{N}}:=Y'$. It should be mentioned that in the quotient construction the map $Y{\rightarrow}Y'$ is not surjective in general. For example, if $({\mathbf{G}},X)$ is a pure Shimura datum and ${\mathbf{Z}}$ is the center of ${\mathbf{G}}$, then the quotient $({\mathbf{G}}^{\mathrm{ad}},X^{\mathrm{ad}})$ of $({\mathbf{G}},X)$ by ${\mathbf{Z}}$ is a pure Shimura datum. The connected components of $X^{\mathrm{ad}}$ and $X$ are all isomorphic to the Hermitian symmetric domain defined by the connected Lie group ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{R}})^+$ as the center of ${\mathbf{G}}({\mathbb{R}})^+$ acts on the domain trivially. However more connected components could appear in $X^{\mathrm{ad}}$ than in $X$, simply because ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{R}})$ could have more connected components. This can be also seen from the exactness of $1{\rightarrow}{\mathbf{Z}}({\mathbb{R}}){\rightarrow}{\mathbf{G}}({\mathbb{R}}){\rightarrow}{\mathbf{G}}^{\mathrm{ad}}({\mathbb{R}})$ where the last arrow is not surjective in general, which is deduced from the exact sequence of linear ${\mathbb{Q}}$-groups $1{\rightarrow}{\mathbf{Z}}{\rightarrow}{\mathbf{G}}{\rightarrow}{\mathbf{G}}^{\mathrm{ad}}{\rightarrow}1$ with ${\mathbf{Z}}$ the center of ${\mathbf{G}}$. When ${\mathbf{N}}$ is unipotent, the map $Y{\rightarrow}Y/{\mathbf{N}}$ is surjective, whose fibers are isomorphic to ${\mathbf{N}}({\mathbb{R}}){\mathbf{U}}_{\mathbf{N}}({\mathbb{C}})$ with ${\mathbf{U}}_{\mathbf{N}}={\mathbf{U}}\cap{\mathbf{N}}$, and in this case we often use the more precise notation $Y/{\mathbf{N}}({\mathbb{R}}){\mathbf{U}}_{\mathbf{N}}({\mathbb{C}})$ in place of the vague expression $Y/{\mathbf{N}}$, cf.[@pink; @thesis] 2.18. In particular, taking ${\mathbf{N}}={\mathbf{U}}$ and ${\mathbf{W}}$ successively, we see that a mixed Shimura datum fits into a sequence $$({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}/{\mathbf{U}},Y/{\mathbf{U}}({\mathbb{C}})){\rightarrow}({\mathbf{P}}/{\mathbf{W}},Y/{\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}}))$$ where $({\mathbf{P}}/{\mathbf{U}},Y/{\mathbf{U}}({\mathbb{C}}))$ is a Kuga datum and $({\mathbf{P}}/{\mathbf{W}},Y/{\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}}))$ is a pure Shimura datum. \(3) As a natural combination of (1) and (2), when a morphism between mixed Shimura data $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$ is given, its image* is the triple $(f({\mathbf{P}}),f({\mathbf{U}}),f_(Y))$. One verifies directly from the definition that the image is a subdatum of $({\mathbf{P}}',{\mathbf{U}}',Y')$ and equals the quotient of $({\mathbf{P}},{\mathbf{U}},Y)$ by ${\mathbf{N}}:={\mathrm{Ker}}(f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}')$. \(4) A pure section* of $({\mathbf{P}},{\mathbf{U}},Y)$ associated to the Levi decomposition ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}$ is a pure Shimura datum $({\mathbf{G}},X)$ which is a subdatum of $({\mathbf{P}},{\mathbf{U}},Y)$ such that the ${\mathbb{Q}}$-group homomorphism ${\mathbf{G}}{\hookrightarrow}{\mathbf{P}}$ is given by the Levi decomposition and the composition $({\mathbf{G}},X){\hookrightarrow}({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}/{\mathbf{W}},Y/{\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}}))$ is an isomorphism. \(5) For $({\mathbf{P}}_i,{\mathbf{U}}_u,Y_i)$ two mixed Shimura data ($i=1,2$), we have the product $({\mathbf{P}}_1\times{\mathbf{P}}_2,{\mathbf{U}}_1\times{\mathbf{U}}_2,Y_1\times Y_2)$ which is a mixed Shimura datum in an evident way, cf.[@pink; @thesis]2.5. \[unipotent radical and Levi decomposition\] Let $({\mathbf{P}},{\mathbf{U}},Y)$ be a mixed Shimura datum, with ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}$ a Levi decomposition. Write ${\mathbf{V}}={\mathbf{W}}/{\mathbf{U}}$. Then: \(1) ${\mathbf{U}}$ and ${\mathbf{V}}$ are commutative, and ${\mathbf{W}}$ is a central extension of ${\mathbf{V}}$ by ${\mathbf{U}}$ i.e. $1{\rightarrow}{\mathbf{U}}{\rightarrow}{\mathbf{W}}{\rightarrow}{\mathbf{V}}{\rightarrow}1$. Writing the group laws on ${\mathbf{U}}$ and on ${\mathbf{V}}$ additively and fixing an isomorphism of ${\mathbb{Q}}$-schemes ${\mathbf{W}}{\cong}{\mathbf{U}}\times{\mathbf{V}}$, the group law on ${\mathbf{W}}$ writes as $$(u,v)\cdot(u',v')=(u+u'+\frac{1}{2}\psi(v,v'),v+v')$$ where the commutator map ${\mathbf{W}}\times{\mathbf{W}}{\rightarrow}{\mathbf{W}}$ has image in ${\mathbf{U}}$ and factors through a unique alternating bilinear map $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$. \(2) For any $y\in Y$, the action of ${\mathbb{S}}_{\mathbb{C}}$ on ${\mathrm{Lie}}{\mathbf{P}}_{\mathbb{C}}$ induces on ${\mathbf{U}}$ resp. on ${\mathbf{V}}$ (both viewed as finite-dimensional ${\mathbb{Q}}$-vector spaces) a Hodge structure of type $(-1,-1)$ resp. of type $\{(-1,0),(0,-1)\}$. \(3) For any $y\in Y$, write $x:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{G}}_{\mathbb{C}}$ for the composition $\pi_{\mathbf{W}}\circ y$. Then $x$ is defined over ${\mathbb{R}}$ and $x\in Y$. Outting $X={\mathbf{G}}({\mathbb{R}})x$ the orbit of $x$ in $Y$ under ${\mathbf{G}}({\mathbb{R}})$ we obtain a pure Shimura subdatum $({\mathbf{G}},X)$ of $({\mathbf{P}},{\mathbf{U}},Y)$, and the composition of the inclusion with the reduction modulo ${\mathbf{W}}$ is an isomorphism: $({\mathbf{G}},X){\hookrightarrow}({\mathbf{P}},{\mathbf{U}},Y){{\twoheadrightarrow}}({\mathbf{P}}/{\mathbf{W}},Y/{\mathbf{W}})$. Moreover the Hodge types of $\rho_{\mathbf{U}}\circ x$ resp. of $\rho_{\mathbf{V}}\circ x$ $(-1,-1)$ resp. $\{(-1,0),(0,-1)\}$, where $\rho_{\mathbf{U}}$ resp. $\rho_{\mathbf{V}}$ are the action of ${\mathbf{G}}$ on ${\mathbf{U}}$ resp. on ${\mathbf{W}}/{\mathbf{U}}={\mathbf{V}}$ by conjugation, and $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ is ${\mathbf{G}}$-equivariant. The representation $\rho_{\mathbf{U}}$ factors through a split ${\mathbb{Q}}$-torus. In particular, $({\mathbf{P}},{\mathbf{U}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ is a split unipotent extension in the sense of [@pink; @thesis] 2.21. \(4) ${\mathbf{P}}^{\mathrm{der}}$ equals ${\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}}$ and it admits no non-trivial compact quotient ${\mathbb{Q}}$-groups. \(1) and (2) are found in [@pink; @thesis] 2.15, 2.16. \(3) Since $\pi_{\mathbf{U}}\circ y$ is already defined over ${\mathbb{R}}$, the homomorphism $\pi_{\mathbf{U}}\circ y:{\mathbb{S}}{\rightarrow}({\mathbf{V}}\rtimes{\mathbf{G}})_{\mathbb{R}}$, whose image is an ${\mathbb{R}}$-torus, factors through some Levi ${\mathbb{R}}$-subgroup of the form $v{\mathbf{G}}_{\mathbb{R}}v^{{-1}}$ for some $v\in{\mathbf{V}}({\mathbb{R}})$. Thus $\pi_{\mathbf{U}}\circ y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}/{\mathbf{U}}_{\mathbb{C}}$ factors through $v{\mathbf{G}}_{\mathbb{C}}v^{{-1}}$. The pre-image of $v{\mathbf{G}}_{\mathbb{C}}v^{{-1}}$ in ${\mathbf{P}}_{\mathbb{C}}$ is ${\mathbf{U}}_{\mathbb{C}}\rtimes(w{\mathbf{G}}_{\mathbb{C}}w^{{-1}})$ for some $w\in{\mathbf{W}}({\mathbb{C}})$ lifting $v$. In ${\mathbf{U}}_{\mathbb{C}}\rtimes w{\mathbf{G}}_{\mathbb{C}}w^{{-1}}$ the maximal reductive ${\mathbb{C}}$-subgroups are Levi ${\mathbb{C}}$-subgroups of the form $w'{\mathbf{G}}_{\mathbb{C}}w'^{{-1}}$ with $w'\in{\mathbf{U}}({\mathbb{C}})w\subset{\mathbf{U}}({\mathbb{C}}){\mathbf{W}}({\mathbb{R}})$. In particular, conjugate $y$ by $w'$ we get $x\in Y$ such that $x({\mathbb{S}}_{\mathbb{C}})\subset{\mathbf{G}}_{\mathbb{C}}\subset{\mathbf{P}}_{\mathbb{C}}$. Since the composition ${\mathbf{G}}{\hookrightarrow}{\mathbf{P}}{{\twoheadrightarrow}}{\mathbf{G}}$ is the identity, we factorize $x:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}$ into the composition ${\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}{{\twoheadrightarrow}}{\mathbf{G}}_{\mathbb{C}}{\hookrightarrow}{\mathbf{P}}_{\mathbb{C}}$. The composition $\pi_{\mathbf{W}}\circ x:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}{{\twoheadrightarrow}}{\mathbf{G}}_{\mathbb{C}}$ is defined over ${\mathbb{R}}$, and the projection ${\mathbf{P}}_{\mathbb{C}}{\rightarrow}{\mathbf{G}}_{\mathbb{C}}$ is defined over ${\mathbb{R}}$ as ${\mathbf{P}}{\rightarrow}{\mathbf{G}}$ is already defined over ${\mathbb{Q}}$. Hence $x$ is defined over ${\mathbb{R}}$. Since $x\in Y$, and ${\mathrm{Lie}}{\mathbf{G}}={\mathrm{Lie}}{\mathbf{P}}/{\mathrm{Lie}}{\mathbf{W}}$, we see that the Hodge structure given by $x:{\mathbb{S}}{\rightarrow}{\mathbf{G}}_{\mathbb{R}}$ on ${\mathrm{Lie}}{\mathbf{G}}$ is of type $\{(-1,1),(0,0),(1,-1)\}$, and the conjugation by $x({\mathbf{i}})$ induces a Cartan involution on ${\mathbf{G}}_{\mathbb{R}}^{\mathrm{ad}}$. The ${\mathbf{G}}({\mathbb{R}})$-orbit $X$ of $x$ inside $Y\subset{\mathfrak{Y}}({\mathbf{P}})$ clearly lies in ${\mathfrak{Y}}({\mathbf{G}})$ (and actually lies in the real part ${\mathfrak{X}}({\mathbf{G}}))$, hence the pair $({\mathbf{G}},X)$ is a pure Shimura datum, and the inclusion $({\mathbf{G}},X){\hookrightarrow}({\mathbf{P}},{\mathbf{U}},Y)$ makes it a pure Shimura subdatum. The claims on Hodge types and the pairing $\psi$ are immediate from (1) and (2). The claim on the action of ${\mathbf{G}}$ on ${\mathbf{U}}$ is clear because ${\mathbf{P}}$ acts on ${\mathbf{U}}$ through a split ${\mathbb{Q}}$-torus by [@pink; @thesis] 2.14 and ${\mathbf{G}}$ acts through ${\mathbf{G}}{\hookrightarrow}{\mathbf{P}}$. \(4) From [@pink; @thesis] 2.10 we know that ${\mathbf{P}}^{\mathrm{der}}$ contains ${\mathbf{W}}$. It clearly contains ${\mathbf{G}}^{\mathrm{der}}$, hence ${\mathbf{P}}^{\mathrm{der}}\supset{\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}}$. The quotient ${\mathbf{P}}/({\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}})$ is already commutative, which gives the inclusion ${\mathbf{P}}^{\mathrm{der}}\subset{\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}}$ in the other direction. From \[mixed Shimura data\] (iv) we know that ${\mathbf{P}}^{\mathrm{der}}$ admits no compact quotient ${\mathbb{Q}}$-groups other than the trivial one. \[group law\] Aside from the group law $(u,v)\cdot(u',v')=(u+u'+\frac{1}{2}\psi(v,v'),v+v')$ and the evident equality $(u,v)^n=(nu,nv)$, the following identities will be useful for elements $(u,v,g)$ in ${\mathbf{P}}{\cong}{\mathbf{U}}\times{\mathbf{V}}\times{\mathbf{G}}$, in which the neutral element is $(0,0,1)$: - multiplication $(u,v,g)(u',v',g')=(u+g(u')+\psi(v,g(v')),v+g(v'),gg')$; - inverse $(u,v,g)^{{-1}}=(-g^{{-1}}(u) , -g^{{-1}}(v), g^{{-1}})$, namely $(w,g)^{{-1}}=(g^{{-1}}(w^{{-1}}),g^{{-1}})$ for $w=(u,v)$ - and the commutator between ${\mathbf{W}}$ and ${\mathbf{G}}$ is $$(u,v,1)(0,0,g)(-u,-v,1)(0,0,g^{{-1}})=(u-g(u),v-g(v),1)$$ where we write $g(u)=gug^{{-1}}=\rho_{\mathbf{U}}(g)(u)$ and similarly for $g(v)$, $g(w)$. We thus prefer treating a general mixed Shimura datum as a split unipotent extension of a pure Shimura datum by two unipotent ${\mathbb{Q}}$-groups subject to certain conditions, and we often reformulate this as the following: \[fibred mixed Shimura data new\] (1) Let $({\mathbf{G}},X)$ be a pure Shimura datum, and let $\rho_{\mathbf{U}}:{\mathbf{G}}{\rightarrow}{\mathbf{GL}}_{\mathbf{U}}$ and $\rho_{\mathbf{V}}:{\mathbf{G}}{\rightarrow}{\mathbf{GL}}_{\mathbf{V}}$ be two finite-dimensional algebraic representation, together with an alternating ${\mathbf{G}}$-equivariant bilinear map $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$, giving rise to a central extension of unipotent ${\mathbb{Q}}$-groups $1{\rightarrow}{\mathbf{U}}{\rightarrow}{\mathbf{W}}{\rightarrow}{\mathbf{V}}{\rightarrow}1$. Assume that - for any $x\in X$, the composition $\rho_{\mathbf{U}}\circ x$ is a rational Hodge structure of type $(-1,-1)$, and $\rho_{\mathbf{V}}\circ x$ is a rational Hodge structure of type $\{(-1,0),(0,-1)\}$; - the connected center of ${\mathbf{G}}$ acts on ${\mathbf{U}}$ and on ${\mathbf{V}}$ through ${\mathbb{Q}}$-tori subject to the condition (iv) in \[mixed Shimura data\]. Then by putting ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}$ and $Y$ the ${\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$-orbit of any $x:{\mathbb{S}}{\rightarrow}{\mathbf{G}}_{\mathbb{R}}{\rightarrow}{\mathbf{P}}_{\mathbb{R}}$, the triple $({\mathbf{P}},{\mathbf{U}},Y)$ thus obtained is a mixed Shimura datum. The canonical projection $({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{G}},X)$ is the quotient by ${\mathbf{W}}$, and $({\mathbf{G}},X)$ is naturally a pure section by the evident inclusions ${\mathbf{G}}{\hookrightarrow}{\mathbf{P}}$ and $X{\hookrightarrow}Y$. In particular, $Y$ can be viewed as a holomorphic vector bundle over $X$, whose fibers are isomorphic to the Lie algebra of ${\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$. We call $({\mathbf{P}},{\mathbf{U}},Y)$ the mixed Shimura datum fibred over $({\mathbf{G}},X)$ by the representations $\rho_{\mathbf{U}}$ and $\rho_{\mathbf{V}}$ and the alternating map $\psi$. We write $({\mathbf{P}},{\mathbf{U}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ and $Y={\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})\rtimes X$ to emphasize that the role of the Levi decomposition. \(2) A morphism between fibred mixed Shimura data is a commutative diagram of the form $$\xymatrix{({\mathbf{P}},{\mathbf{U}},Y)\ar[d]^{\pi_{\mathbf{W}}} \ar[r]^{(f,f_)}&({\mathbf{P}}',{\mathbf{U}}',Y')\ar[d]^{\pi_{{\mathbf{W}}'}}\\ ({\mathbf{G}},X)\ar[r]^{(f,f_)} &({\mathbf{G}}',X')}$$ where the vertical arrows are reductions modulo the unipotent radicals, inducing the bottom horizontal morphism of pure Shimura data from the upper one. Note that the commutative diagram give rise to homomorphisms $\alpha:{\mathbf{V}}{\rightarrow}{\mathbf{V}}'$, $\beta:{\mathbf{U}}{\rightarrow}{\mathbf{U}}'$ and ${\mathbf{W}}{\rightarrow}{\mathbf{W}}'$ with $\beta(\psi(v,v'))=\psi'(\alpha(v),\alpha(v'))$. Identify $({\mathbf{G}},X)$ resp. $({\mathbf{G}}',X')$ as a pure subdatum of $({\mathbf{P}},{\mathbf{U}},Y)$ resp. of $({\mathbf{P}}',{\mathbf{U}}',Y')$ via split unipotent extension as in (1). If the morphism $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$ sends the pure subdatum $({\mathbf{G}},X)$ into $({\mathbf{G}}',X')$, then the morphisms $\alpha$ and $\beta$ are equivariant [[with respect to]{}]{}$f:{\mathbf{G}}{\rightarrow}{\mathbf{G}}'$, and ${\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ can be recovered as $(u,v,g)\mapsto(\beta(u),\alpha(v),f(g))$ when we use the isomorphisms of ${\mathbb{Q}}$-schemes ${\mathbf{P}}={\mathbf{U}}\times{\mathbf{V}}\times{\mathbf{G}}$ and ${\mathbf{P}}'={\mathbf{U}}'\times{\mathbf{V}}'\times{\mathbf{G}}'$. Conversely, assume that fibred mixed Shimura data $({\mathbf{P}},{\mathbf{U}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ and $({\mathbf{P}}',{\mathbf{U}}',Y')=({\mathbf{U}}',{\mathbf{V}}')\rtimes({\mathbf{G}}',X')$ are given. If $(f,f_):({\mathbf{G}},X){\rightarrow}({\mathbf{G}}',X')$ is a morphism of pure Shimura data, together with $f$-equivariant homomorphisms $\alpha:{\mathbf{V}}{\rightarrow}{\mathbf{V}}'$ $\beta:{\mathbf{U}}{\rightarrow}{\mathbf{U}}'$ and $\beta(\psi(v,v'))=\psi'(\alpha(v),\alpha(v'))$. Then $(f,f_):({\mathbf{G}},X){\rightarrow}({\mathbf{G}}',X')$ extends to a morphism of mixed Shimura data $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$, with the ${\mathbb{Q}}$-group homomorphism being $(u,v,g)\mapsto(\beta(u),\alpha(v),f(g))$ under the isomorphism of ${\mathbb{Q}}$-schemes ${\mathbf{P}}{\cong}{\mathbf{U}}\times{\mathbf{V}}\times{\mathbf{G}}$ and ${\mathbf{P}}'={\mathbf{U}}'\times{\mathbf{V}}'\times{\mathbf{G}}'$. \(1) is clear from \[unipotent radical and Levi decomposition\] and [@pink; @thesis] 2.16, 2.17, 2.21. See [@pink; @thesis] 2.18 and 2.19 for the proof for $Y$ being a holomorphic vector bundle over $X$. \(2) When $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$ is a morphism of mixed Shimura data, the Lie algebra map ${\mathrm{Lie}}f:{\mathrm{Lie}}{\mathbf{P}}{\rightarrow}{\mathrm{Lie}}{\mathbf{P}}'$ respects the rational weight filtration and the central extension structures on the unipotent radicals. Hence $f({\mathbf{U}})\subset{\mathbf{U}}'$, $f({\mathbf{W}})\subset{\mathbf{W}}'$, with $\beta(\psi(v,v'))=\psi'(\alpha(v),\alpha(v'))$ for $v,v'\in{\mathbf{V}}$, where $\alpha$ and $\beta$ are induced by $f$. Reduce modulo the unipotent radicals of $(f,f_)$ gives $({\mathbf{G}},X){\rightarrow}({\mathbf{G}}',X')$ together with a commutative diagram of the mentioned form. If moreover $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$ sends $({\mathbf{G}},X)$ into $({\mathbf{G}}',X')$, then the homomorphism $f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ sends the Levi ${\mathbb{Q}}$-subgroup ${\mathbf{G}}$ into ${\mathbf{G}}'$. The homomorphisms between normal unipotent ${\mathbb{Q}}$-groups ${\mathbf{U}}{\rightarrow}{\mathbf{U}}'$ and ${\mathbf{W}}{\rightarrow}{\mathbf{W}}'$ are equivariant [[with respect to]{}]{}${\mathbf{P}}{\rightarrow}{\mathbf{P}}'$, hence we get $\alpha:{\mathbf{V}}{\rightarrow}{\mathbf{V}}'$ and $\beta:{\mathbf{U}}{\rightarrow}{\mathbf{U}}'$ equivariant [[with respect to]{}]{}$f:{\mathbf{G}}{\rightarrow}{\mathbf{G}}'$. The recovery of $f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ by $\alpha$, $\beta$ and $f:{\mathbf{G}}{\rightarrow}{\mathbf{G}}'$ is immediate. Conversely, if we are given fibred mixed Shimura data $({\mathbf{P}},{\mathbf{U}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ and $({\mathbf{P}}',{\mathbf{U}}',Y')=({\mathbf{U}}',{\mathbf{V}}')\rtimes({\mathbf{G}}',X')$, a ${\mathbb{Q}}$-group homomorphism $f:{\mathbf{G}}{\rightarrow}{\mathbf{G}}'$ with $f$-equivariant maps $\alpha$ and $\beta$ naturally gives rise to a unique ${\mathbb{Q}}$-group homomorphism $f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ subject to the formula $(u,v,g)\mapsto(\beta(u),\alpha(v),f(g))$, and $f_:{\mathfrak{Y}}({\mathbf{P}}){\rightarrow}{\mathfrak{Y}}({\mathbf{P}}')$ sends $Y$ the ${\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$-orbit of $X$ into $Y'$ the ${\mathbf{P}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})$-orbit of $X'$. It is easy to verify that for any $y\in Y$, the mixed Hodge structure on ${\mathrm{Lie}}{\mathbf{P}}$ satisfies the constraints in \[mixed Shimura data\] and that $(f,f_):({\mathbf{P}},{\mathbf{U}},Y){\rightarrow}({\mathbf{P}}',{\mathbf{U}}',Y')$ is a morphism of mixed Shimura data, using the Hodge type conditions on ${\mathbf{U}}$, ${\mathbf{V}}$ and ${\mathbf{U}}'$, ${\mathbf{V}}'$ given in (1). In particular we have the following corollaries on pure sections and subdata: \[pure section\] If $({\mathbf{P}},{\mathbf{U}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ is a fibred mixed Shimura datum, then the pure sections of $({\mathbf{P}},{\mathbf{U}},Y){{\twoheadrightarrow}}({\mathbf{G}},X)$ are exactly subdata of the form $(w{\mathbf{G}}w^{{-1}},wX)$ with $w$ running through ${\mathbf{W}}({\mathbb{Q}})$, and they are the same as maximal pure subdata of $({\mathbf{P}},{\mathbf{U}},Y)$. It is clear that each $(w{\mathbf{G}}w^{{-1}},wX)$ is a pure section for any given $w\in{\mathbf{W}}({\mathbb{Q}})$. Conversely, if $({\mathbf{G}}',X')$ is a pure section in the sense of \[morphisms of mixed Shimura data\](3), then ${\mathbf{G}}'=w{\mathbf{G}}w^{{-1}}$ is conjugate to ${\mathbf{G}}$ by some $w\in{\mathbf{W}}({\mathbb{Q}})$, hence $(w^{{-1}}{\mathbf{G}}'w,w^{{-1}}X')=({\mathbf{G}},w^{{-1}}X')$ is a pure subdatum of $({\mathbf{P}},{\mathbf{U}},Y)$. Since ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}$, the composition of the evident maps between ${\mathfrak{Y}}({\mathbf{G}}){\rightarrow}{\mathfrak{Y}}({\mathbf{P}}){\rightarrow}{\mathfrak{Y}}({\mathbf{G}})$ induced by ${\mathbf{G}}{\hookrightarrow}{\mathbf{P}}{{\twoheadrightarrow}}{\mathbf{G}}$ is the identity. Apply the composition to the subset $w^{{-1}}X'\subset{\mathfrak{X}}({\mathbf{G}})\subset{\mathfrak{Y}}({\mathbf{G}})$, we see that its image in ${\mathfrak{Y}}({\mathbf{G}})$ must be $X$ because $({\mathbf{G}},w^{{-1}}X')$ is a pure section, hence $w^{{-1}}X'=X$. The maximality is clear because maximal reductive ${\mathbb{Q}}$-subgroups of ${\mathbf{P}}$ are exactly the Levi ${\mathbb{Q}}$-subgroups, hence conjugate to ${\mathbf{G}}$ by ${\mathbf{W}}({\mathbb{Q}})$. \[structure of subdata\] Let $({\mathbf{P}},{\mathbf{U}},Y)$ be a mixed Shimura datum fibred as $({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$, and let $({\mathbf{P}}',{\mathbf{U}}',Y')$ be a mixed Shimura subdatum. Then there exists a pure Shimura subdatum $({\mathbf{G}}',X')$ of $({\mathbf{G}},X)$, an element $w\in{\mathbf{W}}({\mathbb{Q}})$, and a unipotent ${\mathbb{Q}}$-subgroup ${\mathbf{W}}'$ of ${\mathbf{W}}$, such that ${\mathbf{P}}'={\mathbf{W}}'\rtimes w{\mathbf{G}}' w^{{-1}}$ and $({\mathbf{P}}',{\mathbf{U}}',Y'){\cong}({\mathbf{U}}',{\mathbf{V}}')\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ as a fibred mixed Shimura datum. Here ${\mathbf{V}}'={\mathbf{W}}'/{\mathbf{U}}'$ resp. ${\mathbf{U}}'={\mathbf{U}}\cap{\mathbf{W}}'$ is a ${\mathbb{Q}}$-subspace of ${\mathbf{V}}$ resp. of ${\mathbf{U}}$ stabilized under $w{\mathbf{G}}'w^{{-1}}$, and ${\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ restricts to ${\mathbf{V}}'\times{\mathbf{V}}'{\rightarrow}{\mathbf{U}}'$ and is equivariant under $w{\mathbf{G}}'w^{{-1}}$. The pure subdatum $(w{\mathbf{G}}'w^{{-1}},wX')$ in $({\mathbf{P}},{\mathbf{U}},Y)$ is a pure section of $({\mathbf{P}}',{\mathbf{U}}',Y')$. The idea is the same as [@chen; @kuga] 2.10. Let $({\mathbf{P}}_0,Y_0)$ be a maximal pure Shimura subdatum of $({\mathbf{P}}',{\mathbf{U}}',Y')$, then its image $({\mathbf{G}}',X')$ in $({\mathbf{G}},X)$ is a pure Shimura subdatum. Note that $({\mathbf{P}}',{\mathbf{U}}',Y')$ is a subdatum of ${\mathbf{W}}\rtimes({\mathbf{G}}',X')$ containing a maximal pure subdatum $({\mathbf{P}}_0,Y_0)=(w{\mathbf{G}}'w^{{-1}},w')$ for some $w\in{\mathbf{W}}({\mathbb{Q}})$. We are thus reduced to the case when $({\mathbf{G}}',X')=({\mathbf{G}},X)$. In this case $({\mathbf{P}}_0,Y_0)=(w{\mathbf{G}}w^{{-1}},wX)$, and the unipotent radical ${\mathbf{W}}'$ of ${\mathbf{P}}'$ is naturally a ${\mathbb{Q}}$-subgroup of ${\mathbf{W}}$ stabilized by $w{\mathbf{G}}w^{{-1}}$-conjugation. Using $(w{\mathbf{G}}w^{{-1}},wX)$ as a pure section corresponding to the Levi decomposition ${\mathbf{P}}'={\mathbf{W}}'\rtimes(w{\mathbf{G}}w^{{-1}})$, we see that the intersection ${\mathbf{U}}':={\mathbf{U}}\cap{\mathbf{W}}'$ is the weight -2 part due to the rational weight filtration given by any $y\in wX$, and ${\mathbf{V}}'={\mathbf{W}}'/{\mathbf{U}}'$ equals the image of ${\mathbf{W}}'$ in ${\mathbf{V}}$, which is clearly stable under $w{\mathbf{G}}w^{{-1}}$. The bilinear map $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ clearly restricts to $\psi':{\mathbf{V}}'\times{\mathbf{V}}'{\rightarrow}{\mathbf{U}}'$ and is $w{\mathbf{G}}w^{{-1}}$-equivariant, as immediate consequences of the Lie bracket structure on ${\mathrm{Lie}}{\mathbf{W}}'$ and the Hodge types. The following lemma is the mixed analogue of [@ullmo; @yafaev] Lemma 3.7. \[common Mumford-Tate group\]. Let $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ be a mixed Shimura datum. If ${\mathbf{P}}'\subset{\mathbf{P}}$ is a ${\mathbb{Q}}$-subgroup coming from some subdatum $({\mathbf{P}}',Y')$, then there are only finitely many subdata of the form $({\mathbf{P}}',Y'')$ in $({\mathbf{P}},Y)$. When $({\mathbf{P}},{\mathbf{U}},Y)$ is pure, this is proved in [@ullmo; @yafaev] Lemma 3.7. For a general ${\mathbb{Q}}$-subgroup ${\mathbf{P}}'$, if there exists a subdatum of the form $({\mathbf{P}}',{\mathbf{U}}',Y')$, then ${\mathbf{U}}'={\mathbf{U}}\cap{\mathbf{P}}'$ and the unipotent radical ${\mathbf{W}}'={\mathbf{W}}\cap{\mathbf{P}}'$ in ${\mathbf{P}}'$ are independent of $Y'$ by the constraints of Hodge types. Choose a Levi decomposition ${\mathbf{P}}'={\mathbf{W}}'\rtimes w{\mathbf{G}}' w^{{-1}}$, we have $({\mathbf{P}}',{\mathbf{U}}',Y')={\mathbf{W}}'\rtimes(w{\mathbf{G}}' w^{{-1}},wX')$ for some pure Shimura subdatum $(w{\mathbf{G}}'w^{{-1}},wX')\subset(w{\mathbf{G}}w^{{-1}},wX)$, namely the $({\mathbf{P}}',{\mathbf{U}}',Y')$ is constructed out of $(w{\mathbf{G}}' w^{{-1}},wX')$ by some unipotent ${\mathbb{Q}}$-subgroup ${\mathbf{W}}'$. There are at most finitely many pure Shimura subdatum of the form $(w{\mathbf{G}}'w^{{-1}},wX')$ in $(w{\mathbf{G}}w^{{-1}},wX)$, hence the finiteness of mixed Shimura subdata associated to ${\mathbf{P}}'$ follows. We also include the following result that allow us to generate subdata by “taking orbits”: \[generating subdata\] Let $({\mathbf{P}},{\mathbf{U}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ be a mixed Shimura datum. Let ${\mathbf{P}}'$ be a ${\mathbb{Q}}$-subgroup of ${\mathbf{P}}$ admitting no compact semi-simple quotient ${\mathbb{Q}}$-group, and ${\mathbf{P}}'_{\mathbb{C}}\supset y({\mathbb{S}}_{\mathbb{C}})$ for some $y\in Y$. Then \(1) ${\mathbf{P}}'={\mathbf{W}}'\rtimes w{\mathbf{G}}'w^{{-1}}$ for some reductive ${\mathbb{Q}}$-subgroup ${\mathbf{G}}'$ of ${\mathbf{G}}$ and some $w\in{\mathbf{W}}({\mathbb{Q}})$ and unipotent ${\mathbb{Q}}$-subgroup ${\mathbf{W}}'\subset{\mathbf{W}}$. \(2) if moreover the connected center of $w{\mathbf{G}}'w^{{-1}}$ acts on ${\mathbf{W}}'$ through a ${\mathbb{Q}}$-torus subject to \[mixed Shimura data\](v), then the triple $({\mathbf{P}}',{\mathbf{U}}',Y')$ with ${\mathbf{U}}'={\mathbf{U}}\cap{\mathbf{W}}'$ and $Y'={\mathbf{P}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})y$ is a mixed Shimura subdatum of $({\mathbf{P}},{\mathbf{U}},Y)$. \(3) In particular, if ${\mathbf{P}}'={\mathrm{MT}}(Y^+)$ is the generic Mumford-Tate group of a connected component of $Y$, then (1) and (2) holds for ${\mathbf{P}}'$, with ${\mathbf{P}}'^{\mathrm{der}}={\mathbf{P}}^{\mathrm{der}}$. \(1) The image of ${\mathbf{P}}'$ along $\pi=\pi_{\mathbf{W}}:{\mathbf{P}}{\rightarrow}{\mathbf{G}}$ is a ${\mathbb{Q}}$-subgroup ${\mathbf{G}}'$ of ${\mathbf{G}}$ such that ${\mathbf{G}}'_{\mathbb{C}}\supset x({\mathbb{S}}_{\mathbb{C}})$ for $x=\pi_y$. Since $x$ is already defined over ${\mathbb{R}}$ by \[mixed Shimura data\](i), we have $x({\mathbb{S}})\subset{\mathbf{G}}'_{\mathbb{R}}\subset{\mathbf{G}}_{\mathbb{R}}$. Since the centralizer of $x({\mathbb{S}})$ in ${\mathbf{G}}_{\mathbb{R}}$ is compact, by [@eskin; @mozes; @shah] Lemma 5.1 we see that ${\mathbf{G}}'$ is reductive. The kernel ${\mathbf{W}}':={\mathrm{Ker}}({\mathbf{P}}'{\rightarrow}{\mathbf{G}}')$ is contained in ${\mathbf{W}}$, hence unipotent. Thus ${\mathbf{P}}'$ admits a Levi decomposition of the form ${\mathbf{W}}'\rtimes{\mathbf{H}}'$, where ${\mathbf{H}}'$ is a maximal reductive ${\mathbb{Q}}$-subgroup of ${\mathbf{P}}'$. ${\mathbf{H}}$ extends to a maximal reductive ${\mathbb{Q}}$-subgroup in ${\mathbf{P}}$ of the form $w{\mathbf{G}}w^{{-1}}$, hence $w^{{-1}}{\mathbf{H}}w$ is a reductive ${\mathbb{Q}}$-subgroup of ${\mathbf{G}}$, and it coincides with the image of ${\mathbf{P}}'$ modulo ${\mathbf{W}}'$, which gives ${\mathbf{H}}=w{\mathbf{G}}'w^{{-1}}$. \(2) Note that $w{\mathbf{G}}'w^{{-1}}$ admits no compact semi-simple quotient ${\mathbb{Q}}$-group as this is already true for ${\mathbf{P}}'$. Since the homomorphism $y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}$ factors through ${\mathbf{P}}'_{\mathbb{C}}$, we see that the Lie algebra ${\mathfrak{p}}'={\mathrm{Lie}}{\mathbf{P}}'$ is a rational mixed Hodge substructure of ${\mathfrak{p}}={\mathrm{Lie}}{\mathbf{P}}$, where the weight filtration is induced from the one on ${\mathfrak{p}}$ by restriction, and the Hodge types do not exceed the set $$\{(-1,-1),(-1,0),(0,-1),(-1,1),(0,0),(1,-1)\}.$$ Thus ${\mathbf{U}}'={\mathbf{U}}\cap{\mathbf{P}}'$ is the weight -2 part and ${\mathbf{W}}'$ is the part of weight at most -1. The involution induced by $y({\mathbf{i}})$ in ${\mathbf{G}}_{\mathbb{R}}$ stabilizes ${\mathbf{G}}'_{\mathbb{R}}$, hence it induces further a Cartan involution on ${\mathbf{G}}'^{\mathrm{ad}}_{\mathbb{R}}$ because ${\mathbf{G}}'^{\mathrm{ad}}$ admits no compact ${\mathbb{Q}}$-factors. The remaining conditions in \[mixed Shimura data\] are automatic, hence $({\mathbf{P}}',{\mathbf{U}}',Y')$ is a mixed Shimura datum, and it is clearly a subdatum of $({\mathbf{P}},{\mathbf{U}},Y)$. \(3) When ${\mathbf{P}}'={\mathrm{MT}}(Y^+)$, the image of $Y^+$ in $X$ is a connected component $X^+$ of $X$, and the image ${\mathbf{G}}'$ of ${\mathbf{P}}'$ is a reductive ${\mathbb{Q}}$-subgroup of ${\mathbf{G}}$ such that $x({\mathbb{S}})\subset{\mathbf{G}}'_{\mathbb{R}}$ for all $x\in X^+$. If ${\mathrm{MT}}(X^+)\subsetneq {\mathbf{G}}'$, then the pre-image ${\mathbf{P}}''$ of ${\mathrm{MT}}(X^+)$ in ${\mathbf{P}}'$ is a proper ${\mathbb{Q}}$-subgroup and ${\mathbf{P}}''_{\mathbb{C}}\supset y({\mathbb{S}}_{\mathbb{C}})$ for all $y\in Y^+$, which is absurd, and we get ${\mathbf{G}}'={\mathrm{MT}}(X^+)$. When $x$ runs through $X^+$, using \[common Mumford-Tate group\] we only get finitely many pure subdata of the form $({\mathbf{G}}',X'_{i}={\mathbf{G}}'({\mathbb{R}})x)$, $i=1,\cdots,m$. Each $X'_i$ is an complex submanifold of $X$, whose connected components are Hermitian symmetric subdomains of connected components of $X$, and the finite union $\bigcup_iX'_i$ contains $X^+$. It turns out that at least one of them, written as $X'$, is of dimension equal to $\dim X^+$, and we must have $X'^+=X^+$ for some connected component of $X'$. Since $X'^+$ resp. $X^+$ is homogeneous under ${\mathbf{G}}'^{\mathrm{der}}({\mathbb{R}})^+$ resp. under ${\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$, the inclusion of connected semi-simple Lie groups ${\mathbf{G}}'^{\mathrm{der}}({\mathbb{R}})^+\subset{\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$ has to be an equality, and we get ${\mathbf{G}}'^{\mathrm{der}}={\mathbf{G}}^{\mathrm{der}}$, and only one subdatum of the form $({\mathbf{G}}',X')$ is produced this way: $X'={\mathbf{G}}'({\mathbb{R}})X^+$. In particular, the center of ${\mathbf{G}}'$ is a ${\mathbb{Q}}$-subtorus of ${\mathbf{G}}$, and its action on ${\mathbf{W}}$ satisfies the condition (v) in \[mixed Shimura data\]. The kernel of ${\mathbf{P}}'{\rightarrow}{\mathbf{G}}'$ is unipotent, hence ${\mathbf{P}}'={\mathbf{W}}'\rtimes{\mathbf{G}}'$ for some unipotent ${\mathbb{Q}}$-subgroup ${\mathbf{W}}'\subset{\mathbf{W}}$, which is the extension of ${\mathbf{V}}'={\mathbf{W}}'/{\mathbf{U}}'$ by ${\mathbf{U}}':={\mathbf{U}}\cap{\mathbf{P}}'$. When $y$ runs through $Y^+$, again by \[common Mumford-Tate group\] we only get finitely many subdata of the form $({\mathbf{P}}',{\mathbf{U}}',Y'_i)$ with $Y'_i={\mathbf{P}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})y_i$ for some $y_i\in Y^+$, and each connected component of $Y'_i$ is a complex submanifold of $Y$ homogeneous under ${\mathbf{P}}'({\mathbb{R}})^+{\mathbf{U}}'({\mathbb{C}})$. We thus have a finite union $\bigcup_iY_i$ containing $Y^+$. By [@pink; @thesis] 2.19, each $Y_i^+$ is a complex vector bundle over an Hermitian symmetric domain isomorphic to $X^+$, and the fibers are isomorphic to ${\mathbf{W}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})$. If ${\mathbf{W}}'\subsetneq{\mathbf{W}}$, then the finite union $\bigcup_iY_i$ cannot contain $Y^+$ by dimension arguments because $Y^+$ is isomorphic to a complex vector bundle over $X^+$ with fibers isomorphic to ${\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})$. Hence we must have ${\mathbf{W}}'={\mathbf{W}}$, and thus ${\mathbf{P}}'^{\mathrm{der}}={\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}}={\mathbf{P}}^{\mathrm{der}}$. \[pure irreducibility\] Let $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ be a mixed Shimura datum fibred over a pure one $({\mathbf{G}},X)$. Then $({\mathbf{P}},Y)$ is irreducible [[if and only if]{}]{}$({\mathbf{G}},X)$ is irreducible. If $({\mathbf{P}},Y)$ is irreducible, then $({\mathbf{G}},X)$ is irreducible by [@chen; @kuga] 2.4(2). Conversely, assume that $({\mathbf{G}},X)$ is irreducible, and ${\mathbf{P}}'$ is a ${\mathbb{Q}}$-subgroup of ${\mathbf{P}}$ such that $y({\mathbb{S}}_{\mathbb{C}})\subset{\mathbf{P}}'_{\mathbb{C}}$. Write ${\mathbf{G}}'$ for the image of ${\mathbf{P}}'$ in ${\mathbf{G}}$, then $x({\mathbb{S}})\subset{\mathbf{G}}'_{\mathbb{R}}$ for all $x\in X$, which gives ${\mathbf{G}}'={\mathbf{G}}$, and ${\mathbf{P}}'={\mathbf{W}}'\rtimes w{\mathbf{G}}w^{{-1}}$ for some $w\in{\mathbf{W}}({\mathbb{Q}})$ by \[generating subdata\](1). Since $Y\supset Y^+$ for any connected component $Y^+$ of $Y$, we have ${\mathbf{P}}'\supset{\mathrm{MT}}(Y^+)$, and thus ${\mathbf{P}}'\supset{\mathbf{W}}$ by the arguments in \[generating subdata\](3), which gives ${\mathbf{P}}'={\mathbf{W}}\rtimes w{\mathbf{G}}w^{{-1}}={\mathbf{W}}\rtimes{\mathbf{G}}={\mathbf{P}}$. \[abbreviation of notations\] In a mixed Shimura datum $({\mathbf{P}},{\mathbf{U}},Y)$, the ${\mathbb{Q}}$-group ${\mathbf{U}}$, the unipotent radical ${\mathbf{W}}$, and thus the quotient ${\mathbf{V}}={\mathbf{W}}/{\mathbf{U}}$ as well, are uniquely determined by any $y\in Y$, because the weight filtration of the mixed Hodge structure given by ${\mathrm{Ad}}_{\mathbf{P}}\circ y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}{\rightarrow}{\mathbf{GL}}_{{\mathfrak{p}}{\mathbb{C}}}$ on ${\mathfrak{p}}={\mathrm{Lie}}{\mathbf{P}}$ determines ${\mathrm{Lie}}{\mathbf{U}}$ and ${\mathrm{Lie}}{\mathbf{W}}$, which in turn determine the connected unipotent ${\mathbb{Q}}$-groups ${\mathbf{U}}$ and ${\mathbf{W}}$. We will call ${\mathbf{U}}$ the unipotent part of weight -2 of ${\mathbf{P}}$ or of the datum. In the sequel we simply write $({\mathbf{P}},Y)$ for the datum, and ${\mathbf{U}}$ always denotes the unipotent part of weight -2 if no further use of the notation is specified. As for morphism between mixed Shimura data, we often write $f$ instead of a pair $(f,f_)$. \[mixed shimura varieties\] Let $({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ be a mixed Shimura datum, and let $K\subset{\mathbf{P}}({{\hat{\mathbb{Q}}}})$ be a [[compact open subgroup]{}]{}. The (complex) mixed Shimura variety* associated to $({\mathbf{P}},Y)$ at level $K$ is the quotient space $$M_K({\mathbf{P}},Y)({\mathbb{C}})={\mathbf{P}}({\mathbb{Q}}){\backslash}[ Y\times{\mathbf{P}}({{\hat{\mathbb{Q}}}})/K]{\cong}{\mathbf{P}}({\mathbb{Q}})_+{\backslash}[ Y^+\times{\mathbf{P}}({{\hat{\mathbb{Q}}}})/K]$$ where the last equality makes sense for any connected component $Y^+$ of $Y$ because ${\mathbf{P}}({\mathbb{Q}})_+$ equals the stabilizer of $Y^+$ in ${\mathbf{P}}({\mathbb{Q}})$. Using the finiteness of class numbers in [@platonov; @rapinchuk] 8.1, we see that the double quotient ${\mathbf{P}}({\mathbb{Q}})_+{\backslash}{\mathbf{P}}({{\hat{\mathbb{Q}}}})/K$ is finite. Writing ${\mathcal{R}}$ for a set of representatives, we then have $$M_K({\mathbf{P}},Y)({\mathbb{C}})=\coprod_{a\in{\mathcal{R}}}\Gamma_K(a){\backslash}Y^+$$ with $\Gamma_K(a)={\mathbf{P}}({\mathbb{Q}})_+\cap aKa^{{-1}}$ a congruence subgroup of ${\mathbf{P}}({\mathbb{R}})_+$. Pink has shown in [@pink; @thesis] that such double quotients are normal quasi-projective varieties over ${\mathbb{C}}$, generalizing a theorem of Baily and Borel cf.[@baily; @borel]. He has further shown that mixed Shimura varieties $M_K({\mathbf{P}},Y)$ admit canonical models over their reflex fields $E({\mathbf{P}},Y)$, which are certain number fields embedded in ${\mathbb{C}}$. In this paper, we treat mixed Shimura varieties as algebraic varieties over ${\bar{\mathbb{Q}}}$, and we denote them as $M_K({\mathbf{P}},Y)$, equipped with the Galois action using the canonical model. In Section 2 and 3 we only use complex mixed Shimura varieties, and in Section 4 and 5 we will use some elementary properties of canonical models. Kuga varieties resp. pure Shimura varieties are mixed Shimura varieties associated to Kuga data resp. pure Shimura data. If $({\mathbf{P}},Y){\rightarrow}({\mathbf{P}}',Y')$ is a morphism of mixed Shimura data, then we have the inclusion of reflex fields $E({\mathbf{P}}',Y')\subset E({\mathbf{P}},Y)$, cf. [@pink; @thesis] 11.2. For the moment it suffices to know that the following morphisms are functorially defined with respect to the canonical models: \[morphisms of mixed Shimura varieties and Hecke translates\] \(1) Let $f:({\mathbf{P}},Y){\rightarrow}({\mathbf{P}}',Y')$ be a morphism of mixed Shimura data, with [[compact open subgroups]{}]{}$K\subset{\mathbf{P}}({{\hat{\mathbb{Q}}}})$ and $K'\subset{\mathbf{P}}'({{\hat{\mathbb{Q}}}})$ such that $f(K)\subset K'$, then there exists a unique morphism $M_K({\mathbf{P}},Y){\rightarrow}M_{K'}({\mathbf{P}}',Y')$ of mixed Shimura varieties whose evaluation over ${\mathbb{C}}$-points is simply $[x,aK]\mapsto[f_(x), f(a)K']$. It is actually defined over $E({\mathbf{P}},Y)$. For $({\mathbf{P}},X)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$, the natural projection $\pi:({\mathbf{P}},Y){\rightarrow}({\mathbf{G}},X)$ gives the natural projection onto the pure Shimura variety $$\pi:M_K({\mathbf{P}},Y){\rightarrow}M_{\pi(K)}({\mathbf{G}},X).$$ We can refine this projection into $$M_K({\mathbf{P}},Y){\overset}{\pi_{\mathbf{U}}}{\longrightarrow}M_{\pi_{\mathbf{U}}(K)}({\mathbf{P}}/{\mathbf{U}},Y/{\mathbf{U}}({\mathbb{C}})){\overset}{\pi_{\mathbf{V}}} {\longrightarrow}M_{\pi(K)}({\mathbf{G}},X)$$ as $\pi=\pi_{\mathbf{W}}=\pi_{\mathbf{V}}\circ\pi_{\mathbf{U}}$, and the sequence means that a general mixed Shimura variety is fibred over some Kuga variety. \(2) Let $({\mathbf{P}},Y)$ be a mixed Shimura datum, and $g\in{\mathbf{P}}({{\hat{\mathbb{Q}}}})$. For $K\subset{\mathbf{P}}({{\hat{\mathbb{Q}}}})$ a [[compact open subgroup]{}]{}, there exists a unique isomorphism of mixed Shimura varieties $\tau_g:M_{gKg^{{-1}}}({\mathbf{P}},Y){\rightarrow}M_K({\mathbf{P}},Y)$ whose evaluation on ${\mathbb{C}}$-points is $$\tau_g:[x,agKg^{{-1}}]\mapsto[x,agK].$$ It is actually defined over $E({\mathbf{P}},Y)$, and we call it the Hecke translation* associated to $g$. Later in Section 4 we will use Hecke translation by $w\in{\mathbf{W}}({\mathbb{Q}})$ to obtain isomorphisms between different pure sections of $M_K({\mathbf{P}},Y)$ under suitable constraints on the level structures. We will show later in \[insensitivity of levels\] that the André-Oort conjecture is insensitive to the change of $K$ by smaller [[compact open subgroups]{}]{}, hence in this paper we will mainly work with levels $K$ that are neat, see [@pink; @thesis] Introduction (page 5). Mixed Shimura varieties at neat levels are smooth. We also introduce an auxiliary condition of the [[compact open subgroup]{}]{}$K$: \[levels of product type\] Let $({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ be a fibred mixed Shimura datum. \(1) A [[compact open subgroup]{}]{}$K$ of ${\mathbf{P}}({{\hat{\mathbb{Q}}}})$ is said to be of product type, if it is of the form $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$ for [[compact open subgroups]{}]{}$K_{\mathbf{W}}\subset{\mathbf{W}}({{\hat{\mathbb{Q}}}})$, $K_{\mathbf{G}}\subset{\mathbf{G}}({{\hat{\mathbb{Q}}}})$, with $K_{\mathbf{W}}$ the central extension of a [[compact open subgroup]{}]{}$K_{\mathbf{V}}\subset{\mathbf{V}}({{\hat{\mathbb{Q}}}})$ by a [[compact open subgroup]{}]{}$K_{\mathbf{U}}\subset{\mathbf{U}}({{\hat{\mathbb{Q}}}})$ through the restriction of $\psi$; $K_{\mathbf{U}}$ and $K_{\mathbf{V}}$ are required to be stabilized by $K_{\mathbf{G}}$. \(2) A [[compact open subgroup]{}]{}$K$ in ${\mathbf{P}}({{\hat{\mathbb{Q}}}})$ is said to be of fine product type if - (2-a) it is of product type and $K=\prod_p K_p$ for [[compact open subgroups]{}]{}$K_p\subset{\mathbf{P}}({{\mathbb{Q}_p}})$ for any rational prime $p$, such that for some $\wp$ prime, $K_\wp$ is neat (hence $K$ is neat, and $K_{{\mathbf{G}},p}$ is neat); - (2-b) we also require that $K_{\mathbf{G}}=K_{{\mathbf{G}}^{\mathrm{der}}}K_{\mathbf{C}}$ where ${\mathbf{C}}$ is the connected center of ${\mathbf{G}}$, with [[compact open subgroups]{}]{}$K_{{\mathbf{G}}^{\mathrm{der}}}\subset{\mathbf{G}}^{\mathrm{der}}({{\hat{\mathbb{Q}}}})$ and $K_{\mathbf{C}}\subset{\mathbf{C}}({{\hat{\mathbb{Q}}}})$ both of fine product type in the sense of (a). - (2-c) there exist ${\mathbb{Z}}$-lattices $\Gamma_{\mathbf{U}}\subset{\mathbf{U}}({\mathbb{Q}})$ and $\Gamma_{\mathbf{V}}\subset{\mathbf{V}}({\mathbb{Q}})$ such that - $\psi(\Gamma_{\mathbf{V}}\times\Gamma_{\mathbf{V}})\subset\Gamma_{\mathbf{U}}$, hence they generate a congruence subgroup $\Gamma_{\mathbf{W}}$ in ${\mathbf{W}}({\mathbb{Q}})$; - $K_{\mathbf{U}}$ resp. $K_{\mathbf{V}}$ is the profinite completion of $\Gamma_{\mathbf{U}}$ resp. of $\Gamma_{\mathbf{V}}$, hence the same for $K_{\mathbf{W}}$ [[with respect to]{}]{}$\Gamma_{\mathbf{W}}$. In this case we also write $K_p=K_{{\mathbf{W}},p}\rtimes K_{{\mathbf{G}},p}$ and $K_?=\prod_p K_{?,p}$ for $?\in\{{\mathbf{U}},{\mathbf{V}},{\mathbf{W}},{\mathbf{G}},{\mathbf{P}}\}$. \[two step fibration\] If $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$, then $\pi(K)=K_{\mathbf{G}}$ and we have an evident morphism $\iota(0): M_{K_{\mathbf{G}}}({\mathbf{G}},X){\hookrightarrow}M_K({\mathbf{P}},Y)$, which we called the zero section of the (fibred) mixed Shimura variety defined by $({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$. The natural projection can be refined into $$M_K({\mathbf{P}},Y){\overset}{\pi_{\mathbf{U}}}{\longrightarrow}M_{K_{\mathbf{V}}\rtimes K_{\mathbf{G}}}({\mathbf{V}}\rtimes({\mathbf{G}},X)){\overset}{\pi_{\mathbf{V}}}{\longrightarrow}M_{K_{\mathbf{G}}}({\mathbf{G}},X)$$ where $\pi_{\mathbf{V}}$ is an abelian scheme with zero section $\pi_{\mathbf{U}}\circ \iota(0)$, and $\pi_{\mathbf{U}}$ is a torsor under $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{C}})$. Since ${\mathbf{U}}$ is commutative, $\Gamma_{\mathbf{U}}$ is a ${\mathbb{Z}}$-lattice in the ${\mathbb{Q}}$-vector space ${\mathbf{U}}({\mathbb{Q}})$, and $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{C}}){\cong}({\mathbb{C}}/{\mathbb{Z}})^{\dim{\mathbf{U}}}$ is an algebraic torus, whose character group is naturally identified with $\Gamma_{\mathbf{U}}$. \[Siegel data\] Let ${\mathbf{V}}$ be a finite-dimensional ${\mathbb{Q}}$-vector space, equipped with a symplectic form $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ where ${\mathbf{U}}={{\mathbb{G}_\mathrm{a}}}$ is the one-dimensional rational Hodge structure of type $(-1,-1)$. (1) We have the following data: 1. pure Shimura datum of Siegel type: From the ${\mathbb{Q}}$-group ${\mathrm{GSp}}_{\mathbf{V}}={\mathrm{GSp}}({\mathbf{V}},\psi)$ of symplectic similitude, we obtain the pure Shimura datum $({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$, with ${\mathscr{H}}_{\mathbf{V}}={\mathscr{H}}_{\mathbf{V}}^+\coprod{\mathscr{H}}_{\mathbf{V}}^-$ the Siegel double space associated to $({\mathbf{V}},\psi)$. The pure Shimura varieties it defines are Siegel modular varieties (with suitable level structures). When $({\mathbf{V}},\psi)$ is the standard symplectic structure on ${\mathbb{Q}}^{2g}$, it is often written as $({\mathrm{GSp}}_{2g},{\mathscr{H}}_g)$. 2. Kuga datum of Siegel type: For any $x\in{\mathscr{H}}_{\mathbf{V}}$, the standard representation $\rho_{\mathbf{V}}:{\mathrm{GSp}}_{\mathbf{V}}{\rightarrow}{{\mathbf{GL}}}_{\mathbf{V}}$ defines a rational Hodge structure $({\mathbf{V}},\rho_{\mathbf{V}}\circ x)$ of type $\{(-1,0),(0,-1)\}$, hence we get the Kuga datum ${\mathbf{V}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$, which we denote as $({\mathbf{Q}}_{\mathbf{V}},{\mathscr{V}}_{\mathbf{V}})$. 3. mixed Shimura datum of Siegel type: The symplectic form defines a central extension ${\mathbf{W}}$ of ${\mathbf{V}}$ by ${\mathbf{U}}$, and it is easy to verify that $({\mathbf{P}}_{\mathbf{V}},{\mathscr{U}}_{\mathbf{V}}):=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$ is a mixed Shimura datum fibred over the Siegel datum. Note that when $g=0$, the mixed Shimura datum is of the form ${\mathbb{G}}_{\mathrm{a}}\rtimes({{\mathbb{G}_\mathrm{m}}},{\mathscr{H}}_0)$ with and ${\mathscr{H}}_0$ is a single point. Sometimes we also call Kuga data of Siegel type as mixed Shimura data of Siegel type. \(2) The three classes of mixed Shimura data given above are all irreducible: - For $({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$, ${\mathscr{H}}_{\mathbf{V}}^+$ is the simple Hermitian symmetric domain corresponding to the connected simple Lie group ${\mathrm{Sp}}_{\mathbf{V}}({\mathbb{R}})$. If there is a pure subdatum $({\mathbf{H}},X_{\mathbf{H}})$ with $X_{\mathbf{H}}$ containing ${\mathscr{H}}_{\mathbf{V}}^+$, then $X_{\mathbf{H}}$ is either $X_{\mathbf{H}}^+:={\mathscr{H}}_{\mathbf{V}}^+$ or ${\mathscr{H}}_{\mathbf{V}}$, and $X_{\mathbf{H}}^+$ is a homogeneous space under ${\mathbf{H}}^{\mathrm{der}}({\mathbb{R}})^+$. Since ${\mathbf{H}}^{\mathrm{der}}\subset{\mathrm{Sp}}_{\mathbf{V}}$, the classification of simple Hermitian symmetric domains forces the equality ${\mathbf{H}}^{\mathrm{der}}={\mathrm{Sp}}_{\mathbf{V}}$ because they both give rise to ${\mathscr{H}}_{\mathbf{V}}^+$. Note that the image of ${{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}}\subset{\mathbb{S}}$ (corresponding to ${\mathbb{R}}^\times{\mathbb{C}}^\times$) under any $x\in{\mathscr{H}}_{\mathbf{V}}^+$ is the center ${{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}}$ of ${{\mathbf{GL}}}_{{\mathbf{V}},{\mathbb{R}}}$, namely acting on ${\mathbf{V}}_{\mathbb{R}}$ by the central scaling. Hence ${\mathbf{H}}\supset{{\mathbb{G}_\mathrm{m}}}$, i.e. ${\mathbf{H}}$ contains the center ${{\mathbb{G}_\mathrm{m}}}$ of ${\mathrm{GSp}}_{\mathbf{V}}$, which implies ${\mathbf{H}}={\mathrm{GSp}}_{\mathbf{V}}$. - For $({\mathbf{Q}},{\mathscr{V}})={\mathbf{V}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$, ${\mathscr{V}}$ is the ${\mathbf{V}}({\mathbb{R}})$-orbit of ${\mathscr{H}}_{\mathbf{V}}$ in ${\mathfrak{X}}({\mathbf{Q}})$. If ${\mathbf{Q}}'\subset{\mathbf{Q}}$ is a ${\mathbb{Q}}$-subgroup such that $y({\mathbb{S}})\subset{\mathbf{Q}}'_{\mathbb{R}}$ for all $y\in{\mathscr{V}}$, then restricting to $x\in{\mathscr{H}}_{\mathbf{V}}\subset{\mathscr{V}}$ we get ${\mathbf{Q}}'\supset{\mathrm{GSp}}_{\mathbf{V}}$. The image of ${\mathbf{Q}}'$ in ${\mathrm{GSp}}_{{\mathbf{V}}}$ is clearly equal to ${\mathrm{GSp}}_{\mathbf{V}}$, and the unipotent radical ${\mathbf{V}}'$ of ${\mathbf{Q}}'$ is necessarily a ${\mathbb{Q}}$-subgroup of ${\mathbf{V}}$. Thus a Levi decomposition of ${\mathbf{Q}}'$ over ${\mathbb{Q}}$ is of the form ${\mathbf{V}}'\rtimes {\mathrm{GSp}}_{\mathbf{V}}$. Since the ${\mathbf{V}}$ is irreducible as a representation of ${\mathrm{GSp}}_{\mathbf{V}}$, we must have ${\mathbf{V}}'={\mathbf{V}}$, which gives ${\mathbf{Q}}'={\mathbf{Q}}$. Note that similar arguments show that ${\mathbf{U}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}})$ is an irreducible mixed Shimura datum, using the action of ${\mathrm{GSp}}_{\mathbf{V}}$ on ${\mathbf{U}}={\mathbb{G}}_{\mathrm{a}}$ by the square of the central character. - For $({\mathbf{P}},{\mathscr{U}})=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$, ${\mathbf{W}}$ is the extension of ${\mathbf{V}}$ by ${\mathbf{U}}={\mathbb{G}}_{\mathrm{a}}$ using the symplectic form $\psi$. If ${\mathbf{P}}'\subset{\mathbf{P}}$ is a ${\mathbb{Q}}$-subgroup such that $y({\mathbb{S}}_{\mathbb{C}})\subset{\mathbf{P}}'_{\mathbb{R}}$, then when $y$ runs through points in ${\mathbf{U}}({\mathbb{C}})\rtimes{\mathscr{H}}_{\mathbf{V}}$, the irreducible subdatum ${\mathbf{U}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$ forces the inclusion ${\mathbf{U}}\rtimes{\mathrm{GSp}}_{\mathbf{V}}\subset{\mathbf{P}}'$, and in particular ${\mathrm{GSp}}_{\mathbf{V}}\subset{\mathbf{P}}'$. Hence ${\mathbf{P}}'$ admits a Levi decomposition over ${\mathbb{Q}}$ of the form ${\mathbf{W}}'\rtimes{\mathrm{GSp}}_{\mathbf{V}}$, where ${\mathbf{W}}'$ is a unipotent ${\mathbb{Q}}$-subgroup of ${\mathbf{W}}$ containing ${\mathbf{U}}$. Thus ${\mathbf{W}}'$ is an extension of ${\mathbf{V}}'={\mathbf{W}}'/{\mathbf{U}}$ by ${\mathbf{U}}$ using the restriction of $\psi$. ${\mathbf{W}}'$ and ${\mathbf{U}}'$ being both stable under ${\mathrm{GSp}}_{\mathbf{V}}$, we see that ${\mathbf{V}}'$ is a ${\mathrm{GSp}}_{\mathbf{V}}$-stable ${\mathbb{Q}}$-vector subspace of ${\mathbf{V}}$, hence the equalities ${\mathbf{V}}'={\mathbf{V}}$, ${\mathbf{W}}'={\mathbf{W}}$, and ${\mathbf{P}}'={\mathbf{P}}$, because ${\mathbf{V}}$ is an irreducible representation of ${\mathrm{GSp}}_{\mathbf{V}}$. \(3) Note that in a product of the form $({\mathbf{G}},X)=({\mathrm{GSp}}_{{\mathbf{V}}_1},{\mathscr{H}}_{{\mathbf{V}}_1})\times\cdots\times({\mathrm{GSp}}_{{\mathbf{V}}_n},{\mathscr{H}}_{{\mathbf{V}},n})$, we can construct irreducible subdata of the form $({\mathbf{G}}',X')$ where ${\mathbf{G}}'$ is the ${\mathbb{Q}}$-subgroup generated by ${\mathbf{G}}^{\mathrm{der}}=\prod_j{\mathrm{Sp}}_{{\mathbf{V}}_j}$ plus a split ${\mathbb{Q}}$-torus ${{\mathbb{G}_\mathrm{m}}}$ that acts on each ${\mathbf{V}}_j$ by the central scaling, and $X'$ is the ${\mathbf{G}}'({\mathbb{R}})$-orbit of some $x=(x_1,\cdots,x_n)\in X=\prod_j{\mathscr{H}}_{{\mathbf{V}}_j}$. In fact $x$ sends ${\mathbb{S}}^1$ into $x_1({\mathbb{S}}^1)\times\cdots\times x_n({\mathbb{S}}^1)\in\prod_j{\mathrm{Sp}}_{{\mathbf{V}}_j,{\mathbb{R}}}$, and sends ${{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}}$ to the center of ${{\mathbf{GL}}}_{\oplus_j{\mathbf{V}}_j}$. Hence by \[generating subdata\], $({\mathbf{G}}',{\mathbf{G}}'({\mathbb{R}})x)$ is a subdatum of $({\mathbf{G}},X)$, which is clearly irreducible. However ${\mathbf{G}}({\mathbb{R}})$ has only two connected components, as its center ${{\mathbb{G}_\mathrm{m}}}({\mathbb{R}})$ has only two connected components and ${\mathbf{G}}'^{\mathrm{der}}({\mathbb{R}})=\prod_j{\mathrm{Sp}}_{{\mathbf{V}}_j}({\mathbb{R}})$ is connected, and thus ${\mathbf{G}}'({\mathbb{R}})x$ has only two connected components, while $X=\prod_j{\mathscr{H}}_{{\mathbf{V}}_j}$ has $2^n$ connected components. For a point $x\in X$, we have its signature vector $s_x\in(\pm)^n$, describing whether it is positive or negative definite on ${\mathbf{V}}_j$, $j=1,\cdots,n$. Two points $x=(x_j)$ and $x'=(x'_j)$ in $X$ fall in the same connected component [[if and only if]{}]{}they have the same signature on each ${\mathbf{V}}_j$. Hence $x'\in{\mathbf{G}}'({\mathbb{R}})x$ [[if and only if]{}]{}$s_{x'}=\pm s_x$. When $x$ runs through $X$, we get finitely many irreducible subdata of the form $({\mathbf{G}}',{\mathbf{G}}'({\mathbb{R}})x)$, which follows from \[common Mumford-Tate group\]. It is also clear that the generic Mumford-Tate group of each connected component of $X$ is ${\mathbf{G}}'$. Although we mainly work with Shimura data in the sense of Deligne, we mention that the pair $({\mathbf{G}}',X=\prod_j{\mathscr{H}}_{{\mathbf{V}}_j})$ is a pure Shimura datum in the sense of Pink [@pink; @thesis] 2.1, as each $x\in X$ gives a homomorphism ${\mathbb{S}}{\rightarrow}{\mathbf{G}}'_{\mathbb{R}}$, and $X{\rightarrow}{\mathfrak{X}}({\mathbf{G}}')$ is a ${\mathbf{G}}'({\mathbb{R}})$-equivariant map with finite fibers. Similarly, in the Kuga case, $({\mathbf{P}},Y)=\prod_j({\mathbf{Q}}_j{\mathscr{V}}_j)=(\oplus_j{\mathbf{V}}_j)\rtimes({\mathbf{G}},X)$ admits irreducible subdata of the form $({\mathbf{P}}',Y')=(\oplus_j{\mathbf{V}}_j)\rtimes({\mathbf{G}}',X')$. The general mixed Shimura case of Siegel type is parallel. These irreducible subdata are actually strictly irreducible in the sense of \[special subvarieties\](3). The fact that the connected center is simply a split ${\mathbb{Q}}$-torus ${{\mathbb{G}_\mathrm{m}}}$ will be useful in the estimations \[torsion order in the product case\] and \[torsion order in the embedded case\]. \(4) Assume that for some ${\mathbb{Z}}$-lattice $\Gamma_{\mathbf{V}}$ of ${\mathbf{V}}$, the restriction $\psi:\Gamma_{\mathbf{V}}\times\Gamma_{\mathbf{V}}{\rightarrow}{\mathbb{Q}}(-1)$ has value in ${\mathbb{Z}}(-1)={\mathbb{Z}}(2\pi{\mathbf{i}})^{{-1}}$ and is of discriminant $\pm1$. The profinite completions of lattices $\Gamma_{\mathbf{V}}\subset{\mathbf{V}}$ and ${\mathbb{Z}}(-1)\subset{\mathbb{Q}}(-1)$ are [[compact open subgroups]{}]{}$K_{\mathbf{V}}$ and $K_{\mathbf{U}}$ respectively. Take a [[compact open subgroup]{}]{}$K_{\mathbf{G}}\subset{\mathrm{GSp}}_{\mathbf{V}}({{\hat{\mathbb{Q}}}})$ small enough and stabilizing both $K_{\mathbf{V}}$ and $K_{\mathbf{U}}$, we get the mixed Shimura variety $M_K({\mathbf{P}}_{\mathbf{V}},{\mathscr{U}}_{\mathbf{V}})$ for $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$, $K_{\mathbf{W}}$ being the [[compact open subgroup]{}]{}generated by $K_{\mathbf{U}}$ and $K_{\mathbf{V}}$. We also have the universal abelian scheme over the Siegel moduli space of level $K_{\mathbf{G}}$, namely $${{\mathscr{A}}}=M_{K_{\mathbf{V}}\rtimes K_{\mathbf{G}}}({\mathbf{Q}}_{\mathbf{V}},{\mathscr{V}}_{\mathbf{V}}){\rightarrow}{\mathscr{S}}=M_{K_{\mathbf{G}}}({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$$ and $M_K({\mathbf{P}}_{\mathbf{V}},{\mathscr{U}}_{\mathbf{V}})$ is a ${{\mathbb{G}_\mathrm{m}}}$-torsor over ${{\mathscr{A}}}$. The [[compact open subgroups]{}]{}thus obtained are levels of fine product type when $K_{\mathbf{G}}$ is of fine product type. \[special subvarieties\] Let $({\mathbf{P}},Y)$ be a mixed Shimura datum, with $M=M_K({\mathbf{P}},Y)$ a mixed Shimura variety associated with it. \(1) The map $\wp_{\mathbf{P}}:Y\times{\mathbf{P}}({{\hat{\mathbb{Q}}}})/K{\rightarrow}M({\mathbb{C}}),\ (y,aK)\mapsto [y,aK]$ is called the (complex) uniformization map of $M$. It is clear that the source is not connected in general, but its connected components are simply connected complex manifolds isomorphic to each other. A special subvariety of $M_K({\mathbf{P}},Y)$ is a priori a subset of $M({\mathbb{C}})$ of the form $\wp_{\mathbf{P}}( Y'^+\times aK)$ with $a\in{\mathbf{P}}({{\hat{\mathbb{Q}}}})$ and $Y'^+$ a connected component of some mixed Shimura subdatum $({\mathbf{P}}',Y')\subset({\mathbf{P}},Y)$, where $K'\subset{\mathbf{P}}'({{\hat{\mathbb{Q}}}})$ is the [[compact open subgroup]{}]{}$aKa^{{-1}}\cap{\mathbf{P}}'({{\hat{\mathbb{Q}}}})$. A special subvariety is actually a closed algebraic subvariety of $M_K({\mathbf{P}},Y)$ over ${\bar{\mathbb{Q}}}$: it is a connected component of the image of the morphism $M_{K'}({\mathbf{P}}',Y'){\rightarrow}M_{aKa^{{-1}}}({\mathbf{P}},Y)$ under the Hecke translate $M_{aKa^{{-1}}}({\mathbf{P}},Y){\cong}M_K({\mathbf{P}},Y)$. (2) In Section 2 and 3, we will often work with connected mixed Shimura varieties defined as follows: - a connected mixed Shimura datum is of the form $({\mathbf{P}},Y;Y^+)$ where $({\mathbf{P}},Y)$ is a mixed Shimura datum and $Y^+$ a connected component of $Y$; a morphism between connected mixed Shimura data is $f:({\mathbf{P}}_1,Y_1;Y_1^+){\rightarrow}({\mathbf{P}}_2,Y_2;Y_2^+)$ with $f$ a morphism of mixed Shimura data $({\mathbf{P}}_1,Y_1){\rightarrow}({\mathbf{P}}_2,Y_2)$ sending $Y_1^+$ into $Y_2^+$; in particular, a connected mixed Shimura subdatum is of the form $({\mathbf{P}}',Y';Y'^+)\subset({\mathbf{P}},Y;Y^+)$ with $({\mathbf{P}}',Y')$ a subdatum of $({\mathbf{P}},Y)$ and $Y'^+$ a connected component of $Y'$ contained in $Y^+$; - a connected mixed Shimura variety is a quotient space of the form $M^+=\Gamma{\backslash}Y^+$ where $\Gamma\subset{\mathbf{P}}({\mathbb{Q}})_+$ is a congruence subgroup; such quotients are normal quasi-projective algebraic varieties defined over a finite extension of the reflex field of $({\mathbf{P}},Y)$, and we treat them as varieties over ${\bar{\mathbb{Q}}}$; - for a connected mixed Shimura variety $M^+$ as above we have the (complex) uniformization map $\wp_\Gamma: Y^+{\rightarrow}M^+$ $y\mapsto\Gamma y$, and a special subvariety of $M^+$ is a subset of the form $\wp_\Gamma(Y'^+)$ given by some connected mixed Shimura subdatum $({\mathbf{P}}',Y';Y'^+)$; special subvarieties are closed irreducible algebraic subvarieties defined over ${\bar{\mathbb{Q}}}$, with canonical models defined over some number fields. For example, in the Kuga case $({\mathbf{P}},Y)={\mathbf{V}}\rtimes({\mathbf{G}},X)$, we have explained in Introduction that special subvarieties are certain torsion subschemes of abelian schemes over some pure special subvariety $S'\subset S$. \(3) We also introduce a variant of irreducible data in the connected setting. A connected mixed Shimura data $({\mathbf{P}},Y;Y^+)$ is said to be strictly irreducible if ${\mathbf{P}}={\mathrm{MT}}(Y^+)$. Note that in this case $Y={\mathbf{P}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})Y^+$ is determined by ${\mathbf{P}}$ and $Y^+$, and $({\mathbf{P}},Y)$ is necessarily irreducible. The pair $({\mathbf{P}},Y)$ thus obtained is also said to be strictly irreducible. For example, the pure and mixed Shimura data of Siegel type associated to a symplectic ${\mathbb{Q}}$-space $({\mathbf{V}},\psi)$ gives rise to strictly irreducible connected mixed Shimura data $({\mathbf{P}},Y;Y^+)$, and the data $({\mathbf{G}}',X')$ constructed in \[Siegel data\](3) gives rise to strictly irreducible ones $({\mathbf{G}}',X';X'^+)$. \[strict irreducibility\](1) Let $f:({\mathbf{P}},Y;Y^+){\rightarrow}({\mathbf{P}}',Y';Y'^+)$ be a morphism of connected mixed Shimura data, such that $f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ is surjective. Assume that $({\mathbf{P}}_1,Y_1;Y_1^+)$ is a strictly irreducible connected subdatum of $({\mathbf{P}},Y;Y^+)$. Then its image $({\mathbf{P}}_1',Y_1';Y_1'^+)$ in $({\mathbf{P}}',Y';Y'^+)$ remains strictly irreducible. \(2) Let $({\mathbf{P}},Y;Y^+)={\mathbf{W}}\rtimes({\mathbf{G}},X;X^+)$ be a connected mixed Shimura datum fibred over a connected pure Shimura datum $({\mathbf{G}},X;X^+)$. Then $({\mathbf{P}},Y;Y^+)$ is strictly irreducible [[if and only if]{}]{}so it is with $({\mathbf{G}},X;X^+)$. \(1) Since $f:{\mathbf{P}}{\rightarrow}{\mathbf{P}}'$ is surjective, the map $f_:Y^+{\rightarrow}Y'^+$ is also surjective. Assume that $({\mathbf{P}}_1',Y_1';Y_1'^+)$ is not strictly irreducible. Then there exists ${\mathbf{P}}_2'\subsetneq{\mathbf{P}}_1'$ such that ${\mathbf{P}}_2'={\mathrm{MT}}(Y_1'^+)$, and putting $Y_2'^+=Y_1'^+$ plus $Y_2'={\mathbf{P}}_2'({\mathbb{R}}){\mathbf{U}}_2'({\mathbb{C}})Y_2'^+$, we get a strictly irreducible subdatum $({\mathbf{P}}_2',Y_2';Y_2'^+)$. We have ${\mathbf{P}}_2:=f^{{-1}}({\mathbf{P}}_2)\subsetneq{\mathbf{P}}_1$ by the epimorphism $f:{\mathbf{P}}_1{{\twoheadrightarrow}}{\mathbf{P}}_1'$, and clearly the inclusion ${\mathbf{P}}_{2,{\mathbb{C}}}\supset y({\mathbb{S}}_{\mathbb{C}})$ holds for all $y\in Y_1^+$ because $f({\mathbf{P}}_{2,{\mathbb{C}}})\supset f(y)({\mathbb{S}}_{\mathbb{C}})$, contradicting the strict irreducibility of $({\mathbf{P}}_1,Y_1;Y_1^+)$. \(2) The reduction modulo ${\mathbf{W}}$ gives $\pi:({\mathbf{P}},Y;Y^+){\rightarrow}({\mathbf{G}},X;X^+)$ with $\pi:{\mathbf{P}}{\rightarrow}{\mathbf{G}}$ surjective. If $({\mathbf{P}},Y;Y^+)$ is strictly irreducible, then so it is with its image $({\mathbf{G}},X;X^+)$ by (1). Conversely, assume $({\mathbf{G}},X;X^+)$ is strictly irreducible, then $({\mathbf{G}},X)$ is irreducible, and we get $({\mathbf{P}},Y)$ irreducible by \[pure irreducibility\]. Let ${\mathbf{P}}'\subset{\mathbf{P}}$ be the generic Mumford-Tate group of $Y^+$, then ${\mathbf{P}}'^{\mathrm{der}}={\mathbf{P}}^{\mathrm{der}}={\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}}$ by \[unipotent radical and Levi decomposition\](4) and \[generating subdata\](3). The reduction of ${\mathbf{P}}'$ modulo ${\mathbf{W}}$ is a ${\mathbb{Q}}$-subgroup ${\mathbf{G}}'$ of ${\mathbf{G}}$ such that ${\mathbf{G}}'_{\mathbb{R}}\supset x({\mathbb{S}})$ for all $x\in X^+$, hence ${\mathbf{G}}'={\mathbf{G}}$ and ${\mathbf{P}}'={\mathbf{P}}$. The André-Oort conjecture can be reduced to the case of special subvarieties within a connected mixed Shimura variety, and it suffices to prove it for some level structure sufficiently small, due to the following elementary lemma: \[insensitivity of levels\] Let $({\mathbf{P}},Y;Y^+)$ be a connected mixed Shimura data, giving rise to a morphism of connected mixed Shimura varieties $\pi:M=\Gamma{\backslash}Y^+{\rightarrow}M'=\Gamma'{\backslash}Y^+$ via an inclusion of congruence subgroups $\Gamma\subset\Gamma'$ in ${\mathbf{P}}({\mathbb{R}})_+$. \(1) If $S\subset M$ is a special subvariety, then its image $\pi(S)$ in $M'$ is special; conversely, if $S'\subset M'$ is a special subvariety, then the pre-image $\pi^{{-1}}(S')$ in $M$ is a finite union of special subvarieties. \(2) The André-Oort conjecture holds for $M$ [[if and only if]{}]{}it holds for $M'$. \(1) If $S=\wp_\Gamma(Y_1^+)$ is a special subvariety defined by some conncted subdatum $({\mathbf{P}}_1,Y_1;Y_1^+)$, then $\pi(S)=\wp_{\Gamma'}(Y_1^+)$ is special. Conversely, if $\Gamma'=\coprod\Gamma a_j$ is a decomposition into finitely many cosets, and $S'=\wp_{\Gamma'}(Y_1^+)$ is special given by a connected mixed Shimura subdatum $({\mathbf{P}}_1,Y_1;Y_1^+)$, then $\pi^{{-1}}(S')$ is the finite union of special subvarieties $S_j=\wp_{\Gamma}(a_jY_1^+)$ defined by $(a_j{\mathbf{P}}_1a_j^{{-1}},a_jY_1;a_jY_1^+)$. \(2) If the André-Oort conjecture holds for $M$, and $(S_n')$ is a sequence of special subvarieties in $M'$, then the pre-images $\pi^{{-1}}(S_n')$ form a sequence of special subvarieties, whose Zariski closure is a finite union $\bigcup_jZ_j$ of special subvarieties in $M$. The finite map $\pi:M{\rightarrow}M'$ is closed, hence it sends $\bigcup_jZ_j$ to the Zariski closure of $\bigcup_nS_n'$ and it is a finite union of special subvarieties $\bigcup_j\pi(Z_j)$. Conversely, if a geometrically irreducible subvariety $Z\subset M$ is the Zariski closure of a sequence of special subvarieties $\bigcup_nS_n$, then $Z$ is a geometrically irreducible component of $\pi^{{-1}}(\pi(Z))$, hence special because $\pi(Z)$ is the Zariski closure of a sequence of special subvarieties $(\pi(S_n))$ in $M'$, and $\pi^{{-1}}(\pi(Z))$ is a finite union of special subvarieties by (1). \[congruence subgroups\] Although we have used congruence subgroups in ${\mathbf{P}}({\mathbb{Q}})^+$ to define connected mixed Shimura varieties of the form $\Gamma{\backslash}Y^+$ and their special subvarieties, it makes no harm to use arithmetic subgroups of ${\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$, as long as we only treat them as complex algebraic varieties. In this setting we can also define special subvarieties and formulate the André-Oort conjecture (see (3) below). We assume for simplicity that the arithmetic subgroups involved are torsion-free, since this suffices for the study of André-Oort type conjectures following the idea of \[insensitivity of levels\]. By [@baily; @borel] and [@pink; @thesis], quotients of the form $\Gamma{\backslash}Y^+$ with $\Gamma$ torsion-free arithmetic subgroups of ${\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$ are normal quasi-projective algebraic varieties over ${\mathbb{C}}$, which are also smooth. In fact: \(1) In the pure case $({\mathbf{P}},Y;Y^+)=({\mathbf{G}},X;X^+)$, the Lie group ${\mathbf{G}}({\mathbb{R}})_+$ acts on $X^+$ through ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{R}})^+$. If $\Gamma\subset{\mathbf{G}}^{\mathrm{der}}({\mathbb{Q}})^+$ is an arithmetic subgroup, then using the quotient map ${\mathbf{G}}^{\mathrm{der}}{\rightarrow}{\mathbf{G}}^{\mathrm{ad}}$, its image $\Gamma^{\mathrm{ad}}\subset{\mathbf{G}}^{\mathrm{ad}}({\mathbb{Q}})^+$ is arithmetic by [@borel; @arithmetic] 8.9 and 8.11, and the quotient $\Gamma{\backslash}X^+=\Gamma^{\mathrm{ad}}{\backslash}X^+$ is an algebraic variety. If $\Gamma_{\mathbf{G}}$ is a torsion-free arithmetic subgroup in ${\mathbf{G}}({\mathbb{Q}})_+$, then $\Gamma_{\mathbf{G}}^\dag:=\Gamma_{\mathbf{G}}\cap{\mathbf{G}}^{\mathrm{der}}({\mathbb{Q}})^+$ is a torsion-free arithmetic subgroup of ${\mathbf{G}}^{\mathrm{der}}({\mathbb{Q}})^+$, and $\Gamma_{\mathbf{G}}$ acts on $X^+$ through its image $\Gamma_{\mathbf{G}}^{\mathrm{ad}}\subset{\mathbf{G}}^{\mathrm{ad}}({\mathbb{Q}})^+$, which is an arithmetic subgroup of ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{Q}})^+$ again by [@borel; @arithmetic] using ${\mathbf{G}}{{\twoheadrightarrow}}{\mathbf{G}}^{\mathrm{ad}}$. Again because we only focus on André-Oort type conjectures, following the idea of \[insensitivity of levels\] we only consider the case when $\Gamma_{\mathbf{G}}^{\mathrm{ad}}$ is torsion-free. The group ${\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$ also acts on $X^+$ through ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{R}})^+$, and the evident map $\Gamma_{\mathbf{G}}^\dag{\backslash}X^+{\rightarrow}\Gamma_{\mathbf{G}}{\backslash}X^+$ is the same as $\Gamma'{\backslash}X^+{\rightarrow}\Gamma_{\mathbf{G}}^{\mathrm{ad}}{\backslash}X^+$, where $\Gamma'$ is the image of $\Gamma_{\mathbf{G}}^\dag$ in ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{Q}})^+$. Clearly $\Gamma'$ is also an arithmetic subgroup, contained in $\Gamma_{\mathbf{G}}^{\mathrm{ad}}$ as a subgroup of finite index, and it is torsion-free. Hence $\Gamma_{\mathbf{G}}^\dag{\backslash}X^+{\rightarrow}\Gamma_{\mathbf{G}}{\backslash}X^+$ is a finite morphism between algebraic varieties: since these quotients are given by torsion-free arithmetic subgroups, by [@borel; @metric; @properties] 3.10 we deduce that $\Gamma'{\backslash}X^+{\rightarrow}\Gamma_{\mathbf{G}}^{\mathrm{ad}}{\backslash}X^+$ is algebraic, and in fact it is a finite étale covering using Riemann existence theorem, cf. [@gille; @szamuely] 5.7.4. \(2) In the mixed case, the connected mixed Shimura varieties of interest in our study are often given in a product form, i.e. given as $\Gamma{\backslash}Y^+$ using connected data $({\mathbf{P}},Y;Y^+)={\mathbf{W}}\rtimes({\mathbf{G}},X;X^+)$ with $\Gamma=\Gamma_{\mathbf{W}}\rtimes \Gamma_{\mathbf{G}}$ for arithmetic subgroups $\Gamma_{\mathbf{W}}\subset{\mathbf{W}}({\mathbb{Q}})$ and $\Gamma_{\mathbf{G}}\subset{\mathbf{G}}({\mathbb{Q}})_+$. Write $\Gamma_{\mathbf{G}}^\dag=\Gamma_{\mathbf{G}}\cap{\mathbf{G}}^{\mathrm{der}}({\mathbb{Q}})^+$ and $\Gamma^\dag=\Gamma_{\mathbf{W}}\rtimes\Gamma_{\mathbf{G}}^\dag$, we have $\Gamma^\dag=\Gamma\cap{\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$ as an arithmetic subgroup of ${\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$ using ${\mathbf{P}}^{\mathrm{der}}={\mathbf{W}}\rtimes{\mathbf{G}}^{\mathrm{der}}$. Consider the following diagrams: $$\xymatrix{\Gamma^\dag \ar[r]\ar[d] & \Gamma \ar[d] & & \Gamma^\dag{\backslash}Y^+\ar[r]\ar[d] & \Gamma{\backslash}Y^+\ar[d] \\ \Gamma_{\mathbf{G}}^\dag\ar[r] & \Gamma_{\mathbf{G}}& & \Gamma_{\mathbf{G}}^\dag{\backslash}X^+ \ar[r] & \Gamma_{\mathbf{G}}{\backslash}X^+}$$ where the left one is Cartesian whose arrows are inclusions, and the right one is Cartesian in the category of complex analytic spaces using the group actions from the left one on $Y^+{\rightarrow}X^+$. Hence $\Gamma^\dag {\backslash}Y^+{\rightarrow}\Gamma{\backslash}Y^+$ is a finite morphism between algebraic varieties as it is pulled back from the finite morphism on the bottom. One may also talk about $\Gamma{\backslash}Y^+$ for general (torsion-free) arithmetic subgroups of ${\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$, because such subgroups contain normal subgroups of finite index of the product form above, and we may argue by finite group quotients and Riemann existence theorem. Note that we cannot define mixed Shimura data of the form $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ with ${\mathbf{G}}$ of adjoint type, because in this case, the Hodge structure given by $x\in X$ on any algebraic representation ${\mathbf{V}}$ of ${\mathbf{G}}$ is necessarily of weight zero as the center of ${\mathbf{G}}$ is trivial. Hence in the diagram above it would not make sense to write groups like $\Gamma_{\mathbf{W}}\rtimes\Gamma_{\mathbf{G}}^{\mathrm{ad}}$. \(3) The André-Oort conjecture for special subvarieties still make sense in this setting which only involves complex algebraic varieties. Namely we start with an arithmetic subgroup $\Gamma\subset{\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$, form the uniformization map $\wp_\Gamma:Y^+{\rightarrow}\Gamma{\backslash}Y^+$, and define special subvarieties to be of the form $\wp_\Gamma(Y'^+)$ using connected mixed Shimura subdata $({\mathbf{P}}',Y';Y'^+)\subset({\mathbf{P}},Y;Y^+)$. If $\Gamma\subset{\mathbf{P}}({\mathbb{Q}})_+$ is a torsion-free congruence subgroup, and $\Gamma'\subset{\mathbf{P}}^{\mathrm{der}}({\mathbb{Q}})^+$ is an arithmetic subgroup contained in $\Gamma$, then using the arguments through the universal coverings as in \[insensitivity of levels\] and the finite morphism $\Gamma'{\backslash}Y^+{\rightarrow}\Gamma{\backslash}Y^+$, we see that the André-Oort conjecture for $\Gamma{\backslash}Y^+$ is equivalent to the one for $\Gamma'{\backslash}Y^+$. When we need finer information about the canonical models, we will always work with classical mixed Shimura data with level structures given by compact open subgroups of ${\mathbf{P}}({{\hat{\mathbb{Q}}}})$. The remark above draws our attention to the derived groups. Analogue to modifying congruence subgroups, we can also modify the derived groups: \[insensitivity of isogeny\] Let $f:M{\rightarrow}M'$ be a morphism between connected mixed Shimura varieties given by some morphism of connected mixed Shimura data $(f,f_):({\mathbf{P}},Y;Y^+){\rightarrow}({\mathbf{P}}',Y';Y'^+)$ together with congruence subgroups $\Gamma\subset{\mathbf{P}}({\mathbb{Q}})_+$ and $\Gamma'\subset{\mathbf{P}}'({\mathbb{Q}})_+$ satisfying $f(\Gamma)\subset\Gamma'$. Assume that the ${\mathbb{Q}}$-group homomorphism $f:{\mathbf{P}}^{\mathrm{der}}{\rightarrow}{\mathbf{P}}'^{\mathrm{der}}$ is an isogeny, i.e. surjective of finite kernel. Then \(1) $f_:Y^+{\rightarrow}Y'^+$ is an isomorphism and $f:M{\rightarrow}M'$ is finite; \(2) the André-Oort conjecture holds for $M$ [[if and only if]{}]{}it holds for $M'$. Note that (1) implies that a connected mixed Shimura variety could be realized by different connected mixed Shimura data, and (2) affirms that one might choose any mixed Shimura datum to study the André-Oort conjecture. For example, in the pure case, the evident morphism between pure Shimura data $({\mathbf{G}},X){\rightarrow}({\mathbf{G}}^{\mathrm{ad}},X^{\mathrm{ad}})=({\mathbf{G}},X)/{\mathbf{Z}}$ with ${\mathbf{Z}}$ the center of ${\mathbf{G}}$ satisfies the lemma: ${\mathbf{G}}^{\mathrm{der}}{\rightarrow}{\mathbf{G}}^{\mathrm{ad}}$ is an isogeny. Hence the André-Oort conjecture for pure Shimura varieties is reduced to the case where the ambient Shimura variety is defined by a ${\mathbb{Q}}$-group of adjoint type, which has been used in [@klingler; @yafaev] [@ullmo; @yafaev] etc. \(1) By \[fibred mixed Shimura data new\], we may assume that $({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$, $({\mathbf{P}}',Y')=({\mathbf{U}}',{\mathbf{V}}')\rtimes({\mathbf{G}}',X')$, and $(f,f_)$ is given by $(f,f_):({\mathbf{G}},X){\rightarrow}({\mathbf{G}}',X')$ a morphism of pure Shimura data together with equivariant maps between ${\mathbb{Q}}$-vector spaces $f:{\mathbf{U}}{\rightarrow}{\mathbf{U}}'$ and $f:{\mathbf{V}}{\rightarrow}{\mathbf{V}}'$ compatible with the alternating bilinear maps $\psi$ and $\psi'$. When we regard ${\mathbf{G}}$ as a ${\mathbb{Q}}$-subgroup of ${\mathbf{P}}$, $f({\mathbf{G}})\subset{\mathbf{P}}'$ is a reductive ${\mathbb{Q}}$-subgroup, which extends to some maximal ${\mathbb{Q}}$-subgroup $w'{\mathbf{G}}'w'^{{-1}}$ for some $w'\in{\mathbf{W}}'({\mathbb{Q}})$, and we assume for simplicity that $w'=1$, hence the morphism $({\mathbf{G}},X){\rightarrow}({\mathbf{G}}',X')$ extends to $({\mathbf{P}},Y){\rightarrow}({\mathbf{P}}',Y')$. Since $f:{\mathbf{P}}^{\mathrm{der}}{\rightarrow}{\mathbf{P}}'^{\mathrm{der}}$ is an isogeny, $f$ induces an isomorphism of Lie algebras ${\mathrm{Lie}}{\mathbf{P}}^{\mathrm{der}}{\rightarrow}{\mathrm{Lie}}{\mathbf{P}}'^{\mathrm{der}}$, and thus ${\mathrm{Lie}}{\mathbf{W}}{\cong}{\mathrm{Lie}}{\mathbf{W}}'$ under $f$. Taking $y\in Y$ mapped to $y'=f(y)\in Y'$, we see that the mixed Hodge structures on ${\mathrm{Lie}}{\mathbf{W}}$ and on ${\mathrm{Lie}}{\mathbf{W}}'$ are isomorphic. This forces the ${\mathbb{Q}}$-group homomorphism ${\mathbf{U}}{\rightarrow}{\mathbf{U}}'$ to be an isomorphism because it underlies an isomorphism of rational Hodge structures of type $(-1,-1)$, and so it is with the quotient ${\mathbf{V}}{\rightarrow}{\mathbf{V}}'$, hence $f:{\mathbf{W}}{\rightarrow}{\mathbf{W}}'$ is also an isomorphism. As for the pure part, the isogeny ${\mathbf{P}}^{\mathrm{der}}{\rightarrow}{\mathbf{P}}'^{\mathrm{der}}$ gives an isogeny ${\mathbf{G}}^{\mathrm{der}}{\rightarrow}{\mathbf{G}}'^{\mathrm{der}}$ which gives further an isomorphism ${\mathbf{G}}^{\mathrm{ad}}{\rightarrow}{\mathbf{G}}'^{\mathrm{ad}}$, hence the map $f_:X{\rightarrow}X'$ is an isomorphism on each connected components in $X$. Therefore $f_:Y^+={\mathbf{W}}({\mathbb{R}}){\mathbf{U}}({\mathbb{C}})\rtimes X^+{\rightarrow}Y'^+={\mathbf{W}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})\rtimes X'^+$ is an isomorphism. Assume that $f:\Gamma{\backslash}Y^+{\rightarrow}\Gamma'{\backslash}Y^+$ is associated to congruence subgroups $\Gamma$ and $\Gamma'$ respectively with $f(\Gamma)\subset\Gamma'$, then the corresponding map for the pure quotient $f:\Gamma_{\mathbf{G}}{\backslash}X^+{\rightarrow}\Gamma_{{\mathbf{G}}'}{\backslash}X'^+$ is finite. In fact, the image $\Gamma_{\mathbf{G}}$ of $\Gamma$ in ${\mathbf{G}}({\mathbb{Q}})_+$ resp. $\Gamma_{{\mathbf{G}}'}$ of $\Gamma'$ in ${\mathbf{G}}'({\mathbb{Q}})_+$ acts on $X^+$ through ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{Q}})^+$ resp. on $X'^+$ through ${\mathbf{G}}'^{\mathrm{ad}}({\mathbb{Q}})^+$, and from the isomorphism ${\mathbf{G}}^{\mathrm{ad}}{\cong}{\mathbf{G}}'^{\mathrm{ad}}$ we know that the image of $\Gamma_{\mathbf{G}}$ in ${\mathbf{G}}^{\mathrm{ad}}({\mathbb{Q}})^+$ is n arithmetic subgroup of finite index in the image of $\Gamma_{{\mathbf{G}}'}$ in ${\mathbf{G}}'^{\mathrm{ad}}({\mathbb{Q}})^+$. Since ${\mathbf{W}}{\cong}{\mathbf{W}}'$, we also get $\Gamma\cap{\mathbf{W}}({\mathbb{Q}})$ of finite index in $\Gamma'\cap{\mathbf{W}}'({\mathbb{Q}})$. Hence $f:\Gamma{\backslash}Y^+{\rightarrow}\Gamma'{\backslash}Y'^+$ is finite. \(2) If $S\subset \Gamma{\backslash}Y^+$ is a special subvariety defined by $({\mathbf{P}}_1,Y_1;Y_1^+)$, then its image in $\Gamma'{\backslash}Y'^+$ is a special subvariety defined by the image subdatum $(f({\mathbf{P}}_1),f_(Y_1);f_(Y_1^+))$. Conversely, if $S'$ is a special subvariety of $\Gamma'{\backslash}Y'^+$ defined by $({\mathbf{P}}_1',Y_1';Y_1'^+)$, then we claim that its preimage in $\Gamma{\backslash}Y^+$ is a finite union of special subvarieties which are Hecke translates of a connected subdatum of the form $({\mathbf{P}}_1,Y_1;Y_1^+)$ where - ${\mathbf{P}}_1$ is the neutral component of $f^{{-1}}({\mathbf{P}}_1')$; - $Y_1^+=f_^{{-1}}(Y_1'^+)$ under the isomorphism $f_:Y^+{\rightarrow}Y'^+$; - $Y_1$ is the ${\mathbf{P}}_1({\mathbb{R}}){\mathbf{U}}_1({\mathbb{C}})$-orbit of $Y_1^+$ with ${\mathbf{U}}_1={\mathbf{U}}\cap{\mathbf{P}}_1$. In fact, any $y'\in Y_1'^+$ has a unique preimage $y\in Y^+$ under the isomorphism $f_:Y^+{\rightarrow}Y'^+$, and the inclusion $y'({\mathbb{S}}_{\mathbb{C}})\subset{\mathbf{P}}'_{1,{\mathbb{C}}}$ gives $y({\mathbb{S}}_{\mathbb{C}})\subset {\mathbf{P}}_{1,{\mathbb{C}}}$ because $y({\mathbb{S}}_{\mathbb{C}})$ is necessarily connected. We verify that the ${\mathbb{Q}}$-group ${\mathbf{P}}_1$ satisfies the condition in \[generating subdata\]: ${\mathbf{P}}_1$ is the neutral component of $f^{{-1}}({\mathbf{P}}_1')$, hence its image ${\mathbf{G}}_1$ modulo ${\mathbf{W}}$ in ${\mathbf{G}}$ is the neutral component of $f^{{-1}}({\mathbf{G}}_1')$ with ${\mathbf{G}}_1'$ the reduction of ${\mathbf{P}}_1'$ modulo ${\mathbf{W}}'$ in ${\mathbf{G}}'$. Since the image of $({\mathbf{P}}_1',Y_1')$ in $({\mathbf{G}}',X')$ is a pure Shimura subdatum of the form $({\mathbf{G}}_1',X_1')$, we see that ${\mathbf{G}}_1'^{\mathrm{ad}}$ admits no compact ${\mathbb{Q}}$-factors, hence so it is with ${\mathbf{G}}_1$. By \[generating subdata\], ${\mathbf{P}}_1$ does give rise to a mixed Shimura subdatum $({\mathbf{P}}_1,{\mathbf{U}}_1,Y_1)$ of $({\mathbf{P}},{\mathbf{U}},Y)$ using the element $y$, with ${\mathbf{U}}_1={\mathbf{U}}\cap{\mathbf{P}}_1$ and $Y_1$ being the ${\mathbf{P}}_1({\mathbb{R}}){\mathbf{U}}_1({\mathbb{C}})$-orbit of $y$. The image of $({\mathbf{P}}_1,{\mathbf{U}}_1,Y_1)$ in $({\mathbf{P}},{\mathbf{U}}',Y')$ is clearly contained in $({\mathbf{P}}_1',{\mathbf{U}}_1',Y_1')$. We have ${\mathbf{P}}_1^{\mathrm{der}}\subset{\mathbf{P}}^{\mathrm{der}}$, and the evident homomorphism $f:{\mathbf{P}}_1^{\mathrm{der}}{\rightarrow}{\mathbf{P}}_1'^{\mathrm{der}}$ is an isogeny because it is restricted from $f:{\mathbf{P}}^{\mathrm{der}}{\rightarrow}{\mathbf{P}}'^{\mathrm{der}}$. By the arguments in (1) we have isomorphisms $f:{\mathbf{U}}_1{\rightarrow}{\mathbf{U}}_1'$, $f:{\mathbf{W}}_1{\rightarrow}{\mathbf{W}}_1'$, and $f_:Y_1^+{\rightarrow}Y_1'^+$. Using \[congruence subgroups\](3), the André-Oort conjecture for $\Gamma{\backslash}Y^+$ resp. for $\Gamma{\backslash}Y'^+$ is equivalent to the conjecture for $\Gamma^\dagger{\backslash}Y^+$ resp. for $\Gamma'^\dagger{\backslash}Y'^+$. The isogeny $f:{\mathbf{P}}^{\mathrm{der}}{\rightarrow}{\mathbf{P}}'^{\mathrm{der}}$ induces an isomorphism $Y^+{\rightarrow}Y'^+$ and it sends $\Gamma^\dagger$ into an arithmetic subgroup of $\Gamma'^\dagger$ with finite kernel, hence the arguments in (1) show that the André-Oort conjecture is the same for $\Gamma^\dagger{\backslash}Y^+$ and $\Gamma'^\dagger{\backslash}Y'^+$, hence the same for $\Gamma{\backslash}Y^+$ and $\Gamma'{\backslash}Y'^+$. In the rest of this section, we explain how a general mixed Shimura datum could be embedded, up to isogeny, into the product of a pure Shimura datum with Kuga data and mixed Shimura data defined in \[Siegel data\]. This phenomenon is similar to the reduction lemma in [@pink; @thesis] 2.26, but the proof is easier as we only require embedding up to isogeny. \[reduction lemma\] Let $({\mathbf{P}},Y)$ be an irreducible mixed Shimura datum. Then there exists a morphism of mixed Shimura data $$f:({\mathbf{P}},Y){\rightarrow}({\mathbf{G}}_0,X_0)\times\prod_{i=1,\cdots,r}({\mathbf{P}}_i,{\mathscr{U}}_i)\times ({\mathbf{Q}}_0,{\mathscr{V}}_0)$$ where $({\mathbf{G}}_0,X_0)$ is a pure Shimura datum, $({\mathbf{P}}_i,{\mathscr{U}}_i)=({\mathbf{P}}_{{\mathbf{V}}_i},{\mathscr{U}}_{{\mathbf{V}}_i})$, $({\mathbf{Q}}_0,{\mathscr{V}}_0)=({\mathbf{Q}}_{{\mathbf{V}}_0},{\mathscr{V}}_{{\mathbf{V}}_0})$ defined as in \[Siegel data\] for some symplectic spaces ${\mathbf{V}}_i$ ($i=0,1,\cdots,r$), and that the ${\mathbb{Q}}$-group homomorphism ${\mathbf{P}}{\rightarrow}{\mathbf{G}}\times\prod_i{\mathbf{P}}_i\times {\mathbf{Q}}_0$ is of finite kernel. If moreover $({\mathbf{P}},Y)$ is a Kuga datum, then $f$ can be taken of the form $$({\mathbf{P}},Y)={\mathbf{V}}\rtimes({\mathbf{G}},X){\rightarrow}({\mathbf{G}}_0,X_0)\times({\mathbf{Q}}_0,{\mathscr{V}}_0)=({\mathbf{G}}_0,X_0)\times ({\mathbf{V}}\rtimes({\mathrm{GSp}}_{\mathbf{V}}, {\mathscr{H}}_{\mathbf{V}})).$$ Write $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ with ${\mathbf{W}}$ given by an alternating bilinear map $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ equivariant under ${\mathbf{G}}$. \(1) We first consider the Kuga case, i.e. $\psi=0$ and ${\mathbf{U}}=0$. We claim in this case ${\mathbf{G}}$ preserves a symplectic form $\Psi$ on ${\mathbf{V}}$ up to similitude, and it gives rise to a morphism of Kuga data $({\mathbf{P}},Y){\rightarrow}{\mathbf{V}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$. Using [@pink; @thesis] 1.4, we get a variation of rational Hodge structures ${{\mathbb{V}}}$ on $X$ associated to the representation $\rho_{\mathbf{V}}$, which is pure of weight 1 and type $\{(-1,0),(0,-1)\}$, and the Hodge structure on ${{\mathbb{V}}}_x$ is given by $\rho_{\mathbf{V}}\circ x$; using further [@pink; @thesis] 1.12, this variation is polarized by some $\Psi:{{\mathbb{V}}}\otimes_{{\mathbb{Q}}_X}{{\mathbb{V}}}{\rightarrow}{\mathbb{Q}}(1)_X$, coming from some ${\mathbf{G}}$-equivariant non-degenerate bilinear map $\Psi:{\mathbf{V}}\otimes_{\mathbb{Q}}{\mathbf{V}}{\rightarrow}{\mathbb{G}}_{\mathrm{a}}({\cong}{\mathbb{Q}}(1))$, which is a symplectic form due to the weight and the Hodge type of $\rho_{\mathbf{V}}\circ x$ ($x\in X$). Hence we obtain a map $f_:X{\rightarrow}{\mathscr{H}}_{\mathbf{V}}$ sending $x\in X$ to the polarized rational Hodge structure $(\rho_{\mathbf{V}}\circ x,\Psi)$, and $f_$ is equivariant [[with respect to]{}]{}a ${\mathbb{Q}}$-group homomorphism $f:{\mathbf{G}}{\rightarrow}{\mathrm{GSp}}_{\mathbf{V}}$. Using \[fibred mixed Shimura data new\](2), we get a morphism of Kuga data $f:{\mathbf{V}}\rtimes({\mathbf{G}},X){\rightarrow}{\mathbf{V}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})=:({\mathbf{Q}}_0,{\mathscr{V}}_0)$, and the restriction of the ${\mathbb{Q}}$-group homomorphism $f$ to the unipotent radical ${\mathbf{V}}$ is identity. Let ${\mathbf{G}}'$ be the image of ${\mathbf{G}}$ in ${\mathrm{GSp}}_{\mathbf{V}}$. Since ${\mathfrak{g}}={\mathrm{Lie}}{\mathbf{G}}$ is reductive, the epimorphism ${\mathrm{Lie}}f:{\mathfrak{g}}={\mathrm{Lie}}{\mathbf{G}}{\rightarrow}{\mathfrak{g}}'={\mathrm{Lie}}{\mathbf{G}}'$ gives rise to a decomposition ${\mathfrak{g}}={\mathfrak{g}}'\oplus{\mathfrak{g}}''$ of ideals of ${\mathfrak{g}}$. Now that ${\mathfrak{g}}$ contains a Lie subalgebra ${\mathfrak{g}}'$, ${\mathbf{G}}$ contains a connected normal reductive ${\mathbb{Q}}$-subgroup ${\mathbf{H}}'$ whose Lie algebra is ${\mathfrak{g}}'$. Let $({\mathbf{G}}_0,X_0)$ be the quotient of $({\mathbf{G}},X)$ by ${\mathbf{H}}'$. We have ${\mathbf{G}}_0={\mathbf{G}}/{\mathbf{H}}'$, and thus the homomorphism ${\mathbf{G}}{\rightarrow}{\mathbf{G}}_0\times{\mathbf{G}}'{\hookrightarrow}{\mathbf{G}}_0\times{\mathrm{GSp}}_{\mathbf{V}}$ is of finite kernel because the Lie algebra homomorphism ${\mathfrak{g}}{\rightarrow}({\mathfrak{g}}/{\mathfrak{g}}')\oplus{\mathfrak{g}}'$ is an isomorphism. From the morphism $({\mathbf{G}},X){\rightarrow}({\mathbf{G}}_0,X_0)\times({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$ we get $$({\mathbf{P}},Y)={\mathbf{V}}\rtimes({\mathbf{G}},X){\rightarrow}({\mathbf{G}}_0,X_0)\times({\mathbf{V}}\rtimes({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}}))=({\mathbf{G}}_0,X_0)\times({\mathbf{Q}}_0,{\mathscr{V}}_0)$$ and ${\mathbf{P}}{\rightarrow}{\mathbf{G}}_0\times{\mathbf{Q}}_0$ is of finite kernel. \(2) When ${\mathbf{U}}\neq 0$, by [@pink; @thesis] 2.14, ${\mathbf{G}}$ acts on ${\mathbf{U}}$ through a split ${\mathbb{Q}}$-torus, and ${\mathbf{U}}$ splits into a direct sum of one-dimensional subrepresentations ${\mathbf{U}}=\oplus_\alpha{\mathbf{U}}_\alpha$. We thus get $\psi=\oplus_\alpha\psi_\alpha$ with $\psi_\alpha$ the composition ${\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}{\rightarrow}{\mathbb{G}}_{\mathrm{a}}$ using the $\alpha$-th projection. Write ${\mathbf{W}}_\alpha$ for the extension of ${\mathbf{V}}$ by ${\mathbb{G}}_{\mathrm{a}}$ using $\psi_\alpha$, we have an inclusion ${\mathbf{W}}{\hookrightarrow}\prod_{\alpha}{\mathbf{W}}_\alpha$ which is the identify when restricted to ${\mathbf{U}}$, and it becomes the diagonal embedding ${\mathbf{V}}{\hookrightarrow}\prod_\alpha{\mathbf{V}}$ when reduced modulo ${\mathbf{U}}$. It extends to an inclusion ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{G}}{\hookrightarrow}\prod_\alpha{\mathbf{P}}_\alpha$ with ${\mathbf{P}}_\alpha={\mathbf{W}}_\alpha\rtimes{\mathbf{G}}$, and we get an embedding $$({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X){\hookrightarrow}\prod_{\alpha}({\mathbf{P}}_\alpha,Y_\alpha)=\prod_\alpha{\mathbf{W}}_\alpha\rtimes({\mathbf{G}},X)=\prod_{\alpha}({\mathbb{G}}_{\mathrm{a}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$$ and it remains to prove the lemma for each $({\mathbf{P}}_\alpha,Y_\alpha)$. We thus assume that ${\mathbf{U}}$ is one-dimensional. The radical ${\mathbf{V}}_0$ of $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ is $\{v\in{\mathbf{V}}:\psi(v,v')=0\forall v'\in{\mathbf{V}}\}$ is a subrepresentation in ${\mathbf{V}}$ under ${\mathbf{G}}$, hence we have a splitting ${\mathbf{V}}={\mathbf{V}}_0\oplus{\mathbf{V}}_1$ because ${\mathbf{G}}$ is reductive, and the restriction $\psi:{\mathbf{V}}_1\times{\mathbf{V}}_1{\rightarrow}{\mathbf{U}}$ is non-degenerate, i.e. a symplectic form. We thus get an embedding $$({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X){\hookrightarrow}(({\mathbf{U}},{\mathbf{V}}_1)\rtimes({\mathbf{G}},X))\times({\mathbf{V}}_0\rtimes({\mathbf{G}},X)).$$ The Kuga case ${\mathbf{V}}_0\rtimes({\mathbf{G}},X)$ is already treated in (1). As for $({\mathbf{U}},{\mathbf{V}}_1)\rtimes({\mathbf{G}},X)$, ${\mathbf{U}}$ is one-dimensional and ${\mathbf{G}}$ acts on it by scalars, hence ${\mathbf{G}}$ preserves $\psi$ up to similitude, which gives $({\mathbf{G}},X){\rightarrow}({\mathrm{GSp}}_{{\mathbf{V}}_1},{\mathscr{H}}_{{\mathbf{V}}_1})$ and a morphism $({\mathbf{U}},{\mathbf{V}}_1)\rtimes({\mathbf{G}},X){\rightarrow}({\mathbf{U}},{\mathbf{V}}_1)\rtimes({\mathrm{GSp}}_{{\mathbf{V}}_1},{\mathscr{H}}_{{\mathbf{V}}_1})$, whose restriction to the unipotent radical ${\mathbf{W}}_1$ (extension of ${\mathbf{V}}_1$ by ${\mathbf{U}}$ via $\psi$) is the identity. Repeat the construction in (1) (i.e. lifting the image of ${\mathbf{G}}{\rightarrow}{\mathrm{GSp}}_{{\mathbf{V}}_1}$ into a connected normal ${\mathbb{Q}}$-subgroup of ${\mathbf{G}}$), we get a morphism $$({\mathbf{U}},{\mathbf{V}}_1)\rtimes({\mathbf{G}},X){\rightarrow}({\mathbf{G}}_1,X_1)\times(({\mathbf{U}},{\mathbf{V}}_1)\rtimes({\mathrm{GSp}}_{{\mathbf{V}}_1},{\mathscr{H}}_{{\mathbf{V}}_1})$$ in which the ${\mathbb{Q}}$-group homomorphism is of finite kernel. Hence the claim. \[reduction to subdata of a good product\] When we study the André-Oort conjecture for $M_K({\mathbf{P}},Y)$, it suffices to restrict to each connected component of the form $M^+=\Gamma{\backslash}Y^+$ for $Y^+$ some fixed connected component of $Y$ and $\Gamma$ some suitably defined congruence subgroup of ${\mathbf{P}}({\mathbb{Q}})_+$. In order to use the strategy of [@klingler; @yafaev] and [@ullmo; @yafaev] for $M^+$, it suffices to take the subdatum $({\mathbf{P}}',Y')$ where ${\mathbf{P}}'={\mathrm{MT}}(Y^+)\subset{\mathbf{P}}$ and $Y'={\mathbf{P}}'({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})Y^+$ using \[generating subdata\](3), which is irreducible, hence admits a morphism into $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$ satisfying \[reduction lemma\]. Moreover the reduction modulo the center ${\mathbf{Z}}_0$ of ${\mathbf{G}}_0$ gives $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}}){\rightarrow}({\mathbf{G}}_0^{\mathrm{ad}},X_0^{\mathrm{ad}})\times({\mathbf{L}},Y_{\mathbf{L}})$ satisfying \[insensitivity of isogeny\], hence we may reduce the André-Oort conjecture to mixed Shimura varieties defined by a subdatum of a “good product” of the form $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$ with ${\mathbf{G}}_0$ semi-simple of adjoint type and $({\mathbf{L}},Y_{\mathbf{L}})$ a product of finitely many mixed Shimura data of Siegel type. We will encounter these good products in Section 4 and Section 5, which provide convenient settings for the estimation of degrees of Galois orbits of special subvarieties. Measure-theoretic constructions on mixed Shimura varieties {#Measure-theoretic constructions on mixed Shimura varieties} ========================================================== In this section, we introduce some measure-theoretic constructions associated to connected mixed Shimura varieties. Most of them are analogue to the Kuga case discussed in [@chen; @kuga] Section 2, 2.14-2.18, except that in the general case, we work with the notion of S-spaces. We also introduce the notion of ${{{(\mathbf{T},w)}}}$-special subdata, which is the analogue of ${\mathbf{T}}$-special subdata of [@ullmo; @yafaev] 3.1 in the mixed case. \[lattice spaces and canonical measures\] \(1) A linear ${\mathbb{Q}}$-group ${\mathbf{P}}$ is said to be of type ${\mathscr{H}}$* if it is of the form ${\mathbf{P}}={\mathbf{W}}\rtimes{\mathbf{H}}$ with ${\mathbf{W}}$ a unipotent ${\mathbb{Q}}$-group and ${\mathbf{H}}$ a connected semi-simple ${\mathbb{Q}}$-group without normal ${\mathbb{Q}}$-subgroups ${\mathbf{H}}'\subset{\mathbf{H}}$ of dimension $>0$ such that ${\mathbf{H}}'({\mathbb{R}})$ is compact. For a mixed Shimura datum $({\mathbf{P}},Y)$, the ${\mathbb{Q}}$-group of commutators ${\mathbf{P}}^{\mathrm{der}}$ is of type ${\mathscr{H}}$, due to \[unipotent radical and Levi decomposition\](4). (2) For ${\mathbf{P}}$ a linear group of type ${\mathscr{H}}$ and $\Gamma\subset{\mathbf{P}}({\mathbb{R}})^+$ a congruence subgroup, the quotient $\Omega=\Gamma{\backslash}{\mathbf{P}}({\mathbb{R}})^+$ is called the (connected) lattice space associated to $({\mathbf{P}},\Gamma)$. Since $\Gamma$ is discrete in ${\mathbf{P}}({\mathbb{R}})^+$, the space $\Omega$ is a smooth manifold. We also have the uniformization map $\wp_\Gamma:{\mathbf{P}}({\mathbb{R}})^+{\rightarrow}\Omega,\ a\mapsto\Gamma a$. \(3) Let $\Omega=\Gamma{\backslash}{\mathbf{P}}({\mathbb{R}})^+$ be a lattice space as in (2). The left Haar measure $\nu_{\mathbf{P}}$ on ${\mathbf{P}}({\mathbb{R}})^+$ passes to a measure $\nu_\Omega$ on $\Omega$: choose a fundamental domain $F\subset{\mathbf{P}}({\mathbb{R}})^+$ [[with respect to]{}]{}$\Gamma$, we put $\nu_\Omega(A)=\nu_{\mathbf{P}}(F\cap\wp_\Gamma^{{-1}}A)$ for $A\subset\Omega$ measurable. Following [@chen; @kuga] 2.15 (1), $\nu_\Omega$ is of finite volume and is normalized such that $\nu_\Omega(\Omega)=1$. We call it the canonical measure on $\Omega$. \[lattice space and s-space\] Let $({\mathbf{P}},Y;Y^+)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X;X^+)$ be a connected mixed Shimura datum with pure section $({\mathbf{G}},X;X^+)$. Let $\Gamma$ be a congruence subgroup of ${\mathbf{P}}({\mathbb{R}})_+$, which gives us the connected mixed Shimura variety $M=\Gamma{\backslash}Y^+$. \(1) The lattice space associated to $M$ is $\Omega=\Gamma^\dagger{\backslash}{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$ where $\Gamma^\dagger=\Gamma\cap{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$. It is equipped with the canonical measure $\nu_\Omega$, and we have the uniformization map $\wp_\Gamma:{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+{\rightarrow}\Omega$, $g\mapsto \Gamma^\dagger g$. A lattice subspace of $\Omega$ is of the form $\wp_\Gamma({\mathbf{H}}({\mathbb{R}})^+)$ for some ${\mathbb{Q}}$-subgroup ${\mathbf{H}}\subset{\mathbf{P}}^{\mathrm{der}}$ of type ${\mathscr{H}}$. Since $\Gamma^\dagger$ acts on ${\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$ by translation, we have $\wp_\Gamma({\mathbf{H}}({\mathbb{R}})^+){\cong}(\Gamma\cap{\mathbf{H}}({\mathbb{R}})^+){\backslash}{\mathbf{H}}({\mathbb{R}})^+$ is a lattice space itself, and it is a closed submanifold of $\Omega$. It carries a canonical measure $\nu$ by \[lattice spaces and canonical measures\], and we regard $\nu$ as a probability measure on $\Omega$ with support equal to the submanifold $\wp_\Gamma({\mathbf{H}}({\mathbb{R}})^+)$. \(2) We write ${{\mathscr{Y}}}^+$ for the ${\mathbf{P}}({\mathbb{R}})_+$-orbit of $X^+$ in $Y$, called the real part of $Y^+$. It is a connected real submanifold of $Y^+$. The (connected) S-space associated to $M$ is ${{\mathscr{M}}}=\Gamma{\backslash}{{\mathscr{Y}}}^+$. Since $\Gamma$ contains a neat subgroup of finite index, the quotient ${{\mathscr{M}}}$ is a real analytic space with at most singularities of finite group quotient. We also have the following orbit map associated to any point $y\in{{\mathscr{Y}}}^+$: $$\kappa_y:\Omega=\Gamma^\dagger{\backslash}{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+{\rightarrow}{{\mathscr{M}}}=\Gamma{\backslash}{{\mathscr{Y}}}^+,\ \Gamma^\dagger g\mapsto \Gamma gy.$$ It is surjective because $\Gamma^\dagger\subset\Gamma$ and ${{\mathscr{Y}}}^+$ is a single ${\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$-orbit, as $X^+$ is homogeneous under ${\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$. It is a submersion of smooth real analytic spaces when $\Gamma$ is neat. \[remarks on s-spaces\] The ${\mathbf{P}}({\mathbb{R}})$-orbit ${{\mathscr{Y}}}$ of $X$ in $Y$ is independent of the choice of pure section $({\mathbf{G}},X)$ as different pure sections are conjugate to each other under ${\mathbf{P}}({\mathbb{Q}})\subset{\mathbf{P}}({\mathbb{R}})$. ${{\mathscr{Y}}}^+$ is simply a connected component of ${{\mathscr{Y}}}$, as it is the preimage of $X^+$ under the natural projection ${{\mathscr{Y}}}({\hookrightarrow}Y){{\twoheadrightarrow}}X$ whose fibers are connected (isomorphic to ${\mathbf{W}}({\mathbb{R}}))$. The notion of real part of $Y$ is inspired by the imaginary part of $Y$ defined in [@pink; @thesis] 4.14. Let $({\mathbf{P}},Y;Y^+)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X;X^+)$ be a connected mixed Shimura datum with ${\mathbf{U}}\neq 0$. Then for any congruence subgroup $\Gamma\subset{\mathbf{P}}({\mathbb{Q}})_+$, the S-space $\Gamma{\backslash}{{\mathscr{Y}}}^+$ is dense in $\Gamma{\backslash}Y^+$ for the Zariski topology. In the Kuga case, we have ${\mathbf{U}}=0$, hence the real part ${{\mathscr{Y}}}^+$ equals $Y^+$, and the S-space ${{\mathscr{M}}}$ is just the Kuga variety. In the non-Kuga case, the projection $\pi_{\mathbf{U}}$ gives us the commutative diagram $$\xymatrix{{{\mathscr{Y}}}^+\ar[d]^{\pi_{\mathbf{U}}}\ar[r]^\subset & Y^+\ar[d]^{\pi_{\mathbf{U}}}\\ Y^+/{\mathbf{U}}({\mathbb{C}})\ar[r]^= & Y^+/{\mathbf{U}}({\mathbb{C}})},$$ in which the vertical maps are smooth submersions of manifolds. The right one is a ${\mathbf{U}}({\mathbb{C}})$-torsor, the left one is a ${\mathbf{U}}({\mathbb{R}})$-torsor, and $Y^+={{\mathscr{Y}}}^+\times^{{\mathbf{U}}({\mathbb{R}})}{\mathbf{U}}({\mathbb{C}})$ namely the quotient of ${{\mathscr{Y}}}^+\times{\mathbf{U}}({\mathbb{C}})$ by the diagonal action of ${\mathbf{U}}({\mathbb{R}})$. ${\mathbf{U}}({\mathbb{R}})\subset{\mathbf{U}}({\mathbb{C}})$ is Zariski dense when we view ${\mathbf{U}}({\mathbb{C}})$ as a complex algebraic variety, hence the density of ${{\mathscr{Y}}}$ in $Y$. The proof for ${{\mathscr{M}}}\subset M$ is clear when we restrict to connected components and take quotient by $\Gamma$. The advantage of S-spaces is that they carry canonical measures of finite volumes. Parallel to the Kuga case studied in [@chen; @kuga] 2.17 and 2.18, we have the following: \[canonical measures on s-spaces\] Let $M=\Gamma{\backslash}Y^+$ be a connected mixed Shimura variety associated to $({\mathbf{P}},Y;Y^+)$, with $\Omega=\Gamma^\dagger{\backslash}{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$ the corresponding lattice space, and ${{\mathscr{M}}}=\Gamma{\backslash}{{\mathscr{Y}}}^+$ the S-space. Fix a base point $y\in {{\mathscr{Y}}}^+\subset Y^+$. \(1) The orbit map $\kappa_y:{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+{\rightarrow}{{\mathscr{Y}}}^+,\ g\mapsto gy$ is a submersion with compact fibers. The isotropy subgroup $K_y$ of $y$ in ${\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$ is a maximal compact subgroup of ${\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$. The left invariant Haar measure $\nu_{\mathbf{P}}$ on ${\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$ passes to a left invariant measure $\mu_{{\mathscr{Y}}}=\kappa_{y}\nu_{\mathbf{P}}$ on ${{\mathscr{Y}}}^+$, which is independent of the choice of $y$. (2) Taking quotients by congruence subgroups, the orbit map $\kappa_y:\Gamma^\dagger{\backslash}{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+{\rightarrow}\Gamma{\backslash}{{\mathscr{Y}}}^+,\ \ \Gamma^\dagger g\mapsto\Gamma gy$ is a submersion with compact fibers. The push-forward $\kappa_{y}$ sends $\nu_\Omega$ to a probability measure $\mu_{{{\mathscr{M}}}}$ on ${{\mathscr{M}}}=\Gamma{\backslash}{{\mathscr{Y}}}^+$, independent of the choice of $y$. We call it the canonical measure on ${{\mathscr{M}}}$. \(3) Let $ M'\subset M$ be a special subvariety defined by $({\mathbf{P}}',Y';Y'^+)$, and take $y\in Y'^+\subset Y^+$. Then we have the commutative diagram $$\xymatrix{ \Omega'\ar[r]^\subset\ar[d]^{\kappa_y} & \Omega\ar[d]^{\kappa_y}\\ {{\mathscr{M}}}'\ar[r]^\subset & {{\mathscr{M}}}}$$ with $\Omega'$ the special lattice space associated to $M'$, ${{\mathscr{M}}}'$ the corresponding special S-subspace. In particular we have $\kappa_{y}\nu_{\Omega'}=\mu_{{{\mathscr{M}}}'}$, with $\nu_{\Omega'}$ the canonical measure of the lattice subspace $\Omega'$ associated to ${\mathbf{P}}'^{\mathrm{der}}({\mathbb{R}})^+$. Note that we identify $\nu_{{{\mathscr{M}}}'}$ as a probability measure on ${{\mathscr{M}}}$ with support equal to ${{\mathscr{M}}}'$. Similarly, for the fibration over the pure base $\pi:M{\rightarrow}S=\Gamma_{\mathbf{G}}{\backslash}X^+$ with $\Gamma=\Gamma_{\mathbf{W}}\rtimes\Gamma_{\mathbf{G}}$, we have the submersions $\pi:\Omega{\rightarrow}\Omega_{\mathbf{G}}:=\Gamma_{\mathbf{G}}^\dagger{\backslash}{\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$, $\pi:{{\mathscr{M}}}' {\rightarrow}S$, together with $\pi_\nu_\Omega=\nu_{\Omega_{\mathbf{G}}}$ and $\pi_\mu_{{\mathscr{M}}}=\mu_S$. It suffices to replace the ${\mathbf{V}}$’s etc. in [@chen; @kuga] 2.17 and 2.18 by ${\mathbf{W}}$’s etc. as the proof there already works for general unipotent ${\mathbf{V}}$’s. In the pure case, we have the notion of ${\mathbf{T}}$-special sub-object, where ${\mathbf{T}}$ is the connected center of the ${\mathbb{Q}}$-group defining the subdatum, the special subvarieties, etc. In the mixed case, the connected center is of the form $w{\mathbf{T}}w^{{-1}}$ following the notations in \[structure of subdata\], and we prefer to separate ${\mathbf{T}}$ and $w$, because ${\mathbf{T}}$ provides information on the image in the pure base, and $w$ describes how the pure section has been translated from the given one defined by $({\mathbf{G}},X)\subset({\mathbf{P}},Y)$. In Introduction we have seen motivations for this notion on Kuga varieties via the description of special subvarieties as torsion subschemes in some subfamily of abelian varieties. \[tw-special subdata\] Let $({\mathbf{P}},Y)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ be a mixed Shimura datum, with ${\mathbf{W}}$ the central extension of ${\mathbf{V}}$ by ${\mathbf{U}}$ as the unipotent radical of ${\mathbf{P}}$. Take ${\mathbf{T}}$ a ${\mathbb{Q}}$-torus in ${\mathbf{G}}$ and $w$ an element in ${\mathbf{W}}({\mathbb{Q}})$. \(1) A subdatum $({\mathbf{P}}',Y')$ of $({\mathbf{P}},Y)$ is said to be $({\mathbf{T}},w)$-special* if it is of the form $({\mathbf{U}}',{\mathbf{V}}')\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ presented as in \[structure of subdata\], with ${\mathbf{T}}$ equal to the connected center of ${\mathbf{G}}'$. In the language of [@ullmo; @yafaev], $({\mathbf{G}}',X')$ is a ${\mathbf{T}}$-special subdatum of $({\mathbf{G}},X)$, and the element $w\in{\mathbf{W}}({\mathbb{Q}})$ conjugates it to a pure section of $({\mathbf{P}}',Y')$, cf. \[pure section\]. \(2) Similarly, if $M=\Gamma{\backslash}Y^+$ is a connected mixed Shimura variety defined by $({\mathbf{P}},Y;Y^+)$, then a special subvariety of $M$ is $({\mathbf{T}},w)$-special if it is defined by some (connected) irreducible $({\mathbf{T}},w)$-special subdatum. We also define notions such as $({\mathbf{T}},w)$-special lattice subspaces, $({\mathbf{T}},w)$-special S-subspaces, etc. in the evident way. \(3) When we remove $w\in{\mathbf{W}}({\mathbb{Q}})$ we get the notion of ${\mathbf{T}}$-special sub-objects, similar to the Kuga case studied in [@chen; @kuga] 3.1: a ${\mathbf{T}}$-special subdatum is an irreducible subdatum $({\mathbf{P}}',Y')\subset({\mathbf{P}},Y)$ such that the image of $({\mathbf{P}}',Y')$ under the natural projection is $({\mathbf{G}}',X')$ a pure irreducible subdatum of $({\mathbf{G}},X)$ with ${\mathbf{T}}$ equal to the connected center of ${\mathbf{G}}'$; the notion of ${\mathbf{T}}$-special subvarieties, etc. is understood in the evident way. If $({\mathbf{P}},Y)$ is pure, i.e. ${\mathbf{W}}=1$, then being $({\mathbf{T}},1)$-special is the same as ${\mathbf{T}}$-special pure subdata. We will also use the following variant to state our main results on the equidistribution of special subvarieties, inspired by the pure case studied in [@ullmo; @yafaev]. Subsets of closed subvarieties of a ${\bar{\mathbb{Q}}}$-variety of finite type are always countable, hence we talk about sequences of special subvarieties indexed by ${\mathbb{N}}$ instead of “families”, “collections”, etc. \[bounded sequence\] Let $M=\Gamma{\backslash}Y^+$ be a connected mixed Shimura variety defined by $({\mathbf{P}},Y;Y^+)={\mathbf{W}}\rtimes({\mathbf{G}},X;X^+)$. Fix a finite set $B=\{({\mathbf{T}}_1,w_1),\cdots,({\mathbf{T}}_r,w_r)\}$ with ${\mathbf{T}}_i$ a ${\mathbb{Q}}$-torus in ${\mathbf{G}}$ and $w_i\in{\mathbf{W}}({\mathbb{Q}})$, $i=1,\cdots,r$. We call $B$ a (finite) bounding set. \(1) A special subvariety of $M$ is said to be bounded by $B$ (or $B$-bounded) if it is ${{{(\mathbf{T},w)}}}$-special for some ${{{(\mathbf{T},w)}}}\in B$. A sequence $(M_n)$ of special subvarieties in $M$ is said to be bounded by $B$ if each $M_n$ is $B$-bounded. \(2) Similarly, a sequence of special lattice subspaces resp. of special S-subspaces is bounded by $B$ if its members are defined by ${{{(\mathbf{T},w)}}}$-special subdatum for ${{{(\mathbf{T},w)}}}\in B$. \(3) For $\Omega$ resp. ${{\mathscr{M}}}$ the lattice space resp. the S-space associated to $M$ we write ${\mathscr{P}}_B(\Omega)$ resp. ${\mathscr{P}}_B({{\mathscr{M}}})$ for the set of canonical measures on $\Omega$ resp. on ${{\mathscr{M}}}$ associated to $B$-bounded special subvarieties. Note that when $({\mathbf{P}},Y)=({\mathbf{G}},X)$ is pure, $B$ is simply a finite set of ${\mathbb{Q}}$-tori in ${\mathbf{G}}$. \[conjugation by gamma\] We consider a connected mixed Shimura variety of the form $M=\Gamma{\backslash}Y^+$ defined by $({\mathbf{P}},Y;Y^+)={\mathbf{W}}\rtimes({\mathbf{G}},X;X^+)$ with $\Gamma=\Gamma_{\mathbf{W}}\rtimes\Gamma_{\mathbf{G}}$ and fibred over $S=\Gamma_{\mathbf{G}}{\backslash}X^+$. Let $Z$ be a ${{{(\mathbf{T},w)}}}$-special subvariety, defined by $({\mathbf{P}}',Y')={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}}, wX;wX^+)$, with ${\mathbf{T}}$ the connected center of ${\mathbf{G}}'$. The pre-image of $Z$ under the uniformization $\wp_\Gamma: Y^+{\rightarrow}M$ is the union $\bigcup_{\gamma\in \Gamma}\gamma Y'^+$, hence a subdatum $({\mathbf{P}}'',Y'';Y''^+)$ defines the same special subvariety $Z$ as $({\mathbf{P}}',Y';Y'^+)$ does [[if and only if]{}]{}$({\mathbf{P}}'',Y'';Y''^+)=(\gamma{\mathbf{P}}'\gamma^{{-1}}, \gamma Y'; \gamma Y'^+)$ for some $\gamma\in\Gamma$. In our definition, ${\mathbf{T}}$ only depends on the image of $Z$ in $S$, and we can conjugate ${\mathbf{T}}$ by $\Gamma_{\mathbf{G}}$; in the unipotent radical, since $\Gamma_{\mathbf{W}}$ acts on ${\mathbf{U}}({\mathbb{C}}){\mathbf{W}}({\mathbb{R}})$ by translation, $w$ and $w'$ give rise to the same special subvariety [[if and only if]{}]{}$w=\gamma w'$ for some $\gamma\in\Gamma_{\mathbf{W}}$. We thus conclude that the notion of ${{{(\mathbf{T},w)}}}$-special subvarieties actually only depends on the class $[{\mathbf{T}},w]$, by which we mean the $\Gamma_{\mathbf{G}}$-conjugacy class of ${\mathbf{T}}$ in ${\mathbf{G}}$ and the coset $\Gamma_{\mathbf{W}}w$ in $\Gamma_{\mathbf{W}}{\backslash}{\mathbf{W}}({\mathbb{Q}})$. Bounded equidistribution of special subvarieties {#Bounded equidistribution of special subvarieties} ================================================ We first consider the case when the bound $B$ consists of one single element ${{{(\mathbf{T},w)}}}$, and we write ${\mathscr{P}}_{{{(\mathbf{T},w)}}}({\mathscr{S}})$ in place of ${\mathscr{P}}_B({\mathscr{S}})$ for ${\mathscr{S}}\in\{\Omega,{{\mathscr{M}}}\}$. This is exactly the analogue of the ${\mathbf{T}}$-special case for pure Shimura varieties, and the main theorem of this section will rely on the following theorem of S. Mozes and N. Shah: \[mozes shah\] Let $\Omega=\Gamma{\backslash}{\mathbf{H}}({\mathbb{R}})^+$ be the lattice space associated to a ${\mathbb{Q}}$-group of type ${\mathscr{H}}$ and a congruence subgroup $\Gamma\subset{\mathbf{H}}({\mathbb{R}})^+$. Write ${\mathscr{P}}_h(\Omega)$ for the set of canonical measures on $\Omega$ associated to lattice subspaces defined by ${\mathbb{Q}}$-subgroups of type ${\mathscr{H}}$. Then ${\mathscr{P}}_h(\Omega)$ is compact for the weak topology as a subset of the set of Radon measures on $\Omega$, and the property of “support convergence” holds on it: if $\nu_n$ is a convergent sequence in ${\mathscr{P}}_h(\Omega)$ of limit $\nu$, then we have ${\mathrm{supp}}\nu_n\subset {\mathrm{supp}}\nu$ for $n\geq N$, $N$ being some positive integer, and the union $\bigcup_{n\geq N}{\mathrm{supp}}\nu_n$ is dense in ${\mathrm{supp}}\nu$ for the analytic topology. We begin with the strategy of the proof of the equidistribution of ${{{(\mathbf{T},w)}}}$-special subspaces and S-subspaces, in comparison with the pure case treated in [@clozel; @ullmo] [@ullmo; @yafaev] and the rigid Kuga case in [@chen; @kuga]: 1. For lattice subspaces, it suffices to show that ${\mathscr{P}}_{{{(\mathbf{T},w)}}}(\Omega)$ is a closed subset of ${\mathscr{P}}_h(\Omega)$, namely if $\nu_n$ is a sequence of canonical measures of limit $\nu$, such that each $\nu_n$ is associated to ${\mathbf{P}}_n^{\mathrm{der}}$ from some ${{{(\mathbf{T},w)}}}$-special subdata $({\mathbf{P}}_n,Y_n)$, then $\nu$ is also associated to ${\mathbf{P}}_\nu^{\mathrm{der}}$ from some ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}_\nu,Y_\nu)$. In fact: 1. in the pure case, the ${\mathbb{Q}}$-group ${\mathbf{Q}}$ generated by the union of semi-simple ${\mathbb{Q}}$-groups $\bigcup_{n>>0}{\mathbf{P}}_n^{\mathrm{der}}$ is a semi-simple ${\mathbb{Q}}$-group of type ${\mathscr{H}}$, and is centralized by ${\mathbf{T}}$ the common connected center of the ${\mathbf{P}}_n$, and ${\mathbf{T}}{\mathbf{Q}}$ is the ${\mathbb{Q}}$-group of some ${\mathbf{T}}$-special subdatum; 2. in the Kuga case treated in [@chen; @kuga], the ${\mathbb{Q}}$-group ${\mathbf{Q}}$ generated by the union $\bigcup_{n>>0}{\mathbf{P}}^{\mathrm{der}}_n$ is of the form ${\mathbf{V}}'\rtimes{\mathbf{H}}'$ with ${\mathbf{V}}'$ unipotent and ${\mathbf{H}}'$ semi-simple of type ${\mathscr{H}}$, however there might be infinitely many subdata $({\mathbf{P}}',Y')$ such that ${\mathbf{P}}'^{\mathrm{der}}={\mathbf{Q}}$, because for any $v\in{\mathbf{V}}({\mathbb{Q}})$ fixed by ${\mathbf{G}}'^{\mathrm{der}}$ and ${\mathbf{P}}'={\mathbf{V}}'\rtimes(v{\mathbf{G}}'v^{{-1}})$ we have ${\mathbf{P}}'^{\mathrm{der}}={\mathbf{V}}'\rtimes{\mathbf{G}}'^{\mathrm{der}}$, cf. [@chen; @kuga] 2.19 and 3.6; to exclude this situation we have restricted to the $\rho$-rigid case in [@chen; @kuga], and results like [@chen; @kuga] 3.5 and 4.5 show that the canonical measures associated to $\rho$-rigid subdata form a closed subset of ${\mathscr{P}}_h(\Omega)$; 3. in the general case under the ${{{(\mathbf{T},w)}}}$-special assumption, the situation is similar to the pure case (i-1), and we will construct a ${{{(\mathbf{T},w)}}}$-special subdatum out of the ${\mathbb{Q}}$-group generated by the union $\bigcup_{n>>0}{\mathbf{P}}_n^{\mathrm{der}}$; thanks to the specification of the unipotent element $w$, we do not need any $\rho$-rigidity to ensure that the new datum is well defined. 2. For S-spaces, we follow a similar reduction following the pure case in [@clozel; @ullmo], namely there exists a compact subset $C$ of ${{\mathscr{Y}}}^+$ such that any ${{{(\mathbf{T},w)}}}$-special S-subspace in ${{\mathscr{M}}}$ can be defined by some subdatum $({\mathbf{P}}',Y';Y'^+)$ satisfying ${{\mathscr{Y}}}'^+\cap C\neq \emptyset$, and then we may repeat the remaining arguments in [@clozel; @ullmo]. The following lemma will be useful both in the pure case and in the mixed case. \[maximal TW-special subdata\] For $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ a mixed Shimura datum. If ${{{(\mathbf{T},w)}}}$ a pair as in \[tw-special subdata\], then the set of maximal ${{{(\mathbf{T},w)}}}$-special subdata of $({\mathbf{P}},Y)$ is finite. If $({\mathbf{G}}',X')$ is a maximal ${\mathbf{T}}$-special subdatum of $({\mathbf{G}},X)$, then ${\mathbf{W}}\rtimes({\mathbf{G}}',X')={\mathbf{W}}\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ is a maximal ${{{(\mathbf{T},w)}}}$-special subdatum of $({\mathbf{P}},Y)$ using $w\in{\mathbf{W}}({\mathbb{Q}})$. Hence we are reduced to the pure case. If $({\mathbf{G}}_1,X_1)\subset({\mathbf{G}},X)$ is a ${\mathbf{T}}$-special subdatum, then ${\mathbf{G}}_1$ is contained in the neutral component ${\mathbf{Z}}^\circ$ of the centralizer ${\mathbf{Z}}_{\mathbf{G}}{\mathbf{T}}$, and ${\mathbf{Z}}^\circ$ admits a decomposition into an almost direct product: ${\mathbf{Z}}^\circ={\mathbf{C}}{\mathbf{H}}'{\mathbf{H}}''$ with ${\mathbf{C}}$ a ${\mathbb{Q}}$-torus, ${\mathbf{H}}'$ a semi-simple ${\mathbb{Q}}$-group without compact ${\mathbb{Q}}$-factors, and ${\mathbf{H}}''$ a semi-simple ${\mathbb{Q}}$-group without non-compact ${\mathbb{Q}}$-factors. We put ${\mathbf{G}}'={\mathbf{C}}{\mathbf{H}}'$, then the constructions in [@ullmo; @yafaev] 3.6 gives us a maximal ${\mathbf{T}}$-special subdatum $({\mathbf{G}}',{\mathbf{G}}'({\mathbb{R}})x)$ with $x\in X_1$ arbitrary, cf. \[generating subdata\]. Note that the ${\mathbb{Q}}$-group ${\mathbf{G}}'$ is determined by ${\mathbf{T}}$ and is independent of $({\mathbf{G}}_1,X_1)$, thus maximal ${\mathbf{T}}$-special subdata are associated to ${\mathbf{G}}'$. Hence by [@ullmo; @yafaev] 3.7 there are only finitely many maximal ${\mathbf{T}}$-special subdata. \[equidistribution of TW-special subspaces\] Let ${\mathscr{S}}$ be the lattice space (resp. the S-space) associated to a connected mixed Shimura variety $M=\Gamma{\backslash}Y^+$ defined by $({\mathbf{P}},Y;Y^+)={\mathbf{W}}\rtimes({\mathbf{G}},X;X^+)$. Fix a pair $({\mathbf{T}},w)$ as in \[tw-special subdata\] and put $B=\{{{{(\mathbf{T},w)}}}\}$. Then the set ${\mathscr{P}}_B({\mathscr{S}})$ is compact for the weak topology, and the property of support convergence holds in it in the sense of \[mozes shah\]. We start with the case of lattice subspaces with $({\mathbf{P}},Y)=({\mathbf{G}},X)$ pure. In [@clozel; @ullmo] ${\mathbf{G}}$ was assumed to be of adjoint type, and in [@ullmo; @yafaev] the case of ${\mathbf{T}}$-special subdata of $({\mathbf{G}},X)$ with ${\mathbf{G}}$ of adjoint type was considered. Here we adapt some of their arguments for general reductive ${\mathbf{G}}$. We have $\Omega=\Omega_{\mathbf{G}}=\Gamma_{\mathbf{G}}^\dagger{\backslash}{\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$, hence ${\mathscr{P}}_{\mathbf{T}}(\Omega)$ is a subset of ${\mathscr{P}}_h(\Omega)$ (as there is no unipotent vector $w$ in this case). We proceed to show that ${\mathscr{P}}_{\mathbf{T}}(\Omega)$ is closed in ${\mathscr{P}}_h(\Omega)$ for the weak topology. By the proof of \[maximal TW-special subdata\] all the maximal ${\mathbf{T}}$-subdata of $({\mathbf{G}},X)$ are associated to a common reductive ${\mathbb{Q}}$-subgroup ${\mathbf{G}}^{\mathbf{T}}$ of ${\mathbf{G}}$, and the lattice subspace of ${\mathbf{T}}$-special subdata are actually lattice subspaces of $$\Omega_{{\mathbf{G}}^{\mathbf{T}}}=\wp_{\Gamma_{\mathbf{G}}}(({\mathbf{G}}^{\mathbf{T}})^{\mathrm{der}}({\mathbb{R}})^+){\cong}\Gamma_{{\mathbf{G}}^{\mathbf{T}}}^\dagger{\backslash}({\mathbf{G}}^{\mathbf{T}})^{\mathrm{der}}({\mathbb{R}})^+$$ with $\Gamma_{{\mathbf{G}}^{\mathbf{T}}}^\dagger=({\mathbf{G}}^{\mathbf{T}})^{\mathrm{der}}({\mathbb{R}})^+\cap\Gamma_{\mathbf{G}}^\dagger$. Hence we may identify ${\mathscr{P}}_{\mathbf{T}}(\Omega)$ as a subset of ${\mathscr{P}}_h(\Omega_{{\mathbf{G}}^{\mathbf{T}}})$, the latter being a closed subset of ${\mathscr{P}}_h(\Omega)$. We assume for simplicity that ${\mathbf{G}}={\mathbf{G}}^{\mathbf{T}}$, namely ${\mathbf{T}}$ equals the connected center of ${\mathbf{G}}$. Take a sequence $\nu_n$ of canonical measures, which converges in ${\mathscr{P}}_h(\Omega)$ to some $\nu$. Each $\nu_n$ is associated to a ${\mathbb{Q}}$-group ${\mathbf{G}}_n$ of ${\mathbf{G}}$ coming from some ${\mathbf{T}}$-special subdatum $({\mathbf{G}}_n,X_n)$, with $\Omega_n={\mathrm{supp}}\nu_n=\wp_{\Gamma_{\mathbf{G}}}({\mathbf{G}}_n^{\mathrm{der}}({\mathbb{R}})^+)$. The limit $\nu$ is associated to some connected ${\mathbb{Q}}$-group ${\mathbf{G}}'$ of type ${\mathscr{H}}$, of support $\Omega_\nu=\wp_{\Gamma_{\mathbf{G}}}({\mathbf{G}}'({\mathbb{R}})^+)$. We may assume for simplicity that $\bigcup_{n\geq0}\Omega_n$ is contained in $\Omega_\nu$ as a dense subset by restricting to a subsequence after dropping finitely many terms in the original sequence. In particular, $\Omega_n$ and $\Omega_\nu$ are smooth submanifolds of $\Omega$ the quotient of ${\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$ by translation of the discrete subgroup $\Gamma_{\mathbf{G}}^\dagger$, and the inclusion $\Omega_n\subset\Omega_\nu$ implies the inclusion ${\mathrm{Lie}}{\mathbf{G}}_n^{\mathrm{der}}\subset{\mathrm{Lie}}{\mathbf{G}}'$ by computing the tangent spaces of the common point $\wp_\Gamma(e)$, $e$ being the neutral point of ${\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$. This gives ${\mathbf{G}}_n^{\mathrm{der}}\subset{\mathbf{G}}'\subset{\mathbf{G}}^{\mathrm{der}}$. Since ${\mathbf{T}}$ is the common connected center of ${\mathbf{G}}$ and ${\mathbf{G}}_n$ , we have the equality of centralizers ${\mathbf{Z}}_{\mathbf{G}}{\mathbf{G}}_n={\mathbf{T}}{\mathbf{Z}}_{{\mathbf{G}}^{\mathrm{der}}}{\mathbf{G}}_n^{\mathrm{der}}$ for all $n$. Take any $x_n\in X_n$, ${\mathbf{Z}}_{{\mathbf{G}}}{\mathbf{G}}_n({\mathbb{R}})$ is compact modulo ${\mathbf{T}}$ as it centralizes $x_n({\mathbf{i}})$. Hence ${\mathbf{Z}}_{{\mathbf{G}}^{\mathrm{der}}}{\mathbf{G}}_n^{\mathrm{der}}$ is compact, and ${\mathbf{G}}'$ is reductive by [@eskin; @mozes; @shah] Lemma 5.1. We thus obtain an inclusion chain of connected semi-simple ${\mathbb{Q}}$-groups ${\mathbf{G}}_n^{\mathrm{der}}\subset{\mathbf{G}}'\subset{\mathbf{G}}^{\mathrm{der}}$, which extends to ${\mathbf{G}}_n\subset{\mathbf{T}}{\mathbf{G}}'\subset{\mathbf{G}}$. Put ${\mathbf{G}}_\nu={\mathbf{T}}{\mathbf{G}}'$, then \[generating subdata\] gives further an inclusion chain of ${\mathbf{T}}$-special subdatum $({\mathbf{G}}_n,X_n)\subset({\mathbf{G}}_\nu,X_\nu)\subset({\mathbf{G}},X)$ with $X_\nu={\mathbf{G}}_\nu({\mathbb{R}})x_n$ for any $x_n\in X_n$. Therefore ${\mathbf{G}}'={\mathbf{G}}_\nu^{\mathrm{der}}$ does come from some ${\mathbf{T}}$-special subdatum, and $\nu$ is ${\mathbf{T}}$-special. Note that we have constructed subdata of the form $({\mathbf{G}}_\nu,{\mathbf{G}}_\nu({\mathbb{R}})x_n)$ using an arbitrary $x_n\in X_n$ for all $n\in{\mathbb{N}}$. Only finitely many ${\mathbf{T}}$-subdata are obtained in this way due to \[common Mumford-Tate group\]. From the proof we also obtain: \[generating subgroups\] Using the notations in the proof, ${\mathbf{G}}_\nu$ is generated by $\bigcup_n{\mathbf{G}}_n$. In the proof above we already have ${\mathbf{G}}_n^{\mathrm{der}}\subset{\mathbf{G}}'={\mathbf{G}}_\nu^{\mathrm{der}}$ for all $n$. Thus ${\mathbf{G}}'$ contains ${\mathbf{H}}$ the ${\mathbb{Q}}$-subgroup generated by $\bigcup_n{\mathbf{G}}_n^{\mathrm{der}}$ in ${\mathbf{G}}^{\mathrm{der}}$. If ${\mathbf{H}}\subsetneq{\mathbf{G}}'$, then all the lattice subspaces $\Omega_n=\wp_{\Gamma_{\mathbf{G}}}({\mathbf{G}}_n^{\mathrm{der}}({\mathbb{R}})^+)$ are contained in the subspace $\wp_{\Gamma_{\mathbf{G}}}({\mathbf{H}}({\mathbb{R}})^+)$ which is a proper submanifold of $\Omega_\nu$, contradicting the density of $\bigcup_n\Omega_n$ in $\Omega_\nu$. Hence ${\mathbf{H}}={\mathbf{G}}'$. Now we pass to the general mixed case: For any mixed Shimura subdatum $({\mathbf{P}}',Y')={\mathbf{W}}'\rtimes({\mathbf{G}}',X')$ of $({\mathbf{P}},Y)$, the equality ${\mathbf{P}}'^{\mathrm{der}}={\mathbf{W}}'\rtimes{\mathbf{G}}'^{\mathrm{der}}$ by \[unipotent radical and Levi decomposition\](4) shows that ${\mathbf{P}}'^{\mathrm{der}}$ is of type ${\mathscr{H}}$. Hence for $\Omega=\Gamma^\dagger{\backslash}{\mathbf{P}}^{\mathrm{der}}({\mathbb{R}})^+$, ${\mathscr{P}}_{{{(\mathbf{T},w)}}}(\Omega)$ is a subset of ${\mathscr{P}}_h(\Omega)$, and we need to show that ${\mathscr{P}}_{{{(\mathbf{T},w)}}}(\Omega)$ is closed in ${\mathscr{P}}_h(\Omega)$ for the weak topology, just as the pure case above. We thus take a convergent sequence $\nu_n$ in ${\mathscr{P}}_h(\Omega)$ of limit $\nu$, such that $\nu_n\in{\mathscr{P}}_{{{(\mathbf{T},w)}}}(\Omega)$, is associated to some ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}_n,Y_n)={\mathbf{W}}_n\rtimes(w{\mathbf{G}}_nw^{{-1}},wX_n)$, and the support of $\nu_n$ is the ${{{(\mathbf{T},w)}}}$-special lattice subspace $\Omega_n=\wp_\Gamma({\mathbf{P}}_n^{\mathrm{der}}({\mathbb{R}})^+)$, with ${\mathbf{P}}_n^{\mathrm{der}}={\mathbf{W}}_n\rtimes w{\mathbf{G}}_n^{\mathrm{der}}w^{{-1}}$. The limit $\nu$ is associated to some ${\mathbb{Q}}$-subgroup ${\mathbf{P}}'$ of type ${\mathscr{H}}$, with ${\mathrm{supp}}\nu=\Omega_\nu=\wp_\Gamma({\mathbf{P}}'({\mathbb{R}})^+)$. We assume for simplicity that $\Omega_n\subset\Omega_\nu$ for all $n$, hence $\bigcup_n\Omega_n$ is dense in $\Omega_\nu$ for the analytic topology. Let $\Gamma_{\mathbf{G}}$ be the image of $\Gamma$ in ${\mathbf{G}}({\mathbb{R}})^+$, which is a congruence subgroup of ${\mathbf{G}}({\mathbb{R}})^+$, and we write $\Gamma_{\mathbf{G}}^\dagger=\Gamma_{\mathbf{G}}\cap{\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$, together with $\pi:\Omega{\rightarrow}\Omega_{\mathbf{G}}=\Gamma_{\mathbf{G}}^\dagger{\backslash}{\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})^+$ for the projection deduced from $\pi=\pi_{\mathbf{W}}:{\mathbf{P}}{\rightarrow}{\mathbf{G}}$ the quotient modulo ${\mathbf{W}}$. Then by \[canonical measures on s-spaces\], $\pi_\nu_n$ is the canonical measure associated to $\pi({\mathbf{P}}_n^{\mathrm{der}})={\mathbf{G}}_n^{\mathrm{der}}$. We clearly have the convergence $\lim_{n{\rightarrow}\infty}\pi_\nu_n=\pi_\nu$, hence by the result in the pure case, $\pi_\nu$ is ${\mathbf{T}}$-special, i.e. it is associated to some ${\mathbf{T}}$-special subdatum $({\mathbf{G}}_\nu,X_\nu)$. ${\mathbf{G}}_\nu$ is generated by $\bigcup_n{\mathbf{G}}_n$, and the connected semi-simple ${\mathbb{Q}}$-subgroup ${\mathbf{G}}'={\mathbf{G}}_\nu^{\mathrm{der}}$ is generated by $\bigcup_n{\mathbf{G}}_n^{\mathrm{der}}$. On the other hand, it is direct from the construction that the image $\pi({\mathbf{P}}')$ of ${\mathbf{P}}'$ modulo ${\mathbf{W}}$ in ${\mathbf{G}}^{\mathrm{der}}$ is a ${\mathbb{Q}}$-subgroup of type ${\mathscr{H}}$, and $\wp_{\Gamma_{\mathbf{G}}}(\pi({\mathbf{P}}')({\mathbb{R}})^+)$ equals the support of $\pi_\nu$. Hence $\pi({\mathbf{P}}')={\mathbf{G}}'={\mathbf{G}}_\nu^{\mathrm{der}}$. It is also clear that the unipotent ${\mathbb{Q}}$-subgroup ${\mathbf{W}}':={\mathbf{W}}\cap{\mathbf{P}}'$ is the unipotent radical of ${\mathbf{P}}'$ because ${\mathbf{P}}'/{\mathbf{W}}'={\mathbf{G}}'$, and we write ${\mathbf{V}}'$ for the image of ${\mathbf{W}}'$ in ${\mathbf{V}}={\mathbf{W}}/{\mathbf{U}}$, which makes ${\mathbf{W}}'$ the central extension of ${\mathbf{V}}'$ by ${\mathbf{U}}':={\mathbf{U}}\cap{\mathbf{W}}'$ under the restriction of $\psi:{\mathbf{V}}\times{\mathbf{V}}{\rightarrow}{\mathbf{U}}$. Just as the pure case, we have inclusions of smooth submanifolds $\Omega_n\subset\Omega_\nu$, which gives ${\mathbf{P}}_n^{\mathrm{der}}\subset{\mathbf{P}}'$ for all $n$. We want to show that ${\mathbf{P}}'$ is generated by $\bigcup_n{\mathbf{P}}_n^{\mathrm{der}}$. Let ${\mathbf{W}}''$ be the unipotent ${\mathbb{Q}}$-subgroup of ${\mathbf{W}}$ generated by $\bigcup_n{\mathbf{W}}_n$. Then reduction modulo ${\mathbf{U}}$ shows that ${\mathbf{V}}'':={\mathbf{W}}''/{\mathbf{U}}''$ is generated by $\bigcup_n{\mathbf{V}}_n$ with ${\mathbf{V}}_n={\mathbf{W}}_n/{\mathbf{U}}_n$, and similarly ${\mathbf{U}}'':={\mathbf{U}}\cap{\mathbf{W}}''$ is generated by $\bigcup_n{\mathbf{U}}_n=\bigcup_n{\mathbf{W}}_n\cap{\mathbf{U}}$. The ${\mathbb{Q}}$-groups ${\mathbf{V}}_n$, ${\mathbf{U}}_n$, and ${\mathbf{W}}_n$ are stable under $w{\mathbf{G}}_n^{\mathrm{der}}w^{{-1}}$ and $w{\mathbf{T}}w^{{-1}}$, hence ${\mathbf{W}}''$ is stabilized by $w{\mathbf{G}}'w^{{-1}}$, by $w{\mathbf{T}}w^{{-1}}$, and by $w{\mathbf{G}}_\nu w^{{-1}}$. Thus ${\mathbf{W}}''\rtimes w{\mathbf{G}}'w^{{-1}}$ is already a ${\mathbb{Q}}$-subgroup of type ${\mathscr{H}}$ containing $\bigcup_n{\mathbf{P}}_n^{\mathrm{der}}$. This forces the equality ${\mathbf{P}}'={\mathbf{W}}''\rtimes w{\mathbf{G}}'w^{{-1}}$ due to the density of $\bigcup_n\Omega_n$ in $\Omega_\nu$. In particular ${\mathbf{W}}'={\mathbf{W}}''$ is a central extension of ${\mathbf{V}}'={\mathbf{V}}''$ by ${\mathbf{U}}'={\mathbf{U}}''$, stable under the actions of $w{\mathbf{G}}'w^{{-1}}$, of $w{\mathbf{T}}w^{{-1}}$, and thus of $w{\mathbf{G}}_\nu w^{{-1}}$. We thus put ${\mathbf{P}}_\nu:={\mathbf{P}}'w{\mathbf{T}}w^{{-1}}={\mathbf{W}}'\rtimes w{\mathbf{G}}_\nu w^{{-1}}$. It contains ${\mathbf{P}}_n$ for all $n$, and it is clear that $({\mathbf{P}}_\nu,{\mathbf{U}}',{\mathbf{P}}_\nu({\mathbb{R}}){\mathbf{U}}'({\mathbb{C}})y_n)$ is a ${{{(\mathbf{T},w)}}}$-special subdatum by \[generating subdata\]. The equality ${\mathbf{P}}_\nu^{\mathrm{der}}={\mathbf{W}}'\rtimes w{\mathbf{G}}'w^{{-1}}$ shows that $\nu$ is ${{{(\mathbf{T},w)}}}$-special. The idea is similar to the pure case in [@clozel; @ullmo] and the Kuga case treated in [@chen; @kuga](Section 5), and we merely sketch the main arguments. - There exists a compact subset $K{{{(\mathbf{T},w)}}}$ of ${{\mathscr{Y}}}^+$ such that if ${{\mathscr{M}}}'\subset {{\mathscr{M}}}$ is a ${{{(\mathbf{T},w)}}}$-special S-subspace, then ${{\mathscr{M}}}'=\wp_\Gamma({{\mathscr{Y}}}'^+)$ is given by some connected ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}',Y';Y'^+)$, with real part ${{\mathscr{Y}}}'^+$ meeting $K{{{(\mathbf{T},w)}}}$ non-trivially. In the pure case such a compact subset $K({\mathbf{T}})\subset X^+$ is given in [@clozel; @ullmo] 4.5; in the mixed case it suffices to take a compact subset $C$ of ${\mathbf{W}}({\mathbb{R}})$ containing $w$ and a fundamental domain for the action of $\Gamma_{\mathbf{W}}$ on ${\mathbf{W}}({\mathbb{R}})$, and then $K({{{(\mathbf{T},w)}}}):=(C\cdot X^+)\cap\pi^{{-1}}(K({\mathbf{T}}))$, the proof for which is the same as [@chen; @kuga] 5.4. - The set ${\mathscr{P}}_{{{(\mathbf{T},w)}}}({{\mathscr{M}}})$ is compact for the weak topology: if $\mu_n$ is a sequence of ${{{(\mathbf{T},w)}}}$-special canonical measures on ${{\mathscr{M}}}$ defined by $({\mathbf{P}}_n,Y_n;Y_n^+)$, given as $\mu_n=\kappa_{y_n}\nu_n$ for $y_n\in K{{{(\mathbf{T},w)}}}$ and $\nu_n$ the canonical measure associated to $\Omega_n=\Gamma_n^\dagger{\backslash}{\mathbf{P}}_n^{\mathrm{der}}({\mathbb{R}})^+$, then up to restriction to subsequences, we may assume that $y_n$ converges to some $y\in K{{{(\mathbf{T},w)}}}$ and $(\nu_n)$ converges to some $\nu$ associated to a ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}',Y;Y'^+)$ with $y\in{{\mathscr{Y}}}'^+\cap K{{{(\mathbf{T},w)}}}$. Thus $\mu_n$ converges to $\mu=\kappa_{y}\nu$. The property of support convergence holds similarly. \[bounded equidistribution\] (1) For $B$ a finite bounding set, ${\mathscr{S}}\in\{\Omega,{{\mathscr{M}}}\}$, we have ${\mathscr{P}}_B({\mathscr{S}})=\bigcup_{{{{(\mathbf{T},w)}}}\in B}{\mathscr{P}}_{{{(\mathbf{T},w)}}}({\mathscr{S}})$. In particular, ${\mathscr{P}}_B({\mathscr{S}})$ is compact for the weak topology, in which holds the support convergence. \(2) For ${\mathscr{S}}=\Omega$ (resp. ${\mathscr{S}}={{\mathscr{M}}}$), the closure of a sequence of special lattice subspaces (resp. of special S-subspaces) bounded by $B$ for the analytic topology is a finite union of special lattice subspaces (resp. of special S-subspaces) bounded by $B$. \(1) This is clear because ${\mathscr{P}}_B({\mathscr{S}})$ is a finite union of compact subsets of the set of Radon measures on ${\mathscr{S}}$. The property of support convergence holds because if a sequence $(\mu_n)$ converges to $\mu$, then it contains a subsequence that converges into ${\mathscr{P}}_{{{(\mathbf{T},w)}}}({\mathscr{S}})$ for some ${{{(\mathbf{T},w)}}}\in B$. Hence the $\nu\in{\mathscr{P}}_{{{(\mathbf{T},w)}}}({\mathscr{S}})$. All the convergent subsequence of $(\mu_n)$ are of the same limit, so it is not possible to have an infinite subsequence lying outside ${\mathscr{P}}_{{{(\mathbf{T},w)}}}({\mathscr{S}})$. Hence the sequence itself is in ${\mathscr{P}}_{{{(\mathbf{T},w)}}}({\mathscr{S}})$. \(2) This is clear using the convergence of measures and the property of support convergence. \[bounded André-Oort\] Let $M$ be a connected Shimura variety defined by $({\mathbf{P}},Y;Y^+)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X;X^+)$, with $B$ a finite bounding set. Let $(M_n)$ be a sequence of special subvarieties bounded by $B$. Then the Zariski closure of $\bigcup_nM_n$ is a finite union of special subvarieties bounded by $B$. This is clear because analytic closure is finer than Zariski closure, and S-subspaces are Zariski dense in the corresponding special subvarieties. \[compact tori vs. algebraic tori\] When ${\mathbf{V}}=0$ and $\Gamma=\Gamma_{\mathbf{U}}\rtimes\Gamma_{\mathbf{G}}$ for some lattice $\Gamma_{\mathbf{U}}$ in ${\mathbf{U}}({\mathbb{Q}})$ stabilized by $\Gamma_{\mathbf{G}}$ a congruence subgroup of ${\mathbf{G}}({\mathbb{Q}})_+$, the fibration $M=\Gamma{\backslash}Y^+{\rightarrow}S=\Gamma_{\mathbf{G}}{\backslash}X^+$ is a torus group scheme over $S$, whose fibers are complex tori isomorphic to $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{C}}){\cong}({\mathbb{C}}/{\mathbb{Z}})^d$, $d$ being the dimension of ${\mathbf{U}}$. Thus the S-space ${{\mathscr{M}}}=\Gamma{\backslash}{{\mathscr{Y}}}^+$ is a real analytic subgroup of $M$ relative to the base $S$, whose fibers are compact tori isomorphic to $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{R}}){\cong}({\mathbb{R}}/{\mathbb{Z}})^d$ in the split complex tori $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{C}})$, hence Zariski dense. Using harmonic analysis on $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{R}})$ one can prove that the analytic closure of a sequence of connected closed Lie subtori in it is still a connected closed Lie subtorus, which implies that the Zariski closure of a sequence of connected algebraic subtori in $\Gamma_{\mathbf{U}}{\backslash}{\mathbf{U}}({\mathbb{C}})$ is an algebraic subtorus, cf. [@ratazzi; @ullmo] Section 4.1. This can be viewed as a motivation for our notion of S-spaces. Lower bound of the Galois orbit of a pure special subvariety {#Lower bound of the Galois orbit of a pure special subvariety} ============================================================ The results from this section on rely heavily on [@ullmo; @yafaev], especially the estimation on Galois orbits of ${\mathbf{T}}$-special subvarieties in pure Shimura varieties. Hence we assume that all the mixed Shimura (sub)data we encounter are irreducible in the sense of \[mixed Shimura data\](3). This actually forces the pure part to be irreducible, due to the following lemma, In [@ullmo; @yafaev] Lemma 2.1, a special subvariety $S'$ of a pure Shimura variety $M_K({\mathbf{G}},X)$ is realized as the image of a connected component of some morphism $M_{K'}({\mathbf{G}}',X'){\rightarrow}M_K({\mathbf{G}},X)$, with ${\mathbf{G}}'$ the generic Mumford-Tate ${\mathbb{Q}}$-group of $S'$, and $K'=K\cap{\mathbf{G}}'({{\hat{\mathbb{Q}}}})$. All the estimations concerning the ${\mathbf{T}}$-special subvarieties requires ${\mathbf{T}}$ to be the connected center of the generic Mumford-Tate ${\mathbb{Q}}$-group ${\mathbf{G}}'$. The mixed case is similar: by \[insensitivity of levels\] and the discussion in \[reduction to subdata of a good product\], it suffices to treat special subvarieties in $M^+=\Gamma{\backslash}Y^+$, where $Y^+$ comes from some irreducible mixed Shimura datum $({\mathbf{P}},Y)$ and $\Gamma={\mathbf{P}}({\mathbb{Q}})_+\cap K$ for any fixed [[compact open subgroup]{}]{}$K\subset{\mathbf{P}}({{\hat{\mathbb{Q}}}})$; in $M^+$ special subvarieties are obtained, using the discussion in \[special subvarieties\](1), as the image of $Y'^+\times K$ with $Y'^+\subset Y^+$ coming from some subdatum $({\mathbf{P}}',Y')$, and we may assume that ${\mathbf{P}}'={\mathrm{MT}}(Y'^+)$ because this does not change $Y'^+$. We start with some preliminaries on the reciprocity map describing the Galois action on the set of connected components of pure Shimura varieties. \[connected components\] Let ${\mathbf{G}}$ be a connected reductive ${\mathbb{Q}}$-group. We write ${\overline{\pi}_\circ}({\mathbf{G}})$ for the set $\pi_0({\mathbf{G}}({\mathbb{A}})/{\mathbf{G}}({\mathbb{Q}})^-\rho({\mathbf{H}}({{\hat{\mathbb{Q}}}})))$ where ${\mathbf{G}}({\mathbb{Q}})^-$ stands for the closure of ${\mathbf{G}}({\mathbb{Q}})$ in ${\mathbf{G}}({\mathbb{A}})$, and $\rho:{\mathbf{H}}{\rightarrow}{\mathbf{G}}^{\mathrm{der}}$ is the simply-connected covering of ${\mathbf{G}}^{\mathrm{der}}$. Clearly ${\overline{\pi}_\circ}({\mathbf{G}})=\pi_0({\mathbf{G}}({\mathbb{A}})/{\mathbf{G}}({\mathbb{Q}})^-{\mathbf{G}}({\mathbb{R}})^+\rho({\mathbf{H}}({{\hat{\mathbb{Q}}}}))$. Since ${\mathbf{G}}({{\hat{\mathbb{Q}}}})$ is totally disconnected, the natural action of ${\mathbf{G}}({{\hat{\mathbb{Q}}}})$ on ${\mathbf{G}}({\mathbb{A}})$ by left translation gives an action on ${\overline{\pi}_\circ}({\mathbf{G}})$. For $K\subset{\mathbf{G}}({{\hat{\mathbb{Q}}}})$, we denote the quotient by $K$ of ${\overline{\pi}_\circ}({\mathbf{G}})$ as ${\overline{\pi}_\circ}({\mathbf{G}})/K$. We also have the natural action of $\pi_0({\mathbf{G}}({\mathbb{R}}))$ on ${\overline{\pi}_\circ}({\mathbf{G}})$. From the finiteness of class numbers of linear algebraic group over global fields ([@platonov; @rapinchuk] 8.1), we know that for each $K\subset{\mathbf{G}}({{\hat{\mathbb{Q}}}})$, the quotient ${\overline{\pi}_\circ}({\mathbf{G}})/K$ is a finite abelian group. Hence ${\overline{\pi}_\circ}({\mathbf{G}})={\varprojlim}_K{\overline{\pi}_\circ}({\mathbf{G}})/K$ is a pro-finite abelian group. In particular, if $F$ is a number field, we have the ${\mathbb{Q}}$-torus ${\mathbb{G}}_{\mathrm{m}}^F={\mathrm{Res}}_{F/{\mathbb{Q}}}{{\mathbb{G}_\mathrm{m}}}_F$, and class field theory gives us the reciprocity isomorphism ${{\mathrm{rec}}}^F:{\mathrm{Gal}}(F^{\mathrm{ab}}/F){\cong}{\overline{\pi}_\circ}({\mathbb{G}}_{\mathrm{m}}^F)$. For a pure Shimura variety $S=M_K({\mathbf{G}},X)$, the set of its geometrically connected components is $\pi_0(S)={\overline{\pi}_\circ}({\mathbf{G}})/{\mathbf{G}}({\mathbb{R}})_+K$, with ${\mathbf{G}}({\mathbb{R}})_+$ acts through $\pi_0({\mathbf{G}}({\mathbb{R}})_+)\subset\pi_0({\mathbf{G}}({\mathbb{R}}))$. \[reflex fields and reciprocity maps\] \(1) Let $({\mathbf{P}},Y)$ be a mixed Shimura datum. The reflex field* $E({\mathbf{P}},Y)$ is the smallest subfield $E$ of ${\mathbb{C}}$ such that ${{\mathrm{Aut}}}({\mathbb{C}}/E)$ fixes the ${\mathbf{P}}({\mathbb{C}})$-conjugacy class of $\mu_y:{{\mathbb{G}_\mathrm{m}}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}$, with $\mu_y$ the restriction of $y:{\mathbb{S}}_{\mathbb{C}}{\rightarrow}{\mathbf{P}}_{\mathbb{C}}$ to ${{\mathbb{G}_\mathrm{m}}}\times\{1\}$ via ${\mathbb{S}}_{\mathbb{C}}{\cong}{{\mathbb{G}_\mathrm{m}}}\times{{\mathbb{G}_\mathrm{m}}}$. $E({\mathbf{P}},Y)$ is a number field embedded in ${\mathbb{C}}$. Whenever there is a morphism of mixed Shimura data $({\mathbf{P}},Y){\rightarrow}({\mathbf{P}}',Y')$ we have $E({\mathbf{P}},Y)\supset E({\mathbf{P}}',Y')$. In particular, using the natural projection and the pure section of $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$, we have $E({\mathbf{P}},Y)=E({\mathbf{G}},X)$. \(2) If $({\mathbf{T}},x)$ is a pure Shimura datum with ${\mathbf{T}}$ a ${\mathbb{Q}}$-torus, then $E=E({\mathbf{T}},x)$ is the field of definition of $\mu_x:{{\mathbb{G}_\mathrm{m}}}_{\mathbb{C}}{\rightarrow}{\mathbf{T}}_{\mathbb{C}}$, and the reciprocity map of $({\mathbf{T}},x)$ is the composition $${{\mathrm{rec}}}_x:{\mathrm{Gal}}(E^{\mathrm{ab}}/E){\cong}{\overline{\pi}_\circ}({\mathbb{G}}_{\mathrm{m}}^E){\overset}{\mu_x}{\longrightarrow}{\overline{\pi}_\circ}({\mathbf{T}}^E){\overset}{{\mathrm{Nm}}_{E/{\mathbb{Q}}}}{\longrightarrow}{\overline{\pi}_\circ}({\mathbf{T}})$$ with ${\mathbf{T}}^E={\mathrm{Res}}_{E/{\mathbb{Q}}}T_E$ and ${\mathrm{Nm}}_{E/{\mathbb{Q}}}$ induced by the norm $E^\times{\rightarrow}{\mathbb{Q}}^\times$. For a general pure Shimura datum $({\mathbf{G}},X)$ of reflex field $E=E({\mathbf{G}},X)$, we still have a continuous homomorphism, referred to as the reciprocity map: $${{\mathrm{rec}}}_X:{\mathrm{Gal}}(E^{\mathrm{ab}}/E){\cong}{\overline{\pi}_\circ}({\mathbb{G}}_{\mathrm{m}}^E){\overset}{\mu_X}{\longrightarrow}{\overline{\pi}_\circ}({\mathbf{G}})$$ and the action of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)$ on $\pi_0(M_K({\mathbf{G}},X))$ is through translation by the homomorphism $${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E){\rightarrow}{\mathrm{Gal}}(E^{\mathrm{ab}}/E){\rightarrow}{\overline{\pi}_\circ}({\mathbf{G}}){\rightarrow}{\overline{\pi}_\circ}({\mathbf{G}})/{\mathbf{G}}({\mathbb{R}})_+K.$$ Each connected component of $M_K({\mathbf{G}},X)$ is defined over a finite abelian extension of $E$. The reciprocity maps are functorial [[with respect to]{}]{}morphisms between Shimura data and between Shimura varieties. \[assumption\] In our study of special subvarieties, we will be mainly concerned with the following situation: $M=M_K({\mathbf{P}},Y)$ is a mixed Shimura variety defined by $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ at some level $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$ of fine product type. We fix $Y^+={\mathbf{U}}({\mathbb{C}}){\mathbf{W}}({\mathbb{R}})X^+$ a connected component of $Y$ lying over a connected component $X^+$ in $X$, and we have a fixed connected mixed Shimura variety $M^+=\Gamma{\backslash}Y^+$, with $\Gamma={\mathbf{P}}({\mathbb{Q}})_+\cap K$. We study special subvarieties in $M^+$ that are of the form $\wp_\Gamma(Y'^+)$, coming from connected subdatum $({\mathbf{P}}',Y';Y'^+)$ of $({\mathbf{P}},Y;Y^+)$. Similar to the case of Kuga varieties, cf. [@chen; @kuga] 2.12 and 2.13, all special subvarieties are obtained this way, as long as one passes to different connected components of $M$ using Hecke translates, cf. \[morphisms of mixed Shimura varieties and Hecke translates\]. In particular, the special subvariety $\wp_\Gamma(Y'^+)$ is a connected component of the image $M_{K'}({\mathbf{P}}',Y'){\rightarrow}M_K({\mathbf{P}},Y)$ where $K'$ is some [[compact open subgroup]{}]{}of ${\mathbf{P}}'({{\hat{\mathbb{Q}}}})$ contained in $K$. The fine product condition on $K$ shows that the natural projection $M_K({\mathbf{P}},Y){\rightarrow}S:= M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ has a section given by $({\mathbf{G}},X){\hookrightarrow}({\mathbf{P}},Y)$, so $S$ is identified as a closed subscheme of $M$. Similarly, $M^+$ is fibred over $S^+=\Gamma_{\mathbf{G}}{\backslash}X^+$ with $\Gamma_{\mathbf{G}}={\mathbf{G}}({\mathbb{Q}})_+\cap K_{\mathbf{G}}$ and $S^+$ is a closed subscheme of $M^+$ by the pure section. We write $E$ for the reflex field of $({\mathbf{P}},Y)$, and we study the Galois orbits of the form ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot S'$ for $S'$ a special subvariety in $S^+$, as well as its mixed analogue. Note that the orbit may exceed $S^+$. We can nevertheless restrict to orbits under ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E^+)$ with $E^+$ the field of definition of $S^+$ corresponding to the kernel of ${\mathrm{Gal}}(E^{\mathrm{ab}}/E){\rightarrow}{\overline{\pi}_\circ}({\mathbf{G}})/{\mathbf{G}}({\mathbb{R}})_+K_{\mathbf{G}}$. The difference is bounded by $\#\pi_0(M_{K_{\mathbf{G}}}({\mathbf{G}},X))$ which is constant when we fix $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$. Finally, when we mention irreducible mixed Shimura (sub)data $({\mathbf{P}},Y)$, we require that for some connected component $Y^+$ of $Y$ we have ${\mathbf{P}}={\mathrm{MT}}(Y^+)$. The original estimation in [@ullmo; @yafaev] 2.19 requires ${\mathbf{G}}$ to be of adjoint type. We prefer the following version for general reductive ${\mathbf{G}}$: \[lower bound involving splitting fields\] Let $S=M_K({\mathbf{G}},X)$ be a pure Shimura variety with reflex field $E$ at some level $K\subset{\mathbf{G}}({{\hat{\mathbb{Q}}}})$ of fine product type. Write ${\mathscr{L}}={\mathscr{L}}_K$ for the automorphic line bundle on $S$, namely the ample line bundle of top degree automorphic forms on $S$, such that a fixed positive power of ${\mathscr{L}}$ defines the Baily-Borel compactification of $S$. We also fix an integer $N>0$. Let ${\mathbf{T}}$ be a non-trivial ${\mathbb{Q}}$-torus in ${\mathbf{G}}$, with splitting field $F_{\mathbf{T}}$, arising as the connected center of ${\mathbf{G}}'$ for some irreducible pure subdatum $({\mathbf{G}}',X')$ of $({\mathbf{G}},X)$. Assume that the GRH holds for $F_{\mathbf{T}}$. Then the following inequality holds for any ${\mathbf{T}}$-special subvariety $S'\subset S$ defined by $({\mathbf{G}}',X')$: $$\deg_{\mathscr{L}}({\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot S')\geq c_ND_N({\mathbf{T}})\cdot\prod_{p\in\Delta({\mathbf{T}},K)}{{\mathrm{max}}}\{1,I({\mathbf{T}},K_p)\}$$ where - $D_N({\mathbf{T}})=(\log{D({\mathbf{T}})})^N$ with $D({\mathbf{T}})$ the absolute discriminant of the splitting field of $F_{\mathbf{T}}$; - $\Delta({\mathbf{T}},K)$ is the set of rational primes $p$ such that $K_{{\mathbf{T}},p}\subsetneq K_{{\mathbf{T}},p}^{{\mathrm{max}}}$, with - $K_{{\mathbf{T}},p}={\mathbf{T}}({{\mathbb{Q}_p}})\cap K_p$ - $K_{{\mathbf{T}},p}^{{\mathrm{max}}}$ the maximal [[compact open subgroup]{}]{}of ${\mathbf{T}}({{\mathbb{Q}_p}})$ and $\Delta({\mathbf{T}},K)$ is finite, i.e. $K_{{\mathbf{T}},p}=K_{{\mathbf{T}},p}^{{\mathrm{max}}}$ for all but finitely many $p$; - $I({\mathbf{T}},K_p)=b[K_{{\mathbf{T}},p}^{{\mathrm{max}}}:K_{{\mathbf{T}},p}]$; - $c_N,b\in{\mathbb{R}}_{>0}$ are constants independent of $K,{\mathbf{T}}$; moreover $b$ is independent of $N$. The proof makes use of a few useful uniform bounds , among which we single out the following (cf. [@ullmo; @yafaev] 2.4, 2.5): \[uniform bounds\] Let $({\mathbf{G}},X)$ be a pure Shimura datum, and write $d_{\mathbf{G}}$ for the dimension of ${\mathbf{G}}$. Then: \(1) If ${\mathbf{T}}$ is a ${\mathbb{Q}}$-torus in ${\mathbf{G}}$, then the degree of the splitting field $F_{\mathbf{T}}$ of ${\mathbf{T}}$ is uniformly bounded in terms of $d_{\mathbf{G}}$. \(2) If $({\mathbf{G}}',X')$ is a pure subdatum of $({\mathbf{G}},X)$, then the degree of the reflex field $E'=E({\mathbf{G}}',X')$ is uniformly bounded in terms of $d_{\mathbf{G}}$. In fact we can find a ${\mathbb{Q}}$-torus ${\mathbf{H}}$ in ${\mathbf{G}}$ whose splitting field contains $E({\mathbf{G}}',X')$. Of course by being uniformly bounded in terms of $d_{\mathbf{G}}$ we mean being less than some positive constant that only depends on $d_{\mathbf{G}}$. We adapt the strategy in [@ullmo; @yafaev] Subsection 2.2 (from Definition 2.10 to Theorem 2.19) into two steps: 1. For $({\mathbf{G}}',X')$ a general pure Shimura datum and $S'$ a connected component of $M_{K'}({\mathbf{G}}',X')$, with reflex field $E'=E({\mathbf{G}}',X')$, ${\mathscr{L}}_{K'}$ the automorphic line bundle, ${\mathbf{T}}$ the connected center of ${\mathbf{G}}'$, and $F_{\mathbf{T}}$ the splitting field of ${\mathbf{T}}$, we have $$\deg_{{\mathscr{L}}_{K'}}({\mathrm{Gal}}({\bar{\mathbb{Q}}}/E')\cdot S')\geq c'_ND_N({\mathbf{T}})\cdot\prod_{p\in\Delta({\mathbf{T}},K')}{{\mathrm{max}}}\{1, I({\mathbf{T}},K'_p) \}$$ under the GRH for $F_{\mathbf{T}}$, where $D_N({\mathbf{T}})$ is the $N$-th power of the logarithm of the absolute discriminant of $F_{\mathbf{T}}$, $\Delta({\mathbf{T}},K')$ and $I({\mathbf{T}},K'_p)$ are defined in the same way as in the statement of \[lower bound involving splitting fields\] with $K$ replaced by $K'$. The definition of $I({\mathbf{T}},K'_p)=b'[K'^{{\mathrm{max}}}_{{\mathbf{T}},p}:K'_{{\mathbf{T}},p}]$ involves some absolute constant $b'$ that only depends on the dimension $d_{{\mathbf{G}}'}$ of ${\mathbf{G}}'$ and some fixed faithful representation $\rho':{\mathbf{G}}'{\hookrightarrow}{{\mathbf{GL}}}_{\Lambda,{\mathbb{Q}}}$ with $\Lambda$ some free ${\mathbb{Z}}$-module of finite rank, and the constant $c'_N$ only depends on $d_{{\mathbf{G}}'}$, $\rho'$ and $N$. Note that when ${\mathbf{G}}$ is of adjoint type this is Theorem 2.19 of [@ullmo; @yafaev]. The proof for general ${\mathbf{G}}$ is almost the same, and one needs to modify some estimation of absolute constants: when ${\mathbf{G}}$ is of adjoint type, the Hodge structures defined by $x\in X$ on algebraic representations of ${\mathbf{G}}$ (such as $\Lambda$) are of weight zero; for general ${\mathbf{G}}$ the weight is not necessarily zero, but only one such representation $\Lambda$ is involved, and only finitely many Hodge types arise when $x$ runs through $X$ (and is actually independent of the choice of $x$), hence one obtains estimations similar to [@ullmo; @yafaev] 2.13 and [@yafaev; @duke] 2.13. 2. When we consider ${\mathbf{T}}$-special subvarieties $f(S')$ realized as the image of some connected component $S'$ of $M_{K'}({\mathbf{G}}',X')$ along $f:M_{K'}({\mathbf{G}}',X'){\rightarrow}M_K({\mathbf{G}},X)$ with $K'=K\cap{\mathbf{G}}'({{\hat{\mathbb{Q}}}})$, we have $$\deg_{{\mathscr{L}}}f(S')\geq\deg_{{\mathscr{L}}_{K'}}S'$$ which is adapted from [@klingler; @yafaev] 5.3.10, cf. \[generic injectivity\] below. We use a fixed faithful representation $\rho:{\mathbf{G}}{\hookrightarrow}{{\mathbf{GL}}}_{\Lambda,{\mathbb{Q}}}$ whose restriction to ${\mathbf{G}}'$ gives the representation $\rho'$ in Step 1. Note that $K'=K\cap{\mathbf{G}}'({{\hat{\mathbb{Q}}}})$ hence $\Delta({\mathbf{T}},K')=\Delta({\mathbf{T}},K)$ and $[K'^{{\mathrm{max}}}_{{\mathbf{T}},p}:K'_{{\mathbf{T}},p}]=[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{{\mathbf{T}},p}]$ for $p\in\Delta({\mathbf{T}},K)$. From this the desired estimation on the degree of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot f(S')$ is obtained, after replacing $c'_N$ and $b'$ by some new constants that only depend on $d_{\mathbf{G}}$, $\rho$, and $N$. In particular, the constants $c_N$ and $b$ do not depend on $K$ and ${\mathbf{T}}$. It should be mentioned that the estimation in Step 1 involves the morphism $\pi':M_{K'}({\mathbf{G}}',X'){\rightarrow}M_{K'^m}({\mathbf{G}}',X')$ where $K'^m=K'^m_3\times\prod_{p\neq 3}K'^{{\mathrm{max}}}_p$, where - $K'^{{\mathrm{max}}}_p:=K'_pK^{{\mathrm{max}}}_{{\mathbf{T}},p}$ only enlarges $K'_p$ using the maximal [[compact open subgroup]{}]{}$K^{{\mathrm{max}}}_{{\mathbf{T}},p}$ of ${\mathbf{T}}({{\mathbb{Q}_p}})$; - for $p=3$, $K'^m_3=K'^{{\mathrm{max}}}_3\cap K^\Lambda_3$ where $K^\Lambda_3$ is a fixed neat [[compact open subgroup]{}]{}of ${{\mathbf{GL}}}_\Lambda({\mathbb{Z}}_3)$, and $[K'^{{\mathrm{max}}}_3:K'^m_3]$ is bounded by some constant that only depends on the rank of $\rho'$. $\pi'$ is finite étale of degree $[K'^m:K']$ by [@ullmo; @yafaev] 2.11, and by [@ullmo; @yafaev] 2.12 the degree of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/F_{\mathbf{T}})\cdot S'$ is at least the degree of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/F_{\mathbf{T}})\cdot S'\cap \pi'^{{-1}}\pi'(S')$ times the cardinality of the ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/F_{\mathbf{T}})$-orbit of $\pi'(S')$. Under the GRH for $F_{\mathbf{T}}$, this latter cardinality is at least $D_N({\mathbf{T}})$ up to some absolute constant, following the proof of [@ullmo; @yafaev] 2.13, and the former degree is at least $I({\mathbf{T}},K')$ up to some absolute constant, following [@ullmo; @yafaev] 2.16, 2.17, and 2.18. \[generic injectivity\] Let $({\mathbf{G}}',X')\subset({\mathbf{G}},X)$ be an inclusion of pure Shimura data. Assume that $({\mathbf{G}}',X')$ and $({\mathbf{G}},X)$ are irreducible, and let $K\subset{\mathbf{G}}({{\hat{\mathbb{Q}}}})$ be a neat [[compact open subgroup]{}]{}. Put $K'=K\cap{\mathbf{G}}'({{\hat{\mathbb{Q}}}})$, then \(1) we have ${\mathbf{T}}_{{\mathbf{G}}'}\supset{\mathbf{T}}_{\mathbf{G}}$, where ${\mathbf{T}}_{{\mathbf{G}}'}$ resp. ${\mathbf{T}}_{\mathbf{G}}$ is the connected center of ${\mathbf{G}}'$ resp. of ${\mathbf{G}}$; \(2) the morphism $f:M_{K'}({\mathbf{G}}',X'){\rightarrow}M_K({\mathbf{G}},X)$ is generically injective; \(3) $\deg_{{\mathscr{L}}}f(S')\geq \deg_{{\mathscr{L}}'}S'$ for ${\mathscr{L}}$ resp. ${\mathscr{L}}'$ the automorphic line bundle on $M_K({\mathbf{G}},X)$ resp. on $M_{K'}({\mathbf{G}}',X')$, and $S'$ any connected component of $M_{K'}({\mathbf{G}}',X')$. \(1) Note that ${\mathbf{G}}'$ is a ${\mathbb{Q}}$-subgroup of ${\mathbf{G}}$, and it normalizes ${\mathbf{G}}^{\mathrm{der}}$. Hence ${\mathbf{G}}'{\mathbf{G}}^{\mathrm{der}}$ is already a ${\mathbb{Q}}$-subgroup of ${\mathbf{G}}$. Take an arbitrary $x\in X'$, we have $x({\mathbb{S}})\subset{\mathbf{G}}'_{\mathbb{R}}$. Conjugate $x$ by an arbitrary $g=th\in{\mathbf{G}}({\mathbb{R}})$ with $t\in{\mathbf{T}}_{\mathbf{G}}({\mathbb{R}})$ and $h\in{\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})$, we have $t(x)={\mathrm{Int}}(t)\circ x=x$ because $t$ is central in ${\mathbf{G}}({\mathbb{R}})$ and thus $g(x)=h(x)={\mathrm{Int}}(h)\circ x$ has image in ${\mathbf{G}}'{\mathbf{G}}^{\mathrm{der}}$. Since $X={\mathbf{G}}({\mathbb{R}})x$, by \[generating subdata\] we get a subdatum $({\mathbf{G}}'{\mathbf{G}}^{\mathrm{der}},X={\mathbf{G}}'({\mathbb{R}}){\mathbf{G}}^{\mathrm{der}}({\mathbb{R}})x)$, and the irreducibility of $({\mathbf{G}},X)$ gives ${\mathbf{G}}={\mathbf{G}}'{\mathbf{G}}^{\mathrm{der}}$. Clearly we have ${\mathbf{G}}'^{\mathrm{der}}\subset{\mathbf{G}}^{\mathrm{der}}$, and ${\mathbf{G}}'={\mathbf{T}}_{{\mathbf{G}}'}{\mathbf{G}}'^{\mathrm{der}}$ and ${\mathbf{G}}={\mathbf{T}}_{\mathbf{G}}{\mathbf{G}}^{\mathrm{der}}$, hence the inclusion ${\mathbf{T}}_{{\mathbf{G}}}\subset{\mathbf{T}}_{{\mathbf{G}}'}$. \(2) Let ${\mathbf{N}}:={\mathbf{N}}_{\mathbf{G}}{\mathbf{G}}'$ be the normalizer of ${\mathbf{G}}'$ in ${\mathbf{G}}$. By the arguments in [@ullmo; @yafaev] Lemma 2.2, ${\mathbf{N}}$ is reductive. We claim that the quotient ${\mathbf{N}}/{\mathbf{G}}'$ is compact. Since ${\mathbf{N}}\supset{\mathbf{G}}'\supset{\mathbf{T}}_{\mathbf{G}}$, we have ${\mathbf{N}}/{\mathbf{G}}'={\mathbf{N}}_{\mathrm{ad}}/{\mathbf{G}}'_{\mathrm{ad}}$, where ${\mathbf{G}}'_{\mathrm{ad}}$ is the image of ${\mathbf{G}}'$ in ${\mathbf{G}}_{\mathrm{ad}}:={\mathbf{G}}/{\mathbf{T}}_{\mathbf{G}}$, and ${\mathbf{N}}_{\mathrm{ad}}$ is the normalizer of ${\mathbf{G}}'_{\mathrm{ad}}$ in ${\mathbf{G}}_{\mathrm{ad}}$, equal to the reduction modulo ${\mathbf{T}}_{\mathbf{G}}$ of ${\mathbf{N}}$, and thus the equality ${\mathbf{N}}/{\mathbf{G}}'={\mathbf{N}}_{\mathrm{ad}}/{\mathbf{G}}'_{\mathrm{ad}}$. Since $({\mathbf{G}}'_{\mathrm{ad}},X'_{\mathrm{ad}})=({\mathbf{G}}',X')/{\mathbf{T}}_{\mathbf{G}}$ is a subdatum of $({\mathbf{G}}_{\mathrm{ad}},X_{\mathrm{ad}}):=({\mathbf{G}},X)/{\mathbf{T}}_{\mathbf{G}}$ with ${\mathbf{G}}_{\mathrm{ad}}$ semi-simple, the centralizer of ${\mathbf{G}}'_{\mathrm{ad}}$ in ${\mathbf{G}}_{\mathrm{ad}}$ is compact because it commutes with $x({\mathbf{i}})$ for any $x\in X'_{\mathrm{ad}}$ in ${\mathbf{G}}_{\mathrm{ad}}({\mathbb{R}})$. The neutral component ${\mathbf{N}}_{\mathrm{ad}}^\circ$ admits an almost direct product of the form ${\mathbf{G}}'_{\mathrm{ad}}{\mathbf{L}}'$, with ${\mathbf{L}}$ commuting with ${\mathbf{G}}'_{\mathrm{ad}}$, hence ${\mathbf{L}}$ is compact, from which we get the compactness of ${\mathbf{N}}/{\mathbf{G}}'={\mathbf{N}}_{\mathrm{ad}}/{\mathbf{G}}'_{\mathrm{ad}}$. Since $K$ is neat, we have ${\mathbf{N}}({\mathbb{Q}})\cap K={\mathbf{G}}'({\mathbb{Q}})\cap K$, and repeat the arguments in [@ullmo; @yafaev] gives the generic injectivity of $f:M_{K'}({\mathbf{G}}',X'){\rightarrow}M_{K}({\mathbf{G}},X)$. \(3) The sheaf $\Lambda_{K,K'}=f^{\mathscr{L}}\otimes{\mathscr{L}}'^{{-1}}$ is nef by [@klingler; @yafaev] 5.3.5. It remains to argue as in [@klingler; @yafaev] 5.3.10, using the generic injectivity proved in (2), because the original proof of 5.3.10 requires ${\mathbf{G}}$ to be of adjoint type only for the generic injectivity of $f$ using [@ullmo; @yafaev] Lemma 2.2. The reader might be left with the impression that in order to adapt the strategy in [@klingler; @yafaev] and [@ullmo; @yafaev] for general mixed Shimura varieties one might need to assume the GRH for all the splitting fields $F_{\mathbf{T}}$ for the ${\mathbf{T}}$-special subvarieties involved. Actually we have: \[reduction to the CM case\] In order to prove the André-Oort conjecture, it suffices work with a connected mixed Shimura variety $M=\Gamma{\backslash}Y^+$ defined by a connected mixed Shimura datum $({\mathbf{P}},Y;Y^+)={\mathbf{W}}\rtimes({\mathbf{G}},X;X^+)$ such that if $({\mathbf{P}}_1,Y_1;Y_1^+)$ is an irreducible ${{{(\mathbf{T},w)}}}$-special subdatum of $({\mathbf{P}},Y;Y^+)$, then the splitting field $F_{\mathbf{T}}$ of ${\mathbf{T}}$ is a CM field. By \[insensitivity of isogeny\], \[reduction lemma\], and the discussion in \[reduction to subdata of a good product\], the André-Oort conjecture is already reduced to mixed Shimura varieties defined by subdata of $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$, where ${\mathbf{G}}_0$ is semi-simple of adjoint type, and $({\mathbf{L}},Y_{\mathbf{L}})={\mathbf{N}}\rtimes({\mathbf{H}},X_{\mathbf{H}})$ is a product of finitely many mixed Shimura data of Siegel type. If $({\mathbf{P}}',Y')$ is an irreducible ${{{(\mathbf{T},w)}}}$-special subdatum of $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$, then ${\mathbf{T}}$ is the connected center of ${\mathbf{G}}'$ coming from some irreducible subdatum $({\mathbf{G}}',X')\subset({\mathbf{G}}_0,X_0)\times({\mathbf{H}},X_{\mathbf{H}})$, with ${\mathbf{H}}$ a product of finitely many ${\mathrm{GSp}}_{{\mathbf{V}}_j}$. In particular, the connected center of ${\mathbf{H}}$ is a split ${\mathbb{Q}}$-torus. Consider the image $({\mathbf{G}}'',X'')$ of $({\mathbf{G}}',X')$ along $({\mathbf{G}}_0,X_0)\times({\mathbf{H}}^{\mathrm{ad}},X^{\mathrm{ad}}_{\mathbf{H}})$, where ${\mathbf{H}}^{\mathrm{ad}}$ is the adjoint quotient of ${\mathbf{H}}$. Since the kernel of ${\mathbf{H}}{\rightarrow}{\mathbf{H}}^{\mathrm{ad}}$ is a split ${\mathbb{Q}}$-torus, and the image of ${\mathbf{T}}$ in ${\mathbf{G}}''$ is the connected center ${\mathbf{T}}''$ of ${\mathbf{G}}''$, we see that the kernel ${\mathbf{T}}'$ of ${\mathbf{T}}{\rightarrow}{\mathbf{T}}''$ is a ${\mathbb{Q}}$-group of multiplicative type isogeneous to a split ${\mathbb{Q}}$-torus. In particular, take the character group ${\mathbf{X}}({\mathbf{T}})={\mathrm{Hom}}_{{\bar{\mathbb{Q}}}-{\mathrm{Gr}}}({\mathbf{T}}_{{\bar{\mathbb{Q}}}},{{\mathbb{G}_\mathrm{m}}}_{{\bar{\mathbb{Q}}}})$ we get an commutative diagram with exact rows $$\xymatrix{0\ar[r] & {\mathbf{X}}({\mathbf{T}}'')\ar[r]^\subset \ar[d]^\cap & {\mathbf{X}}({\mathbf{T}})\ar[r] \ar[d]^\cap & {\mathbf{X}}({\mathbf{T}}')\ar[d] & \\ 0\ar[r] & {\mathbf{X}}({\mathbf{T}}'')\otimes_{\mathbb{Z}}{\mathbb{Q}}\ar[r]^\subset &{\mathbf{X}}({\mathbf{T}})\otimes_{\mathbb{Z}}{\mathbb{Q}}\ar[r] & {\mathbf{X}}({\mathbf{T}}')\otimes_{\mathbb{Z}}{\mathbb{Q}}\ar[r] & 0}$$ where the morphisms are equivariant [[with respect to]{}]{}the evident action of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/{\mathbb{Q}})$. The first two vertical maps are inclusion because ${\mathbf{T}}$ and ${\mathbf{T}}''$ are ${\mathbb{Q}}$-torus, and ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/{\mathbb{Q}})$ acts on ${\mathbf{X}}({\mathbf{T}}')\otimes_{\mathbb{Z}}{\mathbb{Q}}$ because ${\mathbf{T}}'$ is a ${\mathbb{Q}}$-subgroup of the split center of ${\mathbf{H}}$. Diagram chasing shows that the actions of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/{\mathbb{Q}})$ on ${\mathbf{X}}({\mathbf{T}}'')$ and on ${\mathbf{X}}({\mathbf{T}})$ have the same kernel, which means ${\mathbf{T}}$ and ${\mathbf{T}}''$ have the same splitting field, which is a CM field by [@yafaev; @duke] 2.3. \[irreducible subdata\] Although we do not repeat all the proofs in [@ullmo; @yafaev], we remark that the condition of ${\mathbf{G}}$ being of adjoint type could be relaxed into requiring $({\mathbf{G}},X)$ to be irreducible for the first half of Section 1 of [@ullmo; @yafaev], using our lemma \[generic injectivity\]. In [@ullmo; @yafaev] 2.13, one needs ${\mathbf{G}}$ to be of adjoint type so that the splitting fields of the connected centers of irreducible ${\mathbf{T}}$-special subdata are CM fields (for ${\mathbf{T}}$ non-trivial). We cannot achieve this for general ${\mathbf{G}}$ unless we make use of the reduction \[reduction to the CM case\] to modify the defining data. In the rest of this section, only the next theorem requires the GRH for the splitting field $F_{\mathbf{T}}$ for the estimation of Galois orbits of pure special subvarieties in the ${{{(\mathbf{T},w)}}}$-special case. The CM version will be needed in the last section, where we work under \[CM splitting fields\] and all the splitting fields are CM fields. \[orbit of a pure special subvariety\] Let $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ be a mixed Shimura datum, with $E$ its reflex field, and $M=M_K({\mathbf{P}},Y)$ the mixed Shimura variety it defines at some level $K$ of fine product type. Write $\pi:M{\rightarrow}S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ for the natural projection and $\iota(0):S{\hookrightarrow}M$ the pure section. Denote by ${\mathscr{L}}$ the pull-back $\pi^{\mathscr{L}}_S$, with ${\mathscr{L}}_S$ the canonical line bundle on $S$. We also fix an integer $N>0$. Let $M'$ be a pure special subvariety of $M$ defined by a subdatum of the form $(w{\mathbf{G}}'w^{{-1}}, wX';wX'^+)$ for some ${\mathbf{T}}$-special pure subdatum $({\mathbf{G}}',X')\subset({\mathbf{G}},X)$ with ${\mathbf{T}}$ non-trivial ${\mathbb{Q}}$-torus and $w\in{\mathbf{W}}({\mathbb{Q}})$. Then we have the following lower bound assuming the GRH for the splitting field $F_{\mathbf{T}}$ of ${\mathbf{T}}$, using the same constants $c_N,b$ and the notations as in \[lower bound involving splitting fields\]:$$\deg_{\mathscr{L}}({\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot M')\geq c_ND_N({\mathbf{T}})\prod_{p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w))}{{\mathrm{max}}}\{1,I({\mathbf{T}},K_{\mathbf{G}}(w))\}$$ where $D_N({\mathbf{T}})=(\log{D({\mathbf{T}})})^N$, $K_{\mathbf{G}}(w)=\{g\in K_{\mathbf{G}}:wgw^{{-1}}g^{{-1}}\in K_{\mathbf{W}}\}$ and $I({\mathbf{T}},K_{\mathbf{G}}(w)_p)=b[K_{{\mathbf{T}},p}^{{\mathrm{max}}}:K_{\mathbf{T}}(w)_p]$ with $K_{\mathbf{T}}(w)=K_{\mathbf{G}}(w)\cap{\mathbf{T}}({{\hat{\mathbb{Q}}}})$. Before entering the proof, we first justify some notations in the statement: In \[orbit of a pure special subvariety\], $K_{\mathbf{G}}(w)_p={\mathbf{G}}({{\mathbb{Q}_p}})\cap K_{\mathbf{G}}(w)$ is a [[compact open subgroup]{}]{}contained in $K_{{\mathbf{G}},p}$, and it is equal to $K_{{\mathbf{G}},p}$ for all but finitely many $p$’s. In particular, $K_{\mathbf{G}}(w)=\prod_pK_{\mathbf{G}}(w)_p$ is of fine product type. For all but finitely many $p$’s, we have $w\in{\mathbf{W}}({\mathbb{Q}})\cap K_{{\mathbf{W}},p}$ and $wgw^{{-1}}g^{{-1}}\in K_{{\mathbf{W}},p}$ for all $g\in K_{{\mathbf{G}},p}$ as $K_{\mathbf{G}}$ stabilizes $K_{\mathbf{W}}$. When $w\notin K_{{\mathbf{W}},p}$, write $w=(u,v)$ for some $u\in{\mathbf{U}}({\mathbb{Q}})$ and $v\in{\mathbf{V}}({\mathbb{Q}})$. We have seen in \[group law\] that $w^n=(nu,nv)$, hence $w^n\in K_{\mathbf{W}}$ for $n$ a multiple of some constant integer $N>0$. In particular, the subgroup $K_{\mathbf{V}}[v]$ generated by $v$ and $K_{\mathbf{V}}$ in ${\mathbf{V}}({{\hat{\mathbb{Q}}}})$ is compact, the subgroup generated by $\psi(K_{\mathbf{V}}[v],K_{\mathbf{V}}[v])$, $u$ and $K_{\mathbf{U}}$ is compact, and thus they generate a [[compact open subgroup]{}]{}$K_{\mathbf{W}}[w]$ of ${\mathbf{W}}({{\hat{\mathbb{Q}}}})$ in which $K_{\mathbf{W}}$ is cofinite, and its stabilizer in $K_{\mathbf{G}}$ is cofinite, hence the claim on $K_{\mathbf{G}}(w)$. The proof of \[orbit of a pure special subvariety\] is easily reduced to the following: \[finite index\] The action of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)$ on $M_{K^w_{\mathbf{G}}}(w{\mathbf{G}}w^{{-1}},wX)$ is identified with its action on $M_{K_{\mathbf{G}}(w)}({\mathbf{G}},X)$ where $K_{\mathbf{G}}^w=w{\mathbf{G}}({{\hat{\mathbb{Q}}}})w^{{-1}}\cap K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$. We notice that $K_{\mathbf{G}}^w=w{\mathbf{G}}({{\hat{\mathbb{Q}}}})w^{{-1}}\cap K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$ is equal to $wK_{\mathbf{G}}(w)w^{{-1}}$, because $(w,1)(1,g)(w^{{-1}},1)=(wg(w^{{-1}}),g)=(wgw^{{-1}}g^{{-1}},g)$ for $w\in{\mathbf{W}}$ and $g\in{\mathbf{G}}$. From the isomorphism $w{\mathbf{G}}w^{{-1}}{\cong}{\mathbf{G}}$ we get an isomorphism of pure Shimura data $(w{\mathbf{G}}w^{{-1}},wX){\cong}({\mathbf{G}},X)$, and thus an isomorphism of pure Shimura varieties $\lambda:M(w):=M_{K_{\mathbf{G}}^w}(w{\mathbf{G}}w^{{-1}},wX){\cong}S(w):=M_{K_{\mathbf{G}}(w)}({\mathbf{G}},X)$. From the equality $w(K_{\mathbf{W}}\rtimes K_{{\mathbf{G}}}(w))w^{{-1}}=wK_{\mathbf{W}}w^{{-1}}\rtimes K_{\mathbf{G}}^w$ as [[compact open subgroups]{}]{}in ${\mathbf{P}}({{\hat{\mathbb{Q}}}})$, we deduce that the Hecke translation $\tau_w$ (defined in \[morphisms of mixed Shimura varieties and Hecke translates\](2)), namely the isomorphism $$\tau_w:M_{wK_{\mathbf{W}}w^{{-1}}\rtimes K_{\mathbf{G}}^w}({\mathbf{P}},Y)=M_{w(K_{\mathbf{W}}\rtimes K_{\mathbf{G}}(w))w^{{-1}}}({\mathbf{P}},Y){\rightarrow}M_{K_{\mathbf{W}}\rtimes K_{\mathbf{G}}(w)}({\mathbf{P}},Y)$$ restricts to the isomorphism $\lambda:M(w){\cong}S(w)$ above, where $M(w)$ resp. $S(w)$ is regarded as a pure section of $M_{wK_{\mathbf{W}}w^{{-1}}\rtimes K_{\mathbf{G}}^w}({\mathbf{P}},Y)$ resp. of $M_{K_{\mathbf{W}}\rtimes K_{\mathbf{G}}(w)}({\mathbf{P}},Y)$ using the equality $({\mathbf{P}},Y)={\mathbf{W}}\rtimes(w{\mathbf{G}}w^{{-1}},wX)$ resp. $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$. Since the Hecke translation $\tau_w$ is an isomorphism defined over the common reflex field $E=E({\mathbf{G}},X)$, it transports the action of ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)$ on $S(w)$ to that on $M(w)$, hence the claim. We have the commutative diagram:$$\xymatrix{M(w)\ar[r]^{\iota(w)} \ar[d]^\lambda & M\ar[d]^\pi\\ S(w)\ar[r]^f & S=M(0)}$$ with $\iota(w)$ the inclusion of the pure special subvariety $M(w){\hookrightarrow}M$. Since $\lambda$ is an isomorphism, the degree of a closed subvariety $Z$ in $M(w)$ against $\iota(w)^\pi^{\mathscr{L}}_S$ is the same as the degree of $\lambda(Z)\subset S(w)$ against $f^{\mathscr{L}}_S={\mathscr{L}}_{S(w)}$, with the last equality by [@klingler; @yafaev] 5.3.2(1). Taking $Z$ to be the pure special subvariety defined by $(w{\mathbf{G}}'w^{{-1}},wX';WX'^+)$, then its image under $\lambda$ is the special subvariety in $S(w)$ defined by $({\mathbf{G}}',X';X'^+)$. Using \[lower bound involving splitting fields\] with $K_{\mathbf{G}}$ replaced by $K_{\mathbf{G}}(w)$ we get $$\deg_{{\mathscr{L}}}({\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot M')=\deg_{{\mathscr{L}}_{S(w)}}({\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot\lambda(M'))\geq c_ND_N({\mathbf{T}})\prod_{p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w))}{{\mathrm{max}}}\{1,I({\mathbf{T}},K_{\mathbf{G}}(w)) \}.$$ \[unipotent Hecke translation\] We have seen in the proof of \[finite index\] that the Hecke translation $\tau_w$ (namely conjugation by $w^{{-1}}$ cf. \[morphisms of mixed Shimura varieties and Hecke translates\](2)) gives $w(K_{\mathbf{W}}\rtimes K_{\mathbf{G}})w^{{-1}}{\cong}(wK_{\mathbf{W}}w^{{-1}})\rtimes K_{\mathbf{G}}^w$ under the assumption $K_{\mathbf{G}}=K_{\mathbf{G}}(w)$, hence the isomorphism $M_{wKw^{{-1}}}({\mathbf{P}},Y){\rightarrow}M_K({\mathbf{P}},Y)$ sending the pure section given by $(w{\mathbf{G}}w^{{-1}}, wX)$ to the one given by $({\mathbf{G}},X)$. In particular, if $\psi=0$, then ${\mathbf{W}}$ is commutative, which gives us equalities $wK_{\mathbf{W}}w^{{-1}}=K_{\mathbf{W}}$ and $w(K_{\mathbf{W}}\rtimes K_{\mathbf{G}})w^{{-1}}{\cong}wK_{\mathbf{W}}w^{{-1}}\rtimes K_{\mathbf{G}}^w$. In this case, if we have $K_{\mathbf{G}}=K_{\mathbf{G}}(w)$, then conjugation by $w^{{-1}}$ defines an automorphism of $M_K({\mathbf{P}},Y)$ translating the pure section $M_{wK_{\mathbf{G}}w^{{-1}}}(w{\mathbf{G}}w^{{-1}}, wX)$ to $M_{K_{\mathbf{G}}}({\mathbf{G}},X)$. If we are in the Kuga case ${\mathbf{U}}=0$, then we are again led to the picture of torsion sections of abelian schemes. The natural projection $\pi:M=M_{K_{\mathbf{V}}\rtimes K_{\mathbf{G}}}({\mathbf{V}}\rtimes{\mathbf{G}},{\mathbf{V}}({\mathbb{R}})X){\rightarrow}S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ is an abelian $S$-scheme. If $v\in{\mathbf{V}}({\mathbb{Q}})$ is of order $n$ in ${\mathbf{V}}({{\hat{\mathbb{Q}}}})/K_{\mathbf{V}}$, then the maximal pure Shimura subvariety defined by $(v{\mathbf{G}}v^{{-1}}, vX)$ is contained in $M[n]$ the $n$-torsion part of $\pi:M{\rightarrow}S$. It is a section to $\pi$ [[if and only if]{}]{}$K_{\mathbf{G}}=K_{\mathbf{G}}(v)$. Similarly, if ${\mathbf{V}}=0\neq {\mathbf{U}}$, then $\pi:M=M_{K_{\mathbf{U}}\rtimes K_{\mathbf{G}}}({\mathbf{U}}\rtimes{\mathbf{G}},{\mathbf{U}}({\mathbb{C}})X){\rightarrow}S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ is an $S$-torus, and in this case an element $u\in{\mathbf{U}}({\mathbb{Q}})$ satisfying $K_{\mathbf{G}}=K_{\mathbf{G}}(u)$ gives a torsion section $M(u)$ using formulas similar to the Kuga case. This also allows us to talk about the case $\psi=0$ where ${\mathbf{W}}{\cong}{\mathbf{U}}\oplus{\mathbf{V}}$ is a commutative unipotent ${\mathbb{Q}}$-group, and the results are parallel. We want to take a closer look at the term $I({\mathbf{T}},K_{\mathbf{G}}(w))$. In [@ullmo; @yafaev] 3.15, the faithful representation $\rho:{\mathbf{G}}{\rightarrow}{{\mathbf{GL}}}_{\Lambda,{\mathbb{Q}}}$ leads to an inequality $I({\mathbf{T}},K_p)\geq c\cdot p$ for all prime $p$ such that $p$ is unramified in the splitting field of ${\mathbf{T}}$ and that $K_p={{\mathbf{GL}}}_{\Lambda}({{\mathbb{Z}_p}})\cap{\mathbf{G}}({{\mathbb{Q}_p}})$. In our case, besides the representation $\rho$ we have further $\rho_{\mathbf{U}}$ and $\rho_{\mathbf{V}}$ in the definition of mixed Shimura data, and we want to show that for $p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$ we have further $I({\mathbf{T}},K_{\mathbf{G}}(w)_p)\geq c\cdot {{\mathrm{ord}}_p(w,K_{\mathbf{W}})}$, using the following definition: Let ${\mathbf{W}}$ be the unipotent radical of ${\mathbf{P}}$ from some mixed Shimura datum $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$, which is a central extension of ${\mathbf{V}}$ by ${\mathbf{U}}$ via $\psi$. The order* of $w$ [[with respect to]{}]{}a [[compact open subgroup]{}]{}$K_{\mathbf{W}}\subset{\mathbf{W}}({{\hat{\mathbb{Q}}}})$ is the smallest integer $n>0$ such that $w^N\in K_{\mathbf{W}}$ for all $N\in n{\mathbb{Z}}$. If $K_{\mathbf{W}}$ is the subgroup of ${\mathbf{W}}({{\hat{\mathbb{Q}}}})$ generated by [[compact open subgroups]{}]{}$K_{\mathbf{U}}\subset{\mathbf{U}}({{\hat{\mathbb{Q}}}})$ and $K_{\mathbf{V}}\subset{\mathbf{V}}({{\hat{\mathbb{Q}}}})$ via $\psi$ (satisfying $\psi(K_{\mathbf{V}}\times K_{\mathbf{V}})\subset K_{\mathbf{U}}$), then by writing $w=(u,v)$ for $u\in{\mathbf{U}}({\mathbb{Q}})$ and $v\in{\mathbf{V}}({\mathbb{Q}})$ we see that ${\mathrm{ord}}(w,K_{\mathbf{W}})$ is the least common multiple of ${\mathrm{ord}}(u,K_{\mathbf{U}})$ and ${\mathrm{ord}}(v,K_{\mathbf{V}})$, where ${\mathrm{ord}}(u,K_{\mathbf{U}})$ is the order of the class $[u]$ in the torsion abelian group ${\mathbf{U}}({{\hat{\mathbb{Q}}}})/K_{\mathbf{U}}$, and similarly for ${\mathrm{ord}}(v,K_{\mathbf{V}})$. The order for ${\mathbf{W}}({{\hat{\mathbb{Q}}}})/K_{\mathbf{W}}$ is thus well-defined, although the quotient is only a pointed set with an action of ${\mathbb{Z}}$, rather than a group. If the $K_{\mathbf{U}}$ and $K_{\mathbf{V}}$ above are of fine product type, then we have ${\mathrm{ord}}(w,K_{\mathbf{W}})=\prod_p{\mathrm{ord}}_p(w,K_{\mathbf{W}})$, where ${\mathrm{ord}}_p(w,K_{\mathbf{W}})$ is the order of $w$ in ${\mathbf{W}}({{\mathbb{Q}_p}})/K_{{\mathbf{W}},p}$. The product makes sense because $w\in K_{{\mathbf{W}},p}$ for all but finitely many $p$’s, i.e. ${\mathrm{ord}}_p(w,K_{\mathbf{W}})=1$ for almost every $p$. We also have ${\mathrm{ord}}_p(w,K_{\mathbf{W}})={{\mathrm{max}}}\{{\mathrm{ord}}_p(u,K_{\mathbf{U}}),{\mathrm{ord}}_p(v,K_{\mathbf{V}})\}$ when we write $w=(u,v)$. Note that the abelian groups ${\mathbf{U}}({{\mathbb{Q}_p}})/K_{{\mathbf{U}},p}$ and ${\mathbf{V}}({{\mathbb{Q}_p}})/K_{{\mathbf{V}},p}$ are $p$-torsion groups, the torsion orders ${\mathrm{ord}}_p(u,K_{\mathbf{U}})$ and ${\mathrm{ord}}_p(v,K_{\mathbf{V}})$ are $p$-powers, hence so it is with ${\mathrm{ord}}_p(w,K_{\mathbf{W}})$. \[torsion order in the siegel case\] We first consider the torsion order in the Siegel case, using the mixed Shimura datum defined in \[Siegel data\]. We have a symplectic form $\psi:{\mathbf{V}}\rtimes{\mathbf{V}}{\rightarrow}{\mathbf{U}}$ with ${\mathbf{U}}={{\mathbb{G}_\mathrm{a}}}$, the extension ${\mathbf{W}}$ of ${\mathbf{V}}$ by ${\mathbf{U}}$, and we have the pure Shimura datum $({\mathbf{G}},X)=({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$, as well as the mixed Shimura datum $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$, the reflex field of which is ${\mathbb{Q}}$. Taking a [[compact open subgroup]{}]{}$K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$ of fine product type, we have the mixed Shimura datum $M=M_K({\mathbf{P}},Y)$ fibred over $S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$. Note that $({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$ is irreducible. In fact ${\mathrm{Sp}}_{\mathbf{V}}$ is the minimal ${\mathbb{Q}}$-subgroup of ${\mathrm{GSp}}_{\mathbf{V}}$ whose base change to ${\mathbb{R}}$ contains all $x({\mathbb{S}}^1)$ for $x\in{\mathscr{H}}_{\mathbf{V}}$ and ${\mathbb{S}}^1={\mathrm{Ker}}({\mathrm{Nm}}_{{\mathbb{C}}/{\mathbb{R}}}:{\mathbb{S}}{\rightarrow}{\mathbb{G}}_{{\mathrm{m}},{\mathbb{R}}})$, otherwise the Hermitian symmetric domain ${\mathscr{H}}_{\mathbf{V}}^+$ could be produced from ${\mathbf{H}}({\mathbb{R}})^+$ by some smaller reductive ${\mathbb{Q}}$-subgroup ${\mathbf{H}}\subsetneq{\mathrm{Sp}}_{\mathbf{V}}$ using \[generating subdata\], contradicting the classification of simple Hermitian symmetric spaces; and for any $x\in{\mathscr{H}}_{\mathbf{V}}$, the image of ${\mathbb{G}}_{{\mathrm{m}},{\mathbb{R}}}$ in ${\mathbb{S}}$ (corresponding to ${\mathbb{R}}^\times\subset{\mathbb{C}}^\times$) along $x$ is a central ${\mathbb{R}}$-torus of ${\mathrm{GSp}}_{{\mathbf{V}},{\mathbb{R}}}$, and coincides with the center of ${\mathrm{GSp}}_{{\mathbf{V}},{\mathbb{R}}}$, hence ${\mathrm{GSp}}_{\mathbf{V}}$ is already the generic Mumford-Tate group of ${\mathscr{H}}_{\mathbf{V}}$. Let $({\mathbf{G}}',X')$ be an irreducible pure subdatum of $({\mathbf{G}},X)$, with ${\mathbf{T}}$ the connected center of ${\mathbf{G}}'$. Since $({\mathrm{GSp}}_{\mathbf{V}},{\mathscr{H}}_{\mathbf{V}})$ is already irreducible, by \[generic injectivity\](1) we see that ${\mathbf{T}}$ contains ${\mathbb{G}}_{\mathrm{m}}$ the center of ${\mathrm{GSp}}_{\mathbf{V}}$. The center ${{\mathbb{G}_\mathrm{m}}}$ of ${\mathbf{G}}={\mathrm{GSp}}_{\mathbf{V}}$ acts on ${\mathbf{V}}$ by central scaling, and it acts on ${\mathbf{U}}$ by the square of central scaling. Taking a [[compact open subgroup]{}]{}$K_{\mathbf{G}}$ of ${\mathbf{G}}({{\hat{\mathbb{Q}}}})$ of the form $K_{{\mathbb{G}_\mathrm{m}}}K_{{\mathbf{G}}^{\mathrm{der}}}$ and $K_{\mathbf{U}}$, $K_{\mathbf{V}}$, $K_{\mathbf{W}}$ as in \[levels of product type\], we see that $K_{\mathbf{T}}={\mathbf{T}}({{\hat{\mathbb{Q}}}})\cap K_{\mathbf{G}}\supset K_{{\mathbb{G}_\mathrm{m}}}$. In particular, for any $w\in{\mathbf{W}}({\mathbb{Q}})$ and $p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$ we have $$[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{\mathbf{T}}(w)_p]\geq [K_{{{\mathbb{G}_\mathrm{m}}},p}^{{\mathrm{max}}}:K_{{\mathbb{G}_\mathrm{m}}}(w)_p].$$ Write $w=(u,v)$ for $u\in{\mathbf{U}}({\mathbb{Q}})$ and $v\in{\mathbf{V}}({\mathbb{Q}})$. $K^{{\mathrm{max}}}_{{{\mathbb{G}_\mathrm{m}}},p}{\cong}{{\mathbb{Z}^\times_p}}$ acts on ${\mathbf{U}}({{\mathbb{Q}_p}})/K_{{\mathbf{U}},p}$ by automorphism $t({{\bar{u}}})=\overline{t^2u}$ where $t\in{{\mathbb{Z}^\times_p}}$ and the bar stands for the class modulo $K_{{\mathbf{U}},p}$. The action preserves the order ${\mathrm{ord}}_p(u,K_{\mathbf{U}})$, and it stabilizes the image of ${{\mathbb{Z}^\times_p}}u$ modulo $K_{\mathbf{U}}$, which is isomorphic to ${{\mathbb{Z}_p}}/p^m$ with $p^m={\mathrm{ord}}_p(u,K_{\mathbf{U}})$. Hence the cardinality of the quotient $[K^{{\mathrm{max}}}_{{{\mathbb{G}_\mathrm{m}}},p}:K_{{{\mathbb{G}_\mathrm{m}}},p}]$ is equal to $$\#\{t^2:t\in({{\mathbb{Z}_p}}/p^m)^\times\}=\frac{1}{2}\#({{\mathbb{Z}_p}}/p^m)=\frac{p-1}{2p}{\mathrm{ord}}_p(u,K_{\mathbf{U}}).$$ The case of ${\mathbf{V}}$ is similar: ${{\mathbb{G}_\mathrm{m}}}$ is the common center of ${{\mathbf{GL}}}_{\mathbf{V}}$ and ${\mathrm{GSp}}_{\mathbf{V}}$, hence $$[K_{{{\mathbb{G}_\mathrm{m}}},p}^{{\mathrm{max}}}:K_{{\mathbb{G}_\mathrm{m}}}(w)_p]\geq\frac{p-1}{p}{\mathrm{ord}}_p(v,K_{\mathbf{V}})$$ and combining it with the case of ${\mathbf{U}}$ we get $$[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{\mathbf{T}}(w)_p]\geq\frac{1}{4}{\mathrm{ord}}_p(w,K_{\mathbf{W}}).$$ \[torsion order in the product case\] Let $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ be an irreducible mixed Shimura subdatum of a product datum of finitely many mixed Shimura data of Siegel type (including Kuga data) $({\mathbf{L}},Y_{\mathbf{L}})={\mathbf{N}}\rtimes({\mathbf{H}},X_{\mathbf{H}})=\prod_j({\mathbf{P}}_j,{\mathscr{U}}_j)\times({\mathbf{Q}},{\mathscr{V}})$, with $({\mathbf{G}},X)\subset({\mathbf{H}},X_{\mathbf{H}})$. Let $K=K_{\mathbf{N}}\rtimes K_{\mathbf{H}}$ be a [[compact open subgroup]{}]{}of fine product type restricting to $K_{\mathbf{P}}=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$. Let $({\mathbf{P}}',Y'):={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ be an irreducible ${{{(\mathbf{T},w)}}}$-special subdatum of $({\mathbf{P}},Y)$, with $w\in{\mathbf{W}}({\mathbb{Q}})$ non-trivial. Keeping the notations as in \[orbit of a pure special subvariety\], we have: \(1) for $p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$ we have $I({\mathbf{T}},K_{\mathbf{G}}(w)_p)\geq c\cdot{\mathrm{ord}}_p(w,K_{\mathbf{W}})$, $c$ being some constant independent of $K$ and ${\mathbf{T}}$; \(2) there is a constant integer $N>0$ such that $w^N\in K_{{\mathbf{W}},p}$ for $p\notin\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$, and $N$ is independent of $({\mathbf{G}}',X')$, ${\mathbf{T}}$, and $K$. Since $({\mathbf{P}}',Y')={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ is irreducible, $({\mathbf{G}}',X')$ is irreducible by \[pure irreducibility\]. Take any connected component $X'^+$ of $X'$, we have ${\mathbf{G}}'':={\mathrm{MT}}(X'^+)$ with ${\mathbf{G}}''^{\mathrm{der}}={\mathbf{G}}'^{\mathrm{der}}$, and strictly irreducible data $({\mathbf{G}}'',X'')$ with $X''={\mathbf{G}}''({\mathbb{R}})X'^+$ and $({\mathbf{P}}'',Y'')={\mathbf{W}}'\rtimes(w{\mathbf{G}}''w^{{-1}},wX'')$. $({\mathbf{G}}'',X'')$ being a strictly irreducible pure Shimura subdatum of $({\mathbf{H}},X_{\mathbf{H}})=({\mathrm{GSp}}_{{\mathbf{V}}_1},{\mathscr{H}}_{{\mathbf{V}}_1})\times\cdots\times({\mathrm{GSp}}_{{\mathbf{V}}_n},{\mathscr{H}}_{{\mathbf{V}}_n})$, we have $X''^+=X'^+\subset X_{\mathbf{H}}^+$ for some connected component $X_{\mathbf{H}}^+$ of $X_{\mathbf{H}}$, and this gives an inclusion of strictly irreducible pure Shimura data $({\mathbf{G}}'',X'')\subset({\mathbf{H}}',X'_{\mathbf{H}}={\mathbf{H}}'({\mathbb{R}})X^+_{\mathbf{H}})$, where ${\mathbf{H}}'$ is the ${\mathbb{Q}}$-subgroup generated by ${\mathbf{H}}^{\mathrm{der}}=\prod{\mathrm{Sp}}_{{\mathbf{V}}_j}$ and a central split ${\mathbb{Q}}$-torus ${{\mathbb{G}_\mathrm{m}}}_m$ which acts on each ${\mathbf{V}}_j$ by the central scaling. From \[generic injectivity\](1) we get ${{\mathbb{G}_\mathrm{m}}}\subset{\mathbf{T}}'$ with ${\mathbf{T}}'$ the connected center of ${\mathbf{G}}'$. Since ${\mathbf{G}}'\subset{\mathbf{G}}$ and ${\mathbf{G}}'^{\mathrm{der}}={\mathbf{G}}^{\mathrm{der}}$, we get ${{\mathbb{G}_\mathrm{m}}}\subset{\mathbf{T}}'\subset{\mathbf{T}}$. We write ${\mathbf{C}}$ for this split ${\mathbb{Q}}$-torus so as to avoid ambiguities with other ${\mathbb{G}}_{\mathrm{m}}$, like those arising as the connected centers of the ${\mathrm{GSp}}_{{\mathbf{V}}_j}$. \(1) The inclusion ${\mathbf{C}}\subset{\mathbf{T}}$ gives $K_{\mathbf{C}}(w)\subset K_{\mathbf{T}}(w)\subset K_{\mathbf{G}}(w)$, and for any prime $p$ we have $K_{\mathbf{C}}(w)_p\subset K_{\mathbf{T}}(w)_p\subset K_{\mathbf{G}}(w)_p$ and $K^{{\mathrm{max}}}_{{\mathbf{C}},p}\subset K^{{\mathrm{max}}}_{{\mathbf{T}},p}$. The cardinality $K^{{\mathrm{max}}}_{{\mathbf{C}},p}/K_{\mathbf{C}}(w)_p$ resp. $K^{{\mathrm{max}}}_{{\mathbf{T}},p}/K_{\mathbf{T}}(w)_p$ equals the cardinality of the $K^{{\mathrm{max}}}_{{\mathbf{C}},p}$-orbit resp. the $K^{{\mathrm{max}}}_{{\mathbf{T}},p}$-orbit of the class of $w$ in the quotient set $K_{{\mathbf{W}},p}{\backslash}{\mathbf{W}}({{\mathbb{Q}_p}})$, hence for $p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$ i.e. $K^{{\mathrm{max}}}_{{\mathbf{T}},p}\supsetneq K_{\mathbf{T}}(w)_p$ we have $$[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{\mathbf{T}}(w)_p]\geq [K^{{\mathrm{max}}}_{{\mathbf{C}},p}:K_{{\mathbf{C}}}(w)_p]\geq \frac{1}{4}{\mathrm{ord}}_p(w,K_{\mathbf{W}})$$ where the last inequality follows from \[torsion order in the siegel case\]: although $w$ comes from ${\mathbf{W}}({\mathbb{Q}})$ with ${\mathbf{W}}$ an extension of ${\mathbf{V}}$ by ${\mathbf{U}}$, what matters is that $K^{{\mathrm{max}}}_{{\mathbf{C}},p}={{\mathbb{Z}^\times_p}}$ acts on ${\mathbf{V}}({{\mathbb{Q}_p}})$ by the central scaling and on ${\mathbf{U}}({{\mathbb{Q}_p}})$ by the square of central scaling, and the estimation in \[torsion order in the siegel case\] applies. It remains to put $c=b/4$ using $I({\mathbf{T}},K_{\mathbf{G}}(w)_p)=b[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{\mathbf{T}}(w)_p]$. \(2) For $p\notin\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$ we have $K^{{\mathrm{max}}}_{{\mathbf{T}},p}=K_{{\mathbf{T}},p}=K_{{\mathbf{T}}}(w)_p$, and in this case $K^{{\mathrm{max}}}_{{\mathbf{C}},p}=K_{{\mathbf{C}},p}{\cong}{{\mathbb{Z}^\times_p}}$: if $K_{{\mathbf{C}},p}=K_{{\mathbf{T}},p}\cap{\mathbf{C}}({{\mathbb{Q}_p}})$ is not maximal, then we get $K^{{\mathrm{max}}}_{{\mathbf{C}},p}K_{{\mathbf{T}},p}\supsetneq K^{{\mathrm{max}}}_{{\mathbf{T}},p}$ which is absurd. For any $g\in K_{{\mathbf{T}},p}$, we have $wgw^{{-1}}g^{{-1}}\in K_{{\mathbf{W}},p}$. Take $g=t\in K_{{\mathbf{C}},p}={{\mathbb{Z}^\times_p}}$ we have $$wgw^{{-1}}g^{{-1}}=(u-t^2u-\psi(v,tv),v-tv,1)=(u-t^2u,v-tv,1)\in K_{{\mathbf{W}},p}$$ where we use $\psi(v,tv)=t\psi(v,v)=0$. Concerning the term $v-tv=(1-t)v$: for $p\geq 3$, we may take $t=2\in{\mathbb{Z}}_p^\times$, and $v-tv\in K_{\mathbf{V}}$ implies $v\in K_{\mathbf{V}}$; for $p=2$, we still have $3\in{\mathbb{Z}}_p^\times$, which gives $2v\in K_{\mathbf{V}}$. Concerning the term $u-t^2u=(1-t^2)u$: for $p\geq 5$, the subgroup $\{t^2:t\in{\mathbb{Z}}_p^\times\}$ is a subgroup of index 2 in ${\mathbb{Z}}_p$, which contains $1+p{\mathbb{Z}}_p$ as a proper subset. In particular we can find $t\in{\mathbb{Z}}_p^\times$ such that $1-t^2$ is a unit in ${\mathbb{Z}}_p$, hence $u\in K_{\mathbf{U}}$ in this case. For $p\leq 3$, we can still find $t\in{\mathbb{Z}}_p^\times$ such that $1-t^2$ divides 12. Hence it suffices to take $N=12$. \[torsion order in the embedded case\] Let $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)=({\mathbf{U}},{\mathbf{V}})\rtimes({\mathbf{G}},X)$ be a subdatum of a product of the form $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$ with ${\mathbf{G}}_0$ of adjoint type, $({\mathbf{L}},Y_{\mathbf{L}})={\mathbf{N}}\rtimes({\mathbf{H}},X_{\mathbf{H}})=({\mathbf{U}}_{\mathbf{N}},{\mathbf{V}}_{\mathbf{N}})\rtimes({\mathbf{H}},X_{\mathbf{H}})$ a finite product of mixed Shimura data of Siegel type and $({\mathbf{G}},X)\subset({\mathbf{G}}_0,X_0)\times({\mathbf{H}},X_{\mathbf{H}})$. We write $({\mathbf{H}},X_{\mathbf{H}})=({\mathrm{GSp}}_{{\mathbf{V}}_1},{\mathscr{H}}_{{\mathbf{V}}_1})\times\cdots\times({\mathrm{GSp}}_{{\mathbf{V}}_n},{\mathscr{H}}_{{\mathbf{V}}_n})$. Let $K=K_{\mathbf{N}}\rtimes(K_{{\mathbf{G}}_0}\times K_{\mathbf{H}})$ be a [[compact open subgroup]{}]{}of fine product type, which restricts to $K_{\mathbf{P}}=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$. If $({\mathbf{P}}',Y')={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ is a strictly irreducible ${{{(\mathbf{T},w)}}}$-subdatum of $({\mathbf{P}},Y)$ for some $w\in{\mathbf{W}}({\mathbb{Q}})$, then using the notations in \[orbit of a pure special subvariety\] we have: (1)$I({\mathbf{T}},K_{\mathbf{G}}(w)_p)\geq c\cdot {\mathrm{ord}}_p(w,K_{\mathbf{W}})$, $c$ being some constant independent of $({\mathbf{G}}',X')$, $K$, and ${\mathbf{T}}$; \(2) there is a constant integer $N>0$ such that $w^N\in K_{{\mathbf{W}},p}$ for $p\notin\Delta({\mathbf{T}},K_{\mathbf{G}}(w))$, and $N$ is independent of $({\mathbf{G}}',X')$, $K$, and ${\mathbf{T}}$. Let $x=(x_0,x_1)$ be a point in $X_0\times X_{\mathbf{H}}$ from the datum $({\mathbf{G}}_0,X_0)\times({\mathbf{H}},X_{\mathbf{H}})$, and let ${{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}}\subset{\mathbb{S}}$ be the split ${\mathbb{R}}$-torus corresponding to ${\mathbb{R}}^\times\subset{\mathbb{C}}^\times$. Then $x_1({{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}})$ acts on ${\mathbf{V}}_{{\mathbf{N}},{\mathbb{R}}}$ via the central scaling and on ${\mathbf{U}}_{{\mathbf{N}},{\mathbb{R}}}$ via the square of the central scaling, while $x_0({{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}})$ is trivial, because by \[mixed Shimura data\](i) $x_0$ sends ${{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}}$ into the center of ${\mathbf{G}}_0$ which is trivial. Let ${\mathbf{C}}$ be the split ${\mathbb{Q}}$-torus isomorphic to ${{\mathbb{G}_\mathrm{m}}}$ in ${\mathbf{H}}={\mathrm{GSp}}_{{\mathbf{V}}_1}\times\cdots\times{\mathrm{GSp}}_{{\mathbf{V}}_n}$ which is the diagonal of ${{\mathbb{G}_\mathrm{m}}}\times\cdots\times{{\mathbb{G}_\mathrm{m}}}$, as we have seen in \[Siegel data\](3) (we write ${\mathbf{C}}$ instead of ${{\mathbb{G}_\mathrm{m}}}$ so as to avoid ambiguities with the connected centers of ${\mathrm{GSp}}_{{\mathbf{V}}_j}$). ${\mathbf{C}}$ is one-dimensional, and we have shown that for any given $x\in X_0\times X_{\mathbf{H}}$, ${\mathbf{C}}$ is the minimal ${\mathbb{Q}}$-subtorus in ${\mathbf{G}}_0\times{\mathbf{H}}$ whose base change to ${\mathbb{R}}$ contains $x({{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}})$, and in fact ${\mathbf{C}}_{\mathbb{R}}=x({{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}})$. When $x$ runs through $X'$, the generic Mumford-Tate group ${\mathbf{G}}'={\mathrm{MT}}(X'^+)$ for some connected component $X'^+$ of $X'$ necessarily contains ${\mathbf{C}}$ because ${\mathbf{G}}'_{\mathbb{R}}\supset x({{\mathbb{G}_\mathrm{m}}}_{\mathbb{R}})={\mathbf{C}}_{\mathbb{R}}$. Clearly ${\mathbf{C}}$ is central in ${\mathbf{G}}_0\times{\mathbf{H}}$, hence it is central in ${\mathbf{G}}'$, and we get ${\mathbf{C}}\subset{\mathbf{T}}$. It remains to argue as in \[torsion order in the product case\]. Note that the constants $c$ and $N$ are the same as in \[torsion order in the product case\]. \[torsion order in general\] \(1) The corollary \[torsion order in the embedded case\] above is sufficient for the study of André-Oort conjecture for mixed Shimura varieties using the reductions \[insensitivity of isogeny\] and \[reduction lemma\]. For a general mixed Shimura datum $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ mapped into $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$ with finite kernel, where $({\mathbf{L}},Y_{\mathbf{L}})={\mathbf{N}}\rtimes({\mathbf{H}},X_{\mathbf{H}})$ is a product of mixed Shimura data of Siegel type with $({\mathbf{G}},X)$ mapped into $({\mathbf{H}},X_{\mathbf{H}})$, the image of a strictly irreducible ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}',Y')={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}},wX')$ in $({\mathbf{L}},Y_{\mathbf{L}})$ is a strictly irreducible subdatum $({\mathbf{P}}'',Y'')={\mathbf{W}}''\rtimes(w''{\mathbf{G}}''w''^{{-1}},w''X'')$, and the connected center ${\mathbf{T}}''$ of ${\mathbf{G}}''$, which is the image of ${\mathbf{T}}$, contains ${\mathbf{C}}$ the split central ${\mathbb{Q}}$-torus constructed in the product case. The pre-image of ${\mathbf{C}}$ in ${\mathbf{T}}$ must contain a split ${\mathbb{Q}}$-torus ${\mathbf{C}}'$ which is mapped onto ${\mathbf{C}}$. We do have $[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{\mathbf{T}}(w)_p]\geq [K^{{\mathrm{max}}}_{{\mathbf{C}}',p}:K_{{\mathbf{C}}'}(w)_p]$, but $[K^{{\mathrm{max}}}_{{\mathbf{C}}',p}:K_{{\mathbf{C}}'}(w)_p]\geq c'[K^{{\mathrm{max}}}_{{\mathbf{C}},p}:K_{\mathbf{C}}(w)_p]$ is not evident. We have an exact sequence $$1{\rightarrow}{\mathbf{C}}''{\rightarrow}{\mathbf{C}}'{\rightarrow}{\mathbf{C}}{\rightarrow}1$$ with ${\mathbf{C}}''$ a finite ${\mathbb{Q}}$-group of degree $d$ (i.e. associated to a commutative Hopf ${\mathbb{Q}}$-algebra of dimension $d$) and we have the exactness of $$1{\rightarrow}{\mathbf{C}}''({{\mathbb{Q}_p}}){\rightarrow}{\mathbf{C}}'({{\mathbb{Q}_p}}){\rightarrow}{\mathbf{C}}({{\mathbb{Q}_p}}){\rightarrow}H^1({\mathrm{Gal}}({\bar{\mathbb{Q}}}_p/{{\mathbb{Q}_p}}),{\mathbf{C}}''({\bar{\mathbb{Q}}}_p).$$ Here the Galois cohomology $H^1({{\mathbb{Q}_p}},{\mathbf{C}}'')$ is of $d$-torsion, which implies that $d$-powers of elements in $K^{{\mathrm{max}}}_{{\mathbf{C}},p}={{\mathbb{Z}^\times_p}}$ fall in the image of $K^{{\mathrm{max}}}_{{\mathbf{C}}',p}$. Using the exponential map [@neukirch; @number; @theory] II.5.5, we can find an open subgroup $U'_p$ in $U_p=1+2p{{\mathbb{Z}_p}}\subset{{\mathbb{Z}^\times_p}}$ with index $[U_p:U'_p]$ uniformly bounded independent of $p$. However $[{{\mathbb{Z}^\times_p}}:U_p]=p-1$ for $p\geq 3$, and using these arguments we can only arrive at an estimation of the form $[K^{{\mathrm{max}}}_{{\mathbf{T}},p}:K_{\mathbf{T}}(w)_p]\geq \frac{c}{p}{\mathrm{ord}}_p(w,K_{\mathbf{W}})$ for some absolute constant $c$, and this is not sufficient for some results in the last section concerning bounded equidistribution. It is for this reason that we do not proceed further for an estimation of torsion order in general. \(2) Some of the arguments in \[finite index\] and in \[torsion order in the siegel case\] have appeared in [@chen; @thesis] 4.2. GAO Ziyang has informed us of his work [@gao; @mixed], where he obtained similar results independently. His work concentrates on Galois orbits of special points, and directly leads to the André-Oort conjecture without repeating the arguments for special subvarieties, due to the powerful machinery of o-minimality. He has restricted to the case that the pure part of the mixed Shimura varieties in question are given by subdata of Siegel type. Using our arguments it is natural to expect similar results valid for general mixed Shimura data that are subdata in some $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$ as in the corollary above. Special subvarieties with bounded test invariants ================================================= In this section we prove the equivalence between bounded sequences of special subvarieties and sequences with bounded test invariants, where the notion of test invariants is introduced as a substitute to the estimation of degrees of lower bounds for Galois orbits. We will also draw some conclusions under the GRH for CM fields, when the following assumption is satisfied: \[CM splitting fields\] The ambient mixed Shimura variety $M_K({\mathbf{P}},Y)$ is defined by a mixed Shimura datum $({\mathbf{P}},Y)={\mathbf{W}}\rtimes({\mathbf{G}},X)$ of some datum of the form $({\mathbf{G}}_0,X_0)\times({\mathbf{L}},Y_{\mathbf{L}})$ where ${\mathbf{G}}_0$ is semi-simple of adjoint type and $({\mathbf{L}},Y_{\mathbf{L}})={\mathbf{N}}\rtimes({\mathbf{H}},{\mathbf{N}})$ is a finite product of mixed Shimura data of Siegel type (including Kuga ones). It is also required that $({\mathbf{G}},X){\hookrightarrow}({\mathbf{G}}_0,X_0)\times({\mathbf{H}},X_{\mathbf{H}})$. When this assumption holds, for any irreducible ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}',Y')$ of $({\mathbf{P}},Y)$, the splitting field $F_{\mathbf{T}}$ of ${\mathbf{T}}$ is a CM field as we have seen in \[reduction to the CM case\], and the André-Oort conjecture can be reduced to this case. We first recall the following criterion for the ergodic-Galois alternative in the pure case: \[bounded galois orbits\] Let $S=M_K({\mathbf{G}},X)$ be a pure Shimura variety, with $E$ its reflex field, and $(S_n)$ a sequence of special subvarieties, defined by $({\mathbf{G}}_n,X_n)$. Write ${\mathbf{T}}_n$ for the connected center of ${\mathbf{G}}_n$, and $D({\mathbf{T}})_n$ the absolute discriminant of its splitting field over ${\mathbb{Q}}$. If there exists some constant $C>0$ such that $$\log D({\mathbf{T}}_n)\cdot\prod_{p\in\Delta({\mathbf{T}}_n,K)}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K_p)\}\leq C, \forall n\in{\mathbb{N}}$$ then there exists finitely many ${\mathbb{Q}}$-tori $\{{\mathbf{C}}_1,\cdots,{\mathbf{C}}_N\}$ in ${\mathbf{G}}$ such that each $S_n$ is ${\mathbf{C}}_i$-special for some $i$. In particular, assume that \[CM splitting fields\] is satisfied, which means, in the pure case, that $({\mathbf{G}},X)$ is a subdatum of a product $({\mathbf{G}}_0,X_0)\times({\mathbf{H}},X_{\mathbf{H}})$ with $({\mathbf{H}},X_{\mathbf{H}})$ a product of finitely many pure Shimura data of Siegel type, and assume the GRH for CM fields, if $\deg_{\pi^{\mathscr{L}}_S}{\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot S_n\leq C, \forall n$ for some constant $C>0$, ${\mathscr{L}}_S$ being the automorphic line bundle on $S$, then the sequence $(S_n)$ is bounded in the sense of \[bounded sequence\]. The original statement was made assuming ${\mathbf{G}}$ being of adjoint type, and from \[lower bound involving splitting fields\] and \[reduction to the CM case\] the modified form above is immediate. Note that the arguments in [@ullmo; @yafaev] 3.13 - 3.21 do not rely on the GRH for CM fields, and the GRH is not involved for sequences of pure special subvarieties with bounded test invariants. It is used when we pass to Galois orbits of bounded degrees. For a sequence of pure special subvarieties in a mixed Shimura variety we immediately get: \[pure special subvarieties of bounded Galois orbits\] Let $M=M_K({\mathbf{P}},Y)$ be a mixed Shimura variety satisfying \[CM splitting fields\], which is defined over the reflex field $E=E({\mathbf{P}},Y)$ as in \[assumption\] with ${\mathscr{L}}_S$ the automorphic line bundle on $S$, and let $(M_n)$ be a sequence of pure special subvarieties, defined by irreducible $({\mathbf{T}}_n,w_n)$-special pure subdata $({\mathbf{P}}_n,Y_n)={\mathbf{W}}_n\rtimes(w_n{\mathbf{G}}_nw_n^{{-1}},w_nX_n)$. If there exists some constant $C>0$ such that $$\log{}D({\mathbf{T}}_n)\prod_{p\in\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K_{\mathbf{G}}(w_n)_p)\}\leq C,\ \forall n\in{\mathbb{N}}$$ then the sequence is $B$-bounded for some $B$ in the sense of \[bounded sequence\]. The analytic closure of $\bigcup_nM_n$ is a finite union of pure special subvarieties bounded by $B$. In particular, under the GRH for CM fields, a sequence of pure special subvarieties $(M_n)$ such that $$\deg_{\pi{\mathscr{L}}_S}{\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot M_n\leq C,\ \forall n$$ for some constant $C>0$ is bounded by some $B$, and the analytic closure of $\bigcup_nM_n$ is a finite union of $B$-bounded pure special subvarieties. Write $\pi:M{\rightarrow}S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ for the natural projection. Then the images $S_n=\pi(M_n)\subset S$ is a sequence of pure special subvarieties, with $S_n$ being ${\mathbf{T}}_n$-special. It is clear that $\Delta({\mathbf{T}}_n,K_{\mathbf{G}})\subset\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))$, and thus $$\log D({\mathbf{T}}_n)\prod_{p\in\Delta({\mathbf{T}}_n,K_{\mathbf{G}})}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K_{\mathbf{G}})\}\leq C$$ which implies that the sequence $(S_n)$ is bounded. In particular, we can choose the defining subdatum for $(M_n)$ to be $(w_n{\mathbf{G}}_nw_n^{{-1}},w_nX_n)$ such that the connected centers of the ${\mathbf{G}}_n$ come from a fixed finite set $\{{\mathbf{T}}_\alpha:\alpha\in A\}$ ($A$ finite), and the absolute discriminants $D({\mathbf{T}}_\alpha)$ assume only finitely many values. Therefore the sequence $I({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))$ is also bounded by some constant $C'$, and ${\mathrm{ord}}_p(w_n,K_{\mathbf{W}})\leq C'/c$ for $p\in\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))$ where $c$ is the constant in \[torsion order in the embedded case\]. We see that - for $p\in\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))$, ${\mathrm{ord}}_p(w,K_{\mathbf{W}})\leq C_1$, with $C_1$ some constant independent of $w_n,{\mathbf{T}}_n,K$; in particular, the union $\bigcup_n\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))$ is finite; - for $p\notin\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w_n))$ and $p$ not dividing $N$ (the constant in \[torsion order in the embedded case\](2)), we have $w\in K_{{\mathbf{W}},p}$; - for $p\notin\Delta({\mathbf{T}},K_{\mathbf{G}}(w_n))$ and $p$ dividing $N$, we have $w_n^N\in K_{{\mathbf{W}},p}$ and ${\mathrm{ord}}_p(w_n,K_{\mathbf{W}})\leq p^{v_p(N)}$ ($v_p$ is the $p$-adic valuation such that $v_p(p)=1$); more precisely we have $N=12$ and for $p=2$ or $p=3$ we have ${\mathrm{ord}}_p(w_n,K_{\mathbf{W}})\leq 4$. Hence there are only finitely many choices for the classes of $w_n=(u_n,v_n)$ modulo $K_{\mathbf{W}}$ and we may take $w_n$’s from a fixed finite subset of ${\mathbf{W}}({\mathbb{Q}})$, which means that the sequence $(M_n)$ is bounded. The claim on sequences whose Galois orbits are of bounded degrees is clear. Note that the conclusion of the corollary above is very restrictive: we have started with a sequence of pure special subvarieties and ended up with finitely many pure special subvarieties. The finitely many choices of the $w_n$’s modulo $K_{\mathbf{W}}$ have forced the sequence to lie in the union of finitely many maximal pure special subvarieties of $M$. In the mixed case, we propose the following substitute for the estimation of Galois orbits. \[test invariants\] Let $M=M_K({\mathbf{P}},Y)$ be a mixed Shimura variety satisfying \[CM splitting fields\], defined at some level $K$ of fine product type with $M^+$ a connected component of $M$ given by $Y^+\subset Y$. For $M'$ a special subvariety defined by a strictly irreducible ${{{(\mathbf{T},w)}}}$-special subdatum $({\mathbf{P}}',Y';Y'^+)={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}},wX';wX'^+)$, we define the test invariant of $M'$ to be $$\tau_M(M'):=\log D({\mathbf{T}})\min_{w'\in{\mathbf{W}}'({\mathbb{Q}})w}\prod_{p\in\Delta({\mathbf{T}},K_{\mathbf{G}}(w'))}{{\mathrm{max}}}\{1,I({\mathbf{T}},K_{\mathbf{G}}(w'))\}$$ where ${\mathbf{T}}$ is the connected center of ${\mathbf{G}}'$, $D({\mathbf{T}})$ is the absolute discriminant of its splitting field. The subdata ${\mathbf{W}}'\rtimes(w'{\mathbf{G}}'w'^{{-1}},w'X';w'X'^+)$ define the same special subvariety $M'$ by \[structure of subdata\], and the minimum over ${\mathbf{W}}'({\mathbb{Q}})w$ is justified by \[torsion order in the embedded case\]. The definition is independent of the choice of the subdata defining $M'$, as one may verify using \[conjugation by gamma\] \[special subvarieties of bounded test invariants\]Let $M=M_K({\mathbf{P}},Y)$ be a mixed Shimura variety satisfying \[CM splitting fields\], with $K=K_{\mathbf{W}}\rtimes K_{\mathbf{G}}$ and reflex field $E$ be as in \[assumption\], and fix $M^+$ the component of $M$ given by $Y^+$ and $\Gamma={\mathbf{P}}({\mathbb{Q}})_+\cap K$. Let $(M_n)$ be a sequence of special subvarieties in $M^+$ defined by strictly irreducible $({\mathbf{T}}_n,w_n)$-special connected subdata $({\mathbf{P}}_n,Y_n;Y_n^+)={\mathbf{W}}_n\rtimes(w_n{\mathbf{G}}_nw_n^{{-1}},w_nX_n;w_nX_n^+) $ such that for some constant $C>0$ we have $$\tau_M(M_n)\leq C,\forall n.$$ Then \(1) the sequence is $B$-bounded for some finite $B$. \(2) Assume further the GRH for CM fields. Then we can find a [[compact open subgroup]{}]{}$K'\subset K$ of fine product type $K'=K'_{\mathbf{W}}\rtimes K'_{\mathbf{G}}$ such that for $M'^+$ the connected component corresponding to $Y^+$ and ${\mathbf{P}}({\mathbb{Q}})_+\cap K'$ in $M'=M_{K'}({\mathbf{P}},Y)$ we have the estimation of Galois orbits $$\deg_{\pi^{\mathscr{L}}_{S'}}{\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot S_n'\geq c_N D_N({\mathbf{T}}_n)\min_{w'\in{\mathbf{W}}_n({\mathbb{Q}})w_n}\prod_{p\in\Delta({\mathbf{T}}_n,K'_{\mathbf{G}}(w'))}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K'_{\mathbf{G}}(w')_p)\}$$ where - $K'_{\mathbf{G}}(w)=\{g\in K'_{\mathbf{G}}:wgw^{{-1}}g^{{-1}}\in K'_{\mathbf{W}}\}$; - ${\mathscr{L}}_{S'}$ is the automorphic line bundle on $S'=M_{K_{\mathbf{G}}'}({\mathbf{G}},X)$; - $S_n'$ is any maximal pure special subvariety in $M_n'$ the special subvariety defined by $({\mathbf{P}}_n,Y_n;Y_n^+)$ in $M'^+$. In other words, the test invariants are potentially the “correct” numerical bounds for Galois orbits in the mixed case, as long as we restrict our attention to bounded sequences. \(1) Write $\pi:M{\rightarrow}S=M_{K_{\mathbf{G}}}({\mathbf{G}},X)$ for the natural projection, and $S_n=\pi(M_n)$. Then similar to \[pure special subvarieties of bounded Galois orbits\], $S_n$ is ${\mathbf{T}}_n$-special, with bounded test invariants $$\log D({\mathbf{T}}_n)\prod_{p\in\Delta({\mathbf{T}}_nK_{\mathbf{G}})}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K_{{\mathbf{G}},p})\}\leq C.$$ Therefore $(S_n)$ is bounded, and the sequence $\log D({\mathbf{T}}_n)$ only takes finitely many values. We may replace $w_n$ by $w_n'\in{\mathbf{W}}_n({\mathbb{Q}})w_n$ which minimizes the following set of values $$\{\prod_{p\in\Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w))}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K_{\mathbf{G}}(w)_p)\}:w\in{\mathbf{W}}_n({\mathbb{Q}})w_n\}$$ without changing the special subvarieties. Then $\prod_{p\in \Delta({\mathbf{T}}_n,K_{\mathbf{G}}(w'_n))}{{\mathrm{max}}}\{1,I({\mathbf{T}}_n,K_{\mathbf{G}}(w'_n)_p)\}\leq C',\ \forall n$ for some constant $C'>0$. We deduce that the classes of $w'_n$ modulo $K_{\mathbf{W}}$ is finite, using \[torsion order in the embedded case\]. Since we may always translate $w'_n$ by elements in $\Gamma_{\mathbf{W}}={\mathbf{W}}({\mathbb{Q}})\cap K_{\mathbf{W}}$, we may take the $w'_n$’s from a fixed finite subset of ${\mathbf{W}}({\mathbb{Q}})$, hence the claim. \(2) Let $B$ be a finite bounding set for $(M_n)$. Write $w=(u,v)$, then $wK_{\mathbf{W}}w^{{-1}}=\{(u'+2\psi(v,v'),v'):u'\in K_{\mathbf{U}}, v'\in K_{\mathbf{V}}\}$. We may shrink $K_{\mathbf{V}}$ to a [[compact open subgroup]{}]{}$K_{\mathbf{V}}'$ such that $2\psi(v,v')\in K_{\mathbf{U}}$ for all $v'\in K_{\mathbf{V}}'$. One may simply take $K_{\mathbf{V}}'=NK_{\mathbf{V}}$ for some integer $N>0$, and thus $K'_{\mathbf{V}}$ is itself stabilized by $K_{\mathbf{G}}$. Take $K'_{\mathbf{G}}:=\bigcap_{{{{(\mathbf{T},w)}}}\in B} K_{\mathbf{G}}(w)$, and take $K_{\mathbf{W}}'$ the subgroup of $K_{\mathbf{W}}$ generated by $K_{\mathbf{U}}$ and $K'_{\mathbf{V}}$. Then $K_{\mathbf{G}}'$ stabilizes $K_{\mathbf{W}}'$, and we take $K'=K'_{\mathbf{W}}\rtimes K'_{\mathbf{G}}$. Thus $wK' w^{{-1}}=K'$ when ${{{(\mathbf{T},w)}}}\in B$, and the Hecke translation by $w^{{-1}}$ gives an automorphism of $M'=M_{K'}({\mathbf{P}},Y)$, sending the pure Shimura subvariety $S'(w)=M_{wK'_{\mathbf{G}}w}(w{\mathbf{G}}w^{{-1}}, wX)$ to $S'(0)=M_{K'_{\mathbf{G}}}({\mathbf{G}},X)$, both of which are sections to the natural projection $\pi:M'{\rightarrow}S'=M_{K'_{\mathbf{G}}}({\mathbf{G}},X)$. Let $M_1$ be ${{{(\mathbf{T},w)}}}$-special subvariety in $M'^+$ is defined by a strictly irreducible subdatum $({\mathbf{P}}',Y';Y'^+)={\mathbf{W}}'\rtimes(w{\mathbf{G}}'w^{{-1}}, wX';wX'^+)$. Then $S_1(w):=M_1\cap S'(w)$ is isomorphic to $S_1:=\pi(M_1)$ using the pure section, and we get the bijection between ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot S_1$, ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot S_1(w)$, and ${\mathrm{Gal}}({\bar{\mathbb{Q}}}/E)\cdot M_1$, from which the estimation follows. \[lower bound of Tsimerman\] The factor $c_ND_N({\mathbf{T}})$ in \[lower bound involving splitting fields\] is as in [@ullmo; @yafaev], which comes from a lower bound of the image of the reciprocity map of the form ${{\mathrm{rec}}}_{\mathbf{T}}:{\mathrm{Gal}}({\bar{\mathbb{Q}}}/F){\rightarrow}{\overline{\pi}_\circ}({\mathbb{G}}_{\mathrm{m}}^F){\rightarrow}{\overline{\pi}_\circ}({\mathbf{T}})/K_{\mathbf{T}}^{{\mathrm{max}}}$ with $F$ the splitting field of the ${\mathbb{Q}}$-torus ${\mathbf{T}}$, proved in [@yafaev; @duke]. In [@tsimerman; @bound] Tsimerman proved a lower bound for a special point $x$ in a Seigel modular variety in the form $C_g (D(Z_x))^{\delta_g}$, where $Z_x$ is the center of the endomorphism algebra of the CM abelian variety parameterized by $x$, and $D(Z_x)$ is the absolute discriminant of $Z_x$, and it is polynomially equivalent to $D({\mathbf{T}}_x)[K^{{\mathrm{max}}}_{{\mathbf{T}}_x}:K_{{\mathbf{T}}_x}]$ with ${\mathbf{T}}_x$ the Mumford-Tate group of $x$ which is a ${\mathbb{Q}}$-torus. The estimation is established unconditionally for CM abelian varieties of dimension at most 6, and it holds in arbitrary dimension under the GRH for CM fields. In our discussion we had preferred a uniform treatment for all Shimura varieties, including pure Shimura varieties that do not admit finite coverings embedded in Siegel modular varieties. Hence we have followed the formulation and the strategy in [@ullmo; @yafaev]. [00]{} Y. André, Six lectures on Shimura varieties, subvarieties and CM points, lectures in Franco-Taiwan Arithmetic Festival 2001, cf. http://www.math.purdue.edu/jyu/notes.andre2001.ps W. Baily and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Annals of Mathematics* 84(2), 442-528, 1966 A. Borel, Introduction aux groupes arithmetiques, Hermann, Paris, 1969 A. Borel, Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem, Journal of Differential Geometry 6, 543-560, 1972 K. Chen, Special subvarieties of mixed Shimura varieties, Ph.D thesis 2009, Université Paris-Sud XI, 2009 K. Chen, On special subvarieties of Kuga varieties, Mathematische Zeitschrift 274, 821-839, 2013 K. Chen, On the degree of special subvarieties in mixed Shimura varieties, in preparation L. Clozel and E. Ullmo, Équidistribution des sous-variétés spéciales, Annals of Mathematics 161(2), 1571-1588, 2005 P. Deligne, Variété des de Shimura: interpretation modulaire, et techniques de construction de modèles canoniques, in Proceedings of Symposia in Pure Mathematics Vol. 33, Part 2, pp.247-290, AMS, 1970 B. Edixhoven and A.Yafaev, Subvarieties of Shimura varieties, Annals of Mathematics 157(2), 621-645, 2003 A. Eskin, S. Mozes, and N. Shah, [Non-divergence of translates of certain algebraic measures]{}, Geometric and functional analysis 7(1997), pp.48-80 Z. Gao, [Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points]{}, preprint, arXiv:1310:1302 P. Gille and T. Szamuely, Galois groups and fundamental groups, Cambridge studies in advanced mathematics Vol. 117, Cambridge University Press 2009 B. Klingler and A. Yafaev, On the André-Oort conjecture, Annals of Mathematics, Vol.180, Issue 3, pp.867-925, 2014 R. L. Long, [Introduction to number theory]{}, Marcel Dekker, New York 1977 J. Milne, Introduction to Shimura varieties, in Harmonic analysis, Shimura varieties, and trace formula, Clay Mathematics Proceedings 4, 265-378, AMS(2005) B. Moonen, Linearity properties of Shimura varieties II, Compositio Mathematica 114(1), 3-35, 1998 S. Mozes and N. Shah, On the space of ergodic invariant measures of unipotent flows, Ergodic theory and Dynamical Systems 15(1), 149-159, 1995 J. Neukirch, Algebraic number theory, Springer Verlag 1999 F. Oort, Canonical liftings and dense sets of CM-points, in Arithmetic geometry (Cortona 1994), pp. 228-234, Symposia Mathematica, Cambridge Univ. Press, Cambridge, 1997 J. Pila, O-minimality and the André-Oort conjecture for ${\mathbb{C}}^n$, Annals of Mathematics, (2), 173(3), 1779-1840, 2011 R. Pink, Arithmetical compactification of mixed Shimura varieties, Bonner Mathematische Schriften vol. 209 R. Pink, A combination of the conjectures of Mordell-Lang and André-Oort, in Geometric methods in algebra and number theory, Progress in Mathematics, vol.253, pp.251-282, 2005 V. Platonov and A. Rapinchuk, Algebraic groups and number theory, Pure and applied mathematics, 139, Academic Press (1994) N. Ratazzi and E. Ullmo, Galois + Equidistribution = Manin-Mumford, in Arithmetic geometry, pp. 419-430, Clay Mathematics Proceedings, vol. 8, AMS, 2009 T. Scanlon, Local André-Oort conjecture for the universal abelian variety, Inventiones mathematicae, 163(1), 191 - 211, 2006 T. Scanlon, A proof of the André-Oort conjecture via mathematical logic, after Pila, Wilkie, and Zannier, Séminaire Bourbaki, Exposé 1037, 2011 J. Tsimerman, Brauer-Siegel theorem for arithmetic tori and lower bounds for Galois orbits of special points, Journal of American Mathematical Society(2012) 25, 1091-1117 E. Ullmo and A. Yafaev, Galois orbits and equidistribution: towards the André-Oort conjecture, with an appendix by P. Gille and L. Moret-Bailey, Annals of Mathematics, Vol.180, Issue 3, pp.823-865,2014 A. Yafaev, A conjecture of Y. André, Duke Mathematics Journal 132(3), 393-407, 2006 A. Yafaev, On a result of Moonen on the moduli space of principally polarized abelian varieties, Compositio Mathematica, 141(5), 1103-1108, 2005 A. Yafaev, Galois orbits and equidistribution: Manin-Mumford and André-Oort, Journal de la théorie des nombres Bordeaux, 21(2), 493-502, 2009
[Effects of acute alcoholic intoxication on the upper respiratory tract function]. Acute alcohol intake may be of potential hazard in anaesthesia emergency procedures because of consciousness alterations. Alcohol ingestion alters indeed the functions of upper airway muscles and increases the risk of obstructive sleep apnea. However, no data are available on the effects of alcohol on the swallowing reflex (SR), which is a major protective mechanism against pulmonary inhalation and on upper airway resistances (UAR) following external inspiratory load application. This study was designed to investigate the effects of acute alcohol intake on SR and UAR in healthy volunteers. After informed consent, 8 male volunteers (29 +/- 3 years) were studied in the supine position. The tip of a catheter was placed through the naris at the epipharynx level for injection of 3 series of 2 volumes of distilled water (0.25 and 1 ml respectively). Swallows were identified by a submental electromyogram. SR efficiency was assessed by recording 1) the latency (L) between injection and the first swallow, and 2) the number of swallows (N) elicited by each bolus. The subjects were breathing through a facial mask connected to a pneumotachograph. Supraglottic airway pressures (UAP) were recorded using a small balloon catheter placed at the tip of the epiglottis. UAR were calculated as the ration of UAP (cmH2O) on air-flow (l.s-1) at the airflow's peak. After a control set of measurements (TC), including SR assessment and UAR at rest (UARo) and during application of an external inspiratory resistive load (12 cmH2O.l-1 x s-1) (UARr) to sensitize the experiment, the subjects ingested 1 ml.kg-1 of alcohol as 40 degrees vodka.(ABSTRACT TRUNCATED AT 250 WORDS)
--- abstract: 'In this paper, half inverse spectral problem for diffusion operator with jump conditions dependent on the spectral parameter and discontinuoty coefficient is considered. The half inverse problems is studied of determining the coefficient and two potential functions of the boundary value problem its spectrum by Hocstadt- Lieberman and Yang-Zettl methods. We show that two potential functions on the whole interval and the parameters in the boundary and jump conditions can be determined from spectrum.' address: \| Cumhuriyet University\ Vocational School of Sivas\ Sivas.\ 58140\ Turkey author: - Abdullah ERGÜN bibliography: - 'mmnsample.bib' title: 'A half-inverse problem for the Singular Diffusion Operator with Jump Conditions' --- Introduction and preliminaries. ================================ We consider the boundary value problem of the form $$\label{1)} l\left(y\right):=-y''+\left[2\lambda p\left(x\right)+q\left(x\right)\right]y=\lambda ^{2} \delta \left(x\right)y,\, \, x\in \left[0,\pi \right]/\left\{a_{1} ,a_{2} \right\}$$ with the boundary conditions $$\label{2)} y'\left(0\right)=0,y\left(\pi \right)=0$$ and the jump conditions $$\label{3)} y\left(a_{1} +0\right)=\alpha _{1} y\left(a_{1} -0\right)$$ $$\label{4)} y'\left(a_{1} +0\right)=\beta _{1} y'\left(a_{1} -0\right)+i\lambda \gamma _{1} y\left(a_{1} -0\right)$$ $$\label{5)} y\left(a_{2} +0\right)=\alpha _{2} y\left(a_{2} -0\right)$$ $$\label{6)} y'\left(a_{2} +0\right)=\beta _{2} y'\left(a_{2} -0\right)+i\lambda \gamma _{2} y\left(a_{2} -0\right)$$ Where $\lambda $ is a spectral parameter, $p(x)\in W_{2}^{1} \left[0,\pi \right]$, $q(x)\in L_{2} \left[0,\pi \right]$ are real valued functions, $a_{1} \in \left[0,\frac{\pi }{2} \right]$, $a_{2} \in \left[\frac{\pi }{2} ,\pi \right]$ , $\alpha _{1} ,\alpha _{2} ,\gamma _{1} ,\gamma _{2} $ are real numbers, $\left\|\alpha _{i} -1\right\|^{2} +\gamma _{i} ^{2} \ne 0\, \, \left(\alpha _{i} >0;i=1,2\right)$, $\beta _{i} =\frac{1}{\alpha _{i} } \left(i=1,2\right)$ and\ $\delta \left(x\right)=\left\{\begin{array}{l} {\alpha ^{2} ,\, \, \, \, x\in \left(0,\frac{\pi }{2} \right)} \\ {\beta ^{2} ,\, \, \, \, x\in \left(\frac{\pi }{2} ,\pi \right)} \end{array}\right. $ where $0<\alpha <\beta <1$,$\alpha +\beta >1$. The inverse problems consist in recoverint the coefficients of an operator from their spectral characteristics. A lot of study were done the inverse spectral problem for Sturm-Liouville operators and diffusion operators [@Acan; @Gala; @Amirov; @Carlson; @Ergün-1; @F.Yang-1; @Gesztes; @Hryniv; @Huang; @Keldysh; @Levin; @Markus; @Sakhnovich; @Yang; @Yang-1; @Yurko; @alpay; @hald; @hochstadt; @Gala-1; @koyunbakan; @levitan; @ozkan; @wei; @10]. The first results an inverse problems theory of Sturm-Liouville operators where given by Ambarzumyan $\left[2\right]$. The half inverse problems for Sturm-Liouville equations; the known potential in half interval is determined by the help of a one spectrum over the interval. First the obtained results the half inverse problem by Hochstadt and Lieberman [@hochstadt]. They proved that spectrum of the problem $$-y''+q\left(x\right)y=\lambda y,\, \, x\in \left[0,1\right]$$ $$y'\left(0\right)-hy\left(0\right)=0$$ $$y'\left(1\right)+Hy\left(1\right)=0$$ and potential $q\left(x\right)$ on the $\left(\frac{1}{2} ,1\right)$uniquely determine the potential $q\left(x\right)$ on the whole interval $\left[0,1\right]$ almost everywhere. Hald [@hald] proved similar results in the case when there exists a impulsive conditions inside the interval. Many studies have been done by different authours for half invers problems using this methods [@koyunbakan; @Sakhnovich]. In the work [@Sakhnovich] studied the existence of the solution for he half-inverse problem of Sturm-Liouville problems and gave method of reconstructing this solution under same conditions by Sakhnovich $\left[16\right]$. Recently, same new uniqueness results on the inverse or half inverse spectral analysis of differential operators have been given. Koyunbakan and Panakhov [@koyunbakan] proved the half inverse problem for diffusion operator on the finite interval $\left[0,\pi \right]$. Ran Zhang, Xiao-Chuan Xu, Chuan-Fu Yang and Natalia Pavlovna Bondarenko, proved the determination of the impulsive Sturm-Liouville operator from a set of eigenvalues [@10] . Purpose of this study is to prove half inverse problem by using the Hocstadt- Lieberman and Yang-Zettl methods for the following equations $$\label{7)} \tilde{l}\left(y\right):=-y''+\left[2\lambda \tilde{p}\left(x\right)+\tilde{q}\left(x\right)\right]y=\lambda ^{2} \tilde{\delta }\left(x\right)y,\, \, x\in \left[0,\pi \right]/\left\{a_{1} ,a_{2} \right\}$$ $$\label{8)} y'\left(0\right)=0,y\left(\pi \right)=0$$ $$\label{9)} y\left(a_{1} +0\right)=\tilde{\alpha }_{1} y\left(a_{1} -0\right)$$ $$\label{10)} y'\left(a_{1} +0\right)=\tilde{\beta }_{1} y'\left(a_{1} -0\right)+i\lambda \tilde{\gamma }_{1} y\left(a_{1} -0\right)$$ $$\label{11)} y\left(a_{2} +0\right)=\tilde{\alpha }_{2} y\left(a_{2} -0\right)$$ $$\label{12)} y'\left(a_{2} +0\right)=\tilde{\beta }_{2} y'\left(a_{2} -0\right)+i\lambda \tilde{\gamma }_{2} y\left(a_{2} -0\right).$$ \[lem:1\] Let $p\left(x\right)\in W_{2}^{1} \left(0,\pi \right)$ ,$q\left(x\right)\in L_{2} \left(0,\pi \right)$. $M\left(x,t\right)$ ,$N\left(x,t\right)$ are summable functions on $\left[0,\pi \right]$ such that the representation for each $x\in \left[0,\pi \right]/\left\{a_{1} ,a_{2} \right\}$. $\; \varphi \left(x,\lambda \right)$ solution of the equations $\left(1.1\right)$ , providing boundary conditions $\left(1.2\right)$ and discontinuity conditions $\left(1.3\right)-\left(1.6\right)$ $$\varphi \left(x,\lambda \right)=\varphi _{0} \left(x,\lambda \right)+\int _{0}^{x}M\left(x,t\right) \cos \lambda tdt+\int _{0}^{x}N\left(x,t\right) \sin \lambda tdt$$ is satisfied, for $0<x<\frac{\pi }{2} $, $$\label{13)} \begin{array}{l} {\varphi _{0} \left(x,\lambda \right)=} \\ {\left(\beta _{1} ^{+} +\frac{\gamma _{1} }{2\alpha } \right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{1}{\alpha } \int _{a_{1} }^{x}p\left(t\right)dt \right]+\left(\beta _{1} ^{-} -\frac{\gamma _{1} }{2\alpha } \right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{1}{\alpha } \int _{a_{1} }^{x}p\left(t\right)dt \right]} \end{array}$$ for $\frac{\pi }{2} <x\le \pi $, $$\label{14)} \begin{array}{l} {\varphi _{0} \left(x,\lambda \right)=\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]} \\ {+\left(\beta _{2} ^{-} +\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda k^{-} \left(\pi \right)-\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]} \\ {+\left(\beta _{2} ^{-} -\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda s^{+} \left(\pi \right)+\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]} \\ {+\left(\beta _{2} ^{+} -\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda s^{-} \left(\pi \right)+\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]} \end{array}$$ where $\xi ^{\pm } \left(x\right)=\pm \alpha x\mp \alpha a_{1} +a_{1} $ , $k^{\pm } \left(x\right)=\xi ^{+} \left(a_{2} \right)\pm \beta x\mp \beta a_{2} $,\ $s^{\pm } \left(x\right)=\xi ^{-} \left(a_{2} \right)\pm \beta x\mp \beta a_{2} $,$\beta _{1} ^{\mp } =\frac{1}{2} \left(\alpha _{1} \mp \frac{\beta _{1} }{\alpha } \right)$ , $\beta _{2} ^{\mp } =\frac{1}{2} \left(\alpha _{2} \mp \frac{\alpha \beta _{2} }{\beta } \right)$ . Thus, following the relations hold; If $p\left(x\right)\in W_{2}^{2} \left(0,\pi \right),\, q\left(x\right)\in W_{2}^{1} \left(0,\pi \right)$ $$\left\{\begin{array}{l} {\frac{\partial ^{2} M\left(x,t\right)}{\partial x^{2} } -\rho \left(x\right)\frac{\partial ^{2} M\left(x,t\right)}{\partial t^{2} } =2p\left(x\right)\frac{\partial N\left(x,t\right)}{\partial t} +q\left(x\right)M\left(x,t\right)} \\ {\frac{\partial ^{2} N\left(x,t\right)}{\partial x^{2} } -\rho \left(x\right)\frac{\partial ^{2} N\left(x,t\right)}{\partial t^{2} } =-2p\left(x\right)\frac{\partial M\left(x,t\right)}{\partial t} +q\left(x\right)N\left(x,t\right)} \end{array}\right. \,$$ $$M\left(x,\varsigma ^{+} \left(x\right)\right)\cos \frac{\beta \left(x\right)}{\alpha } +N\left(x,\varsigma ^{+} \left(x\right)\right)\sin \frac{\beta \left(x\right)}{\alpha } =\left(\beta _{1} ^{+} +\frac{\gamma _{1} }{2\alpha } \right)\int _{0}^{x}\left(q\left(t\right)+\frac{p^{2} \left(t\right)}{\alpha ^{2} } \right) dt\,$$ $$M\left(x,\varsigma ^{+} \left(x\right)\right)\sin \frac{\beta \left(x\right)}{\alpha } -N\left(x,\varsigma ^{+} \left(x\right)\right)\cos \frac{\beta \left(x\right)}{\alpha } =\left(\beta _{1} ^{+} +\frac{\gamma _{1} }{2\alpha } \right)\left(p\left(x\right)-p\left(0\right)\right)\,$$ $$\begin{array}{l} {M\left(x,k^{+} \left(x\right)+0\right)-M\left(x,k^{+} \left(x\right)-0\right)=} \\ {-\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\left(p\left(x\right)-p\left(0\right)\right)\, \sin \frac{\omega \left(x\right)}{\beta } -\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\int _{0}^{x}\left(q\left(t\right)+\frac{p^{2} \left(t\right)}{\beta ^{2} } \right) dt\, \cos \frac{\omega \left(x\right)}{\beta } } \end{array}$$ $$\begin{array}{l} {N\left(x,k^{+} \left(x\right)+0\right)-N\left(x,k^{+} \left(x\right)-0\right)=} \\ {\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\left(p\left(x\right)-p\left(0\right)\right)\, \cos \frac{\omega \left(x\right)}{\beta } -\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\int _{0}^{x}\left(q\left(t\right)+\frac{p^{2} \left(t\right)}{\beta ^{2} } \right) dt\, \sin \frac{\omega \left(x\right)}{\beta } } \end{array}$$ $$\left. \frac{\partial M\left(x,t\right)}{\partial t} \right\|_{t=0} =N\left(x,0\right)=0$$ where $\beta \left(x\right)=\int _{0}^{x}p\left(t\right)dt $,$\omega \left(x\right)=\int _{a_{2} }^{x}p\left(t\right)dt +\int _{0}^{a_{1} }p\left(t\right)dt $. The proof is done as in [@Ergün-1]. Definition. The function $\Delta \left(\lambda \right)$ is called the characteristic function of the eigenvalues $\left\{\lambda _{n} \right\}$of the problem $\left(1.1\right)-\left(1.6\right)$. $\tilde{\Delta }\left(\lambda \right)$ is called the characteristic function of the eigenvalues $\left\{\tilde{\lambda }_{n} \right\}$of the problem $\left(1.7\right)-\left(1.12\right)$. Let $\lambda =s^{2} ,s=\sigma +i\tau \, ,\, \sigma ,\tau \in {\rm R}$. The solution $\varphi \left(x,\lambda \right)$ of $\left(1.1\right)-\left(1.6\right)$ have the following asymptotic formulas hold on for $\left\|\lambda \right\|\to \infty $, for $0<x<\frac{\pi }{2} $, $$\varphi \left(x,\lambda \right)=\frac{1}{2} \left(\frac{\alpha _{1} }{2} \mp \frac{\beta _{1} }{2\alpha } +\frac{\gamma _{1} }{2\alpha } \right)\exp \left(-i\left(\lambda \xi ^{+} \left(x\right)-\frac{v\left(x\right)}{\alpha } \right)\right)\left(1+O\left(\frac{1}{\lambda } \right)\right)$$ for $\frac{\pi }{2} <x\le \pi $ , $$\varphi \left(x,\lambda \right)=\frac{1}{2} \left(\frac{\alpha _{2} }{2} +\frac{\alpha \beta _{2} }{2\beta } +\frac{\gamma _{2} }{2\beta } \right)\exp \left(-i\left(\lambda k^{+} \left(x\right)-\frac{t\left(x\right)}{\beta } \right)\right)\left(1+O\left(\frac{1}{\lambda } \right)\right).$$ where $v\left(x\right)=\int _{a_{1} }^{x}p\left(t\right)dt $, $t\left(x\right)=\int _{a_{2} }^{x}p\left(t\right)dt $. In this study, if $q\left(x\right)$ and $p\left(x\right)$ to be known almost everywhere $\left(\frac{\pi }{2} ,\pi \right)$, sufficient to determine uniquely $p\left(x\right)$ and $q\left(x\right)$ whole interval $\left(0,\pi \right)$ . main result =========== If $\varphi_{0} \left(x,\lambda \right)$ a nontrivial solution of equation $\left(1.1\right)$ with conditions $\left(1.2\right)$-$\left(1.6\right)$, then $\lambda _{0} $ is called eigenvalue. Additionally, $\varphi_{0} \left(x,\lambda \right)$ is called the eigenfunction of the problem corresponding to the eigenvalue $\lambda _{0} $. $\left\{\lambda _{n} \right\}$ are eigenvalues of the problem. \[lem:1\] If $\lambda _{n} =\tilde{\lambda }_{n} $, $\frac{\alpha }{\tilde{\alpha }} =\frac{\beta }{\tilde{\beta }} $ then $\alpha =\tilde{\alpha }$ and $\beta =\tilde{\beta }$ for all $n\in {\rm N}$. Since $\lambda _{n} =\tilde{\lambda }_{n} $ and $\Delta \left(\lambda \right),\, \tilde{\Delta }\left(\lambda \right)$are entire functions in $\lambda $ of order one by Hadamard factorization theorem for $\lambda \in {\rm C}$ $$\Delta \left(\lambda \right)\equiv C\, \tilde{\Delta }\left(\lambda \right)$$ On the other hand, $\left(1.1\right)$ can be written as $$\Delta _{0} \left(\lambda \right)-C\, \tilde{\Delta }_{0} \left(\lambda \right)=C\left[\tilde{\Delta }\left(\lambda \right)-\, \tilde{\Delta }_{0} \left(\lambda \right)\right]-\left[\Delta \left(\lambda \right)-\, \Delta _{0} \left(\lambda \right)\right]$$ Hence $$\label{15)} \begin{array}{l} {C\left[\tilde{\Delta }\left(\lambda \right)-\, \tilde{\Delta }_{0} \left(\lambda \right)\right]-\left[\Delta \left(\lambda \right)-\, \Delta _{0} \left(\lambda \right)\right]=} \\ {\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right]+\left(\beta _{2} ^{-} +\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda k^{-} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right]} \\ {+\left(\beta _{2} ^{-} -\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda s^{+} \left(\pi \right)+\frac{w\left(\pi \right)}{\beta } \right]+\left(\beta _{2} ^{+} -\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda s^{-} \left(\pi \right)+\frac{w\left(\pi \right)}{\beta } \right]} \\ {-C\left(\tilde{\beta }_{2} ^{+} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]-C\left(\tilde{\beta }_{2} ^{-} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda k^{-} \left(\pi \right)-\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]} \\ {-C\left(\tilde{\beta }_{2} ^{-} -\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda s^{+} \left(\pi \right)+\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]-C\left(\tilde{\beta }_{2} ^{+} -\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda s^{-} \left(\pi \right)+\frac{\tilde{w}\left(\pi \right)}{\beta } \right]} \end{array}$$ If we multiply both sides of $\left(2.1\right)$ by $\cos \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right]$ and integrate with respect to $\lambda $ in $\left(\varepsilon ,T\right)$, ($\varepsilon $ is sufficiently small positive number) for any positive real number $T$, then we get $$\begin{array}{l} {\int _{\varepsilon }^{T}\left(C\left[\tilde{\Delta }\left(\lambda \right)-\, \tilde{\Delta }_{0} \left(\lambda \right)\right]-\left[\Delta \left(\lambda \right)-\, \Delta _{0} \left(\lambda \right)\right]\right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right] d\lambda =} \\ {+\int _{\varepsilon }^{T}\left\{\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right]+\left(\beta _{2} ^{-} +\frac{\gamma _{2} }{2\beta } \right)\cos \right. \left[\lambda k^{-} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right] } \\ {+\left(\beta _{2} ^{-} -\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda s^{+} \left(\pi \right)+\frac{w\left(\pi \right)}{\beta } \right]+\left(\beta _{2} ^{+} -\frac{\gamma _{2} }{2\beta } \right)\cos \left[\lambda s^{-} \left(\pi \right)+\frac{w\left(\pi \right)}{\beta } \right]} \\ {-C\left(\tilde{\beta }_{2} ^{+} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]-C\left(\tilde{\beta }_{2} ^{-} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda k^{-} \left(\pi \right)-\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]} \\ {\left. -C\left(\tilde{\beta }_{2} ^{-} -\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda s^{+} \left(\pi \right)+\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]-C\left(\tilde{\beta }_{2} ^{+} -\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda s^{-} \left(\pi \right)+\frac{\tilde{w}\left(\pi \right)}{\beta } \right]\right\}d\lambda } \end{array}$$ And so $$\begin{array}{l} {\int _{\varepsilon }^{T}\left(C\left[\tilde{\Delta }\left(\lambda \right)-\, \tilde{\Delta }_{0} \left(\lambda \right)\right]-\left[\Delta \left(\lambda \right)-\, \Delta _{0} \left(\lambda \right)\right]\right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right] d\lambda =} \\ {\int _{\varepsilon }^{T}\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\cos ^{2} \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right] d\lambda } \\ {-C\int _{\varepsilon }^{T}\left(\tilde{\beta }_{2} ^{+} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right]\cos \left[\lambda k^{+} \left(\pi \right)-\frac{\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right] d\lambda } \end{array}$$ $$\begin{array}{l} {=\int _{\varepsilon }^{T}\frac{1}{2} \left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)+\frac{1}{2} \left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)\cos \left[2\lambda k^{+} \left(\pi \right)-\frac{2w\left(\pi \right)}{\beta } \right] d\lambda } \\ {-C\int _{\varepsilon }^{T}\frac{1}{2} \left(\tilde{\beta }_{2} ^{+} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)\left(\cos \left[2\lambda k^{+} \left(\pi \right)-\frac{\tilde{w}\left(\pi \right)+w\left(\pi \right)}{\beta } \right]+\cos \left[\frac{w\left(\pi \right)-\tilde{w}\left(\pi \right)}{\tilde{\beta }} \right]\right) d\lambda } \end{array}$$ $\Delta \left(\lambda \right)-\Delta _{0} \left(\lambda \right)=O\left(\frac{1}{\left\|\lambda \right\|} e^{\left\|Im\lambda \right\|k^{+} \left(\pi \right)} \right)$, $\tilde{\Delta }\left(\lambda \right)-\tilde{\Delta }_{0} \left(\lambda \right)=O\left(\frac{1}{\left\|\lambda \right\|} e^{\left\|Im\lambda \right\|k^{+} \left(\pi \right)} \right)$ for all $\lambda $ in $\left(\varepsilon ,T\right)$. $$\frac{C}{2} \left(\tilde{\beta }_{2} ^{+} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} \right)-\frac{1}{2} \left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)=O\left(\frac{1}{T} \right)$$ By letting $T$ tend to infinity we see that $$C=\frac{\tilde{\beta }_{2} ^{+} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} }{\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } }$$ Similarly, if we multiply both side of $\left(2.1\right)$ $\cos \left[\lambda k^{-} \left(\pi \right)-\frac{w\left(\pi \right)}{\beta } \right]$ and integrate again with respect to $\lambda $ in $\left(\varepsilon ,T\right)$ and by letting $T$ tend to infinity, then we get $$C=\frac{\tilde{\beta }_{2} ^{-} +\frac{\tilde{\gamma }_{2} }{2\tilde{\beta }} }{\beta _{2} ^{-} +\frac{\gamma _{2} }{2\beta } }$$ But since $\alpha ,\beta $ and $\tilde{\alpha },\tilde{\beta }$ are positive, since $w^{+} \left(\pi \right)-\tilde{w}^{+} \left(\pi \right)=w^{-} \left(\pi \right)-\tilde{w}^{-} \left(\pi \right)$ we conclude that $C=1$. Hence $\frac{\tilde{\beta }_{2} ^{+} }{\beta _{2} ^{+} } =\frac{\tilde{\beta }_{2} ^{-} }{\beta _{2} ^{-} } $ is obtained. We have therefore proved since $\alpha =\tilde{\alpha }$ that $\beta =\tilde{\beta }$. The proof is completed. \[lem:1\]If $\lambda _{n} =\tilde{\lambda }_{n} $ then $\alpha _{i} =\tilde{\alpha }_{i} $ and $\gamma _{i} =\tilde{\gamma }_{i} $ $\left(i=1,2\right)$for all $n\in {\rm N}$. The proof is done as in [@Ergün-1]. \[1\] Let $\left\{\lambda _{n} \right\}$ a eigenvalues of both problem $\left(1.1\right)-\left(1.6\right)$ and $\left(1.7\right)-\left(1.12\right)$. If $p\left(x\right)=\tilde{p}\left(x\right)$ and $q\left(x\right)=\tilde{q}\left(x\right)$ on $\left[\frac{\pi }{2} ,\pi \right]$ , then $p\left(x\right)=\tilde{p}\left(x\right)$ and $q\left(x\right)=\tilde{q}\left(x\right)$ almost everywhere on $\left[0,\pi \right]$. Let function $\varphi \left(x,\lambda \right)$ the solution of equation $\left(1.1\right)$ under the conditions $\left(1.2\right)-\left(1.6\right)$ and the function $\tilde{\varphi }\left(x,\lambda \right)$ the solution of equation $\left(1.7\right)$ under the conditions $\left(1.8\right)-\left(1.12\right)$in $\left[0,\frac{\pi }{2} \right]$. The integral forms of the functions $\varphi \left(x,\lambda \right)$ and $\tilde{\varphi }\left(x,\lambda \right)$ can be obtained as follows $$\label{16)} \begin{array}{l} {\varphi \left(x,\lambda \right)=\left(\beta _{1} ^{+} +\frac{\gamma _{1} }{2\alpha } \right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{1}{\alpha } \int _{a_{1} }^{x}p\left(t\right)dt \right]} \\ {+\left(\beta _{1} ^{-} -\frac{\gamma _{1} }{2\alpha } \right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{1}{\alpha } \int _{a_{1} }^{x}p\left(t\right)dt \right]+\int _{0}^{x}M\left(x,t\right)\cos \lambda tdt +\int _{0}^{x}N\left(x,t\right)\sin \lambda tdt } \end{array}$$ and $$\label{17)} \begin{array}{l} {\tilde{\varphi }\left(x,\lambda \right)=\left(\tilde{\beta }_{1} ^{+} +\frac{\tilde{\gamma }_{1} }{2\alpha } \right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{1}{\alpha } \int _{a_{1} }^{x}\tilde{p}\left(t\right)dt \right]} \\ {+\left(\tilde{\beta }_{1} ^{-} -\frac{\tilde{\gamma }_{1} }{2\alpha } \right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{1}{\alpha } \int _{a_{1} }^{x}\tilde{p}\left(t\right)dt \right]+\int _{0}^{x}\tilde{M}\left(x,t\right)\cos \lambda tdt +\int _{0}^{x}\tilde{N}\left(x,t\right)\sin \lambda tdt } \end{array}$$ If we multiply equations $\left(2.2\right)$ and $\left(2.3\right)$\ $\begin{array}{l} {\varphi \left(x,\lambda \right)\cdot \tilde{\varphi }\left(x,\lambda \right)=\frac{S^{+} \tilde{S}^{+} }{2} \left[\cos \left(2\lambda \xi ^{+} \left(x\right)-K\left(x\right)\right)+\cos L\left(x\right)\right]} \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \left[\cos \left(2\lambda a_{1} t-L\left(x\right)\right)+\cos \left(2\lambda \alpha \left(x-a_{1} \right)-K\left(x\right)\right)\right]} \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \left[\cos \left(2\lambda a_{1} +L\left(x\right)\right)+\cos \left(2\lambda \alpha \left(x-a_{1} \right)+K\left(x\right)\right)\right]} \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \left[\cos \left(2\lambda \xi ^{-} \left(x\right)+L\left(x\right)\right)+\cos K\left(x\right)\right]} \\ {+S^{+} \int _{0}^{x}\tilde{M}\left(x,t\right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{t\left(x\right)}{\alpha } \right] \cos \lambda tdt} \\ {+S^{+} \int _{0}^{x}\tilde{N}\left(x,t\right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{t\left(x\right)}{\alpha } \right] \sin \lambda tdt} \\ {+S^{-} \int _{0}^{x}\tilde{M}\left(x,t\right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{t\left(x\right)}{\alpha } \right] \cos \lambda tdt} \\ {+S^{-} \int _{0}^{x}\tilde{N}\left(x,t\right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{t\left(x\right)}{\alpha } \right] \sin \lambda tdt} \\ {+\tilde{S}^{+} \int _{0}^{x}M\left(x,t\right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right] \cos \lambda tdt} \\ {+\tilde{S}^{+} \int _{0}^{x}N\left(x,t\right)\cos \left[\lambda \xi ^{+} \left(x\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right] \sin \lambda tdt} \\ {+\tilde{S}^{-} \int _{0}^{x}M\left(x,t\right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{\tilde{t}\left(x\right)}{\alpha } \right] \cos \lambda tdt} \\ {+\tilde{S}^{-} \int _{0}^{x}N\left(x,t\right)\cos \left[\lambda \xi ^{-} \left(x\right)+\frac{\tilde{t}\left(x\right)}{\alpha } \right] \sin \lambda tdt} \\ {+\left(\int _{0}^{x}M\left(x,t\right)\cos \lambda tdt \right)\left(\int _{0}^{x}\tilde{M}\left(x,t\right)\cos \lambda tdt \right)} \\ {+\left(\int _{0}^{x}N\left(x,t\right)\sin \lambda tdt \right)\left(\int _{0}^{x}\tilde{N}\left(x,t\right)\sin \lambda tdt \right)} \\ {+\left(\int _{0}^{x}M\left(x,t\right)\cos \lambda tdt \right)\left(\int _{0}^{x}\tilde{N}\left(x,t\right)\sin \lambda tdt \right)} \\ {+\left(\int _{0}^{x}\tilde{M}\left(x,t\right)\cos \lambda tdt \right)\left(\int _{0}^{x}N\left(x,t\right)\sin \lambda tdt \right)} \end{array}$ $$\label{18)} \begin{array}{l} {\varphi \left(x,\lambda \right)\cdot \tilde{\varphi }\left(x,\lambda \right)=\frac{S^{+} \tilde{S}^{+} }{2} \left[\cos \left(2\lambda \xi ^{+} \left(x\right)-K\left(x\right)\right)+\cos L\left(x\right)\right]} \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \left[\cos \left(2\lambda a_{1} t-L\left(x\right)\right)+\cos \left(2\lambda \alpha \left(x-a_{1} \right)-K\left(x\right)\right)\right]} \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \left[\cos \left(2\lambda a_{1} +L\left(x\right)\right)+\cos \left(2\lambda \alpha \left(x-a_{1} \right)+K\left(x\right)\right)\right]} \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \left[\cos \left(2\lambda \xi ^{-} \left(x\right)+L\left(x\right)\right)+\cos K\left(x\right)\right]} \\ {+\frac{1}{2} \left\{\int _{0}^{x}U_{c} \left(x,t\right)\cos \left(2\lambda t-K\left(t\right)\right)dt -\int _{0}^{x}U_{s} \left(x,t\right)\sin \left(2\lambda t-K\left(t\right)\right)dt \right\}} \end{array}$$ is obtained, being $S^{\pm } =\left(\beta _{1} ^{\pm } \mp \frac{\gamma _{1} }{2\alpha } \right)$, $\tilde{S}^{\pm } =\left(\tilde{\beta }_{1} ^{\pm } \mp \frac{\tilde{\gamma }_{1} }{2\alpha } \right)$, $K\left(x\right)=\frac{t\left(x\right)+\tilde{t}\left(x\right)}{2} $, $L\left(x\right)=\frac{t\left(x\right)-\tilde{t}\left(x\right)}{2} $,\ $\begin{array}{l} {U_{c} \left(x,t\right)=S^{+} \tilde{M}\left(x,\xi ^{+} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {+S^{-} \tilde{M}\left(x,\xi ^{-} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {+\tilde{S}^{+} M\left(x,\xi ^{+} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {+\tilde{S}^{-} M\left(x,\xi ^{-} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {-S^{-} \tilde{N}\left(x,\xi ^{+} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {-S^{-} \tilde{N}\left(x,\xi ^{-} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {-\tilde{S}^{+} N\left(x,\xi ^{+} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {-\tilde{S}^{-} N\left(x,\xi ^{-} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {+K_{1} \left(x,t\right)\cos K\left(t\right)+K_{2} \left(x,t\right)\cos K\left(t\right)} \\ {+M_{1} \left(x,t\right)\sin K\left(t\right)+M_{2} \left(x,t\right)\sin K\left(t\right)} \end{array}$\ $\begin{array}{l} {U_{s} \left(x,t\right)=S^{+} \tilde{M}\left(x,\xi ^{+} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {+S^{-} \tilde{M}\left(x,\xi ^{-} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {+\tilde{S}^{+} M\left(x,\xi ^{+} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {+\tilde{S}^{-} M\left(x,\xi ^{-} \left(x\right)-2t\right)\sin \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {+S^{+} \tilde{N}\left(x,\xi ^{+} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {+S^{-} \tilde{N}\left(x,\xi ^{-} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{t\left(x\right)}{\alpha } \right)} \\ {+\tilde{S}^{+} N\left(x,\xi ^{+} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {+\tilde{S}^{-} N\left(x,\xi ^{-} \left(x\right)-2t\right)\cos \left(K\left(t\right)-\frac{\tilde{t}\left(x\right)}{\alpha } \right)} \\ {+K_{1} \left(x,t\right)\sin K\left(t\right)+K_{2} \left(x,t\right)\sin K\left(t\right)} \\ {-M_{1} \left(x,t\right)\cos K\left(t\right)-M_{2} \left(x,t\right)\cos K\left(t\right)} \end{array}$ $$K_{1} \left(x,t\right)=\int _{-x}^{x-2t}M\left(x,s\right)\tilde{M}\left(x,s+2t\right) ds+\int _{2t-x}^{x}M\left(x,s\right)\tilde{M}\left(x,s+2t\right) ds$$ $$K_{2} \left(x,t\right)=\int _{-x}^{x-2t}N\left(x,s\right)\tilde{N}\left(x,s+2t\right) ds+\int _{2t-x}^{x}n\left(x,s\right)\tilde{N}\left(x,s+2t\right) ds$$ $$M_{1} \left(x,t\right)=\int _{-x}^{x-2t}M\left(x,s\right)\tilde{N}\left(x,s+2t\right) ds-\int _{2t-x}^{x}M\left(x,s\right)\tilde{N}\left(x,s+2t\right) ds$$ $$M_{2} \left(x,t\right)=-\int _{-x}^{x-2t}N\left(x,s\right)\tilde{M}\left(x,s+2t\right) ds+\int _{2t-x}^{x}N\left(x,s\right)\tilde{M}\left(x,s+2t\right) ds$$ Let $\varphi \left(x,\lambda \right)$ and $\tilde{\varphi }\left(x,\lambda \right)$ are substituted into $\left(1.1\right)$ and $\left(1.7\right)$, $$\label{19)} -\varphi ''\left(x,\lambda \right)+\left(2\lambda p\left(x\right)+q\left(x\right)\right)\varphi \left(x,\lambda \right)=\lambda ^{2} \rho \left(x\right)\varphi \left(x,\lambda \right)$$ $$\label{20)} -\tilde{\varphi }''\left(x,\lambda \right)+\left(2\lambda p\left(x\right)+q\left(x\right)\right)\tilde{\varphi }\left(x,\lambda \right)=\lambda ^{2} \rho \left(x\right)\tilde{\varphi }\left(x,\lambda \right)$$ The following equations is obtained $\left(2.5\right)$ and $\left(2.6\right)$\ $\begin{array}{l} {\int _{0}^{\frac{\pi }{2} }\varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)\left[2\lambda \left(p\left(x\right)-\tilde{p}\left(x\right)\right)+\left(q\left(x\right)-\tilde{q}\left(x\right)\right)\right] dx} \\ {=\left[\tilde{\varphi }'\left(x,\lambda \right)\varphi \left(x,\lambda \right)-\varphi '\left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)\right]_{0}^{\frac{\pi }{2} } +\left. \right\|_{\frac{\pi }{2} }^{\pi } } \end{array}$ $$\label{21)} \begin{array}{l} {\int _{0}^{\frac{\pi }{2} }\varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)\left[2\lambda \left(p\left(x\right)-\tilde{p}\left(x\right)\right)+\left(q\left(x\right)-\tilde{q}\left(x\right)\right)\right] dx} \\ {+\tilde{\varphi }'\left(\pi ,\lambda \right)\varphi \left(\pi ,\lambda \right)-\varphi '\left(\pi ,\lambda \right)\tilde{\varphi }\left(\pi ,\lambda \right)=0} \end{array}$$ Let $Q\left(x\right)=q\left(x\right)-\tilde{q}\left(x\right)$ and $P\left(x\right)=p\left(x\right)-\tilde{p}\left(x\right)$ $$U\left(\lambda \right)=\int _{0}^{\frac{\pi }{2} }\left[2\lambda P\left(x\right)+Q\left(x\right)\right] \varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)dx$$ It is obvious that the functions $\varphi \left(x,\lambda \right)$ and $\tilde{\varphi }\left(x,\lambda \right)$are the solutions which satisfy boundary value conditions of $\left(1.2\right)$ and $\left(1.8\right)$, recpectively, then if we consider this facts in equation $\left(2.7\right)$, we obtain the following equation $$\label{22)} U\left(\lambda _{n} \right)=0$$ for each eigenvalue $\lambda _{n} $. Let us marked $$U_{1} \left(\lambda \right)=\int _{0}^{\frac{\pi }{2} }P\left(x\right) \varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)dx, U_{2} \left(\lambda \right)=\int _{0}^{\frac{\pi }{2} }Q\left(x\right) \varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)dx$$ Then equations $\left(2.7\right)$ can be rewritten as $$2\lambda _{n} U_{1} \left(\lambda _{n} \right)+U_{2} \left(\lambda _{n} \right)=0.$$ From $\left(2.4\right)$ ve $\left(2.7\right)$ we obtain $$\label{23)} \left\|U\left(\lambda \right)\right\|\le \left(C_{1} +C_{2} \left\|\lambda \right\|\right)\exp \left(\tau \pi \right)$$ $C_{1} ,C_{2} >0$ are constants. For all complex $\lambda $. Because $\lambda _{n} =\tilde{\lambda }_{n} $, $\Delta \left(\lambda \right)=\varphi \left(\pi ,\lambda \right)=\tilde{\varphi }\left(\pi ,\lambda \right)$. Thus, $$U\left(\lambda \right)=\int _{0}^{\frac{\pi }{2} }\left[2\lambda P\left(x\right)+Q\left(x\right)\right] \varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)dx=\Delta \left(\lambda \right)\left[\varphi \left(\pi ,\lambda \right)-\tilde{\varphi }\left(\pi ,\lambda \right)\right] .$$ The function $\phi \left(\lambda \right)=\frac{U\left(\lambda \right)}{\Delta \left(\lambda \right)} $ is an entire function with respect to $\lambda $. It follows from $\Delta \left(\lambda \right)\ge \left(\left\|\lambda \beta \right\|-C\right)\exp \left(\tau \xi ^{+} \left(x\right)\right)$ and $\left(2.9\right)$, $\phi \left(\lambda \right)=O\left(1\right)$ for sufficient large $\left\|\lambda \right\|$. We obtain $\phi \left(\lambda \right)=C$, for all $\lambda $ by Liouville’s Theorem.\ $U\left(\lambda \right)=C\Delta \left(\lambda \right)$\ $\begin{array}{l} {\int _{0}^{\frac{\pi }{2} }\varphi \left(x,\lambda \right)\tilde{\varphi }\left(x,\lambda \right)\left[2\lambda P\left(x\right)+Q\left(x\right)\right] dx=} \\ {=C\left[\left(\beta _{2} ^{+} +\frac{\gamma _{2} }{2\beta } \right)R_{1} \left(a_{2} \right)\cos \left[\lambda k^{+} \left(\pi \right)-\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]\right. } \\ {+\left(\beta _{2} ^{-} +\frac{\gamma _{2} }{2\beta } \right)R_{2} \left(a_{2} \right)\cos \left[\lambda k^{-} \left(\pi \right)-\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]} \\ {+\left(\beta _{2} ^{-} -\frac{\gamma _{2} }{2\beta } \right)R_{1} \left(a_{2} \right)\cos \left[\lambda s^{+} \left(\pi \right)+\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]} \\ {\left. +\left(\beta _{2} ^{+} -\frac{\gamma _{2} }{2\beta } \right)R_{2} \left(a_{2} \right)\cos \left[\lambda s^{-} \left(\pi \right)+\frac{1}{\beta } \int _{a_{2} }^{\pi }p\left(t\right)dt \right]\right]+O\left(\exp \left(\tau k^{+} \left(\pi \right)\right)\right)} \end{array}$\ By the Riemann-Lebesgue lemma, for $\lambda \to \infty $ , $\lambda \in {\rm R}$ we get $C=0$. Then,\ $\begin{array}{l} {2U_{1} \left(\lambda \right)=S^{+} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos \left(2\lambda \xi ^{+} \left(x\right)-K\left(x\right)\right)dx } \\ {+S^{+} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos L\left(x\right) dx} \\ {+S^{+} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos \left(2\lambda a_{1} t-L\left(x\right)\right)dx } \\ {+S^{+} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos \left(2\lambda \alpha \left(x-a_{1} \right)-K\left(x\right)\right)dx } \\ {+S^{-} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos \left(2\lambda a_{1} +L\left(x\right)\right)dx } \\ {+S^{-} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos \cos \left(2\lambda \alpha \left(x-a_{1} \right)+K\left(x\right)\right)dx } \\ {+S^{-} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos \left(2\lambda \xi ^{-} \left(x\right)+L\left(x\right)\right)dx } \\ {+S^{-} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos K\left(x\right)dx } \\ {+\int _{0}^{\frac{\pi }{2} }P\left(x\right)\left(\int _{0}^{x}U_{c} \left(x,t\right)\cos \left(2\lambda t-K\left(t\right)\right)dt \right) dx} \\ {-\int _{0}^{\frac{\pi }{2} }P\left(x\right)\left(\int _{0}^{x}U_{s} \left(x,t\right)\sin \left(2\lambda t-K\left(t\right)\right)dt \right) dx.} \end{array}$\ where $\xi ^{\pm } \left(x\right)=\pm \alpha x\mp \alpha a_{1} +a_{1} $ , $k^{\pm } \left(x\right)=\mu ^{+} \left(a_{2} \right)\pm \beta x\mp \beta a_{2} $,\ $s^{\pm } \left(x\right)=\mu ^{-} \left(a_{2} \right)\pm \beta x\mp \beta a_{2} ,\beta _{1} ^{\mp } =\frac{1}{2} \left(\alpha _{1} \mp \frac{\beta _{1} }{\alpha } \right) , \beta _{2} ^{\mp } =\frac{1}{2} \left(\alpha _{2} \mp \frac{\alpha \beta _{2} }{\beta } \right) .$\ $\begin{array}{l} {2U_{1} \left(\lambda \right)=\frac{S^{+} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{-i\left(K\left(t\right)\right)} e^{i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt +\frac{S^{+} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{i\left(K\left(t\right)\right)} e^{-i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt } \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{-i\left(L\left(t\right)\right)} e^{i\left(2\lambda a_{1} t\right)} dt +\frac{S^{+} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{i\left(L\left(t\right)\right)} e^{-i\left(2\lambda a_{1} t\right)} dt } \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{-i\left(K\left(t\right)\right)} e^{i\left(2\lambda \alpha \left(t-a_{1} \right)\right)} dt ++\frac{S^{+} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{i\left(K\left(t\right)\right)} e^{-i\left(2\lambda \alpha \left(t-a_{1} \right)\right)} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{i\left(L\left(t\right)\right)} e^{i\left(2\lambda a_{1} t\right)} dt +\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{-i\left(L\left(t\right)\right)} e^{i\left(2\lambda a_{1} t\right)} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{i\left(K\left(t\right)\right)} e^{i\left(2\lambda \alpha \left(t-a_{1} \right)\right)} dt +\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{-i\left(K\left(t\right)\right)} e^{i\left(2\lambda \alpha \left(t-a_{1} \right)\right)} dt } \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{i\left(L\left(t\right)\right)} e^{-i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt +\frac{S^{-} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }P\left(t\right)e^{-i\left(L\left(t\right)\right)} e^{i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt } \\ {+S^{+} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos L\left(x\right) dx+S^{-} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos K\left(x\right)dx } \\ {+\int _{0}^{\frac{\pi }{2} }P\left(x\right)\left(\int _{0}^{x}U_{c} \left(x,t\right)\cos \left(2\lambda t-K\left(t\right)\right)dt \right) dx} \\ {-\int _{0}^{\frac{\pi }{2} }P\left(x\right)\left(\int _{0}^{x}U_{s} \left(x,t\right)\sin \left(2\lambda t-K\left(t\right)\right)dt \right) dx} \end{array}$ if necessary operations are performed and integrals are calculated\ $\begin{array}{l} {2U_{1} \left(\lambda \right)=\frac{S^{+} \tilde{S}^{+} }{2} \left[\frac{T_{1} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{i\left(2\lambda \xi ^{+} \left(\frac{\pi }{2} \right)\right)} -\frac{T_{1} \left(0\right)}{2i\lambda \alpha } e^{2i\lambda \left(\alpha a_{1} +a_{1} \right)} -\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{1} ^{{'} } \left(t\right)e^{i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt \right]} \\ {+\frac{S^{+} \tilde{S}^{+} }{2} \left[-\frac{T_{2} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{-i\left(2\lambda \xi ^{+} \left(\frac{\pi }{2} \right)\right)} +\frac{T_{2} \left(0\right)}{2i\lambda \alpha } e^{-2i\lambda \left(\alpha a_{1} +a_{1} \right)} +\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{2} ^{{'} } \left(t\right)e^{-i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt \right]} \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \left[\frac{T_{3} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{i\lambda a_{1} } -\frac{T_{3} \left(0\right)}{2i\lambda \alpha } -\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{3} ^{{'} } \left(t\right)e^{2ia_{1} t} dt \right]} \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \left[-\frac{T_{4} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{i\lambda a_{1} } +\frac{T_{4} \left(0\right)}{2i\lambda \alpha } +\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{4} ^{{'} } \left(t\right)e^{-2ia_{1} t} dt \right]} \\ {+\frac{S^{+} S^{-} }{2} \left[\frac{T_{1} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{2i\lambda \alpha \left(\frac{\pi }{2} -a_{1} \right)} -\frac{T_{1} \left(0\right)}{2i\lambda \alpha } e^{-2i\lambda \alpha a_{1} } -\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{1} ^{{'} } \left(t\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt \right]} \\ {+\frac{S^{+} S^{-} }{2} \left[-\frac{T_{2} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{-2i\lambda \alpha \left(\frac{\pi }{2} -a_{1} \right)} +\frac{T_{2} \left(0\right)}{2i\lambda \alpha } e^{2i\lambda \alpha a_{1} } +\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{2} ^{{'} } \left(t\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt \right]} \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \left[-\frac{T_{3} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{-i\lambda a_{1} \pi } +\frac{T_{3} \left(0\right)}{2i\lambda \alpha } +\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{3} ^{{'} } \left(t\right)e^{-2ia_{1} t} dt \right]} \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \left[\frac{T_{4} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{i\lambda a_{1} \pi } -\frac{T_{4} \left(0\right)}{2i\lambda \alpha } -\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{4} ^{{'} } \left(t\right)e^{2ia_{1} t} dt \right]} \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \left[-\frac{T_{1} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{-2i\lambda \alpha \left(\frac{\pi }{2} -a_{1} \right)} +\frac{T_{1} \left(0\right)}{2i\lambda \alpha } e^{2i\lambda \alpha a_{1} } +\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{1} ^{{'} } \left(t\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt \right]} \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \left[\frac{T_{2} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{2i\lambda \alpha \left(\frac{\pi }{2} -a_{1} \right)} -\frac{T_{2} \left(0\right)}{2i\lambda \alpha } e^{-2i\lambda \alpha a_{1} } -\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{2} ^{{'} } \left(t\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt \right]} \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \left[-\frac{T_{4} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{i\left(2\lambda \xi ^{-} \left(\frac{\pi }{2} \right)\right)} +\frac{T_{4} \left(0\right)}{2i\lambda \alpha } e^{2i\lambda \left(\alpha a_{1} +a_{1} \right)} +\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{4} ^{{'} } \left(t\right)e^{i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt \right]} \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \left[\frac{T_{3} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda \alpha } e^{-i\left(2\lambda \xi ^{-} \left(\frac{\pi }{2} \right)\right)} -\frac{T_{3} \left(0\right)}{2i\lambda \alpha } e^{2i\lambda \left(\alpha a_{1} -a_{1} \right)} -\frac{1}{2i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{3} ^{{'} } \left(t\right)e^{-i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt \right]} \\ {+S^{+} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos L\left(x\right) dx+S^{-} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos K\left(x\right)dx } \\ {+\left[\frac{T_{5} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda } e^{i\pi \lambda } -\frac{T_{5} \left(0\right)}{2i\lambda } -\frac{1}{2i\lambda } \int _{0}^{\frac{\pi }{2} }T'_{1} \left(t\right)e^{2i\lambda t} dt \right]} \\ {+\left[-\frac{T_{6} \left({\raise0.7ex\hbox{$ \pi $}\!\mathord{\left/ {\vphantom {\pi 2}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 2 $}} \right)}{2i\lambda } e^{-i\pi \lambda } +\frac{T_{6} \left(0\right)}{2i\lambda } +\frac{1}{2i\lambda } \int _{0}^{\frac{\pi }{2} }T'_{6} \left(t\right)e^{-2i\lambda t} dt \right]} \end{array}$ where $T_{1} \left(t\right)=P\left(t\right)e^{-i\left(K\left(t\right)\right)} $, $T_{2} \left(t\right)=P\left(t\right)e^{i\left(K\left(t\right)\right)} $, $T_{3} \left(t\right)=P\left(t\right)e^{-i\left(L\left(t\right)\right)} $, $T_{4} \left(t\right)=P\left(t\right)e^{i\left(L\left(t\right)\right)} $, $P_{1} \left(t\right)=\int _{t}^{\frac{\pi }{2} }P\left(x\right)U_{c} \left(x,t\right) dx, P_{2} \left(t\right)=\int _{t}^{\frac{\pi }{2} }P\left(x\right)U_{s} \left(x,t\right) dx$\ $ , T_{5} \left(t\right)=\frac{P_{1} \left(t\right)+iP_{2} \left(t\right)}{2} e^{-iK\left(t\right)} ,T_{6} \left(t\right)=\frac{P_{1} \left(t\right)-iP_{2} \left(t\right)}{2} e^{iK\left(t\right)} $ By the Riemann-Lebesgue lemma $\int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos L\left(x\right) dx=0\, \, ,\, \,\\ \int _{0}^{\frac{\pi }{2} }P\left(x\right)\cos K\left(x\right)dx =0$ and $P\left(\frac{\pi }{2} \right)=0$ for $\lambda \to \infty $.\ Thus, $$\label{24)} \begin{array}{l} {2U_{1} \left(\lambda \right)=-\frac{S^{+} \tilde{S}^{+} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{1} ^{{'} } \left(t\right)e^{i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt +\frac{S^{+} \tilde{S}^{+} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{2} ^{{'} } \left(t\right)e^{-i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt } \\ {-\frac{S^{+} \tilde{S}^{-} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{3} ^{{'} } \left(t\right)e^{2ia_{1} t} dt +\frac{S^{+} \tilde{S}^{-} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{4} ^{{'} } \left(t\right)e^{-2ia_{1} t} dt } \\ {-\frac{S^{+} S^{-} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{1} ^{{'} } \left(t\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt +\frac{S^{+} S^{-} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{2} ^{{'} } \left(t\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{3} ^{{'} } \left(t\right)e^{-2ia_{1} t} dt -\frac{S^{-} \tilde{S}^{+} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{4} ^{{'} } \left(t\right)e^{2ia_{1} t} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{1} ^{{'} } \left(t\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt +\frac{S^{-} \tilde{S}^{+} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{2} ^{{'} } \left(t\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt } \\ {+\frac{S^{-} \tilde{S}^{-} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{4} ^{{'} } \left(t\right)e^{i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt -\frac{S^{-} \tilde{S}^{-} }{4i\lambda \alpha } \int _{0}^{\frac{\pi }{2} }T_{3} ^{{'} } \left(t\right)e^{-i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt } \\ {+\frac{i}{2\lambda } \int _{0}^{\frac{\pi }{2} }T'_{5} \left(t\right)e^{2i\lambda t} dt -\frac{i}{2\lambda } \int _{0}^{\frac{\pi }{2} }T'_{6} \left(t\right)e^{-2i\lambda t} dt } \end{array}$$ $\begin{array}{l} {2U_{2} \left(\lambda \right)=S^{+} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\frac{e^{i\left(2\lambda \xi ^{+} \left(x\right)-K\left(x\right)\right)} +e^{-i\left(2\lambda \xi ^{+} \left(x\right)-K\left(x\right)\right)} }{2} \right)dx } \\ {+S^{+} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\frac{e^{i\left(2\lambda a_{1} t-L\left(x\right)\right)} +e^{-i\left(2\lambda a_{1} t-L\left(x\right)\right)} }{2} \right)dx } \\ {+S^{+} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\frac{e^{i\left(2\lambda \alpha \left(x-a_{1} \right)-K\left(x\right)\right)} +e^{-i\left(2\lambda \alpha \left(x-a_{1} \right)-K\left(x\right)\right)} }{2} \right)dx } \\ {+S^{-} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\frac{e^{i\left(2\lambda a_{1} t+L\left(x\right)\right)} +e^{-i\left(2\lambda a_{1} t+L\left(x\right)\right)} }{2} \right)dx } \\ {+S^{-} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\frac{e^{i\left(2\lambda \alpha \left(x-a_{1} \right)+K\left(x\right)\right)} +e^{-i\left(2\lambda \alpha \left(x-a_{1} \right)+K\left(x\right)\right)} }{2} \right)dx } \\ {+S^{-} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\frac{e^{i\left(2\lambda \xi ^{-} \left(x\right)+L\left(x\right)\right)} +e^{-i\left(2\lambda \xi ^{-} \left(x\right)+L\left(x\right)\right)} }{2} \right)dx } \\ {+S^{+} \tilde{S}^{+} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\cos L\left(x\right) dx+S^{-} \tilde{S}^{-} \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\cos K\left(x\right)dx } \\ {+\int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\int _{0}^{x}U_{c} \left(x,t\right)\cos \left(2\lambda t-K\left(t\right)\right)dt \right) dx} \\ {-\int _{0}^{\frac{\pi }{2} }Q\left(x\right)\left(\int _{0}^{x}U_{s} \left(x,t\right)\sin \left(2\lambda t-K\left(t\right)\right)dt \right) dx} \end{array}$ where $R_{1} \left(t\right)=Q\left(t\right)e^{-i\left(K\left(t\right)\right)} $, $R_{2} \left(t\right)=Q\left(t\right)e^{i\left(K\left(t\right)\right)} $, $R_{3} \left(t\right)=Q\left(t\right)e^{-i\left(L\left(t\right)\right)} $, $R_{4} \left(t\right)=Q\left(t\right)e^{i\left(L\left(t\right)\right)} ,Q_{1} \left(t\right)=\int _{t}^{\frac{\pi }{2} }P\left(x\right)U_{c} \left(x,t\right) dx,$\ $ Q_{2} \left(t\right)=\int _{t}^{\frac{\pi }{2} }P\left(x\right)U_{s} \left(x,t\right) dx, R_{5} \left(t\right)=\frac{Q_{1} \left(t\right)+iQ_{2} \left(t\right)}{2} e^{-iK\left(t\right)} , $ $R_{6} \left(t\right)=\frac{Q_{1} \left(t\right)-iQ_{2} \left(t\right)}{2} e^{iK\left(t\right)} $\ By the Riemann-Lebesgue lemma\ $\int _{0}^{\frac{\pi }{2} }Q\left(x\right)\cos L\left(x\right) dx=0\, \, ,\, \, \int _{0}^{\frac{\pi }{2} }Q\left(x\right)\cos K\left(x\right)dx =0$. Thus, $$\label{25)} \begin{array}{l} {2U_{2} \left(\lambda \right)=\frac{S^{+} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }R_{1} \left(t\right)e^{i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt +\frac{S^{+} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }R_{2} \left(t\right)e^{-i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt } \\ {+\frac{S^{+} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }R_{3} \left(t\right)e^{2ia_{1} t} dt +\frac{S^{+} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }R_{4} \left(t\right)e^{-2ia_{1} t} dt } \\ {+\frac{S^{+} S^{-} }{2} \int _{0}^{\frac{\pi }{2} }R_{1} \left(t\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt +\frac{S^{+} S^{-} }{2} \int _{0}^{\frac{\pi }{2} }R_{2} \left(t\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }R_{3} \left(t\right)e^{-2ia_{1} t} dt +\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }R_{4} \left(t\right)e^{2ia_{1} t} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }R_{1} \left(t\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt +\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }R_{2} \left(t\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt } \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }R_{4} \left(t\right)e^{i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt +\frac{S^{-} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }R_{3} \left(t\right)e^{-i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt } \\ {+\frac{i}{2\lambda } \int _{0}^{\frac{\pi }{2} }R_{5} \left(t\right)e^{2i\lambda t} dt +\frac{i}{2\lambda } \int _{0}^{\frac{\pi }{2} }R_{6} \left(t\right)e^{-2i\lambda t} dt } \end{array}$$ $$\label{26)} 2\lambda U_{1} \left(\lambda \right)+U_{2} \left(\lambda \right)=0.$$ If $\left(2.10\right)$ and $\left(2.11\right)$ are substituted into $\left(2.12\right)$, we get\ $\begin{array}{l} {\frac{S^{+} \tilde{S}^{+} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{1} \left(t\right)+iT'_{1} \left(t\right)\right)e^{i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt +\frac{S^{+} \tilde{S}^{+} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{2} \left(t\right)-iT'_{2} \left(t\right)\right)e^{-i\left(2\lambda \xi ^{+} \left(t\right)\right)} dt } \\ {+\frac{S^{+} \tilde{S}^{-} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{3} \left(t\right)+iT'_{3} \left(t\right)\right)e^{2ia_{1} t} dt +\frac{S^{+} \tilde{S}^{-} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{4} \left(t\right)-iT'_{4} \left(t\right)\right)e^{-2ia_{1} t} dt } \\ {+\frac{S^{+} S^{-} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{1} \left(t\right)+iT'_{1} \left(t\right)\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt +\frac{S^{+} S^{-} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{2} \left(t\right)-iT'_{2} \left(t\right)\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{4} \left(t\right)+iT'_{4} \left(t\right)\right)e^{-2ia_{1} t} dt +\frac{S^{-} \tilde{S}^{+} }{2\alpha } \int _{0}^{\frac{\pi }{2} }\left(R_{3} \left(t\right)-iT'_{3} \left(t\right)\right)e^{2ia_{1} t} dt } \\ {+\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }\left(R_{2} \left(t\right)+iT'_{2} \left(t\right)\right)e^{2i\lambda \alpha \left(t-a_{1} \right)} dt +\frac{S^{-} \tilde{S}^{+} }{2} \int _{0}^{\frac{\pi }{2} }\left(R_{1} \left(t\right)-iT'_{1} \left(t\right)\right)e^{-2i\lambda \alpha \left(t-a_{1} \right)} dt } \\ {+\frac{S^{-} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }\left(R_{4} \left(t\right)-iT'_{4} \left(t\right)\right)e^{i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt +\frac{S^{-} \tilde{S}^{-} }{2} \int _{0}^{\frac{\pi }{2} }\left(R_{3} \left(t\right)+iT'_{3} \left(t\right)\right)e^{-i\left(2\lambda \xi ^{-} \left(t\right)\right)} dt } \\ {+\int _{0}^{\frac{\pi }{2} }\left(R_{5} \left(t\right)+iT'_{5} \left(t\right)\right)e^{2i\lambda t} dt +\int _{0}^{\frac{\pi }{2} }\left(R_{6} \left(t\right)-iT'_{6} \left(t\right)\right)e^{-2i\lambda t} dt =0} \end{array}$\ Since the systems $\left\{e^{\pm 2i\lambda \xi ^{+} \left(t\right)} :\, \, \lambda \in {\rm R}\right\}$ , $\left\{e^{\pm 2i\lambda a_{1} t} :\, \, \lambda \in {\rm R}\right\}$, $\left\{e^{\pm 2i\lambda \alpha \left(t-a_{1} \right)} :\, \, \lambda \in {\rm R}\right\}$ and $\left\{e^{\pm 2i\lambda t} :\, \, \lambda \in {\rm R}\right\}$ are entire in $L_{2} \left(-\frac{\pi }{2} ,\frac{\pi }{2} \right)$, it follows $$\begin{array}{l} {R_{1} \left(t\right)+iT'_{1} \left(t\right)=0\, \, ,\, \, R_{2} \left(t\right)-iT'_{2} \left(t\right)=0\, \, ,\, \, R_{3} \left(t\right)+iT'_{3} \left(t\right)=0} \\ {R_{4} \left(t\right)-iT'_{4} \left(t\right)=0\, \, ,\, \, R_{1} \left(t\right)+iT'_{1} \left(t\right)=0\, \, ,\, \, R_{2} \left(t\right)-iT'_{2} \left(t\right)=0} \\ {R_{4} \left(t\right)+iT'_{4} \left(t\right)=0\, \, ,\, \, R_{3} \left(t\right)-iT'_{3} \left(t\right)=0\, \, ,\, \, R_{2} \left(t\right)+iT'_{2} \left(t\right)=0} \\ {R_{1} \left(t\right)-iT'_{1} \left(t\right)=0\, \, ,\, \, R_{4} \left(t\right)-iT'_{4} \left(t\right)=0\, \, ,\, \, \, R_{3} \left(t\right)+iT'_{3} \left(t\right)=0} \\ {R_{5} \left(t\right)+iT'_{5} \left(t\right)=0\, \, ,\, \, R_{6} \left(t\right)-iT'_{6} \left(t\right)=0} \end{array}$$ Then, we get the following system. $$\begin{array}{l} {R_{5} \left(t\right)+iT'_{5} \left(t\right)=0\, \, } \\ {R_{6} \left(t\right)-iT'_{6} \left(t\right)=0} \end{array}$$ and hence, $$\left\{\begin{array}{l} {\left[Q_{1} \left(t\right)+P_{1} \left(t\right)K'\left(t\right)-P_{2} ^{{'} } \left(t\right)\right]+i\left[Q_{2} \left(t\right)+P_{2} \left(t\right)K'\left(t\right)+P_{1} ^{{'} } \left(t\right)\right]=0} \\ {\left[Q_{1} \left(t\right)+P_{1} \left(t\right)K'\left(t\right)-P_{2} ^{{'} } \left(t\right)\right]-i\left[Q_{2} \left(t\right)+P_{2} \left(t\right)K'\left(t\right)+P_{1} ^{{'} } \left(t\right)\right]=0} \end{array}\right.$$ and hence, $$\left\{\begin{array}{l} {Q_{1} \left(t\right)+P_{1} \left(t\right)K'\left(t\right)-P_{2} ^{{'} } \left(t\right)=0} \\ {Q_{2} \left(t\right)+P_{2} \left(t\right)K'\left(t\right)+P_{1} ^{{'} } \left(t\right)=0} \end{array}\right.$$ $$\label{27)} \left\{\begin{array}{l} {P'\left(t\right)=U_{c} \left(t,t\right)P\left(t\right)} \\ {-\int _{t}^{\frac{\pi }{2} }U_{s} \left(x,t\right)Q\left(x\right)dx-\int _{t}^{\frac{\pi }{2} }\left(K'\left(t\right)U_{s} \left(x,t\right)+\frac{\partial H_{s} \left(x,t\right)}{\partial t} \right)P\left(x\right)dx } \\ {} \\ {P\left(t\right)=-\int _{t}^{\frac{\pi }{2} }P'\left(x\right)dx } \\ {} \\ {Q\left(t\right)=-\left(K'\left(t\right)+U_{s} \left(t,t\right)\right)P\left(t\right)} \\ {-\int _{t}^{\frac{\pi }{2} }U_{c} \left(x,t\right)Q\left(x\right)dx-\int _{t}^{\frac{\pi }{2} }\left(K'\left(t\right)U_{c} \left(x,t\right)-\frac{\partial H_{s} \left(x,t\right)}{\partial t} \right)P\left(x\right)dx } \end{array}\right.$$ If we mark this $$S\left(t\right)=\left(Q\left(t\right),P\left(t\right),P'\left(t\right)\right)^{T}$$ and $$K\left(x,t\right)=\left(\begin{array}{ccc} {U_{c} \left(x,t\right)} & {K'\left(t\right)U_{c} \left(x,t\right)-\frac{\partial U_{s} \left(x,t\right)}{\partial t} } & {-\left(K'\left(t\right)+U_{s} \left(t,t\right)\right)} \\ {0} & {0} & {1} \\ {U_{s} \left(x,t\right)} & {K'\left(t\right)U_{s} \left(x,t\right)+\frac{\partial U_{s} \left(x,t\right)}{\partial t} } & {U_{c} \left(x,t\right)} \end{array}\right)$$ Equations $\left(2.13\right)$ can be reduced to a vector from $$\label{28)} S\left(t\right)+\int _{t}^{\frac{\pi }{2} }K\left(x,t\right)S\left(x\right)dx=0$$ for $0<t<\frac{\pi }{2} $. Since the equation $\left(2.14\right)$is a homogenous Volterra integral equations. Equation $\left(2.14\right)$ only has the trivial solution. Thus, we obtain $S\left(t\right)=0$ for $0<t<\frac{\pi }{2} $. This gives us $Q\left(t\right)=P\left(t\right)=0$ for $0<t<\frac{\pi }{2} $. Thus, we obtain $q\left(x\right)=\tilde{q}\left(x\right)$ and $p\left(x\right)=\tilde{p}\left(x\right)$ on $\left(0,\pi \right)$. The proof is comleted. Acknowledgement {#acknowledgement .unnumbered} =============== Not applicable.
How to Save for a House Down Payment It's easy to dream about buying a house. It is much harder to save up for your house down payment. For most Americans, buying a house means coming up with a substantial down payment. LendingTree data showed that average down payments increased in the final quarter of 2014 to 17.59 percent, up from 16.01 percent the previous quarter. In dollars, the average down payment amount also increased year-over-year to $47,585. That's a ton of money! However, you do have options. Many applicants qualify for first-time buyer programs or FHA home loans, which reduce the required down payment to three or 3.5 percent. The National Association of Realtors (NAR) says that in 2014, "The typical first-time buyer purchased a 1,570 square-foot home costing $169,000." For a typical starter home, then, the three percent down payment required for Fannie Mae's My Community Mortgage program comes to $5,070. That's a more manageable amount, and with these tips you should be able to get a respectable down payment together in months, not years. Money Saving Tips for Down Payment Here are four saving tips that can put thousands of dollars in your home purchase fund. 1. Save $1,000 on Cable According to Consumers Union (the company that publishes Consumer Reports), cable rates have increased 30 percent over the past five years. Forbes reports that in 2011, just the television portion of a cable bill alone was $78 per month. Rounding up, that is just shy of $1,000 a year. Canceling your cable can get you about one fifth of the way to your down payment. One survey of 2,000 TV viewers found that about 12 percent of people under 35 said they get all of their TV and movie programming online, without any paid broadcast or cable TV programming. Saving Trick #1:Streaming services cost a fraction of the price ofcable. If you live in or near a major metropolitan area, you can still get your broadcast channels with the help of a simple antenna. 2. Save $600 on Your Phone It's time to cut the landline. Unless you have truly no cell phone coverage, it is silly to pay for a second phone at your house. What will it save you? Roughly $20 a month for basic calling, $50 if you are on an unlimited calling plan. That's up to $600 per year. While you are downsizing your calling plans, take a cold, hard look at your family's cell phone and data usage. Your teens, for instance, do not need you to finance their iPhone bills or comprehensive data plans. Shop around for the least expensive plan possible. SavingTrick #2:Who cares about the newest iPhone? Not you--if you are trying to buy a house, that is. Keep your cell phone until it actually stops working.Then, when it is time for a new one, find a plan that offers a free phone as part of the deal. 3.Save $2,000 on Lunch According to the USDA, American households spend 43 percent of their food dollars on restaurants or prepared food. A 2012 survey by Accounting Principles points to lunch as a main culprit. Two thirds of American workers buy lunch out instead of bringing it from home, resulting in a whopping $37 a week average or nearly $2,000 a year. A figure like that certainly makes homemade lunch seem much more appetizing. Saving Trick #3: Double your nightly dinner recipes, then divide the leftovers into individually sized storage containers. This makes bringing lunch from home easier and, often, more delicious than trying to pack a sandwich during the morning rush out the door. 4. Save $1,000 on Coffee Half of American workers spend $20 a week on coffee. That means you are pouring $1,000 a year down your throat. For comparison, one bag of coffee beans costs under $10 and can yield around 60 cups of coffee. Saving Trick#4: Can't live without your latte? Make one at home with your own milk frother. They are relatively inexpensive ($10-$20). For that true cafe sweetness, just add a tablespoon of real maple syrup to your drink. Save Big By Thinking Small These four tweaks could save you $4,600 in a year – practically your whole down payment. It's not that the individual expenses here are so large, rather that consistently spending small amounts over time can really add up. On the other side of the coin, small savings do add up. Here are a few small tricks for trimming your spending, to get yourself the rest of the way to that $5,070 down payment. Curb your impulse shopping: Train yourself out of making impulse purchases -- from gum at the checkout line to a t-shirt at a baseball game. One of the best ways to do this is to limit the amount of cash you have on hand. It's easy to talk yourself into spending an extra five dollars here or there if it's burning a hole in your pocket. Kick-start savings with a garage sale: Grab anything you no longer need / use and sell it – eBay, Craigslist, whatever. Deposit a nice chunk into your house fund to get things going. Make a list, check it twice: Before you go to the store -- for groceries or shoes -- have a clear idea of what you need and what you can spend. Stick to it. Avoid theurge to splurge: Sticking to a budget can be as hard as sticking to a diet. This is a good argument for allowing yourself little indulgences from time to time. Just be sure your indulgences are small, meaningful, and rare. You can't afford for one purchase to wipe out all your spending gains for the month. Make saving automatic: Set up an automatic deposit from your paycheck to your savings account, even if it's just 50 dollars a month. You can always add more, and socking away even a small portion of your earnings every month will keep you on track. Alternatively, set yourself a savings goal for the next year, divide by 12 and set up an automatic monthly deposit for that amount. At first, the amount in your savings might seem pitifully small. But stick with the plan, watch your savings grow, and before long you'll be shopping for your first house.
Introduction {#s1} ============ Body mass index (BMI) and waist circumference (WC) have been widely used to predict risks of cardiovascular disease including type II diabetes, hypertension, and dyslipidemia [@pone.0077897-Nguyen1]--[@pone.0077897-Weng1]. The World Health Organization (WHO) has classified BMI \<18.5 kg/m^2^ as underweight, between 18.5--24.9 kg/m^2^ as normal weight, between 25.0--29.9 kg/m^2^ as overweight, and ≥30.0 kg/m^2^ as obese, WHO cut points for WC are classified as ≥94.0 cm for men and WC ≥80.0 cm for women to reflect central obesity [@pone.0077897-World1]. These classifications are based mainly on studies from Western populations [@pone.0077897-World1]. Increasingly, epidemiological and clinical studies have shown a significant association of BMI and WC at lower cutoff points with risks of metabolic disorders among Asian populations [@pone.0077897-Weng1], [@pone.0077897-Wildman1]--[@pone.0077897-Chiu1]. A BMI threshold of ≥23.0 kg/m^2^ has been found to be associated with diabetes among Indian people [@pone.0077897-Snehalatha1]. In China, BMI of 22.5--24.0 kg/m^2^ was found to be associated with hypertension [@pone.0077897-Nguyen1], [@pone.0077897-Tuan1], while this association was found at a lower BMI cutoff in Indonesia (from 21.5--22.5 kg/m^2^) and Vietnam (from 20.5--21.0 kg/m^2^) [@pone.0077897-Tuan1]. To define central obesity, measures of WC ≥90.0 cm for men and ≥80.0 cm for women are widely used for Asian people [@pone.0077897-WHOExpert1], [@pone.0077897-Inoue1]. In India, diabetes was found to be associated with those who had even lower WC (85.0 cm and 80.0 cm for men and women, respectively) [@pone.0077897-Snehalatha1]. In China, WC of 80.0 cm for both men and women was found as the threshold to confer risks of cardiovascular disease [@pone.0077897-Wildman1]. In Cambodia, BMI classification from the WHO [@pone.0077897-World1] (BMI cutoff point of ≥25.0 kg/m^2^ for overweight) still has been used to identify people at greater risks of non-communicable diseases (NCDs). Men with WC of 85.0--94.0 cm and women with WC of 81.0--88.0 cm are classified as having moderate risk of NCDs. Using these classifications, a national STEP survey of risk factors for NCDs conducted by Department of Preventive Medicine, Ministry of Health, Cambodia in 2010 found that 10.5% of men and 16.3% of women were classified as overweight; and 11.8% of men and 16.9% of women were classified as having central obesity [@pone.0077897-Sophal1]. This prevalence is low compared to other neighboring countries such as Thailand [@pone.0077897-Jitnarin1] (overweight: 17.1%, obese: 23.8%) and Vietnam [@pone.0077897-Trinh1] (overweight: 27.5%, obese: 5.7%), where Asian BMI cutoffs is used. The report of the Cambodian national STEP survey did not address the question of whether the usage of using lower BMI and WC classifications would be appropriate for estimating people at increased risks of NCDs in Cambodia. The question remains as to whether Cambodia should use the "Asian" BMI cutoffs of ≥23.0 kg/m^2^ for overweight and ≥28.0 kg/m^2^ for obesity and the "Asian" WC cutoffs of ≥90.0 cm for men and ≥80.0 cm for women for central obesity versus WHO recommendations. This lack of information needs to be answered in order to appropriately inform policy makers and those who are concerned with controlling NCDs in Cambodia. Therefore, the objectives of this study were to determine appropriate BMI and WC cutoff for overweight and central obesity and their associations with CVD risk factors for adults aged 25 to 64 years in Cambodia and to determine whether those cutoffs are more appropriate than the WHO cutoffs. Methods {#s2} ======= Ethics Statement {#s2a} ---------------- All participants were fully explained about the nature and possible consequences of the study. Privacy and anonymity of respondents were fully guaranteed. Respondents have right to quit from the research at any time without any explanation or reason. Verbal explanation was done with those who were illiterate. A written informed consent was obtained from all subjects prior to data collection. This study was approved by the National Ethics Committee for Health Research, Ministry of Health, Cambodia. Study Population {#s2b} ---------------- We used data from the 2010 STEP survey conducted by the Department of Preventive Medicine, Ministry of Health, Cambodia. It is a nationwide cross-sectional survey that was carried out from February to April 2010 using the WHO STEPwise approach to chronic disease risk factor surveillance methodology [@pone.0077897-World2]. The survey was led by a research team from the University of Health Sciences with technical support from the WHO. A multistage-cluster sampling was used to randomly select participants. Communes were randomly selected as the primary sampling unit, followed by villages as the secondary sampling unit and households as elementary units. In total, 5,643 participants were randomly selected accounting for equivalent distribution of gender and age groups (10-years age groups). Of those, 5,433 individuals aged 25 to 64 years participated in the survey, a response rate of 96.3%. For these analyses, we excluded all subjects who had missing values in main variables such as blood pressure (n = 118), height (n = 5), fasting blood sugar (n = 188), and total cholesterol (n = 19). We also excluded 87 pregnant women and one subject with abnormal values in the main variables from the analysis. In total, 418 subjects were excluded resulting in a total of 5,015 persons analyzed here. Variables and Measurements {#s2c} -------------------------- ### Physical and biological measurements {#s2c1} Blood pressure was measured three times on the left arm at sitting position using NISSEL digital blood pressure monitor (model DS-500) automatic digital blood pressure equipment. The 1^st^ measurement of blood pressure was taken after 15 mn rest and the 2^nd^ and 3^rd^ measurements were made after 3 mn interval. Hypertension was defined as systolic blood pressure or diastolic blood pressure, calculated from the means of the last two readings, of ≥140 mmHg and ≥90 mmHg, respectively. Participants who were currently on anti-hypertensive medication were also classified as hypertensive cases. Weight and height were measured using Linkfold electronic body scale, HCS-200-RT model, made by Shanghai Medical Instrument Co. Ltd with the capacity to measure weight up to 200 kg and height up to 210 cm with a precision of 100 grams and 0.5 cm for weight and height, respectively. Weight was measured in light indoor clothing and without footwear. BMI was calculated as the weight in kilograms divided by the square of the height in metre square. A tape with mm(s) precision made from linoleum was used to measure WC. It was measured at standing position at midpoint of the last palpable rib and the iliac crest. A blood sample was drawn after subjects had fasted overnight. Fasting blood glucose and total cholesterol were measured by trained laboratory technicians using capillary drop of blood from participants' finger. Accutrend Plus instruments were used for these measurements and Accutrend control glucose and cholesterol solutions were used to calibrate each instrument at least twice a week. Diabetes mellitus was defined as subjects who had fasting blood glucose of ≥126 mg/dl or those who were currently on medications for diabetes. Hypercholesterolemia was defined as those with total cholesterol of ≥190 mg/dl. ### Socio-demographic characteristics and living behaviors {#s2c2} Measures from the STEPS survey included age (continuous), sex (male or female), residence (rural or urban), ethnicity (Khmer or other), education level (completed primary school, completed secondary school, and post high school), marital status (married, single, other), employment status (employed, unemployed), cigarette smoking status (yes or no), smokeless tobacco use status (yes or no), alcohol drinking status (yes or no), fruit and/or vegetable consumption ≥5 servings per day (yes or no) and using lard/suet as cooking oil (yes or no). These data were collected by trained interviewers using a questionnaire adapted from WHO STEPwise after translating into Khmer language by taking into consideration specific country characteristics. The interview took approximately 30 minutes. Statistical Snalyses {#s2d} -------------------- Data analyses were performed using STATA version 11.0. BMI was stratified as \<18.5 kg/m^2^, 18.5--\<23.0 kg/m^2^, 23.0--\<27.5 kg/m^2^, and ≥27.5 kg/m^2^. This classification was adapted from WHO expert panel recommendation potential BMI categories for public health action in people of Asian ethnicity [@pone.0077897-Inoue1]. A BMI of 18.5--\<23.0 kg/m^2^ was taken as reference. WC was also categorized in units of 10 cm for both sexes. WC of ≤70.0 cm and \>90.0 cm were used as the lowest and highest unit, respectively, and WC of \>70.0--80.0 cm was used as reference group. Prevalence and means of socio-demographic characteristics and NCD risk factors of participants were calculated and differences were tested using Chi-square, Fisher's Exact test for categorical variables and Student t-test for continuous variables. Associations with BMI and WC categories with hypertension, diabetes mellitus, and hypercholesterolemia were examined. Crude and adjusted odds ratio and 95% confidence interval (CI) were calculated using bivariate and multivariate logistic regression analysis, respectively. Based on previous literature [@pone.0077897-Yang1]--[@pone.0077897-Jo1], potential confounders were adjusted. In Model 1, we adjusted for age, sex, and residence. In model 2, we additionally adjusted for physical activities, cigarette smoking, alcohol drinking, fruit and/or vegetable consumption, and using lard/suet as cooking oil. Two-sided p-values of ≤0.05 were regarded as statistically significant. In order to test whether the lower cutoffs have at least as great a biologic plausibility for assessing risks as for the WHO cutoffs, we constructed receiver operating characteristic (ROC) curves for the ability of each of the cutoffs of BMI and WC to detect one or more components of the metabolic syndrome. Areas under the curve (AUC) were computed for the different cut-points of BMI and WC [@pone.0077897-Zweig1]. Results {#s3} ======= Socio-demographic characteristics of the study subjects are shown in [Table 1](#pone-0077897-t001){ref-type="table"}. Of 5,015 subjects who were included in the analysis, 35.6% (n = 1,786) were men, and 64.4% (n = 3,229) were women. Mean age was 43.0 years (SD = 11.2 years) for men and 43.6 years (SD = 10.9 years) for women. Annual income for both sexes was not significantly different (USD 1,121± USD 1,545 for men vs. USD1,230± USD 2,358 for women). The distribution of men and women in urban (17.2% vs. 18.0%) and rural (82.8% vs. 82.0%) was also similar. Compared to women, men were significantly more likely to have completed high school education (18.7% vs. 7.7%), to be married (90.6% vs. 65.5%), to be employed (96.6% vs. 83.4%), to be current cigarette smokers (55.9% vs 6.4%), to be former daily smokers (38.0% vs. 2.9%), to be alcohol drinkers (89.4% vs. 56.4%), and to do regular physical activities (66.1% vs. 52.6%). However, women were more likely to be smokeless tobacco users than men (0.8% in men vs. 1.5% in women). 10.1371/journal.pone.0077897.t001 ###### Socio-demographic of participants. ![](pone.0077897.t001){#pone-0077897-t001-1} Men Women p-value -------------------------------------------------------------------------------- ----------------- ----------------- ----------- Subject, n (%) 1,786 (35.6) 3,229 (64.4) Age in year (mean ± sd) 43.0±11.2 43.6±10.9 0.96 Annual income in USD (mean ± sd) 1,121.2±1,545.5 1,230.8±2,358.0 0.95 Residence, n (%) Urban 307 (17.2) 581 (18.0) 0.47 Rural 1,479 (82.8) 2,648 (82.0) Education level, n (%) Completed Primary School 1,418 (79.4) 2,969 (91.9) \<0.001 Completed High School 334 (18.7) 250 (7.7) \>High School 33 (1.8) 10 (0.3) Ethnicity, n (%) Khmer 1,761 (99.8) 3,190 (99.4) 0.04 Other 3 (0.2) 18 (0.6) Marital status, n (%) Single 66 (3.7) 188 (5.8) \<0.001 Married 1,619 (90.6) 2,116 (65.5) Other[\](#nt101){ref-type="table-fn"} 101 (5.7) 924 (28.6) Employment status, n (%) Employed 1,726 (96.6) 2,694 (83.4) \<0.001 Unemployed 60 (3.4) 535 (16.6) Current cigarette smokers, n (%) Yes 999 (55.9) 207 (6.4) \<0.001 No 787 (44.1) 3,022 (93.6) Former daily smokers, n (%) Yes 333 (38.0) 89 (2.9) \<0.001 No 543 (62.0) 2,973 (97.1) Current smokeless tobacco users* [\\](#nt102){ref-type="table-fn"}, n (%) Yes 46 (2.6) 622 (19.3) \<0.001 No 1,740 (97.4) 2,607 (80.7) Former daily smokeless tobacco users, n (%) Yes 15 (0.8) 41 (1.5) 0.05 No 1,747 (99.1) 2,622 (98.5) Ever drink alcohol, n (%) Yes 1,597 (89.4) 1,821 (56.4) \<0.001 No 189 (10.6) 1,408 (43.6) Physical activity [\\\](#nt103){ref-type="table-fn"}, n (%) Yes 1,180 (66.1) 1,700 (52.6) \<0.001 No 606 (33.9) 1,529 (47.3) Separated, Divorced, Widowed. Snuff, chewing tobacco, betel. Physical activity is defined as vigorous-intensity aerobic physical activity for at least 75 mm throughout the week. [Table 2](#pone-0077897-t002){ref-type="table"} shows the prevalence of risk factors of NCD across different categories of BMI and WC. The proportion of participants in BMI category of 18.5--\<23.0 kg/m^2^, 23.0--\<27.5 kg/m^2^, and ≥27.5 kg/m^2^ was 53.9%, 25.5%, and 6.9%, respectively. Of total, 20.0% of participants had WC between \>80.0--90.0 cm, and only 6.9% of them had WC of \>90.0 cm. In general, women, older people, urban residents, those who did not do regular physical activities, non-smokers, and those who did not use lard or suet as cooking oil were significantly more likely to have BMI ≥23.0 kg/m^2^ (p-values \<0.001) in relation to their comparison groups. Similarly, women, older people, urban residents, and those who did not do physical activities, non-smokers, and those who did not use lard or suet as cooking oil were significantly more likely to have WC \>80.0--90.0 cm (p-values \<0.01) in relation to their comparison groups. 10.1371/journal.pone.0077897.t002 ###### Prevalence of risk factors of non-communicable diseases (NCDs) across different stratifications of body mass index (BMI) and waist circumference (WC). ![](pone.0077897.t002){#pone-0077897-t002-2} BMI Category (kg/m^2^) WC Category (cm) ------------------------------------------------------- ------------------------ ------------------ -------------- ------------ --------- -------------- -------------- -------------- ------------ --------- Subject distribution* 683 (13.6) 2,705 (53.9) 1,279 (25.5) 348 (6.9) 1,514 (30.2) 2,080 (41.5) 1,003 (20.0) 418 (6.9) Gender Male 179 (10.0) 1,123 (62.9) 409 (22.9) 75 (4.2) \<0.001 437 (24.5) 896 (50.2) 330 (18.5) 123 (6.9) \<0.001 Female 504 (15.6) 1,582 (49.0) 870 (26.9) 273 (8.4) 1,077 (33.3) 1,184 (36.7) 673 (20.8) 295 (9.1) Age 25--34 150 (11.8) 822 (64.8) 249 (19.6) 48 (3.8) \<0.001 519 (40.9) 561 (44.2) 156 (12.3) 33 (2.6) \<0.001 35--44 151 (10.8) 738 (52.9) 399 (28.6) 108 (7.7) 386 (27.6) 595 (42.6) 296 (21.2) 119 (8.5) 45--54 184 (13.4) 670 (48.7) 408 (29.6) 115 (8.3) 325 (23.6) 562 (40.8) 344 (25.0) 146 (10.6) 55--64 198 (20.3) 475 (48.8) 223 (22.9) 77 (7.9) 284 (29.2) 362 (37.2) 207 (21.3) 120 (12.3) Residence Urban 68 (7.7) 354 (39.9) 333 (37.5) 133 (15.0) \<0.001 155 (17.4) 296 (33.3) 261 (29.4) 176 (19.8) \<0.001 Rural 615 (14.9) 2,351 (57.0) 946 (22.9) 215 (5.2) 1,359 (32.9) 1,784 (43.2) 742 (18.0) 242 (5.9) Physical activities Yes 678 (13.1) 1,653 (57.4) 675 (23.4) 174 (6.0) \<0.001 916 (31.8) 1,253 (43.5) 516 (17.9) 195 (6.8) \<0.001 No 305 (14.3) 1,052 (49.3) 604 (28.3) 174 (8.1) 598 (28.0) 827 (38.4) 487 (22.8) 223 (10.4) Cigarette smoking Yes 164 (13.6) 767 (63.6) 232 (19.2) 43 (3.6) \<0.001 340 (28.2) 598 (49.6) 195 (16.2) 73 (6.1) \<0.001 No 519 (13.6) 1,938 (50.9) 1,047 (27.5) 305 (8.0) 1,174 (30.8) 1,482 (38.9) 808 (21.2) 345 (9.1) Alcohol drinking [1](#nt104){ref-type="table-fn"} Yes 227 (9.8) 1,337 (58.0) 600 (26.0) 141 (6.2) 0.05 608 (25.4) 1,063 (46.1) 470 (20.4) 164 (7.1) \<0.001 No 67 (13.2) 271 (53.2) 132 (25.9) 39 (7.7) 161 (31.6) 201 (39.5) 98 (19.2) 49 (9.6) Fruit/veg. consumption ≥5 serving/day Yes 236 (13.4) 963 (54.6) 437 (24.8) 128 (7.3) 0.7 524 (29.7) 729 (41.3) 345 (19.6) 166 (9.4) 0.5 No 441 (13.8) 1,716 (53.6) 830 (25.9) 214 (6.7) 974 (30.4) 1,333 (41.6) 646 (20.2) 248 (7.7) Using lard/suet as cooking oil Yes 118 (16.0) 425 (57.6) 165 (22.4) 30 (4.1) \<0.001 255 (34.5) 314 (42.5) 130 (17.6) 39 (5.3) 0.003 No 564 (13.2) 2,280 (53.3) 1,114 (26.0) 318 (7.4) 1,258 (29.4) 1,766 (41.3) 873 (20.4) 379 (8.9) Drink alcohol within the last 30 day. [Table 3](#pone-0077897-t003){ref-type="table"} shows non-adjusted and adjusted odds ratios for the association between hypertension, diabetes mellitus, and hypercholesterolemia and levels of BMI in men and women separately in three statistical models. BMI category of 18.5--\<23.0 kg/m^2^ was used as reference group. In men, compared to the reference category, those with BMI of 23.0--\<27.5 kg/m^2^ were significantly more likely to have hypertension in all models (OR = 2.4, 95% CI = 1.8--3.2; OR = 2.1, 95% CI = 1.6--2.9; OR = 2.4, 95% CI = 1.7--3.3 in model 0, model 1, and model 2, respectively). The increased risk of hypertension was also found in men in BMI category of ≥27.5 kg/m^2^ compared to those in reference category in all models (OR = 4.9, 95% CI = 3.0--8.1; OR = 3.6, 95% CI = 2.1--6.2; OR = 3.3, 95% CI = 1.8--6.1 in model 0, model 1, and model 2, respectively). Similarly, men in BMI category of 23.0--\<27.5 kg/m^2^ were significantly more likely to have hypercholesterolemia compared to those in reference category in all three models (OR = 3.0, 95% CI = 2.3--4.0; OR = 2.7, 95% CI = 2.0--3.6; OR = 2.9, 95% CI = 2.1--4.0 in model 0, model 1, and model 2, respectively). The increased risk of hypercholesterolemia among men in BMI category of ≥27.5 kg/m^2^ compared to men in reference category was also statistically significant in all models (OR = 6.7, 95% CI = 4.1--10.8; OR = 5.1, 95% CI = 3.1--8.4; OR = 4.9, 95% CI = 2.8--8.6 in model 0, model 1, and model 2, respectively). Compared to men in reference category, men in BMI category of 23.0--\<27.5 kg/m^2^ were significantly more likely to be diabetic in all models (OR = 4.0, 95% CI = 1.9--8.5; OR = 3.9, 95% CI = 1.4--6.4; OR = 3.4, 95% CI = 1.3--9.3 in model 0, model 1, and model 2, respectively). However, the increased risk of diabetes mellitus among men in BMI category of ≥27.5 kg/m^2^ compared to those in reference category was statistically significant only in the unadjusted model (OR = 5.2, 95% CI = 1.6--16.6). 10.1371/journal.pone.0077897.t003 ###### Odd ratio (OR) of hypertension, diabetes mellitus and hypercholesterolemia across body mass index (BMI) category. ![](pone.0077897.t003){#pone-0077897-t003-3} BMI Category (kg/m^2^) --------------------------- ------------------------------------------------ ----- ------------------------------------------------ ------------------------------------------------- MEN Hypertension Model 0 0.8 (0.4--1.3) 1.0 2.4[c](#nt107){ref-type="table-fn"} (1.8--3.2) 4.9[c](#nt107){ref-type="table-fn"} (3.0--8.1) Model 1 0.6 (0.3--1.0) 1.0 2.1[c](#nt107){ref-type="table-fn"} (1.6--2.9) 3.6[c](#nt107){ref-type="table-fn"} (2.1--6.2) Model 2 0.7 (0.4--1.4) 1.0 2.4[c](#nt107){ref-type="table-fn"} (1.7--3.3) 3.3[c](#nt107){ref-type="table-fn"}(1.8--6.1) Diabetes mellitus Model 0 1.0 (0.2--4.7) 1.0 4.0[c](#nt107){ref-type="table-fn"} (1.9--8.5) 5.2[b](#nt106){ref-type="table-fn"} (1.6--16.6) Model 1 0.9 (0.2--3.6) 1.0 3.0[b](#nt106){ref-type="table-fn"} (1.4--6.4) 2.5 (1.7--8.4) Model 2 2.1 (0.4--10.4) 1.0 3.4[a](#nt105){ref-type="table-fn"} (1.3--9.3) 2.6 (0.5--13.6) Hypercholesterolemia Model 0 0.8 (0.5--1.3) 1.0 3.0[c](#nt107){ref-type="table-fn"} (2.3--4.0) 6.7[c](#nt107){ref-type="table-fn"} (4.1--10.8) Model 1 0.7 (0.4--1.2) 1.0 2.7[c](#nt107){ref-type="table-fn"} (2.0--3.6) 5.1[c](#nt107){ref-type="table-fn"} (3.1--8.4) Model 2 0.7 (0.3--1.4) 1.0 2.9[c](#nt107){ref-type="table-fn"} (2.1--4.0) 4.9[c](#nt107){ref-type="table-fn"} (2.8--8.6) WOMEN Hypertension Model 0 0.8 (0.6--1.2) 1.0 2.4[c](#nt107){ref-type="table-fn"} (1.9--3.1) 3.9[c](#nt107){ref-type="table-fn"} (2.8--5.3) Model 1 0.6[b](#nt106){ref-type="table-fn"} (0.4--1.0) 1.0 2.3[c](#nt107){ref-type="table-fn"} (1.8--2.9) 3.3[c](#nt107){ref-type="table-fn"} (2.3--4.6) Model 2 0.8 (0.4--1.5) 1.0 2.0[c](#nt107){ref-type="table-fn"} (1.3--3.0) 2.9[c](#nt107){ref-type="table-fn"}(1.7--5.1) Diabetes mellitus Model 0 0.3 (0.1--1.0) 1.0 2.0[b](#nt106){ref-type="table-fn"} (1.2--3.1) 2.7[c](#nt107){ref-type="table-fn"} (1.5--5.0) Model 1 0.3[a](#nt105){ref-type="table-fn"} (0.1--0.8) 1.0 1.6[a](#nt105){ref-type="table-fn"} (1.0--2.6) 1.9[a](#nt105){ref-type="table-fn"} (1.0--3.6) Model 2 0.8 (0.2--4.2) 1.0 1.4 (0.5--4.0) 3.0 (0.9--9.2) Hypercholesterolemia Model 0 0.8 (0.6--1.1) 1.0 2.1[c](#nt107){ref-type="table-fn"} (1.2--2.6) 2.9[c](#nt107){ref-type="table-fn"} (2.2--3.7) Model 1 0.8[a](#nt105){ref-type="table-fn"} (0.6--1.0) 1.0 1.9[c](#nt107){ref-type="table-fn"} (1.6--2.3) 2.3[c](#nt107){ref-type="table-fn"} (1.7--3.0) Model 2 1.1 (0.7--1.8) 1.0 2.1[c](#nt107){ref-type="table-fn"} (1.5--2.9) 2.0[b](#nt106){ref-type="table-fn"} (1.2--3.2) BOTH SEXES Hypertension Model 0 0.8 (0.6--1.0) 1.0 2.3[c](#nt107){ref-type="table-fn"} (1.9--2.8) 3.9[c](#nt107){ref-type="table-fn"} (3.0--5.0) Model 1 0.6[b](#nt106){ref-type="table-fn"} (0.4--0.8) 1.0 2.2[c](#nt107){ref-type="table-fn"} (1.8--2.7) 3.3[c](#nt107){ref-type="table-fn"} (2.5--4.4) Model 2 0.8 (0.5--1.2) 1.0 2.2[c](#nt107){ref-type="table-fn"} (1.7--2.9) 3.1[c](#nt107){ref-type="table-fn"}(2.1--4.6) Diabetes mellitus Model 0 0.5 (0.2--1.2) 1.0 2.5[c](#nt107){ref-type="table-fn"} (1.7--3.7) 3.4[c](#nt107){ref-type="table-fn"} (2.0--5.9) Model 1 0.4[a](#nt105){ref-type="table-fn"} (0.2--0.9) 1.0 1.9[b](#nt106){ref-type="table-fn"} (1.3--2.9) 2.0[a](#nt105){ref-type="table-fn"} (1.1--3.6) Model 2 1.3 (0.4--3.9) 1.0 2.2[a](#nt105){ref-type="table-fn"} (1.3--2.9) 3.0[a](#nt105){ref-type="table-fn"} (1.2--7.7) Hypercholesterolemia Model 0 0.9 (0.7--1.1) 1.0 2.5[c](#nt107){ref-type="table-fn"} (2.1--2.9) 3.7[c](#nt107){ref-type="table-fn"} (2.9--4.7) Model 1 0.8[a](#nt105){ref-type="table-fn"} (0.6--1.0) 1.0 2.1[c](#nt107){ref-type="table-fn"} (1.8--2.5) 2.7[c](#nt107){ref-type="table-fn"} (2.1--3.5) Model 2 1.0 (0.7--1.4) 1.0 2.4[c](#nt107){ref-type="table-fn"} (1.9--3.0) 2.8[c](#nt107){ref-type="table-fn"} (2.0--4.0) p-value \<0.05; p-value \<0.01; p-value \<0.001. Model 0: Non adjusted. Model 1: Adjusted for age, sex, residence, Model 2: Adjusted for age, sex, residence, physical activities, cigarette smoking, alcohol drinking, fruit and/or vegetable consumption, using lard/suet. In women, compared to those in the reference category, women in BMI category of 23.0-- \<27.5 kg/m^2^ were significantly more likely to have hypertension in all models (OR = 2.4, 95% CI = 1.9--3.1; OR = 2.3, 95% CI = 1.8--2.9; OR = 2.0, 95% CI = 1.3--3.0 in model 0, model 1, and model 2, respectively). As expected, the increased risk of hypertension was found in the comparison of women in BMI category of ≥27.5 kg/m^2^ and those in reference category (OR = 3.9, 95% CI = 2.8--5.3; OR = 3.3, 95% CI = 2.3--4.6; OR = 2.9, 95% CI = 1.7--5.1 in model 0, model 1, and model 2, respectively). Similarly, women in BMI category of 23.0--\<27.5 kg/m^2^ were significantly more likely to have hypercholesterolemia in all models (OR = 2.1, 95% CI = 1.2--2.6; OR = 1.9, 95% CI = 1.6--2.3; OR = 2.1, 95% CI = 1.5--2.9 in model 0, model 1, and model 2, respectively) compared to those in reference category. The increased risk of hypercholesterolemia also remained statistically significant in comparisons of women in BMI category of ≥27.5 kg/m^2^ with those in reference category in all models (OR = 2.9, 95% CI = 2.2--3.7; OR = 2.3, 95% CI = 1.7--3.0; OR = 2.0, 95% CI = 1.2--3.2 in model 0, model 1, model 2, respectively). However, women in BMI category of 23.0--\<27.5 kg/m^2^ were significantly more likely to have diabetes mellitus only in the unadjusted model (OR = 2.0, 95% CI = 1.2--3.1) and model 1 (OR = 1.9, 95% CI = 1.6--2.3) in comparison with reference group. The statistical association disappeared after additional adjustment in model 2. In men, the ROC analysis showed greater area under curve (AUC) for a BMI cut-off of 23.0 kg/m^2^ (0.63) than for BMI cut-off of 25.0 kg/m^2^ (0.61) with p-value \<0.001 ([Figure 1](#pone-0077897-g001){ref-type="fig"}). The sensitivity for detecting one of the metabolic syndrome components (diabetes, hypertension, or hypercholesterolemia) using a BMI cut-off of 23.0 kg/m^2^ was 45.0% compared to only 26.0% if a BMI cutoff of 25.0 kg/m^2^ was used to reflect overweight status. The corresponding specificities were 80.0% and 93.0% when BMI cutoff of 23.0 kg/m^2^ and 25.0 kg/m^2^ were used, respectively. Similarly, in women, the AUC from the ROC analysis was significantly greater for a BMI cut-off of 23.0 kg/m^2^ (0.62) than for BMI cut-off of 25.0 kg/m^2^ (0.60) with p-value \<0.001 ([Figure 2](#pone-0077897-g002){ref-type="fig"}). The sensitivity for detecting one of the metabolic syndrome components using BMI cut-off of 23.0 kg/m^2^ was 49.0% compared to only 30.0% if BMI cutoff of 25.0 kg/m^2^ was used for overweight. The corresponding specificities were 71.0% and 84.0% when BMI cutoff of 23.0 kg/m^2^ and 25.0 kg/m^2^ were used, respectively. ![ROC curve comparing two BMI categories for predicting hypertension, diabetes mellitus and hypercholesterolemia in men.](pone.0077897.g001){#pone-0077897-g001} ![ROC curve comparing two BMI categories for predicting hypertension, diabetes mellitus and hypercholesterolemia in women.](pone.0077897.g002){#pone-0077897-g002} Non-adjusted and adjusted odds ratios of the association of hypertension, diabetes mellitus, and hypercholesterolemia across stratifications of WC in men and women are shown in [Table 4](#pone-0077897-t004){ref-type="table"}. WC of \>70.0--80.0 cm was used as the reference category. In general, men and women with WC \>80.0 cm were at significantly increased risk of hypertension, diabetes mellitus, and hypercholesterolemia (all p-value \<0.05) except diabetes mellitus in Model 2 (p-value \>0.05). 10.1371/journal.pone.0077897.t004 ###### Odd ratio (OR) of diabetes mellitus, hypertension and hypercholesterolemia across waist circumference (WC) category. ![](pone.0077897.t004){#pone-0077897-t004-4} WC Category (cm) --------------------------- ------------------------------------------------ ----- ------------------------------------------------- ------------------------------------------------- MEN Hypertension Model 0 0.6[b](#nt112){ref-type="table-fn"} (0.4--0.9) 1.0 2.2[c](#nt113){ref-type="table-fn"} (1.6--3.0) 5.2[c](#nt113){ref-type="table-fn"} (3.4--7.8) Model 1 0.6[b](#nt112){ref-type="table-fn"} (0.5--0.9) 1.0 1.9[c](#nt113){ref-type="table-fn"} (1.7--2.6) 3.9[c](#nt113){ref-type="table-fn"} (2.5--6.1) Model 2 0.7 (0.4--1.1) 1.0 1.9[b](#nt112){ref-type="table-fn"} (1.3--2.8) 4.2[c](#nt113){ref-type="table-fn"} (2.6--6.9) Diabetes mellitus Model 0 0.4 (0.1--1.9) 1.0 4.8[c](#nt113){ref-type="table-fn"} (2.2--10.6) 4.5[b](#nt112){ref-type="table-fn"} (1.6--12.7) Model 1 0.4 (0.1--1.9) 1.0 3.6[b](#nt112){ref-type="table-fn"} (1.6--8.0) 2.2 (0.7--6.5) Model 2 0.7(0.1--3.6) 1.0 3.3[a](#nt111){ref-type="table-fn"} (1.2--9.1) 1.8 (0.4--7.7) Hypercholesterolemia Model 0 0.8 (0.6--1.2) 1.0 3.5[c](#nt113){ref-type="table-fn"} (2.6--4.8) 6.5[c](#nt113){ref-type="table-fn"} (4.3--9.8) Model 1 0.8 (0.6--1.2) 1.0 3.2[c](#nt113){ref-type="table-fn"} (2.4--2.4) 5.0[c](#nt113){ref-type="table-fn"} (3.3--7.6) Model 2 0.9 (0.5--1.3) 1.0 3.2[c](#nt113){ref-type="table-fn"} (2.2--4.6) 5.4[c](#nt113){ref-type="table-fn"} (3.3--8.7) WOMEN Hypertension Model 0 0.7[a](#nt111){ref-type="table-fn"} (0.5--1.0) 1.0 2.5[c](#nt113){ref-type="table-fn"} (1.9--3.3) 4.7[c](#nt113){ref-type="table-fn"} (3.4--6.4) Model 1 0.8 (0.6--1.1) 1.0 2.2[c](#nt113){ref-type="table-fn"} (1.7--2.9) 3.5[c](#nt113){ref-type="table-fn"} (2.5--4.8) Model 2 0.9 (0.6--1.5) 1.0 2.1[c](#nt113){ref-type="table-fn"} (1.4--3.3) 3.4[c](#nt113){ref-type="table-fn"} (2.0--6.0) Diabetes mellitus Model 0 0.4[a](#nt111){ref-type="table-fn"} (0.2--0.8) 1.0 2.4[b](#nt112){ref-type="table-fn"} (1.4--4.1) 5.1[c](#nt113){ref-type="table-fn"} (2.9--8.9) Model 1 0.4[a](#nt111){ref-type="table-fn"} (0.2--0.9) 1.0 2.0[a](#nt111){ref-type="table-fn"} (1.1--3.4) 3.3[c](#nt113){ref-type="table-fn"} (1.8--5.9) Model 2 0.4 (0.1--1.8) 1.0 1.4 (0.5--3.9) 2.8 (0.9--8.4) Hypercholesterolemia Model 0 0.6[c](#nt113){ref-type="table-fn"} (0.5--0.7) 1.0 2.1[c](#nt113){ref-type="table-fn"} (1.7--2.6) 2.8[c](#nt113){ref-type="table-fn"} (2.2--3.7) Model 1 0.6[c](#nt113){ref-type="table-fn"} (0.5--0.8) 1.0 1.9[c](#nt113){ref-type="table-fn"} (1.5--2.3) 2.1[c](#nt113){ref-type="table-fn"} (1.6--2.8) Model 2 0.7[a](#nt111){ref-type="table-fn"} (0.5--1.0) 1.0 1.9[c](#nt113){ref-type="table-fn"} (1.4--2.7) 1.9[b](#nt112){ref-type="table-fn"} (1.2--3.1) BOTH SEXES Hypertension Model 0 0.7[b](#nt112){ref-type="table-fn"} (0.5--0.8) 1.0 2.3[c](#nt113){ref-type="table-fn"} (1.9--2.9) 4.6[c](#nt113){ref-type="table-fn"} (3.6--5.9) Model 1 0.7[b](#nt112){ref-type="table-fn"} (0.5--0.9) 1.0 2.1[c](#nt113){ref-type="table-fn"} (1.7--2.6) 3.5[c](#nt113){ref-type="table-fn"} (2.7--4.6) Model 2 0.7[b](#nt112){ref-type="table-fn"} (0.6--0.9) 1.0 2.1[c](#nt113){ref-type="table-fn"} (1.7--2.5) 3.5[c](#nt113){ref-type="table-fn"} (2.7--4.6) Diabetes mellitus Model 0 0.4[a](#nt111){ref-type="table-fn"} (0.2--0.8) 1.0 3.1[c](#nt113){ref-type="table-fn"} (2.0--4.8) 5.3[c](#nt113){ref-type="table-fn"} (3.3--8.7) Model 1 0.4[a](#nt111){ref-type="table-fn"} (0.2--0.8) 1.0 2.4[c](#nt113){ref-type="table-fn"} (1.5--3.8) 3.2[c](#nt113){ref-type="table-fn"} (1.9--5.3) Model 2 0.4[a](#nt111){ref-type="table-fn"} (0.2--1.8) 1.0 2.3[c](#nt113){ref-type="table-fn"} (1.5--3.7) 3.1[c](#nt113){ref-type="table-fn"} (1.9--5.3) Hypercholesterolemia Model 0 0.7[c](#nt113){ref-type="table-fn"} (0.6--0.8) 1.0 2.6[c](#nt113){ref-type="table-fn"} (2.2--3.1) 3.8[c](#nt113){ref-type="table-fn"} (3.1--4.8) Model 1 0.7[c](#nt113){ref-type="table-fn"} (0.6--0.8) 1.0 2.2[c](#nt113){ref-type="table-fn"} (1.8--2.6) 2.6[c](#nt113){ref-type="table-fn"} (2.1--3.3) Model 2 0.7[c](#nt113){ref-type="table-fn"} (0.6--0.8) 1.0 2.2[c](#nt113){ref-type="table-fn"} (1.8--2.6) 2.6[b](#nt112){ref-type="table-fn"} (2.1--3.3) p-value \<0.05; p-value \<0.01; p-value \<0.001. Model 0: Non Adjusted. Model 1: Adjusted for age, sex, residence, Model 2: Adjusted for age, sex, residence, physical activities, cigarette smoking, alcohol drinking, fruit and/or vegetable consumption, using lard/suet. For men, the areas under the ROC curve comparing a WC cutoff of 80 cm and 94 cm (the cutoff recommended by WHO for men) were 0.65 and 0.55, respectively, with p-value \<0.001 ([Figure 3](#pone-0077897-g003){ref-type="fig"}). The sensitivities for detecting hypertension or diabetes mellitus or hypercholesterolemia using a WC cut-off of 80 cm and 94 cm were 49.2% and 11.2% respectively, and the corresponding specificities were 80.5% and 98.7%, respectively. ![ROC curve comparing two WC categories for predicting hypertension, diabetes mellitus and hypercholesterolemia in men.](pone.0077897.g003){#pone-0077897-g003} Discussion {#s4} ========== To the best of our knowledge, this is the first study using nationwide data to examine the appropriate BMI and WC cutoff for overweight and central obesity among adults in Cambodia. In general, the significant association of subjects with hypertension and hypercholesterolemia was found in those with BMI ≥23.0 kg/m^2^ and with WC \>80.0 cm in both sexes in all three models. The AUC was significantly greater in both sexes when BMI of 23.0 kg/m^2^ was used as the cutoff point for overweight compared to that using the WHO BMI classification for overweight (BMI ≥25.0 kg/m^2^) for detecting the three cardiovascular risk factors. Similarly, the AUC was also higher in men when WC of 80.0 cm was used as cutoff point for central obesity compared to that recommended by WHO (WC ≥94.0 cm in men). Based on these results, the prevalence of overweight was almost doubled, from 13.5% to 25.5%. The prevalence of central obesity was also significantly augmented from 11.8% in men and 16.9% in women to 20.0% in both sexes. These findings are similar to results in some studies in Asian populations [@pone.0077897-Nguyen1], [@pone.0077897-Weng1], [@pone.0077897-Wildman1], [@pone.0077897-Tuan1]. The associations were independent of the effects of potential confounders such as age, sex, residence, physical activities, cigarette smoking, alcohol drinking, fruit or vegetable consumption, and using lard or suet as cooking oil. The risks of developing metabolic syndrome increased significantly in accordance with the increase of BMI and WC. These findings are also consistent with those found in other studies in Asia [@pone.0077897-Pan1]--[@pone.0077897-Li1]. The risk of hypertension for both sexes was similar at a given BMI and WC levels. However, the risk of diabetes mellitus and hypercholesterolemia was higher in men than in women at the same BMI levels. This result suggests that men are more likely to develop diabetes and hypertension than women at a lower BMI and WC levels. This result is consistent with findings in other studies which found that men tend to develop metabolic syndrome at earlier ages than women [@pone.0077897-Zweig1], [@pone.0077897-Worachartcheewan1], [@pone.0077897-Villegas1]. Significant associations between WC and hypertension, diabetes mellitus, and hypercholesterolemia were generally seen among those with WC \>80.0 cm in both sexes in all three models. Therefore, WC of 80 cm appears to be an appropriate cutoff point to define central obesity for adults aged 25--64 years in Cambodia. This finding is similar to findings in other studies which aimed to determine an appropriate cut-off of WC for Asians [@pone.0077897-Wildman1], [@pone.0077897-Aye1]. After including potential risk factors into the models (model 1 and 2), risk of diabetes among men with WC \>90.0 cm were approximately two fold higher than that in the reference group (WC \>70.0--80.0 cm), but this association was not statistically significant. In women, diabetes mellitus was not significantly associated with those with WC \>80.0 cm in model 2. It is observed that men with WC \>90.0 cm had more than two times the risk of hypercholesterolemia than women with the same WC size. The strengths of this study include the large nationally representative samples. Moreover, research methodology used in this study was adapted from WHO STEPwise approach to surveillance (STEPS) which is a simple, standardized method for collecting, analyzing, and disseminating data in WHO member countries [@pone.0077897-World2]. In addition, blood pressure, blood glucose, cholesterol, and other anthropometric variables used in this study were based on real measurements, not based on self-report. However, several limitations should also be considered. Originally, data were collected from 5,433 subjects. In our analyses, 418 participants were excluded because of some missing or abnormal values. Thus only 5,015 participants were included in our analyses. This might affect the validity of the study. Additionally, data from a cross-sectional design was used in this study. Thus a causal relationship cannot be definitively established. The final limitation of this study concerns self-reported measures for many variables which may lead to over or under ascertainment of the true measurement. In conclusion, the increased risk of hypertension, diabetes mellitus, and hypercholesterolemia was statistically significant in both sexes with a BMI of ≥23.0 kg/m^2^ and WC of \>80.0 cm. As the definition of the cutoff value for "normal" BMI and WC in a population should depend on identifying the risk association with non-communicable diseases, our findings may be used to derive the normal cutoff values of BMI and WC. Therefore, we suggest that a BMI cutoff of 23.0 kg/m^2^ and WC cutoff of 80.0 cm may be appropriate for the designation of over-weight and central obesity in adult men and women in Cambodia. Our findings are useful for policy makers as well as for the Ministry of Health of Cambodia for development of strategies to prevent NCDs which are gradually emerging in Cambodia. The authors wish to thank the Department of Preventive Medicine, Ministry of Health, Cambodia for providing the data source used in this study. [^1]: Competing Interests:The authors have declared that no competing interests exist. [^2]: Conceived and designed the experiments: PRP SO. Performed the experiments: PRP SO. Analyzed the data: YA SY AF VG JPL. Wrote the paper: YA SY AF JPL.
A spectrophotometric study of Am(III) complexation with nitrate in aqueous solution at elevated temperatures. The complexation of americium(iii) with nitrate was studied at temperatures from 10 to 85 °C in 1 M HNO3-HClO4 by spectrophotometry. The 1 : 1 complex species, AmNO3(2+), was identified and the stability constants were calculated from the absorption spectra recorded for titrations at several temperatures. Specific ion interaction theory (SIT) was used for ionic strength corrections to obtain the stability constants of AmNO3(2+) at infinite dilution and variable temperatures. The absorption spectra of Am(iii) in diluted HClO4 were also reviewed, and the molar absorptivity of Am(iii) at around 503 nm and 813 nm was re-calibrated by titrations with standardized DTPA solutions to determine the concentration of Am(iii).
Cyclone Fay Cyclone Fay was an intense, late-season tropical cyclone which struck Western Australia during the 2003–04 Australian region cyclone season. Forming from an area of low pressure on 12 March, Fay was the only Category 5 cyclone during the season. The system had a minimum pressure of 910 mbar (hPa; 26.87 inHg) and maximum sustained winds of . Moving towards the southwest and eventually towards the south, Fay gradually strengthened as it paralleled the northwestern coast of Australia, and made landfall on the Pilbara coast on the morning of 27 March as a Category 4 cyclone. While no fatalities were reported, the cyclone brought record-breaking rainfall to Australia, which led to a sharp decrease in the country's gold output. The cyclone also caused minor damage in the Pilbara region of Western Australia. In the spring of 2005, the Australian Bureau of Meteorology retired the name Fay from use, and it will never be used again as a cyclone name. Meteorological history The low pressure system that later developed into Fay formed in the Gulf of Carpentaria on 12 March 2004. Through 15 March satellite imagery indicated increasing convection and organisation of the system, as well as decreasing wind sheer aloft, adding to the favourable conditions for strengthening. On 16 March, the system was designated Tropical Cyclone 18S by the Joint Typhoon Warning Center, with winds of . The system then crossed Melville and Bathurst Islands and moved into the Timor Sea, where it intensified, and was given the name Fay by the Australian Bureau of Meteorology. Fay began to turn southward on 17 March; simultaneously, the cyclone continued to intensify due to a weakening of vertical wind shear, and well-defined outflow became apparent on satellite imagery. The following day, a steering ridge to the south of the system strengthened and pushed the cyclone away from the coast and to the northwest. At the same time, the system continued to intensify due to the favourable environment in the upper atmosphere. However, hot, dry air flowing into the system from the south, combined with vertical wind sheer, kept the storm from strengthening as much at its maximum potential rate. By 19 March Fay's track had turned to the west-southwest, and over the next day it continued to strengthen in due to favourable upper level outflow and weak vertical sheer. On 21 March, Fay became a Category 5 cyclone on the Australian Region Tropical Cyclone Intensity Scale. A mid-latitude trough caused the steering ridge to weaken, and subsequently, Fay to turn to the south. Over the next two days, the environmental shear around the cyclone decreased, which would normally have led to intensification; however, as the shear decreased, the cyclone also moved over an area of dry air, weakening the system. By 23 March, Fay had moved in a loop, and the system weakened to a Category 2. Over the next day, favourable outflow counteracted the dry air that had weakened the system, and a banding eye feature was observed on satellite imagery. Fay then encountered moister air as it moved southward, leading it to re-intensify on 25 March. A weak eye of 10 nm was observed on 26 March which grew to 15 nm as the day went on. Strengthening into a Category 4 system early on 27 March, Fay made landfall on the Pilbara coast between 8 am and 9 am AWST (0000 and 0100 UTC) with winds of , weakening below cyclone strength somewhere between the towns of Nullagine and Telfer. Preparations, Impact, and aftermath Evacuation centres were set up in the Kimberley region of Western Australia. Schools and businesses were also closed, and flights in and out of the area were cancelled. Shelters were set up for people who could not take shelter in their own homes. Residents of the Bidyadanga Aboriginal community were warned of particularly dangerous storm tide as the centre of the cyclone passed to their west. The communities of Sandfire and Pardoo were also warned of dangerous storm tide. Cyclone warnings were issued for areas threatened by the system, and communities in the path of the system were warned of expected high rainfall, as amounts greater than were expected. Minor damage to buildings and limited tree damage were reported in the vicinity of Port Hedland. In the town of Nullagine, 120 residents were evacuated to the town's police station, as heavy rain caused flooding. Flooding of the De Grey and Oakover Rivers led to the town being segmented into 4 sections. As the system passed near the Yarrie mine 200 workers were forced to go under lockdown for 8 hours. The cyclone overturned accommodation units, "shredded" water tanks, cut power lines, and damaged the rail line connecting the mine to Port Hedland. Heavy rainfall was reported along the track of the cyclone, with a two-day total of reported at the Nifty Copper Mine and reported in Telfer. The rain from the cyclone delayed the construction of a gas pipeline at the mine for over 7 months, while the pipeline company waited for the floodwaters to dissipate. According to Newcrest Mining, the rainfall amounts at Telfer exceeded the records going back at least 100 years. The heavy rainfall from both Cyclone Monty in February and Cyclone Fay caused gold output in Australia for the quarter to be the lowest in 10 years. A survey performed by the Australian Institute of Marine Science discovered that the Scott Reef suffered "severe damage," and many coral colonies were uprooted or damaged. Because of the record-breaking rainfall produced across northwestern Australia, the Bureau of Meteorology retired the name Fay after its usage. See also 2003–04 Australian region cyclone season Cyclone Chris Cyclone Kristy References External links Category:2003–04 Australian region cyclone season Category:2004 in Australia Category:Retired Australian region cyclones Category:Category 5 Australian region cyclones
Pas De Rouge CLOE Black leather fringed sling-back wedge sandals €235.00 Select your color Black Sold out Product Code W5638365-01 Details Pas De Rouge CLOE Wedges are Stylish and easy to wear. This light-form pair of sandals is expertly crafted in Italy from black martellato leather, detailed with suede fringes over instep and finished with a striped cork wedge heel.You can try them with everything from boho dresses to flared jeans.
Q: Why is my input not working with my database? Why is my input not working with my database? My prof. showed us an example of the code and I wrote it, like I need it for my website. Sry for my bad english but I'm exhausted of solving the problem. <script type="text/javascript"> var db = null; function openDB(){ db = openDatabase('myfirstdb','1.0','dbsys',110241024); } function tabelleErzeugen(tx){ console.log(tx); tx.executeSql("CREATE TABLE IF NOT EXISTS LogIn(benutzer,passwort)",[],SQLSuccess,SQLFail); } function SQLSuccess(){ console.log("erfolgreich"); } function SQLFail(){ console.log("nicht erfolgreich"); } function addBenutzer(tx){ let benutzer = document.getElementById('benutzer').value; let passwort = document.getElementById('passwort').value; tx.executeSql("INSERT INTO LogIn VALUES(benutzer,passwort)",[],SQLSuccess,SQLFail); } openDB(); db.transaction(tabelleErzeugen); </script> <div class="container"> <div id="create"> <h1>Datensatz hinzufügen</h1> <input type="text" id="benutzer" min="1" /><br /> <input type="password" id="passwort" min="1" /><br /> <input type="button" onclick="db.transaction(addBenutzer)" value="Kontakt speichern" /> </div> </div> A: See html5 web sql for an example how to insert with dynamic values. It should work like this: tx.executeSql("INSERT INTO LogIn (benutzer,passwort) VALUES (?,?)",[benutzer, passwort],SQLSuccess,SQLFail);
In blow molding processes, molten resin must form into stable parisons for a time long enough to permit a mold to enclose the parison. If these molten resins do not possess sufficient "melt strength" or melt viscosity, the parisons will tend to elongate or draw under their own weight and either not be blow moldable or result in blow molded articles which have non-uniform wall thicknesses, low surface gloss, poorly defined sample shape, and a large number of pitmarks. Polymers such as polyesters, polyamides, polyethers, and polyamines when melted generally form thin liquids having low melt viscosities and poor melt strengths. These low melt viscosity materials are unsuited or are only poorly suited for the manufacture of extruded shapes, tubes, deep-drawn articles, and large blow molded articles. In order to overcome this disadvantage and to convert these polymers to a form better suited for the above-mentioned manufacturing techniques it is known to add compounds to the plastics which will increase their melt viscosities. The materials which are added to increase the melt viscosity of the plastics are generally cross linking agents, as described, for example, in U.S. Pat. No. 3,378,532. Such cross linking agents may be added during the condensation reaction by which the plastics are formed, and/or to the plastics after their formation (prior to, or during their melting). Examples of cross linking agents which may be added to the plastics after their formation and before or after their melting in order to increase the melt viscosity include compounds containing at least two epoxy or isocyanate groups in the molecule, organic phosphorus compounds, peroxides, bishaloalkylaryl compounds, and polyesters of carbonic acid. These known cross linking agents which are added to increase the melt viscosity of the polymer are not completely satisfactory. They may, for instance, cause an excessively rapid and large increase in viscosity or form reaction products which have an adverse influence on the quality of the plastics. Furthermore, the results obtained with the use of these known cross linking agents are not always uniform or reproducible. For example, when polyesters of carbonic acid are used to increase the melt viscosity, the degree of viscosity increase is generally dependent not only upon the amount of additive used but also upon its molecular weight and on the stage of the polycondensation reaction at which the addition takes place. Besides having sufficient melt viscosity or "melt strength", polymers which are to be used in blow molding and related applications should also possess sufficient die swell, i.e., the molten polymer should expand as it is released from the extrusion die. This die swell is important for blow molding applications since (a) the larger the diameter of the extruded polymer, the easier it is for air to be blown into the parison, and (b) the greater the die swell the greater the expansion of the molten polymer to fit the particular mold. Polyesters having low intrinsic viscosities are particularly difficult to blow mold. The prior art illustrates the use of numerous additives to modify various properties of polyesters. For example, U.S. Pat. No. 3,376,272 discloses a process for the preparation of branched chain, high molecular weight thermoplastic polyesters having a multiplicity of linear non-cross linked polyester branched chains from dicarboxylic acid anhydrides, monoepoxides, and an alcohol compound by reacting these compounds at a temperature below 150.degree. C. However, the polyesters described in this patent are formed from anhydrides and are therefore not crystalline. Non-crystalline polymers tend to take longer time to set up in a mold and thus are not suited or are only poorly suited for blow molding and related applications. As indicated above, compounds containing epoxy groups in the molecule have been used to increase the melt viscosity of polyesters (see, for example, U.S. Pat. No. 2,830,031). But although the use of epoxies as cross linking agents for polyesters is known, little appears known about the use of epoxies as reactants which promote the branching (and hence increase the "melt strength") but not the cross linking of polyesters. U.S. Pat. No. 3,547,873 discloses the production of thermoplastic molding compositions from linear saturated polyesters and polyfunctional epoxides. This process, however, also yields products which lack the melt strength and die swell necessary for blow molding applications. Furthermore, U.S. Pat. No. 3,692,744 discloses the preparation of polyester molding materials which can be injection molded by having present in the polyesterification mixture, besides the terephthalic acid and diol components, 0.05-3 moles percent, on the acid component, of a compound containing at least three ester forming groups such as a polycarboxylic acid, a polyhydric alcohol, or a hydroxy carboxylic acid. The use of epoxy compounds is not disclosed, however. Copending United States patent application Ser. No. 669,066, which was filed on Mar. 22, 1976 and which is also assigned to the assignee of the present invention, generically discloses and claims a process for preparing branched chain thermoplastic polymers having increased melt strength and which are useful in extrusion applications. Said copending application is entitled "Improved Polymers for Extrusion Applications" and is filed in the name of John R. Costanza and Frank M. Berardinelli. This process comprises reacting at least one thermoplastic polymer which is in the molten state with at least one branching agent which may be selected from the group consisting of epoxy having a functionality of at least two and isocyanate having a functionality of at least three. Branched chain, high melt strength thermoplastic polymers useful in extrusion applications are obtained from this process. In the above described process, reaction between the thermoplastic polymer and the isocyanate branching agent is sufficiently rapid that catalysts are not necessary. However, the reaction between the thermoplastic polymer and the epoxy branching agent requires the use of a catalyst. Typical acid acceptor type catalysts such as diethylamine tend to rapidly produce the improved melt strength polymer products, but these products, while acceptable for many uses, in some instances tend to be rather brittle and somewhat colored.
package org.nativescript.staticbindinggenerator.generating.writing; import java.util.List; public interface ClassWriter extends JavaCodeWriter { void writeBeginningOfChildClass(String className, String extendedClassName, List<String> implementedInterfacesNames); void writeBeginningOfNamedChildClass(String className, String jsFileName, String extendedClassName, List<String> implementedInterfacesNames); void writeClassEnd(); }
# Live Templates for MobX ## Add Live Templates ### Android Studio 1. Copy file `MobX.xml` to: - Windows: `C:\Users\<userName>\.AndroidStudio<version>\config\templates\` - macOS: `/Users/<userName>/Library/Preferences/AndroidStudio<version>/templates/` 1. Restart Android Studio ### Intellij A similar process can be followed for _Intellij Ultimate_. The paths can differ based on how you are installing it. If you use the _Jetbrains Toolbox_ app to manage the app versions, the default location would be in > `/Users/<userName>/Library/Application Support/JetBrains/Toolbox/apps/IDEA-U` ## List of Live Templates `str`: ```dart part 'store.g.dart'; class Store = _Store with _$Store; abstract class _Store with Store { } ``` `obs`: ```dart @observable int value = 0; ``` `act`: ```dart @action void fooBar() { } ```
95 F.3d 53 Willisv.Interocean Management* NO. 95-31097 United States Court of Appeals,Fifth Circuit. July 30, 1996 Appeal From: E.D.La., No. 94-CV-2701-E 1 AFFIRMED. * Fed.R.App.P. 34(a); 5th Cir.R. 34.2
*2 + 15q - 2. Let b be c(5). What is the tens digit of (-1)/b-12470/(-15)? 8 Suppose 0 = -t - q - 35, -6t + 2t = 5q + 141. Let k = t - -82. What is the tens digit of k? 4 Suppose 47d = 8d + 75075. What is the units digit of d? 5 Let f(q) = 88q3 + q2 - 2q + 1. Let x(v) = 3v + 10. Let n be x(-3). What is the tens digit of f(n)? 8 Let o(r) = 204r2 + 3r - 2. Let c be o(1). Suppose -w - 2w + c = 5g, -2g = -4w - 82. What is the tens digit of g? 4 Suppose 5i + 3l - 31 = -6, -4i = 5l - 20. Suppose -g - 30 = -io, 1 = -5g + 2o - 172. What is the units digit of (14/g)/(1/(-55))? 2 Let r(p) = 0 + 4 - 2p2 + 1 + p2 - p*3 + 2p. Let j be r(-3). Suppose -14m = -jm + 150. What is the units digit of m? 0 Let q(s) = 2s2 + 7s + 14. What is the tens digit of q(9)? 3 Let v(r) be the third derivative of r5/60 - r4/8 - 29r3/6 - 6r*2. What is the tens digit of v(-9)? 7 Suppose -4q + 10 = -6. Suppose 5u + 5n - 123 = 3u, -254 = -qu - 2n. What is the tens digit of u? 6 Let w(z) = -z3 + 5z + 5. Let q be w(-6). Suppose 0 = 5n - 59 - q. What is the units digit of ((-680)/n)/(2/(-5))? 4 Suppose -4 = -2t - 0t. Suppose 0 = i - 6i + 5y - 5, -3i = 3y - 15. Suppose -tx = 2f + ix - 66, -3x = 5f - 158. What is the units digit of f? 1 Suppose -5c - 550 = -10c - 3b, 0 = -2b - 10. Suppose 4d - 1 = -5, -f - 71 = -5d. Let h = f + c. What is the units digit of h? 7 Let l(j) = 2j + 11j2 - 1 + 2 - j2 - 7j2. Let b be l(2). Let t = 24 - b. What is the units digit of t? 7 Let w = -702 - -2124. What is the tens digit of w? 2 Let i(p) = 5p*3 - 6p*2 - 3p - 34. Let j(l) = 11l3 - 13l*2 - 7l - 68. Let z(n) = 13i(n) - 6j(n). What is the units digit of z(-6)? 4 Suppose -l - 5 = x - 4, 4x - 5l + 31 = 0. What is the tens digit of x/(-3)(-828)/(-24)? 4 Let l(m) = m - 13. Let s be l(4). Let t = 31 - 11. Let y = t + s. What is the tens digit of y? 1 Let x(w) = -w3 - 6w*2 - 2w + 8. Let h be (-1)/((-4)/6)-6. Let j(n) = n2 + 9n - 6. Let t be j(h). What is the tens digit of x(t)? 2 Suppose 0 = 4g - 4k - 3472, -2k = g + 3k - 892. What is the units digit of g? 2 What is the tens digit of (-12657)/(-21) + 2/7? 0 Suppose 6f + 324 = 3f. Let c = -60 - f. What is the units digit of c? 8 Suppose -3j = -2t + 2j + 760, 5t + 5j - 1830 = 0. What is the tens digit of t? 7 Let y be 5/2551. Let w(l) = 15l - 1. Let u be w(y). Suppose 4t = u + 26. What is the units digit of t? 0 Let l(c) = -4c - 10c + 13c + 2. Suppose -4w = 20 - 0. What is the units digit of l(w)? 7 Let c(z) = -z2 - 7z + 10. Let d be c(-8). What is the tens digit of 15((-20)/(-6))/d? 2 Let x(h) = -h2 - 5h. Let l be x(-4). Let j be (6/(-5))/(30/(-250)). Suppose 53 = lq + 5p, -4q + 5p + j = q. What is the units digit of q? 7 Let q be ((-2022)/4)/(15/(-90)). Suppose -8g = 337 - q. What is the hundreds digit of g? 3 Suppose 0 = -5y + 6y - 16. Let m be 1y(-6 + 12). Let o = m + -53. What is the tens digit of o? 4 Let s(o) = -o3 + 7o*2 - 5o - 1. Let y = 24 + -20. Let d be s(y). What is the units digit of (d - 0)/((-6)/(-8))? 6 What is the tens digit of (18 - -2)/5391? 6 Suppose 2t - 14 + 4 = 0. Suppose -l = -2l + t. Suppose -4u = -f - u + 21, 0 = 2f - lu - 41. What is the units digit of f? 8 What is the units digit of 1 - 4 - (-15258)/15? 5 Suppose g - 5g + 56 = 0. Suppose -7n + 14 = -g. Suppose 16 = nr, -d = r - 8 + 1. What is the units digit of d? 3 Suppose -5q - 145 + 2400 = 0. What is the tens digit of q? 5 Let z(l) be the first derivative of l4/24 + l3/3 - 3l*2 - 4. Let q(f) be the second derivative of z(f). What is the units digit of q(-1)? 1 Let z be (-8)/(1 - (4 - 2)). What is the tens digit of -734/z-2? 7 Suppose 2x - 220 = 4f, -5f + 0x = -3x + 277. What is the tens digit of ((-13)/13)/(1/f)? 5 Let k(t) = t*2 - 9t - 147. What is the hundreds digit of k(-21)? 4 Suppose -12 = -6a + 3a. Let b be 0/(a/126). Suppose -54 = -2h - bn + 5n, 5h - 4n - 135 = 0. What is the units digit of h? 7 Suppose r + 3 = 5. Suppose -ra = 5 - 13. Suppose 228 = al - 5j, -3l + 140 = -0l + 4j. What is the units digit of l? 2 Let v(q) = -q + 1. Let i(w) = 29w - 7. Let l(k) = i(k) + 6v(k). Let u be l(7). Suppose -3g + u = 2g. What is the units digit of g? 2 Let l = 13 + -53. Let n = l + 77. What is the tens digit of n? 3 What is the units digit of (-7)/(7/(-1188)) + (20 - 25)? 3 Suppose 4g - 5x = 1 - 10, -3 = -g - 4x. Suppose 9v - 8v = 4o - 49, 4o - 46 = -2v. What is the units digit of -2 + 3 + g + o? 2 Let q = -11 - -4. Let i = 5 - q. What is the units digit of 4/(2/i4)? 6 Suppose 0f + 4f - 8 = 3a, 0 = -5f + 3a + 7. Let h be (-10)/(-4) - f/(-2). Suppose -hx = -0x - 30. What is the units digit of x? 5 Let n = -60 - 2. Let l = -29 - n. Suppose -5i + 3i + 14 = y, 5i - l = -2y. What is the units digit of y? 4 Let t(h) = -4h + 25 + 11h + 3h + 3h. What is the tens digit of t(5)? 9 Suppose -5a + 80 - 2 = 2i, 0 = -a + 4i - 2. What is the units digit of a? 4 Let d be ((-112)/(-7))/4 + 0. Suppose 3g = -3o + 78, -o + 3g - 101 = -5o. Suppose x - d = o. What is the units digit of x? 7 Suppose z - r = -4r + 14, 2z - 33 = -r. Suppose y - 5s + 4 = -14, 0 = 2y - 5s + 26. Let x = z + y. What is the units digit of x? 9 Suppose -5h = -104 + 589. Let l = h - -139. What is the tens digit of l? 4 Suppose 4l + 10 = 6l. Suppose 0 = -v + lv - 392. What is the units digit of v? 8 Suppose 3d - 2d = 4c - 60, d + 2c + 66 = 0. Let i = d - -119. What is the units digit of (2 + 2)/(10/i)? 2 Suppose -6o = 3d - 3o - 12, 4o - 8 = 0. Suppose 0 = da + a + 57. Let l = 31 + a. What is the tens digit of l? 1 Let t be 2 - -344/3. Suppose -t = 4k - 150. What is the tens digit of k? 2 Suppose -2c + 4z - 30 = 0, 5z = 5c + 55 + 30. Let w = -7 - c. Let g = 4 + w. What is the tens digit of g? 1 Let c(d) = -14d*2 - 4d + 7. Let b(a) = -14a2 - 3a + 6. Suppose -3x = 2x - 25. Let n(r) = xc(r) - 6b(r). What is the units digit of n(-1)? 5 Let b = -14 - -17. Let l be (-7)/(14/(-20)) + 1. Suppose -bq + 55 = -l. What is the tens digit of q? 2 Let w(a) = 25a*2 - a + 1. Let v be w(1). Suppose 2r + 17 = -4d + 5r, 5d + 35 = r. Let l = d + v. What is the tens digit of l? 1 Suppose -3046 = -14p - 736. What is the units digit of p? 5 Let w be (48/4)/((-24)/(-16)). Suppose -4t - 2p - 43 = 3p, -38 = 5t + p. Let i = w + t. What is the units digit of i? 1 Let f = -237 + 252. What is the tens digit of f? 1 Suppose 0 = -2k - m - 5, -2m = 4k + 2m + 12. Let d(a) = -a - 1. Let s(h) = -6h + 1. Let x(u) = 3d(u) + s(u). What is the tens digit of x(k)? 1 Let c(i) = 3i + 4. Let y(v) = 3v + 3. Let t(a) = -6c(a) + 5y(a). Let o be 1/((-2)/81). What is the units digit of t(o)? 3 Suppose -23l = -28l + 230. What is the tens digit of l? 4 Suppose -4f - 30 = f. Let c be (3/(-2) + 1)f. Let t(q) = 3q*2 - 2q - 1. What is the tens digit of t(c)? 2 Suppose 4y - 31 = -y - 3b, -4y + 2b = -16. Suppose -2l - 25 = -0z - yz, -20 = l - 4z. Suppose -3q + l = -12. What is the units digit of q? 4 What is the tens digit of ((-4848)/(-9))/(121/18)? 0 Let o be (-4 - -3)/(3/267). Let h = -28 - o. Suppose h - 12 = q. What is the tens digit of q? 4 Let n = 1384 - 759. What is the hundreds digit of n? 6 What is the units digit of (0/3 - 4)/((-5)/1255)? 4 Let f be (-2)/(-12)29. Suppose 9 = 5c - 11. Suppose -k + 33 = -a, 4a + 91 + c = fk. What is the tens digit of k? 3 Let w(r) = -r3 - 7r*2 - 6r + 9. Let k(o) = -4o + 9. Let c be k(4). What is the units digit of w(c)? 1 Suppose 93 = 3x - 15. Let q be 117/x + (-3)/(-4). Let b(l) = l*3 - 5l*2 + 5l - 1. What is the units digit of b(q)? 3 Suppose 1 = s, 0 = 7m - 2m - 3s - 2822. What is the units digit of m? 5 Let d = 15 - 19. What is the tens digit of 5 + (d - -37 - -4)? 4 Let g(x) = x3 + 5x. Suppose -3p + b + 20 = 0, -2b = -2p + 5p - 5. What is the tens digit of g(p)? 5 What is the hundreds digit of -6 - -2 - (-1 + -1904)? 9 Let j(v) = -39v3 - v2 - v - 1. Let u(o) = -o - 6. Suppose -3a = -2 + 17. Let t be u(a). What is the tens digit of j(t)? 3 Let z(p) = p - 51. Let b be z(5). Let r be 240/3 + 2/(-1). Let j = b +
The efficacy of ketotifen in a controlled double-blind food challenge study in patients with food allergy. The effectiveness of oral ketotifen was compared with that of placebo in 26 patients with food allergy in a randomized, double-blind parallel study. Patients were selected on the basis of food allergy as established by history, clinical improvement after an exclusion diet, and reappearance of the symptoms after a challenge with the food. Thirteen patients were given ketotifen and 13, placebo. Ketotifen or placebo were administered twice daily for 1 month after the first oral provocation test and the last dose was given 12 hours before the second oral provocation test. Ketotifen protected patients (7/13) significantly more than placebo (2/13; P less than .05). The results of this study suggest that ketotifen may be useful for some patients with food allergy.
Q: Unable to run php artisan migrate:refresh command in Php Storm Terminal Unable to run the php artisan migrate:refresh & php artisan migrate command in the terminal. I created the Migration File in the directory, and then deleted it manually from the sidebar rather than make it drop through Drop command. Now, I am unable to run the migrate commands plus the raw sql queries. Anyone, who can help me out? Can I restore the file which I deleted? A: You apparently deleted a migration called 'Add Column' and now migrate is searching for it, but can't find it. Delete this particular row manually in the migrations table in your database and the migrate should run.
/* * Copyright 2013 The Android Open Source Project * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. / package org.apache.harmony.security.utils; /* * Provides a mapping source that the {@link AlgNameMapper} can query for * mapping between algorithm names and OIDs. */ public interface AlgNameMapperSource { public String mapNameToOid(String algName); public String mapOidToName(String oid); }
[Thought-provoking adaptation of otorhinolaryngologic surgery]. Global budgeting was partially replaced by activity-based funding in 1999 in order to improve productivity and reduce waiting lists. The aim of this study is to estimate otolaryngologic surgery rates after the introduction of Diagnosis Related Groups funding. National data on outpatient and inpatient otolaryngologic surgical procedures over the period 1999 to 2002 were provided by the Norwegian Patient Register; an estimate was made of the proportion undergoing uvuloplasty for sleep apnea or snoring. From 1999 to 2002, there was an overall increase in otolaryngologic procedures of 12%. Inter-procedural variation ranged from a 110% increase in uvuloplasties to a 12 % decrease in tonsillectomies. There was a particular increase in procedures requiring neither general anaesthesia nor a highly specialised surgeon. In spite of the increased rates of uvuloplasty, the proportion of patients selected for surgery remained unchanged. The substantial increase in certain procedures may give rise to several interpretations: better medical technology, reallocation of surgical resources to disorders that had been inadequately covered, or a shift towards procedures for which marginal costs do not exceed treatment costs.
<?php /** * @author MyBB Group * @version 2.0.0 * @package mybb/core * @license http://www.mybb.com/licenses/bsd3 BSD-3 / namespace MyBB\Core\Presenters\Moderations; use Illuminate\Contracts\View\Factory as ViewFactory; use McCool\LaravelAutoPresenter\BasePresenter; use MyBB\Core\Content\ContentInterface; use MyBB\Core\Form\RenderableInterface; abstract class AbstractModerationPresenter extends BasePresenter implements ModerationPresenterInterface { /* * @var ViewFactory / protected $viewFactory; /* * @param object $resource * @param ViewFactory $viewFactory / public function __construct($resource, ViewFactory $viewFactory) { parent::__construct($resource); $this->viewFactory = $viewFactory; } /* * @return RenderableInterface[] / public function fields() { return []; } /* * @return string / public function key() : string { return $this->getWrappedObject()->getKey(); } /* * @return string / public function name() : string { return $this->getWrappedObject()->getName(); } /* * @return string / abstract protected function getDescriptionView() : string; /* * @param array $contentCollection * @param ContentInterface $source * @param ContentInterface $destination * * @return string */ public function describe( array $contentCollection, ContentInterface $source = null, ContentInterface $destination = null ) : string { $content = reset($contentCollection); $count = count($contentCollection); $type = null; if ($count > 1) { $type = trans('content.type.' . $content->getType() . '.plural'); } else { $type = trans('content.type.' . $content->getType()); } return $this->viewFactory->make($this->getDescriptionView(), [ 'type' => $type, 'title' => $count > 1 ? null : $content->getTitle(), 'url' => $content->getUrl(), 'count' => $count > 1 ? $count : 'a', 'source_title' => $source ? $source->getTitle() : null, 'source_url' => $source ? $source->getUrl() : null, 'destination_title' => $destination ? $destination->getTitle() : null, 'destination_url' => $destination ? $destination->getUrl() : null, ]); } }
Editor\'s Note: This Manuscript was accepted for publication on September 5, 2019. The authors have no funding, financial relationships, or conflicts of interest to disclose. INTRODUCTION {#lary28320-sec-0007} ============ Laryngopharyngeal reflux (LPR) results in 10% of otolaryngology consultations.[1](#lary28320-bib-0001){ref-type="ref"}, [2](#lary28320-bib-0002){ref-type="ref"} The clinical challenge is to determine if primarily present symptoms such as hoarseness, frequent throat clearing, cough, or asthma‐like symptoms are related to an exacerbated gastroesophageal reflux disease (GERD) or are caused by other potential etiologies such as allergies, sinusitis, chronic bronchitis, or a postnasal drip syndrom.[3](#lary28320-bib-0003){ref-type="ref"} The main problems are that the current standard methods are not sufficient and accurate enough to definitively diagnose LPR.[4](#lary28320-bib-0004){ref-type="ref"}, [5](#lary28320-bib-0005){ref-type="ref"} The lack of LPR‐specific tests often leads to evaluation of an empirical treatment response to GERD or multichannel intraluminal impedance pH throughout 24‐h monitoring (MII‐pH), which is still the gold standard measurement tool to assess if present extraesophageal symptoms are caused by GERD.[5](#lary28320-bib-0005){ref-type="ref"} However, MII‐pH is an invasive and costly method and cannot be performed on all patients with suspicion to suffer from LPR.[6](#lary28320-bib-0006){ref-type="ref"}, [7](#lary28320-bib-0007){ref-type="ref"} There is a need for noninvasive and inexpensive methods that allow for a more sensitive and accurate diagnosis of LPR to optimize the treatment strategies for this patient cohort. Recently, a few studies reported that oropharyngeal pH monitoring using the Restech measurement system (Dx‐pH) appears to be more sensitive than MII‐pH in the evaluation of patients with LPR, although the authors state that Dx‐pH is still limited due to a lack of consensus on normal and abnormal cutoff values, as well as missing well‐controlled prospective studies.[8](#lary28320-bib-0008){ref-type="ref"}, [9](#lary28320-bib-0009){ref-type="ref"} Controversial data is provided by Willhelm et al., who reported that 60% of asymptomatic gastrectomy patients showed positive results in Dx‐pH. Therefore, the authors state that Dx‐pH is not useful to guide any diagnostic or therapeutic decisions.[10](#lary28320-bib-0010){ref-type="ref"} As another diagnostic method, pepsin determination in saliva has been proposed as a tool to improve the diagnosis of GERD as well as LPR. Pepsin is a proteolytic enzyme, which is activated by its precursor pepsinogen in the stomach and can be detected in saliva as well as secretion samples from the lung, sinus, middle ear, trachea, and exhaled breath condensate.[11](#lary28320-bib-0011){ref-type="ref"}, [12](#lary28320-bib-0012){ref-type="ref"}, [13](#lary28320-bib-0013){ref-type="ref"}, [14](#lary28320-bib-0014){ref-type="ref"}, [15](#lary28320-bib-0015){ref-type="ref"} Hayat et al. showed the value of salivary pepsin to discriminate patients with GERD. The authors speculate that this noninvasive Peptest (Peptest, RDBiomed, Hull, U.K.) could lead to an improvement in the diagnosis of patients with GERD as well as patients with LPR.[7](#lary28320-bib-0007){ref-type="ref"} A recently published state‐of‐the‐art review on the evaluation and management of LPR disease by Lechien et al. underlines these speculations, although the authors state that a multiparameter diagnostic approach should be established.[5](#lary28320-bib-0005){ref-type="ref"} Nevertheless, the role of pepsin determination in saliva and Dx‐pH for the diagnosis of LPR remains controversial. The aim of this prospective study was to compare the value of salivary pepsin determination and Dx‐pH measurement as tools in a multiparameter diagnostic pathway for patients with LPR. MATERIALS AND METHODS {#lary28320-sec-0008} ===================== Study Population {#lary28320-sec-0009} ------------------ From October 2015 to May 2018, 635 patients with typical and atypical clinical symptoms related to GERD were assessed for eligibility in the Department of Surgery at Ordensklinikum Linz Sisters of Charity Hospital in Linz, Austria (Fig. [1](#lary28320-fig-0001){ref-type="fig"}). Seventy patients with primarily atypical GERD symptoms and suspicion to suffer from LPR were included in the study. A multiparameter diagnostic approach, including gastroscopy, barium esophagography, high‐resolution esophageal manometry (HRM), MII‐pH, Dx‐pH, and measurement of salivary pepsin concentration was performed. Only patients with primary laryngopharyngeal/atypical reflux symptoms despite treatment with a proton‐pump inhibitor (PPI) for at least 6 months were considered. ![Flowchart showing patient recruitment process and classification. ENT = ear, nose and throat; GIQLI (mean normal 122.6) = Gastrointestinal Quality of Life Index; RFS = Belafsky Reflux Finding Score; RSI = Belafsky Reflux Symptom Index; MII‐pH = multichannel intraluminal impedance pH throughout 24‐h monitoring; Dx‐pH = oropharyngeal pH monitoring using the Restech measurement system.](LARY-130-1780-g001){#lary28320-fig-0001} Patient exclusion criteria were the following: age younger than 18 years, American Society of Anesthesiologists physical status classification \>II, previous esophageal or gastric surgery, pregnancy, presence of higher grade esophageal dysmotility (e.g., achalasia), and other potential causes of laryngopharyngeal/atypical reflux symptoms (e.g., heterotopic gastric mucosa of the cervical esophagus). Written informed consent for participation in the study was obtained from all patients, and study approval was obtained by the institution\'s ethical committee. Study Design and Study Run {#lary28320-sec-0010} ---------------------------- The study design is a prospective single‐center trial on the value of pepsin dtermination in saliva and Dx‐pH as sufficient tools to diagnose LPR. All measurements took place in an inpatient setting, with patients off PPIs for at least 10 days. On day 1, patients had to undergo gastroscopy and HRM. On day 2, MII‐pH simultaneously to Dx‐pH were performed, as well as the collection of three saliva samples to determine the pepsin concentration. On day 3, patients had to undergo an ENT examination including assessment of the Belafskys Reflux Finding Score (RFS) score. Furthermore, during the study period from day 1 through day 3, quality of life and clinical symptoms were assessed in all patients by the GIQLI and Belafsky Reflux Symptom Index (RSI) score, respectively. High‐Resolution Esophageal Manometry {#lary28320-sec-0011} -------------------------------------- All patients had to undergo the measurement after an overnight fast in the supine position. HRM using the Sierra system ManoScan Z, Model A200 (Given Imaging, Duluth, GA) was performed in order to evaluate patients for esophageal motility disorders. A structurally defective lower esophageal sphincter (LES) was defined as an overall length below 2.4 cm, an intraabdominal length below 0.9 cm, and/or the presence of a hiatal hernia. Pressure levels beyond \<29.8 or \> 180.2 mmHg were rated as abnormal, and detected motility disorders were classified according to the Chicago Classification, version 3.0.[16](#lary28320-bib-0016){ref-type="ref"} Quality‐of‐Life Evaluation {#lary28320-sec-0012} ---------------------------- Quality‐of life was assessed by means of the German Gastrointestinal Quality of Life Index (GIQLI).[17](#lary28320-bib-0017){ref-type="ref"} This questionnaire has been validated in German language and it is recommended by the European Study Group for Antireflux Surgery.[18](#lary28320-bib-0018){ref-type="ref"} The GIQLI includes 36 items, which are divided into five subdimensions: gastrointestinal symptoms, emotional status, social functions, physical functions, and a single item for stress of medical treatment, for a minimum of 0 and a maximum of 144 points. A better QoL is indicated by higher points. The mean normal in the healthy population is set at 122.6 points.[17](#lary28320-bib-0017){ref-type="ref"}, [18](#lary28320-bib-0018){ref-type="ref"} Multichannel Intraluminal Impedance pH Throughout 24‐Hour Monitoring {#lary28320-sec-0013} ---------------------------------------------------------------------- All patients had to be off antisecretory therapy for at least 10 days before examination. Furthermore, all patients were encouraged to maintain their normal activities and to remain upright during the day, except for one short nap allowed. Patients were asked to have three main meals a day, without eating snacks in between. The Digitrapper‐multichannel intraluminal impedance‐pH monitoring system (Medtronic, Minneapolis, MN) was used for assessment. A 2.1 mm nasogastric probe was inserted with two antimony pH electrodes located 5 cm above the manometrically located LES and 15 cm more distal the LES and eight impedance electrodes, allowing measurement of intraluminal impedance in six segments at 3, 5, 7, 9, 15, and 17 cm above LES.[19](#lary28320-bib-0019){ref-type="ref"} GERD was diagnosed if the reflux‐related composite pH score according to DeMeester exceeded 14.7, in combination with a total number of reflux events in 24 hours of more than 73.[19](#lary28320-bib-0019){ref-type="ref"}, [20](#lary28320-bib-0020){ref-type="ref"}, [21](#lary28320-bib-0021){ref-type="ref"}, [22](#lary28320-bib-0022){ref-type="ref"} Belafsky Reflux Symptom Index {#lary28320-sec-0014} ------------------------------- Laryngopharyngeal/extra‐esopahgeal reflux symptoms were evaluated using the standardized RSI questionnaire. The RSI includes nine items and it is self‐administered. The score range for each item is between 0 (no problem) and 5 (severe problem) points, with a maximum total score of 45. An RSI of \>13 is considered to indicate the presence of reflux.[23](#lary28320-bib-0023){ref-type="ref"}, [24](#lary28320-bib-0024){ref-type="ref"} Belafskys Reflux Finding Score {#lary28320-sec-0015} -------------------------------- An ear, nose, and throat (ENT) examination was performed by an otolaryngologist, including a fiberoptic laryngoscopy and photographic documentation. Furthermore, the RFS was determined. RFS ranges were set from the lowest possible score of 0 (normal larynx) to the highest possible score of 26. A score of \>7 was defined as pathological.[23](#lary28320-bib-0023){ref-type="ref"}, [25](#lary28320-bib-0025){ref-type="ref"} Oropharyngeal pH Monitoring {#lary28320-sec-0016} ----------------------------- Simultaneous to MII‐pH, patients had to undergo Dx‐pH as well. The Restech Dx‐pH measurement system, version 1.0 (Restech Dx‐pH, Restech, San Diego, CA) was used. Therefore, a probe was placed in a standardized way, as recommended by the provider in the oropharynx above the upper esophageal sphincter. The measurements are evaluated by the Ryan score, which was considered to be pathological when higher 9.4 in the upright position (pH \< 5.5) or higher 6.8 in the supine position (pH \< 5.0).[26](#lary28320-bib-0026){ref-type="ref"} Pepsin Determination in Saliva {#lary28320-sec-0017} -------------------------------- Subjects collected the saliva samples on waking, 1 hour after finishing lunch, and 1 hour after finishing dinner during the MII‐pH and simultaneous Dx‐pH monitoring period. The early morning sample was collected before eating, drinking, smoking, or brushing the teeth of the patients. Saliva was collected into tubes containing 0.5 mL of 0.01 M citric acid. Subjects returned the samples immediately after collection, and the samples were sent to the laboratory. Samples were refrigerated at 4°C and analyzed within 2 days after collection. Pepsin values were determined in a standardized procedure using Peptest (RDBiomed), as previously described.[7](#lary28320-bib-0007){ref-type="ref"} The value of 16 ng/mL was used as cutoff for a positive sample (as determined by the manufacturer). Samples with a pepsin concentration above the upper limit of 500 ng/mL had 501 ng/mL in the results. The mean value out of three samples was used to perform correlation analysis. Statistical Analysis {#lary28320-sec-0018} ---------------------- Statistical analysis was performed using SPSS statistical analysis software, version 25.0 (SPSS Inc., Chicago, IL). Data were compared using a paired t test or the Wilcoxon signed rank test. If normally distributed, datasets were additionally presented as means and standard deviation. Multiple group comparisons were performed using a one‐way analysis of variance, followed by Kolmogorov--Smirnov Test for normal distributed data and the Kruskall--Wallis Test with Dunns comparison for non‐normal data. Receiver operating characteristic (ROC) curves were constructed to determine and compare the sensitivity and specificity of different pepsin cutoff concentrations and their predictive value to diagnose or refute the diagnosis of GERD and extra‐esophagel/laryngophyrangeal reflux‐related symptoms. Likelihood ratios were calculated, and P \< 0.05 was regarded as statistically significant. RESULTS {#lary28320-sec-0019} ======= Patient Characteristics and Classification {#lary28320-sec-0020} -------------------------------------------- Seventy patients were enrolled in the study. There were 30 (42.9%) male and 40 (57.1%) female patients with a mean age of 54.44 (±13.23) years. The mean body mass index (BMI) was 23.21 (±3.2) kg/m^2^. Patients were objective classified according to a pathological DeMeester score (\>14.72), and having more than 73 reflux events in 24 hours to suffer from laryngopharyngeal/extra‐esophageal reflux symptoms related to GERD. Finally, 41 patients (58.6%) were included in the group showing a pathological DeMeester score and were classified having "true" LPR (LPR group). Twenty‐nine patients (41.4%) built the group with clinical symptoms of LPR and normal results in MII‐pH (non‐LPR group) (Fig. [1](#lary28320-fig-0001){ref-type="fig"}). In each group, none of the patients showed high‐grade esophageal motility disorders, a paraesophageal hiatal hernia, or upside‐down stomach in barium esophagography. In gastroscopy, 24 of 41 patients (58.5%) in the LPR group showed signs of esophagitis (grade I or II) compared to four of 29 patients (13.8%) in the non‐LPR group (P = 0.0001). Differences in ages, BMI, and sex distribution of subjects among the two groups were not significant (P \> 0.05 for all). Except for RFS score measurements, reflux episodes detected in MII‐pH, and DeMeester scores, no significant differences in the mean values of RSI score, as well as Ryan score and GIQLI, were seen (Table [1](#lary28320-tbl-0001){ref-type="table"}). However, significantly more patients in the LPR group (32 of 41; 78.0%) showed a pathological result in the RSI score compared to the non‐LPR group (14 of 29; 48.3%) (P = 0.045). ###### Demographic Data and Mean Values of MII‐pH, Reflux Episodes, Dx‐pH, RSI Score, RFS Score, and GIQLI Score For Each Group of Patients. Mean Values When DeMeester Score Pathological (n = 41) Mean Values When DeMeester Score Normal (n = 29) Significance -------------------------------------------------- -------------------------------------------------------- -------------------------------------------------- -------------- Sex (male) 21 (51.2%) 12 (41.4%) P = 0.724 Age (years) 55.2 (SD ± 12.4) 53.2 (SD ± 14.1) P = 0.758 Body mass index (kg/m^2^) 24.3 (SD ± 3.5) 23.2 (SD ± 3.2) P = 0.841 DeMeester score 40.8 (SD ± 36.2) 8.8 (SD ± 3.7) P = 0.000 Total acid exposure time (%) 12.3 (SD ± 6.1) 2.3 (SD ± 1.1) P = 0.000 Reflux episodes MII‐pH (total) 141.7 (SD ± 111.2) 41.8 (SD ± 22.0) P = 0.000 Reflux episodes MII‐pH (proximal; total) 38.7 (SD ± .27.8) 8.2 (SD ± 4.4) P = 0.000 Reflux episodes MII‐pH (proximal; acidic) 25.7 (SD ± .20.1) 4.4 (SD ± 2.3) P = 0.000 Reflux episodes MII‐pH (proximal; weakly acidic) 12.9 (SD ± .7.7) 3.8 (SD ± 2.1) P = 0.000 Reflux episodes MII‐pH (proximal; nonacidic) 2.1 (SD ± .2.0) 0.5 (SD ± 0.5) P = 0.887 GIQLI score (points) 96.5 (SD ± 22.6) 101.6 (SD ± 21.9) P = 0.327 RSI score (points) 18.1 (SD ± 8.4) 15.7 (SD ± 10.2) P = 0.276 RFS score (points) 5.7 (SD ± 2.1) 4.5 (SD ± 2.6) P = 0.048 Ryan Score upright position (\< 9.41) 43.3 (SD ± 102.4) 29.3 (SD ± 49.3) P = 0.472 Ryan Score supine position (\< 6.79) 4.7 (SD ± 9.8) 3.3 (SD ± 5.0) P = 0.467 GIQLI (mean normal 122.6) = Gastrointestinal Quality of Life Index; RFS = Belafsky Reflux Finding Score; Dx‐pH = oropharyngeal pH monitoring using the Restech measurement system; MII‐pH = multichannel intraluminal impedance pH throughout 24‐h monitoring; RSI = Belafsky Reflux Symptom Index; Ryan Score (upright and supine position) = results of oropharyngeal pH monitoring with Restech Dx‐pH Measurement System (Restech, San Diego, CA); SD = standard deviation. There were no significant differences considering the number of patients with a pathological RFS score between both groups (P \> 0.05). Prevalence of Positive Pepsin Detection/Concentration in Saliva {#lary28320-sec-0021} ----------------------------------------------------------------- In total, 35 of 41 (85.4%) patients with a pathological DeMeester score (LPR group) had one or more saliva samples positive for pepsin. In comparison, 21 of 29 (72.4%) patients in the non‐LPR group showed at least one positive sample (P \> 0.05). The prevalence in the LPR group of having a positive sample was 61.0% on waking, 68.3% on lunch, and 56.1% on dinner. In the non‐LPR group, the prevalence of having a positive sample was 65.5% prevalence on waking, 89.7% prevalence on lunch, and 58.6% prevalence on dinner. The mean salivary pepsin concentration out of three samples in the LPR group was 216 (±127) ng/mL, whereas patients in the non‐LPR group had a mean concentration of 161 (±114) ng/mL (Table [2](#lary28320-tbl-0002){ref-type="table"}). ###### Concentrations of Pepsin in Saliva for Each Group of Patients. n = 70 Mean Concentration of Positive Samples (± SEM) Median Concentration (25‐75th centiles), 95th Centile Highest Pepsin Concentration (median (25--75th centile), 95th Centile) --------------------------------------- ------------------------------------------------ ------------------------------------------------------- ------------------------------------------------------------------------ DeMeester score pathological (n = 41) 216 (± 127) 171 (103--271), 378 313 (139--501), 501 DeMeester score normal (n = 29) 161 (± 114) 92.5 (30--319), 501 233 (78--501), 501 Unit of concentrations: ng/mL. SEM = standard error of the mean. Neither mean concentrations of pepsin on waking (LPR vs. non‐LPR:100 \[±150\] ng/mL vs. 115 \[±158\] ng/mL) or after lunch (LPR vs. non‐LPR:192 \[±189\] ng/mL vs. 208 \[±180\] ng/mL) or dinner (LPR vs. non‐LPR:204 \[±209\] ng/mL vs. 202 \[±202\] ng/mL) showed significant differences when comparing both groups. Values of Salivary Pepsin Concentration to Differentiate Patients With LPR From Patients With Non‐LPR {#lary28320-sec-0022} ------------------------------------------------------------------------------------------------------- Using the ROC curve, we identified the optimal cutoff value of salivary pepsin concentration to differentiate patients with LPR from non‐LPR patients. The area under the ROC curve was 0.658 ±0.084 (95% CI, 0.387 to 0.720, P \< 0.05). The best cutoff value was determined to be 216 ng/mL, and the value of the Youden index was largest. The specificity of the Peptest (RDBiomed, Hull, U.K.) was 86.2%, and the sensitivity was 41.5% at the measured optimal cutoff value. If at least one sample was positive (\>16 ng/mL), the test showed a specificity of 85.4% and a sensitivity of 27.6%, with a negative predictive value of 57.1%. With one sample positive, the usefulness of the test depends on the pepsin concentration, which is shown beside predictive values and likelihood ratios in Table [3](#lary28320-tbl-0003){ref-type="table"}. ###### Patients With at Least One Positive Sample, Sensitivities, Specificities, Positive and Negative Predictive Values, and Likelihood Ratios for a Range of Pepsin Concentrations and Their Ability to Identify Patients with LPR. n = 70 DeMeester Score Pathological (%) DeMeester Score Nomal (%) Sensitivity (%) Specificity (%) PPV (%) NPV (%) +ve Likelihood Ratio − ve Likelihood Ratio -------------------------------- ---------------------------------- --------------------------- ----------------- ----------------- --------- --------- ---------------------- ------------------------ At least 1 sample \> 16 ng/mL 35/41 (85.4) 21/29 (72.4) 85.4 27.6 62.5 57.1 1.18 0.53 At least 1 sample \> 50 ng/mL 32/41 (78.1) 17/29 (58.6) 78.1 41.4 65.3 57.1 1.33 0.53 At least 1 sample \> 100 ng/mL 28/41 (68.3) 12/29 (41.4) 68.3 58.6 70.0 56.7 1.65 0.54 At least 1 sample \> 150 ng/mL 22/41 (53.7) 9/29 (31.0) 53.7 69.0 71.0 51.3 1.73 0.67 At least 1 sample \> 216 ng/mL 17/41 (41.5) 4/29 (13.8) 41.5 86.2 81.0 51.0 3.00 0.69 LPR = laryngopharyngeal reflux; NPV = negative predictive value; PPV = positive predictive value. Correlation Between Pepsin in Saliva/Dx‐pH and RFS, RSI, and GIQLI {#lary28320-sec-0023} -------------------------------------------------------------------- The mean values of RSI score, RFS score, and GIQLI are presented in Table [1](#lary28320-tbl-0001){ref-type="table"}. Significant correlations between GIQLI score and RSI score (r = −0.419; P = 0.000), as well as between GIQLI score and RFS score (r = −0.262; P = 0.026), were recognized in all patients. Patients with a pathological result in MII‐pH showed a significant correlation between the values of salivary pepsin and the measurements of RSI score (r = 0.344; P = 0.046). Furthermore, the pepsin test with the highest level out of three samples in each patient of both groups (LPR + non‐LPR) showed a significant correlation with the RFS score (r = 0.246; P = 0.043). Correlation Between Pepsin in Saliva/Dx‐pH and HRM As Well As MII‐pH {#lary28320-sec-0024} ---------------------------------------------------------------------- Lower esophageal sphincter resting pressure (LESP) was significantly lower in the LPR group with a mean of 17.69 (±9.01) mmHg compared to non‐LPR group with a mean of 27.49 (±13.3) mmHg (P = 0.0001). All patients showed normal values of the upper esophageal sphincter pressure and integrated relaxation pressure as well as distal contractile integral. None of the patients presented higher‐grade esophageal motility disorders. There were no significant correlations between LESP measurements and the results of pepsin determination in saliva, as well as results of Dx‐pH (Ryan score in upright and supine position) and LESP measurements in both groups (P \> 0.05). In addition, correlation analysis between the DeMeester score and salivary pepsin values as well as between pepsin values and the results of Ryan score (supine + upright) showed no significant correlations either (P \> 0.05). Furthermore, there were no significant correlations between the mean pepsin values or the highest pepsin test out of three samples in the LPR‐ and non‐LPR group and the number of proximal reflux episodes (total count and separated acidic, weakly acidic, nonacidic events) measured by MII‐pH. Oropharyngeal pH Monitoring {#lary28320-sec-0025} ----------------------------- In summary, elevated Dx‐pH measurements showed no significant correlations with either the DeMeester score, RSI score, RFS score, GIQLI score, outcomes of HRM, or the results of pepsin measurement in saliva. DISCUSSION {#lary28320-sec-0026} ========== The accurate value of salivary pepsin and DX‐pH in the diagnosis of LPR remains controversial because of heterogeneous data and the lack of multiparameter prospective studies and adequate cutoff values.[5](#lary28320-bib-0005){ref-type="ref"}, [27](#lary28320-bib-0027){ref-type="ref"} For patients, who seem to suffer from LPR, no optimal cutoff values for a pepsin measurement with the Peptest (RDBiomed) exist thus far. The aim of our prospective trial was to close that gap. Thus far, this is the largest‐scale prospective study in which the diagnostic value of the Peptest (RDBiomed) and Restech Dx‐pH measurement system (Restech) for the objective diagnosis of LPR confirmed by MII‐pH is assessed. To date, two studies in which the value of pepsin in saliva for the diagnosis of GERD has been assessed have provided cutoff values.[7](#lary28320-bib-0007){ref-type="ref"}, [28](#lary28320-bib-0028){ref-type="ref"} Hayat et al. recently reported that the optimal cutoff was at \>210 ng/mL, showing a sensitivity of 44.0% and a specificity of 98.2% to diagnose patients with GERD.[7](#lary28320-bib-0007){ref-type="ref"} Du et al. stated that the Pepstest (RDBiomed) had a sensitivity of 73% and a specificity of 88.3 for diagnosing GERD using the optimal cutoff value of 76 ng/mL. The authors explained that the differences in their results from those in the study of Hayat et al. are due to use of a different study protocol and MII‐pH plus endoscopy to lower the rate of false negative results.[28](#lary28320-bib-0028){ref-type="ref"} A metanalysis performed by Wang et al. encompassing 11 studies described a moderate value of pepsin determination in saliva for the diagnosis of LPR, with a pooled sensitivity of 64% (95% CI 43 to 80%) and specificity of 68% (95% CI 55 to 78) due to heterogeneous study designs, lack of confirmation by reliable parameters such as results of MII‐pH, and different time points of pepsin collection.[29](#lary28320-bib-0029){ref-type="ref"} In addition, several studies showed promising results using Dx‐pH to determine whether extraesophageal symptoms can be attributed to GERD, whereas other studies have already reported the lack of correlation between Dx‐pH and catheter‐based MII‐pH during simultaneous measurements.[30](#lary28320-bib-0030){ref-type="ref"}, [31](#lary28320-bib-0031){ref-type="ref"}, [32](#lary28320-bib-0032){ref-type="ref"} Furthermore, Willhelm et al. already stated that, based on their measurements, Dx‐pH is not useful to guide any diagnostic or therapeutic decisions.[10](#lary28320-bib-0010){ref-type="ref"} The optimal cutoff value for pepsin in saliva of 216 ng/mL that we used to differentiate between patients with LPR and non‐LPR is quite similar to 210 ng/mL used by Hayet et al. to differentiate between patients with GERD and healthy subjects. Nevertheless, specificity (86.2% vs. 98.2%) of the Pepstest (RDBiomed) was lower in our study group compared to the results reported by Hayet et al., whereas sensitivity was quite similar (41.5% vs. 44.0%).[7](#lary28320-bib-0007){ref-type="ref"} This could be explained by the different study design and patient cohorts. It should be noted that both Hayat et al. and Du et al. have assessed the value of pepsin in saliva to diagnose GERD, whereas we are focusing hereto on patients with symptoms of LPR. We also hypothesized that atypical symptoms are a result of laryngeal or pharyngeal alterations due to increased stress with higher pepsin levels, although the patients had a normal DeMeester score. This can be underlined by the fact that the mean value of the RSI score in both study groups proved to be pathological. In addition, there were signs of reflux esophagitis seen in the LPR and non‐LPR group, which can be due to the fact that catheter‐based pH monitoring may fail to diagnose patients with GERD and patients may show a day‐to‐day variability during measurement.[20](#lary28320-bib-0020){ref-type="ref"}, [33](#lary28320-bib-0033){ref-type="ref"} There also might be some kind of silent reflux present that cannot be detected adequately by MII‐pH. Those combined reasons could explain the low sensitivity of the Peptest (RDBiomed) of 41.5% in our patient cohort. The results of our trial also showed that patients with LPR had a higher mean pepsin concentration out of three samples than patients with primarily LPR‐related symptoms and a normal DeMeester score. Furthermore, a significant correlation between the values of salivary pepsin and the measurements of RSI score in patients with a pathological result in MII‐pH was recognized, and significantly more patients in the LPR group showed a pathological result in the RSI score compared to the non‐LPR group. Based on these findings, a combined application of the cutoff value for pepsin in saliva of 216 ng/mL and the use of the RSI score could increase the specificity and sensitivity of those diagnostic tests to discriminate patients with LPR in clinical practice. This would be a useful, noninvasive, and inexpensive option to diagnose LPR. In addition, the fact that the pepsin test with the highest level in each patient showed that a significant correlation with the RFS score could also allow a combined multiparameter approach of the Peptest (RDBiomed), RSI score, and RFS score to diagnose LPR. Further specific research is necessary to prove that hypothesis. Na et al. reported the best moment to determine the presence of pepsin in saliva, showing the highest values was upon waking.[34](#lary28320-bib-0034){ref-type="ref"} The results of our study cannot confirm this observation. Our patients showed the highest values of pepsin after lunch and dinner, which can be explained by the fact that heartburn likewise generally occurs 1 or 2 hours after a meal.[35](#lary28320-bib-0035){ref-type="ref"} Furthermore, based on the evidence above, it seems that postprandial salivary samples may have a more powerful ability to differentiate GERD patients from non‐GERD patients as well as patients with LPR from non‐LPR. For that reason, the mean value of three samples was used to perform correlation analysis in our trial. Moreover, the pepsin level had no influence on the esophageal motility, which our results share with those of previous studies.[28](#lary28320-bib-0028){ref-type="ref"} All in all, the results of our study underline the role of pepsin in the pathophysiology of laryngopharyngeal/extraesophageal reflux symptoms and encourage performing further research. Nevertheless, correlation analysis between results of Dx‐pH and measurements of objective parameters such as MII‐pH, pepsin in saliva, and RFS score, as well as subjective parameters such as RSI and GIQLI, was not conclusive in our patient cohort. These findings underline the results of previous published trials[10](#lary28320-bib-0010){ref-type="ref"}, [30](#lary28320-bib-0030){ref-type="ref"}, [31](#lary28320-bib-0031){ref-type="ref"}, [32](#lary28320-bib-0032){ref-type="ref"}; therefore, Dx‐pH may have no value in the diagnosis of patients with LPR. Limitations of our study are the lack of follow‐up data to assess treatment outcomes after diagnostic decision based on salivary pepsin testing and that standardization of meals was not included. The patients were only asked to have three main meals so we could best simulate the patient\'s real life. CONCLUSION {#lary28320-sec-0027} ========== The results of this study show that salivary pepsin could be an alternative, cost‐effective, noninvasive measurement tool to assist office‐based diagnosis of LPR, whereas Dx‐pH appears not to be an adequate test. However, larger controlled trials are required to reach more definite conclusions. We want to thank Astrid Reizner and Friedrich Radlmair from the laboratory of the Department of Nuclear Medicine, Ordensklinikum Linz Sisters of Charity Hospital for analyzing the saliva samples. We also want to thank Mag. Christian Steinlechner for statistical support.
Fox Drops the Ball on Iraq War Coverage Fox News continues to divert their readers and viewers attention away from the war in Iraq with any number of "tabloid-type" stories. On a day when the U.S. military announced 14 U.S. troops had been killed in Iraq, the three lead stories on the Fox News web site were: (1) a story about a 13-year old who had her feet severed on a Kentucky amusement park ride, (2) how the search for the missing Canton, Ohio mother was called off because of thunderstorms, and (3) how sewage spilled out of the toilets on a Continental Airlines flight. Not one mention of the 14 U.S. soldiers killed in Iraq on the front page of the Fox News web site The same treatment of the deaths of the 14 U.S. soldiers was evident on all the Fox News television programs where "tabloid-type" stories took precedence over the death of 14 young Americans in Iraq. Here is a round-up of some of the other stories out of Iraq and about the U.S. military which Fox News skipped over in place of the latest on Paris Hilton, Mike Nifong or the missing person du jour. FOX NEWS RANKS LAST ON COVERAGE OF IRAQ WAR The Project for Excellence in Journalism found FOX NEWS spent almost as much time on covering the Anna Nicole Smith story as they did on the Iraq War. In fact, among the three cable news stations, FOX NEWS came in dead last on Iraq War coverage. Bill O'Reilly, host of "The Factor" on FOX NEWS, has been blowing his top saying FOX NEWS doesn't cover the daily car bombings in Iraq because they are so redundant. O'Reilly mistakenly said FOX NEWS does cover the "important" stories about the Iraq War. Apparently the deaths of 14 American troops is not an "important story" in the eyes of FOX NEWS' Bill O'Reilly. But the Project for Excellence in Journalism found overall FOX NEWS devoted only 15 percent of their airtime to the Iraq War while MSNBC spent 31 percent on the war and CNN 25 percent. ARMY RECRUITER GOES TO JAIL FOR SOLICITING 16-YEAR OLD An Army recruiter told a 16-year old high school girl that he could help her get in the Army if she provided him with oral sex. Army Sgt. Robert W. Scott was ordered to jail for a year and will be on probation for five years and will have to pay a fine of $3,020 for the sex offense against the high school gir MARINE WAR VET STRIPPED OF HONORABLE DISCHARGE FOR WAR PROTEST Marine Corporal Adam Kokesh, an Iraq War veteran, has been stripped of his Honorable Discharge and given a General Discharge because he participated in a war protest in Washington wearing parts of his Marine uniform. Kokesh made sure his medals and rank insignia were not on the items he wore during the protest, but a panel of Marine officers still found he was guilty of violating use of his Marine uniform when he appeared at a war protest in Washington. So instead of being able to keep his Honorable Discharge with all the benefits accrued from eight years in the United States Marine Corps, Kokesh has now been given a General Discharge. Kokesh may also have to pay back to the United States government the $10,000 he was given on his GI Bill to attend college. MENTAL HEALTH SYSTEM FOR WAR VETS SUCKS Thanks to the Washington Post, a series appeared on the deplorable conditions wounded veterans face when seeking mental health help after returning from Iraq and Afghanistan. The gut-wrenching account was off the Fox New radar screen. NO DROP IN VIOLENCE IN IRAQ Three months into the new U.S. military strategy that has sent tens of thousands of additional troops into Iraq, overall levels of violence in the country have not decreased, as attacks have shifted away from Baghdad and Anbar, where American forces are concentrated, only to rise in most other provinces, according to a Pentagon report. ARMY NEEDS MORE PSYCHIATRISTS FOR IRAQ WAR VETS The United States Army doesn't have enough mental health workers to handle the enormous number of soldiers returning from Iraq with severe mental health problems. The Army Times reported the Army plans to hire 200 more mental health pros to handle the avalanche of soldiers returning from Iraq with crippling mental health problems. Surveys of troops in Iraq have shown that 15 percent to 20 percent of Army soldiers have signs and symptoms of post-traumatic stress, which can cause flashbacks of traumatic combat experiences and other severe reactions. About 35 percent of soldiers are seeking some kind of mental health treatment a year after returning home under a program that screens returning troops for physical and mental health. FOX AVOIDS REPORTING MASS EXODUS OF IRAQIS The U.N. High Commissioner for Refugees said people fleeing from Iraq has swelled the world's refugee population for the first time in five years. Thousands of Iraqi citizens have fled their homeland for sanctuary in other Middle East countries as the violence spiked again in Iraq with 111 people killed earlier this week , including 30 in Baghdad. Fox News, the Bush White House cheerleader, of course skipped over the mass exodus of Iraqis from Iraq to report on "Operation Arrowhead Ripper," the latest U.S. offensive involving 10,000 U.S. troops searching for Al Qaeda in Baquba, the capital city of Diyala, Province in Iraq. What FOX NEWS doesn't report and what is most troubling to American GIs involved in the offensive is how do they tell who is a member of Al Qaeda. It isn't like they wear uniforms or a T-shirt saying they are a member of Al Qaeda. NO MORE FREE FOOD FOR RETURNING VETS AT AIRPORT In still another display of just how Fox News pays scant attention to our troops serving in Iraq and Afghanistan, the Bangor, Maine international airport has decided to ban a food giveaway to troops returning from combat overseas. The Army Times reported for years, troops stopping for a layover at Bangor International Airport en route to or from Iraq and Afghanistan could count on being offered a chocolate brownie, whoopie pie or other homemade treat. But the free food and beverages came to a halt about a month ago after airport officials served notice to the area's volunteer Maine Troop Greeters that it was enforcing a ban against such giveaways. DIDN'T WE TELL YOU TO STAY INSIDE? Leaflets were dropped from American planes on the city of Baquba, Iraq telling residents to stay inside while American and Iraqi troops scour the area looking for members of Al Qaeda. The leaflets apparently had little impact on the residents of Baquba who were seen mingling on the streets, and even some university students walking to class at the local university. The U.S. military is fanning out all around Baquba, Iraq in hopes of containing Al Qaeda before they move to another area of Iraq and set up their death and suicide squads again. Called "Operation Arrowhead Ripper," the latest U.S. military offense in Iraq has a compliment of 10,000 U.S. troops and Iraqi support troops searching for Al Qaeda. But because the residents of Baquba aren't paying any attention to the leaflets dropped by American helicopters telling them to stay inside, it is becoming impossible for U.S. troops to distinguish Al Qaeda from regular Baquba citizens.
Q: Get value returned from another method In a Template helper, is it possible to get from a method a value returned by another method? In example Template.postsList.helpers({ posts: function () { return Posts.find({}); }, nextPath: function () { // how to return here the number of posts from the query // in the posts method? } }); A: You can just refactor the code so you have a shared way to obtain the posts cursor: var postsCursor = function() { return Posts.find(); }; Template.postsList.helpers posts: postsCursor, nextPath: function () { var count = postsCursor().count(); // do something with count } });
Field Various features relate to an integrated device that includes a capacitor, and more specifically to a capacitor that includes multiple pins and at least one pin that traverses a plate of the capacitor. Background FIG. 1 illustrates a configuration of an integrated device that includes a die. Specifically, FIG. 1 illustrates an integrated device 100 that includes a first die 102 and a package substrate 106. The package substrate 106 includes a dielectric layer and a plurality of interconnects 110. The package substrate 106 is a laminated substrate. The plurality of interconnects 110 includes traces, pads and/or vias. The first die 102 is coupled to the package substrate 106 through a first plurality of solder balls 112. The package substrate 106 is coupled to a printed circuit board (PCB) 108 through a second plurality of solder balls 116. FIG. 1 illustrates that a capacitor 120 is mounted on the PCB 108. The capacitor 120 is located externally of the integrated device 100, and takes up a lot real estate on the PCB 108. A drawback of the capacitor 120 shown in FIG. 1 is that it creates a device with a form factor that may be too large for the needs of mobile computing devices and/or wearable computing devices. This may result in a device that is either too large and/or too thick. That is, the combination of the integrated device 100, the capacitor 120 and the PCB 108 shown in FIG. 1 may be too thick and/or have a surface area that is too large to meet the needs and/or requirements of mobile computing devices and/or wearable computing devices. Therefore, there is a need for an integrated device that includes a compact form factor, while at the same time meeting the needs and/or requirements of mobile devices, Internet of Things (IoT) devices, computing devices and/or wearable computing devices.
The US connection: Melina Mercouri and her friend Dr Andrew Horton Andrew Horton speaks to Helen Velissaris on his life in Greece with the Junta, his friend Melina Mercouri and the script he’s writing on her life Node Tools Comments: (0) Rate This 4 1 vote Your rating: None Melina Mercouri the subejct of Horton's new screenplay. 12 Dec 2012 "Of course I was familiar with protest movements in the USA against the Vietnam War, but I had never seen anything like tanks in the streets, students being arrested and tortured..." World acclaimed screenwriter and author, Dr Andrew Horton, lived in Greece in the '60s and '70s and witnessed the Junta period first hand. Making the trip to teach English at Athens University in 1966, Horton had no idea what he'd be thrown into. "I totally understood what it meant to try and survive under such a dictatorship and to somehow make an effort to protest and look forward to democracy again," he says. Despite the turbulent times, Dr Horton easily fell in love with Greece. Now he organizes trips to Greece for interested students at Oklahoma University, where he teaches film. In 1973, Horton became the film critic to The Athenian Magazine where he got his in with the Greek film scene. Everyone from Theodoros Angelopoulos, Mihalis Cacoyannis and Jules Dassin passed by his office constantly. But it was his friendship with the great Melina Mercouri which left a lasting mark on him. The two met in 1974 when he was writing for the Athenian Magazine and stayed in touch until her death in 1994. He followed her life as a singer, actress and always saw her passion for activism and philanthropy in everything she put her mind to. "She was not just an actress who could sing and dance and make people laugh, but she had a passion to 'make a difference' with her films and in any way possible to 'help Greeks' in the best sense," he says. He remembers her humour the most, an ability to open doors for herself with a couple of laughs, all in the name of a good cause. Mercouri devoted her life to her country, even becoming Minister of Culture in the Greek Parliament. She would reach out with theatre groups, travel to villages to perform for schools and little islands. She even set up the Greek Film Centre to help budding filmmakers help make their films with financial help from the centre. Now, Horton is undertaking the role of writing a script on the life of his much-loved friend. He hopes the project will be picked up by a talented crew to make it into a mainstream film, not just for a Greek audience but for everyone. "I want it to be a real film with a well known director and yes a well known actress and thus it has to be more than just a 'Greek crew' working on it and I am talking to people in Hollywood, yes, of the Greek community and Europe and we'll see what happens," he says. His high profile will hopefully boost the project and get it to the production stage. Horton has penned some well known films, including Brad Pitt's first feature film, The Dark Side of the Sun and the much awarded Something in Between (1983, Yugoslavia, dir. Srdjan Karanovic). Along with his screen writing pursuits he has written over 20 books on the industry. The push to write the script came from the kind words of his friend 10 years ago, production designer Phedon Papamichael. "Andrew, you have to write a script about her life that can be a popular film not just a biography so the world knows about her, because you know her and you know Greece," Papamichael said. Already under his belt, Horton has written screenplays for Renos Haralambidis and one with Lakis Lazopoulos, including a few more in the works.
// Copyright 2018 The Operator-SDK Authors // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. package olmcatalog import ( "bytes" "crypto/sha256" "encoding/json" goerrors "errors" "fmt" "sort" "strings" "github.com/operator-framework/operator-registry/pkg/registry" "github.com/operator-framework/operator-sdk/internal/generate/olm-catalog/descriptor" "github.com/operator-framework/operator-sdk/pkg/k8sutil" "github.com/ghodss/yaml" operatorsv1alpha1 "github.com/operator-framework/operator-lifecycle-manager/pkg/api/apis/operators/v1alpha1" log "github.com/sirupsen/logrus" appsv1 "k8s.io/api/apps/v1" corev1 "k8s.io/api/core/v1" rbacv1 "k8s.io/api/rbac/v1" apiextv1beta1 "k8s.io/apiextensions-apiserver/pkg/apis/apiextensions/v1beta1" "k8s.io/apimachinery/pkg/apis/meta/v1/unstructured" "k8s.io/apimachinery/pkg/runtime/schema" "k8s.io/apimachinery/pkg/version" ) // manifestCollection holds a collection of all manifests relevant to CSV updates. type manifestCollection struct { Roles []rbacv1.Role ClusterRoles []rbacv1.ClusterRole Deployments []appsv1.Deployment CustomResourceDefinitions []apiextv1beta1.CustomResourceDefinition CustomResources []unstructured.Unstructured Others []unstructured.Unstructured } // addRoles assumes add manifest data in rawManifests are Roles and adds them // to the collection. func (c manifestCollection) addRoles(rawManifests ...[]byte) error { for _, rawManifest := range rawManifests { role := rbacv1.Role{} if err := yaml.Unmarshal(rawManifest, &role); err != nil { return fmt.Errorf("error adding Role to manifest collection: %v", err) } c.Roles = append(c.Roles, role) } return nil } // addClusterRoles assumes add manifest data in rawManifests are ClusterRoles // and adds them to the collection. func (c manifestCollection) addClusterRoles(rawManifests ...[]byte) error { for _, rawManifest := range rawManifests { role := rbacv1.ClusterRole{} if err := yaml.Unmarshal(rawManifest, &role); err != nil { return fmt.Errorf("error adding ClusterRole to manifest collection: %v", err) } c.ClusterRoles = append(c.ClusterRoles, role) } return nil } // addDeployments assumes add manifest data in rawManifests are Deployments // and adds them to the collection. func (c manifestCollection) addDeployments(rawManifests ...[]byte) error { for _, rawManifest := range rawManifests { dep := appsv1.Deployment{} if err := yaml.Unmarshal(rawManifest, &dep); err != nil { return fmt.Errorf("error adding Deployment to manifest collection: %v", err) } c.Deployments = append(c.Deployments, dep) } return nil } // addOthers assumes add manifest data in rawManifests are able to be // unmarshalled into an Unstructured object and adds them to the collection. func (c manifestCollection) addOthers(rawManifests ...[]byte) error { for _, rawManifest := range rawManifests { u := unstructured.Unstructured{} if err := yaml.Unmarshal(rawManifest, &u); err != nil { return fmt.Errorf("error adding manifest collection: %v", err) } c.Others = append(c.Others, u) } return nil } // filter applies filtering rules to certain manifest types in a collection. func (c manifestCollection) filter() { c.filterCustomResources() } // filterCustomResources filters "other" objects, which contain likely // Custom Resources corresponding to a CustomResourceDefinition, by GVK. func (c manifestCollection) filterCustomResources() { crdGVKSet := make(map[schema.GroupVersionKind]struct{}) for _, crd := range c.CustomResourceDefinitions { for _, version := range crd.Spec.Versions { gvk := schema.GroupVersionKind{ Group: crd.Spec.Group, Version: version.Name, Kind: crd.Spec.Names.Kind, } crdGVKSet[gvk] = struct{}{} } } customResources := []unstructured.Unstructured{} for _, other := range c.Others { if _, gvkMatches := crdGVKSet[other.GroupVersionKind()]; gvkMatches { customResources = append(customResources, other) } } c.CustomResources = customResources } // apply applies the manifests in the collection to csv. func (c manifestCollection) apply(csv operatorsv1alpha1.ClusterServiceVersion) error { strategy := getCSVInstallStrategy(csv) switch strategy.StrategyName { case operatorsv1alpha1.InstallStrategyNameDeployment: c.applyRoles(&strategy.StrategySpec) c.applyClusterRoles(&strategy.StrategySpec) c.applyDeployments(&strategy.StrategySpec) } csv.Spec.InstallStrategy = strategy c.applyCustomResourceDefinitions(csv) if err := c.applyCustomResources(csv); err != nil { return fmt.Errorf("error applying Custom Resource: %v", err) } return nil } // Get install strategy from csv. func getCSVInstallStrategy(csv operatorsv1alpha1.ClusterServiceVersion) operatorsv1alpha1.NamedInstallStrategy { // Default to a deployment strategy if none found. if csv.Spec.InstallStrategy.StrategyName == "" { csv.Spec.InstallStrategy.StrategyName = operatorsv1alpha1.InstallStrategyNameDeployment } return csv.Spec.InstallStrategy } // applyRoles updates strategy's permissions with the Roles in the collection. func (c manifestCollection) applyRoles(strategy operatorsv1alpha1.StrategyDetailsDeployment) { perms := []operatorsv1alpha1.StrategyDeploymentPermissions{} for _, role := range c.Roles { perms = append(perms, operatorsv1alpha1.StrategyDeploymentPermissions{ ServiceAccountName: role.GetName(), Rules: role.Rules, }) } strategy.Permissions = perms } // applyClusterRoles updates strategy's cluserPermissions with the ClusterRoles // in the collection. func (c manifestCollection) applyClusterRoles(strategy operatorsv1alpha1.StrategyDetailsDeployment) { perms := []operatorsv1alpha1.StrategyDeploymentPermissions{} for _, role := range c.ClusterRoles { perms = append(perms, operatorsv1alpha1.StrategyDeploymentPermissions{ ServiceAccountName: role.GetName(), Rules: role.Rules, }) } strategy.ClusterPermissions = perms } // applyDeployments updates strategy's deployments with the Deployments // in the collection. func (c manifestCollection) applyDeployments(strategy operatorsv1alpha1.StrategyDetailsDeployment) { depSpecs := []operatorsv1alpha1.StrategyDeploymentSpec{} for _, dep := range c.Deployments { setWatchNamespacesEnv(&dep) // Make sure "olm.targetNamespaces" is referenced somewhere in dep, // and emit a warning of not. if !depHasOLMNamespaces(dep) { log.Warnf(`No WATCH_NAMESPACE environment variable nor reference to "%s"`+ ` detected in operator Deployment. For OLM compatibility, your operator`+ ` MUST watch namespaces defined in "%s"`, olmTNMeta, olmTNMeta) } depSpecs = append(depSpecs, operatorsv1alpha1.StrategyDeploymentSpec{ Name: dep.GetName(), Spec: dep.Spec, }) } strategy.DeploymentSpecs = depSpecs } const olmTNMeta = "metadata.annotations['olm.targetNamespaces']" // setWatchNamespacesEnv sets WATCH_NAMESPACE to olmTNString in dep if // WATCH_NAMESPACE exists in a pod spec container's env list. func setWatchNamespacesEnv(dep appsv1.Deployment) { envVar := newEnvVar(k8sutil.WatchNamespaceEnvVar, olmTNMeta) overwriteContainerEnvVar(dep, k8sutil.WatchNamespaceEnvVar, envVar) } func overwriteContainerEnvVar(dep appsv1.Deployment, name string, ev corev1.EnvVar) { for _, c := range dep.Spec.Template.Spec.Containers { for i := 0; i < len(c.Env); i++ { if c.Env[i].Name == name { c.Env[i] = ev } } } } func newEnvVar(name, fieldPath string) corev1.EnvVar { return corev1.EnvVar{ Name: name, ValueFrom: &corev1.EnvVarSource{ FieldRef: &corev1.ObjectFieldSelector{ FieldPath: fieldPath, }, }, } } // OLM places the set of target namespaces for the operator in // "metadata.annotations['olm.targetNamespaces']". This value should be // referenced in either: // - The Deployment's pod spec WATCH_NAMESPACE env variable. // - Some other Deployment pod spec field. func depHasOLMNamespaces(dep appsv1.Deployment) bool { b, err := dep.Spec.Template.Marshal() if err != nil { // Something is wrong with the deployment manifest, not with CLI inputs. log.Fatalf("Marshal Deployment spec: %v", err) } return bytes.Contains(b, []byte(olmTNMeta)) } // applyCustomResourceDefinitions updates csv's customresourcedefinitions.owned // with CustomResourceDefinitions in the collection. // customresourcedefinitions.required are left as-is, since they are // manually-defined values. func (c manifestCollection) applyCustomResourceDefinitions(csv operatorsv1alpha1.ClusterServiceVersion) { ownedDescs := []operatorsv1alpha1.CRDDescription{} descMap := map[registry.DefinitionKey]operatorsv1alpha1.CRDDescription{} for _, owned := range csv.Spec.CustomResourceDefinitions.Owned { defKey := registry.DefinitionKey{ Name: owned.Name, Version: owned.Version, Kind: owned.Kind, } descMap[defKey] = owned } for _, crd := range c.CustomResourceDefinitions { for _, ver := range crd.Spec.Versions { defKey := registry.DefinitionKey{ Name: crd.GetName(), Version: ver.Name, Kind: crd.Spec.Names.Kind, } if owned, ownedExists := descMap[defKey]; ownedExists { ownedDescs = append(ownedDescs, owned) } else { ownedDescs = append(ownedDescs, operatorsv1alpha1.CRDDescription{ Name: defKey.Name, Version: defKey.Version, Kind: defKey.Kind, }) } } } csv.Spec.CustomResourceDefinitions.Owned = ownedDescs } // updateDescriptions parses APIs in apisDir for code and annotations that // can build a verbose crdDescription and updates existing crdDescriptions in // csv. If no code/annotations are found, the crdDescription is appended as-is. func updateDescriptions(csv operatorsv1alpha1.ClusterServiceVersion, apisDir string) error { updatedDescriptions := []operatorsv1alpha1.CRDDescription{} for _, currDescription := range csv.Spec.CustomResourceDefinitions.Owned { group := currDescription.Name if split := strings.Split(currDescription.Name, "."); len(split) > 1 { group = strings.Join(split[1:], ".") } // Parse CRD descriptors from source code comments and annotations. gvk := schema.GroupVersionKind{ Group: group, Version: currDescription.Version, Kind: currDescription.Kind, } newDescription, err := descriptor.GetCRDDescriptionForGVK(apisDir, gvk) if err != nil { if goerrors.Is(err, descriptor.ErrAPIDirNotExist) { log.Debugf("Directory for API %s does not exist. Skipping CSV annotation parsing for API.", gvk) } else if goerrors.Is(err, descriptor.ErrAPITypeNotFound) { log.Debugf("No kind type found for API %s. Skipping CSV annotation parsing for API.", gvk) } else { // TODO: Should we ignore all CSV annotation parsing errors and simply log the error // like we do for the above cases. return fmt.Errorf("failed to set CRD descriptors for %s: %v", gvk, err) } // Keep the existing description and don't update on error updatedDescriptions = append(updatedDescriptions, currDescription) } else { // Replace the existing description with the newly parsed one newDescription.Name = currDescription.Name updatedDescriptions = append(updatedDescriptions, newDescription) } } csv.Spec.CustomResourceDefinitions.Owned = updatedDescriptions return nil } // applyCustomResources updates csv's "alm-examples" annotation with the // Custom Resources in the collection. func (c manifestCollection) applyCustomResources(csv operatorsv1alpha1.ClusterServiceVersion) error { examples := []json.RawMessage{} for _, cr := range c.CustomResources { crBytes, err := cr.MarshalJSON() if err != nil { return err } examples = append(examples, json.RawMessage(crBytes)) } examplesJSON, err := json.Marshal(examples) if err != nil { return err } examplesJSON, err = prettifyJSON(examplesJSON) if err != nil { return err } if csv.GetAnnotations() == nil { csv.SetAnnotations(make(map[string]string)) } csv.GetAnnotations()["alm-examples"] = string(examplesJSON) return nil } // prettifyJSON returns a JSON in a pretty format func prettifyJSON(b []byte) ([]byte, error) { var out bytes.Buffer err := json.Indent(&out, b, "", " ") return out.Bytes(), err } // deduplicate removes duplicate objects from the collection, since we are // collecting an arbitrary list of manifests. func (c manifestCollection) deduplicate() error { hashes := make(map[string]struct{}) roles := []rbacv1.Role{} for _, role := range c.Roles { hasHash, err := addToHashes(&role, hashes) if err != nil { return err } if !hasHash { roles = append(roles, role) } } c.Roles = roles clusterRoles := []rbacv1.ClusterRole{} for _, clusterRole := range c.ClusterRoles { hasHash, err := addToHashes(&clusterRole, hashes) if err != nil { return err } if !hasHash { clusterRoles = append(clusterRoles, clusterRole) } } c.ClusterRoles = clusterRoles deps := []appsv1.Deployment{} for _, dep := range c.Deployments { hasHash, err := addToHashes(&dep, hashes) if err != nil { return err } if !hasHash { deps = append(deps, dep) } } c.Deployments = deps crds := []apiextv1beta1.CustomResourceDefinition{} for _, crd := range c.CustomResourceDefinitions { hasHash, err := addToHashes(&crd, hashes) if err != nil { return err } if !hasHash { crds = append(crds, crd) } } c.CustomResourceDefinitions = crds crs := []unstructured.Unstructured{} for _, cr := range c.CustomResources { b, err := cr.MarshalJSON() if err != nil { return err } hash := hashContents(b) if _, hasHash := hashes[hash]; !hasHash { crs = append(crs, cr) hashes[hash] = struct{}{} } } c.CustomResources = crs return nil } // marshaller is an interface used to generalize hashing for deduplication. type marshaller interface { Marshal() ([]byte, error) } // addToHashes calls m.Marshal(), hashes the returned bytes, and adds the // hash to hashes if it does not exist. addToHashes returns true if m's hash // was not in hashes. func addToHashes(m marshaller, hashes map[string]struct{}) (bool, error) { b, err := m.Marshal() if err != nil { return false, err } hash := hashContents(b) _, hasHash := hashes[hash] if !hasHash { hashes[hash] = struct{}{} } return hasHash, nil } // hashContents creates a sha256 md5 digest of b's bytes. func hashContents(b []byte) string { h := sha256.New() _, _ = h.Write(b) return string(h.Sum(nil)) } // sortUpdates sorts all fields updated in csv. // TODO(estroz): sort other modified fields. func sortUpdates(csv operatorsv1alpha1.ClusterServiceVersion) { sort.Sort(descSorter(csv.Spec.CustomResourceDefinitions.Owned)) sort.Sort(descSorter(csv.Spec.CustomResourceDefinitions.Required)) } // descSorter sorts a set of crdDescriptions. type descSorter []operatorsv1alpha1.CRDDescription var _ sort.Interface = descSorter{} func (descs descSorter) Len() int { return len(descs) } func (descs descSorter) Less(i, j int) bool { if descs[i].Name == descs[j].Name { if descs[i].Kind == descs[j].Kind { return version.CompareKubeAwareVersionStrings(descs[i].Version, descs[j].Version) > 0 } return descs[i].Kind < descs[j].Kind } return descs[i].Name < descs[j].Name } func (descs descSorter) Swap(i, j int) { descs[i], descs[j] = descs[j], descs[i] }
Q: How to get all the required values using jquery or javascript I am having 2 kendo grids which are coming dynamically and the rows and the columns in the grid are also coming dynamically.I have only single save button at the end of grids. My question is when i click the save button i want to save all the values that are modified in the grids. Hope you understand my question.How can i able to do that.Can any one please provide me help Thanks and Regards, Srinivas A: Assuming that you have something like: var grid1 = $("#grid1").kendoGrid({...}).data("kendoGrid"); var grid2 = $("#grid2").kendoGrid({...}).data("kendoGrid"); $("#save_both").click(function() { grid1.saveChanges(); grid2.saveChanges(); }); Basically, when the button is clicked you invoke the saveChanges method of both grids (see http://docs.kendoui.com/api/web/grid#savechanges for more information on saveChanges).
The Story of Mike Danton Mike Danton (left), whose real name was Mike Jefferson, grew up in the Toronto suburb of Brampton. He went on to star for the Quinte Hawks of the Metro Junior Hockey League in 1996-97. The team was coached by David Frost, who would become his agent and alleged svengali. In the years that followed, Danton would become estranged from his parents. Mike Danton (left), whose real name was Mike Jefferson, grew up in the Toronto suburb of Brampton. He went on to star for the Quinte Hawks of the Metro Junior Hockey League in 1996-97. The team was coached by David Frost, who would become his agent and alleged svengali. In the years that followed, Danton would become estranged from his parents. David Frost is a controversial figure who coached a wildly undisciplined Brampton Junior A team that was threatened with suspension in 1993-94. He was accused of hitting one of his players in 1997 and banned from Central A Junior Hockey League arenas after a dispute with the league in 2004. In 2006, he was charged with multiple counts (all dismissed) of sexual exploitation for allegedly hosting alcohol-fueled sex parties involving teenagers. David Frost is a controversial figure who coached a wildly undisciplined Brampton Junior A team that was threatened with suspension in 1993-94. He was accused of hitting one of his players in 1997 and banned from Central A Junior Hockey League arenas after a dispute with the league in 2004. In 2006, he was charged with multiple counts (all dismissed) of sexual exploitation for allegedly hosting alcohol-fueled sex parties involving teenagers. Danton's father, Steve Jefferson, insisted that David Frost had an undue influence and control over his son. Mike had lived with Frost and his wife during his time in junior hockey and Steve Jefferson later said of Frost that he "stole Michael from us [and has taken] Michael's mind from him." Danton's father, Steve Jefferson, insisted that David Frost had an undue influence and control over his son. Mike had lived with Frost and his wife during his time in junior hockey and Steve Jefferson later said of Frost that he "stole Michael from us [and has taken] Michael's mind from him." A scrappy forward, Danton, right, was drafted by the New Jersey Devils in the fifth round of the 2000 NHL draft. He played parts of two seasons for the team, appearing in 19 games and scoring two points, before he was traded to St. Louis. A scrappy forward, Danton, right, was drafted by the New Jersey Devils in the fifth round of the 2000 NHL draft. He played parts of two seasons for the team, appearing in 19 games and scoring two points, before he was traded to St. Louis. During his only full season in the NHL, Danton appeared in 68 games for the Blues, scoring seven goals and 12 points while racking up 141 penalty minutes. But there were signs of trouble off the ice. "I had a big problem with being alone," he told SI. He hung out in strip clubs, drank a lot, stayed up all night and exhibited signs of mental instability. "I couldn't make decisions. I was a 23-year-old infant who wasn't in the right mind frame to be an adult, much less an NHL player." During his only full season in the NHL, Danton appeared in 68 games for the Blues, scoring seven goals and 12 points while racking up 141 penalty minutes. But there were signs of trouble off the ice. "I had a big problem with being alone," he told SI. He hung out in strip clubs, drank a lot, stayed up all night and exhibited signs of mental instability. "I couldn't make decisions. I was a 23-year-old infant who wasn't in the right mind frame to be an adult, much less an NHL player." In April 2004, Danton was arrested at an airport in San Jose and charged with conspiring to have a man killed, a man who was said to be coming to St. Louis to murder him over money owed. Prosecutors contended that the man in question was David Frost. Danton insisted the man was his father, Steve, and he attempted suicide in Santa Clara (Calif.) County Jail shortly after his arrest. He later reached a plea deal and was sentenced to 90 months in federal prison. The judge said, "In over 18 years on the bench, I have [never] been faced with a case as bizarre as this one." In April 2004, Danton was arrested at an airport in San Jose and charged with conspiring to have a man killed, a man who was said to be coming to St. Louis to murder him over money owed. Prosecutors contended that the man in question was David Frost. Danton insisted the man was his father, Steve, and he attempted suicide in Santa Clara (Calif.) County Jail shortly after his arrest. He later reached a plea deal and was sentenced to 90 months in federal prison. The judge said, "In over 18 years on the bench, I have [never] been faced with a case as bizarre as this one." After serving 65 months in prison, during which time he received intensive therapy, Danton was freed in the fall of 2009. Now 30 years old, he is studying psychology (with a near 4.0 GPA) at St. Mary's University in Halifax, Nova Scotia and playing for the Huskies, the school's hockey team. "I know this is going to sound nuts," he told SI, "but I'm glad I went to prison...because the negative-downward spiral that would have happened would be been 10 times worse. It saved me in a way." After serving 65 months in prison, during which time he received intensive therapy, Danton was freed in the fall of 2009. Now 30 years old, he is studying psychology (with a near 4.0 GPA) at St. Mary's University in Halifax, Nova Scotia and playing for the Huskies, the school's hockey team. "I know this is going to sound nuts," he told SI, "but I'm glad I went to prison...because the negative-downward spiral that would have happened would be been 10 times worse. It saved me in a way." Get expert analysis, unrivaled access, and the award-winning storytelling only SI can provide - from Peter King, Tom Verducci, Lee Jenkins, Seth Davis, and more - delivered straight to you, along with up-to-the-minute news and live scores.
MotoGP Racing Blog Monlau Repsol Technical School Wednesday, December 18, 2013 Top racers rely on a skilled crew to keep the motorcycle in prime performing order before, during and after a race. At the Monlau Repsol Technical School in Spain, up-and-coming technicians receive training in practical circumstances, working with real riders at real circuits so they can be completely prepared for top-level competition work after graduation. Curriculum follows guidelines set out by the FIM and FIA, theory is provided by professionals in the field and master classes are taught by experts. In 2012/2013 alone, Repsol gave over 20 grants to cover costs for courses for select students. See the video below for a closer look at the Monlau Repsol Technical School.
/* * Copyright 2015 Daniel Bechler * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package de.danielbechler.diff.identity import de.danielbechler.diff.ObjectDiffer import de.danielbechler.diff.ObjectDifferBuilder import de.danielbechler.diff.path.NodePath import spock.lang.Specification class IdentityStrategyAT extends Specification { static class ObjectWithListProperty { List<?> collection = [] } static class NonMatchingIdentityStrategy implements IdentityStrategy { @Override boolean equals(Object working, Object base) { return false } } def 'configure IdentityStrategy for property of specific type'() { def strategy = new NonMatchingIdentityStrategy() ObjectDiffer objectDiffer = ObjectDifferBuilder.startBuilding() .identity().ofCollectionItems(ObjectWithListProperty, 'collection').via(strategy) .and().build() def working = new ObjectWithListProperty(collection: ['a']) def base = new ObjectWithListProperty(collection: ['a']) when: def node = objectDiffer.compare(working, base) then: node.untouched } def 'configure IdentityStrategy for element at specific path'() { def strategy = new NonMatchingIdentityStrategy() ObjectDiffer objectDiffer = ObjectDifferBuilder.startBuilding() .identity() .ofCollectionItems(NodePath.with('collection')).via(strategy) .and().build() def working = new ObjectWithListProperty(collection: ['a']) def base = new ObjectWithListProperty(collection: ['a']) when: def node = objectDiffer.compare(working, base) then: node.untouched } def 'configure custom IdentityStrategyResolver'() { given: def strategy = new IdentityStrategy() { boolean equals(Object working, Object base) { return working.getAt('id') == base.getAt('id') } } def objectDiffer = ObjectDifferBuilder.startBuilding() .identity() .setDefaultCollectionItemIdentityStrategy(strategy) .and() .build() when: def node = objectDiffer.compare([[id: '1', value: 'original']], [[id: '1', value: 'changed']]) then: node.getChild(NodePath.startBuilding().collectionItem([id:'1']).build()).changed } }
Turnbull, David. 2000. Masons, Tricksters, and Cartographers: Comparative Studies in the Sociology of Scientific and Indigenous Knowledge. New York: Routledge Turnbull aims to show that all knowledge production, including the technoscientific, is “motley”—i.e. a messy meshwork of places, practices, contingencies, and creativity. “The process of knowledge assemblage is a dialectical one in which forms of social space are coproduced. The interactive, contingent assemblage of space and knowledge, sustained and created by social labour, results in what I call a ‘knowledge space’” (4). The knowledge spaces discussed in the book include the construction practices of gothic cathedrals by masons, the production of maps by colonial and European state-makers, indigenous Pacific navigators, scientists and governments seeking a malaria vaccines, and turbulence research. He considers all of these assemblages “forms of local knowledge,” which he says can be compared “so that their differential power effects can be explained but without privileging any of them epistemologically” (6). The question is how does this knowledge travel beyond the site of its production? And how does this assemblage of people, places, practices etc etc become linked and what kind of space does this ensemble produce? The gothic cathedral was built without architects, plans, or common measures; it brought together a vast array of people with different “specialized” but not “expert” knowledges into a knowledge space. With the map and state being co-produced, a cartographic knowledge space is produced, while the Pacific islanders organized knowledge spatially in colonizing the worlds largest ocean. With malaria, the techno-scientific knowledge space being produced by their search for a “global” vaccine is unable to match (or admit) the utter messiness and localness of malaria itself. While turbulence research seeks to impose order to something that might be only defined as chaos. I really liked this book and it’s important for my research. My main critiques are two: 1) I wish that Turnbull’s positioning of himself as a “trickster” would have come out in a more playful manner as I was expecting. I guess an intellectual boundary-snapping trickster is better than no trickster at all. 2) The “space” of “knowledge spaces” is a bit weird. On the one hand, I recognize that he is pointing out how knowledge is always emplaced and embodied via practice and that various assemblages are being produced—sometimes quite contingently—by all these human endeavors, but the production of space itself shines through much more in the chapters on masons, mapping, and islanders, than in the much more ambient chapters on malaria and turbulence, which are much more about knowledge than space-and-knowledge per se. (One more quibble: the book is more a series of “case studies” than genuinely comparative.) The bridging of material, ideal, and practice has many resonances with a lot I’ve been reading, particularly from Lefebvre and other Marxists. But applied to science and technology it has a much different twist with compelling affinities: The motley of scientific practice, its situated messiness, is given a spatial coherence through the social labour of creating equivalences and connections. Such knowledge spaces acquire their taken for granted air and seemingly unchallengeable naturalness through the suppression and denial of work involved in their construction. However, since they are motleys, they are polysemous and are capable of many possible modes of assemblage and of providing alternative interpretations and meanings. Hence all knowledge spaces are potential sites of resistance. (20) The major difference between knowledge systems is produced by power. The power of science over, say, indigenous systems “lies not in the nature of scientific knowledge but in its greater ability to move and apply the knowledge it produces beyond the site of its production” (39). In this sense, particular configurations of people and place make particular kinds of knowledges possible. Knowledge spaces are motley affairs of practice and this is true of indigenous and technoscientific knowledge:
Structure of beta-antithrombin and the effect of glycosylation on antithrombin's heparin affinity and activity. Antithrombin is a member of the serpin family of protease inhibitors and the major inhibitor of the blood coagulation cascade. It is unique amongst the serpins in that it circulates in a conformation that is inactive against its target proteases. Activation of antithrombin is brought about by a conformational change initiated upon binding heparin or heparan sulphate. Two isoforms exist in the circulation, alpha-antithrombin and beta-antithrombin, which differ in the amount of glycosylation present on the polypeptide chain; beta-antithrombin lacks the carbohydrate present at Asn135 in alpha-antithrombin. Of the two forms, beta-antithrombin has the higher affinity for heparin and thus functions as the major inhibitor in vivo even though it is the less abundant form. The reason for the differences in heparin affinity between the alpha and beta-forms have been shown to be due to the additional carbohydrate changing the rate of the conformational change. Here, we describe the most accurate structures of alpha-antithrombin and alpha-antithrombin+heparin pentasaccharide reported to date (2.6A and 2.9A resolution, respectively, both re-refinements using old data), and the structure of beta-antithrombin (2.6A resolution). The new structures have a remarkable degree of ordered carbohydrate and include parts of the antithrombin chain not modeled before. The structures have allowed a detailed comparison of the conformational differences between the three. They show that the structural basis of the lower affinity for heparin of alpha-antithrombin over beta-antithrombin is due to the conformational change that occurs upon heparin binding being sterically hindered by the presence of the additional bulky carbohydrate at Asn135.
KARACHI: A suspected suicide explosion targeting President Asif Ali Zardari's chief security officer killed at least three people in Karachi on Wednesday, police said. Eleven others were injured in the powerful explosion which rocked the busy New Town neighbourhood in the heart of Karachi, less than a kilometre from the Quaid's mausoleum. “Three people, including the president’s chief security officer, Bilal Sheikh, were killed in the bombing,” said Superintendent Police Usman Bajwa. Pakistan's President Asif Ali Zardari said that "Bilal had rendered many sacrifices for the PPP and that he was not just a bodyguard but more like a son." President Zardari also appealed to party workers to offer fateha for Bilal. The president added that Bilal had accompanied Benazir Bhutto when she was attacked in Karachi on Oct 18, 2007. Bilal Sheikh was an active worker of the Pakistan People’s Party, the ruling party in Sindh province. A spokesman for the Bilawal House, President Zardari's private residence in Karachi, had earlier confirmed Sheikh’s death. Sheikh's driver was also killed in the explosion. Bajwa said the attack appeared to be a suicide bombing. “Bilal Sheikh’s vehicle was the target of the attack,” he said. Officials said the wounded included six police officers and one FIA personnel. The injured were shifted to a local hospital where a state of emergency was imposed. Bilal Sheikh was said to be a trusted aide of President Asif Ali Zardari, had previously been in charge of Zardari's private residence in Karachi, and was also responsible for the security in Karachi of Bilawal Bhutto-Zardari, the president’s son and PPP co-chairman. Sheikh had also been in charge of security for Zardari's wife, former prime minister Benazir Bhutto when she returned to Karachi from exile on October 18, 2007, two months before her assassination. The explosion came on the eve of the holy Muslim month of Ramazan, due to be observed in Pakistan from Thursday. Bajwa said Sheikh and his driver had gone to buy food for Ramazan, the fasting month, when his vehicle was targeted. "He had never taken this route before, and he always had security with him," he said. Sheikh had survived two previous attempts on his life. No militant group has claimed responsibility of the attack as yet, but the Tehrik-i-Taliban Pakistan have previously targeted the Pakistan People's Party for it's "secular views". President Zardari and Prime Minister Nawaz Sharif “strongly condemned” the attack, state media said. In a statement, Bilawal Bhutto-Zardari also condemned the attack, blaming an "anti-democratic and extremist mindset" to be behind the bombing. "We will not be intimidated by such cowardly acts and such acts will not deter our resolve to fight terrorism," he said.
Q: copy constructor of a class which has self-pointer to itself in C++? I wanted to ask that how will we implement a copy constructor of a class which has self pointer to itself as its data member, i want to implement a deep copy, class City { string name; City* parent; public: City(string nam, double dcov); City(string nam, double dcov, City* c); City(const City& obj) { this-> name = obj.name; // how to assign parent parent = new City(??) } ~City(); void setName(string name1); void setDistanceCovered(int dist); string getName(); double getDistanceCovered(); City* getParent(){return parent;} }; I am confused that this line // how to assign parent parent = new City(??)will call constructor again instead of deep copy? Regards. A: How about if (obj.parent != NULL) parent = new City(*obj.parent) else parent = NULL; This should work unless you have cycles in the parent hierarchy.
California. September 12th marked the expiration of the Long Ridge timber harvest plan (THP) in the Mattole watershed. After 5 years of fierce direct action and multiple months-long road blockades, tree-sits, and tripods to save the Mattole forest, this day conjures both somber and celebratory emotions. Originally publushed by Save the Mattole’s Ancient Forest Facebook page. Image above: Rally at Foxcamp Gate – September 8th, 2019 2014 Despite the fact that HRC managed to log and herbicide a portion of this ancient forest, relentless resistance from the community and devoted forest defenders succeeded in saving a significant amount of forest that would have other wise been logged by HRC. Tremendous love and gratitude to the hundreds of people who showed up over the years and threw down hard to protect this precious ecosystem. These forests are safe because of you! Worth celebrating are the 512 acres of helicopter logging that was dropped from the original THP thanks to the 2014 blockade. The successful blocking of the 2017 “road to nowhere” saved a hillside excavation and protected a grove of ancient Bay trees from destruction. Big love to Rook for holding it down this summer in the canopy for 60 days and effectively saving an old growth Douglas fir. Love to Pascal for sitting in a giant candalabra tree in Unit 1 – a beautiful grove of mixed forest and magnificent Douglas fir trees which still stands. And of course the forest fought for itself, with a landslide in 2016 making parts of that forest unharvestable. None of these accomplishments could have been possible without the support of the community and all the wonderful people who traveled from near and far and those no longer with us to #savethemattolesancientforest! 2014 Thank you everyone for all the love and continued support over the years. This is not the end, but the continuation of decades of resistance in this bioregion. Sending love and gratitude to forest defenders, #waterprotecters, and #earthdefenders all over the world fighting to #protectwhatyoulove! The fight isn’t over yet y’all! #forestdefenseisclimatedefense (Photos from the recent rally at Fox camp gate September 8th, 2019 and from the road blockade of 2014 that kicked this chapter off) 2014 RIP: Bunny, Scout, Squirrel, Dave’s Not Here, Jungle, Nature Boy, Oat Groat, Root, Thorn, Bagel, and Roots 2014 Support Enough 14 Donation for our work in the Enough 14 info-café and our independent reporting on our blog and social media channels. Even 1€ can make a difference. €1.00 Keep the Enough 14 blog and the Enough 14 Info-Café going. You can do that with a donation here, or by ordering stickers, posters, t-shirts , hoodies or one of the other items here or click at the image below. Support Enough 14! Share this: Twitter Facebook Reddit Tumblr Pinterest LinkedIn Print Email Pocket Telegram WhatsApp Skype Like this: Like Loading...
--- title: "@casl/ability/extra API" categories: [api] order: 15 meta: keywords: ~ description: ~ --- ## rulesToQuery This is a helper iterator function that allows to convert permissions into database query. Handles common scenarios like trying to get rules for an action that is not defined. The function adjust the amount of parameters depending on passed in `TAbility` generic parameters. * Parameters: * `ability: TAbility` * `action: string` * `subject: Subject` * `convert: (rule: RuleOf<TAbility>) => object` * Returns `null` if user is not allowed to specified `action` on specified `subject`, otherwise returns an object of optional `$and` and `$or` fields. `$and` contains results of transformation from inverted rules and `$or` contains results of direct rules. * See also: [Ability to database query](../../advanced/ability-to-database-query), [@casl/mongoose](../../package/casl-mongoose#accessible-records-plugin) ## rulesToFields This is a helper function that allows to extract field values from `Ability` conditions. This may be useful to get default values for a new object based on permissions. The function adjust the amount of parameters depending on passed in `TAbility` generic parameters. * Parameters: * `ability: TAbility` * `action: string` * `subject: Subject` * Returns an object with values from conditions. * Usage\ This function only processes values of conditions that are not objects: ```ts import { defineAbility } from '@casl/ability'; import { rulesToFields } from '@casl/ability/extra'; const ability = defineAbility((can) => { can('read', 'Article', { authorId: 1 }); can('read', 'Article', { public: true }); can('read', 'Article', { title: { $regex: /^\[Draft\]/i } }); }); const defaultValues = rulesToFields(ability, 'read', 'Article'); console.log(defaultValues); // { public: true, authorId: 1 } const newArticle = { ...defaultValues, title: '...', description: '...' }; ``` ## permittedFieldsOf This function returns fields of `subject` which specified `action` may be applied on. Accepts single generic parameter `TAbility` (`T` to be short). * Parameters * `ability: T` * `action: string` * `subject: SubjectType` * `options?: PermittedFieldsOptions<T>` * Returns an array of fields * Usage\ This function is especially useful for backend API because it allows to filter out from request only permittedFields (e.g., in [expressjs](https://expressjs.com/) middleware) ```ts import { defineAbility } from '@casl/ability'; import { permittedFieldsOf } from '@casl/ability/extra'; import { pick, isEmpty } from 'lodash'; const ability = defineAbility((can) => { can('read', 'Article'); can('update', 'Article', ['title', 'description']); }); app.patch('/api/articles/:id', async (req, res) => { const updatableFields = permittedFieldsOf(ability, 'update', 'Article'); const changes = pick(req.body, updatableFields); if (isEmpty(changes)) { res.status(400).send({ message: 'Nothing to update' }); return; } await updateArticleById(id, changes); }); ``` So, now even if user try to send fields that he is not allowed to update, `permittedFieldsOf` will filter them out! * See also: [Restricting fields access](../../guide/restricting-fields), [@casl/mongoose](../../package/casl-mongoose#accessible-fields-plugin) ## packRules This function reduces serialized rules size in 2 times (in comparison to its raw representation), by converting objects to arrays. This is useful if you plan to cache rules in [JWT](https://en.wikipedia.org/wiki/JSON_Web_Token) token. > Don’t use directly result returned by packRules, its format is not public and may change in future versions. * Parameters: * `rules: TRawRule[]` * `packSubject?: (subjectType: SubjectType) => string` - we need to pass this parameter only if we use classes as subject types. It should return subject type's string representation. * Returns `PackRule<TRawRule>[]` * Usage ```ts import { packRules } from '@casl/ability/extra'; import jwt from 'jsonwebtoken'; import { defineRulesFor } from '../services/appAbility'; app.post('/session', (req, res) => { const token = jwt.sign({ id: req.user.id, rules: packRules(defineRulesFor(req.user)) }, 'jwt secret', { expiresIn: '1d' }); res.send({ token }); }); ``` * See also: [Cache abilities](../../cookbook/cache-rules), [`unpackRules`](#unpack-rules) ## unpackRules This function is unpacks rules previously packed by [`packRules`](#pack-rules), so they can be consumed by `Ability` instance. * Parameters: * `rules: PackRule<TRawRule>[]` * `unpackSubject?: (type: string) => SubjectType` - we need to pass this parameter only if we use classes as subject types. It should return subject type out of its string representation. * Returns `TRawRule[]` * Usage\ If backend sends use packed rules, we need to use `unpackRules` before passing them into `Ability` instance: ```ts import { unpackRules } from '@casl/ability/extra' import jwt from 'jsonwebtoken'; import ability from '../services/appAbility'; export default class LoginComponent { login(params) { return http.post('/session') .then((response) => { const token = jwt.decode(response.token); ability.update(unpackRules(token.rules)) }); } } ``` * See also: [Cache abilities](../../cookbook/cache-rules), [`packRules`](#pack-rules)
The shifting politics of patient activism: From bio-sociality to bio-digital citizenship. Digital media provide novel tools for patient activists from disease- and condition-specific communities. While those with debilitating conditions or disabilities have long recognised the value of collective action for advancing their interests, digital media offer activists unparalleled opportunities to fulfil their goals. This article explores the shifting politics of 'activism' in the increasingly digitally mediated, commercialised context of healthcare, asking: what role have digital media played in the repertoire of activists' strategies? And, to what extent and how has the use of such media impacted the very concept of activism? Building on sociological ideas on emergent forms of 'biological citizenship' and drawing on findings from an analysis of available media, including television and print news reportage, online communications, published histories and campaign material and other information produced by activists in HIV/AIDS and breast cancer communities, we argue that digital media have profoundly shaped how 'activism' is enacted, both the goals pursued and the strategies adopted, which serve to broadly align contemporary patient communities' interests with those of science and business. This alignment, which we characterise as 'bio-digital citizenship', has involved a fundamental reorientation of 'activism' from less of a struggle for rights to more of a striving to achieve a public profile and attract funding. We conclude by calling for a reconceptualisation of 'activism' to more adequately reflect the workings of power in the digital age, whereby the agency and hopes of citizens are central to the workings of political rule.
“[We had a] good work day yesterday, [good] preparation. [Iowa is] one of the good football teams, especially a team that, capacity-wise, they’re playing well when you look at taking care of the football, turnovers, and the running game from an offensive line standpoint. They’re typical Iowa where they’re going to get on you and they’re going to do a great job in the zone schemes. Defensively they’re going to play very tight up front and let the linebackers flow. You see that. In the kicking game, they’ve got some real weapons in their kickoff return and their kick coverage and in the kickoff that they’ve done a nice job with. For us we had a good practice. Like I said, it was a good work day. Need another good work day today.” Day to day on your quarterbacks? “Yes. Good answer.” Would you say the last two weeks were the best performances you’ve seen from your receivers? “There’s other times where I think they’ve played pretty well, especially in getting on people and blocking. They’re probably stepping up like they should. I think Roy’s caught the ball well with his hands when you watch it fundamentally. I think they played well.” Has senior day ever been a distraction in your experience? “For the seniors? Not really. I think this group, it will be an emotional time and it should be. A lot of these guys have been playing since they were in third grade, and there will be some of them who will never play again. A lot of them.” You have a lot of personal traditions. Do you do anything specific with the seniors this week? “We’ll do something Saturday.” Can you talk about some of the guys on special teams and coverage teams that have done a good job? “Well Hawthorne is a guy. Him and Floyd Simmons, they’re two seniors who are on a lot of those teams and we expect a lot out of them. I think in the kickoff return phase of it and being a gunner on punt, I think Norfleet has brought some excitement and done a nice job. When you look at the guys, Joe Bolden’s got a lot of snaps out there. Wilson’s -- Jarrod’s had a lot of snaps, which are very valuable for young guys, but I’d say from Paul Gyarmati to the seniors that are out there with Floyd and Brandin, I think those guys are the guys who are on a lot of those teams.” Do you grade those guys like you do with your offense and defense? “Yeah. They’re all graded. Dan does that with every special team. We watch it and evaluate, critique.” When you evaluated Mike Kwiatkowski when you first got here, did you think he would get to this point in terms of production? “I think that’s all part of it. As you go through the process of coaching what you want to do offensively, the encouragement and the evaluation that you give on a daily basis is important. I think Mike is a guy who has gotten better, obviously. He’s done a good job inside that tight end room helping the young guys.” You said he was more of a lineman. Did you think to move him immediately? “Well I think it was a need as much as anything else. We play with tight end a lot. I don’t think that was part of the offense as much before we got here.” Would you say the biggest thing Quinton Washington has done this year is improve the use of his hands? “Yeah, I think that’s part of it. I think his confidence is a big part of where Quinton has established himself a little more. Probably starting with the Illinois game as much as anything. He is a better technician. He is visually keen [with] what he needs to be looking at with more focus. He just -- there’s so much further we can get him.” How do you know with any player when the confidence starts to kick in? “Uh. It’s a really good question. I think probably because of how … maybe you don’t get as many questions? Might be part of it. I think the speed that they play with is part of it.” Al said yesterday it’s been a cram course preparing Devin the last couple of weeks. How hard is it to get someone up to speed that quickly? “I think from the standpoint of the intricacies of the position and the checks and the different things you have to do, I think even people in here could take a snap where it’s a little bit more than that. It’s more than the protections, more than what you seen coverage-wise, the ball handling, the footwork, all those things. That’s where you get more and more as far as a mental piece to playing the position. I think the one thing is that Devin is a very intelligent young man. He is into the football part of it when you look at film and study an opponent.” Is he playing at the highest level at quarterback that you’ve seen from him? “I think he’s been pretty consistent. I think he’s managing games, and that’s a word that is probably overused, but you know, managing an offense, that starts with how your approach is in the huddle and how you talk to those ten other guys and those teammates. I thought on Saturday at the end of the game, just watching him run down the field to spike the ball, he showed great poise and showed great leadership with it.” Can you quantify how hard it is to relearn all that? “Yeah. I don’t know if that’s fair for me to say how hard it is for him. I think it’s difficult. I would think. He had some carryover obviously, and some guys -- and I think there’s some carryover, too when you look at him play wide receiver and studying coverages, if it’s two-deep or one-high, inside leverage and those things. I think that all helped him.” How big is this for him moving forward into 2013? “Let’s worry about Iowa.” On the spike, it looked like Devin Funchess had to run off and dive over the sideline -- “He really didn’t have to. He was a little more dramatic.” Why was there switching going on? “We were in a hurry-hurry situation from an offensive standpoint. If you’re making a substitution, he’s getting ready to make that substitution and not waste time.” So he was going to make the substitution after the play? “Started to, yeah. But when he saw where the ball was, it was, ‘Hey, I’m going to get off the field.’ ” Long snapper is sort of a thankless position. Can you talk about the job Jareth Glanda has done? “I think he’s done a very good job. We always talk about the guys kicking the field goals and we critique punters a lot, but I think Jareth has been very consistent. It’s not easy in protection all the time to snap and protect. A lot of teams don’t ask those guys to do that as much, but within our system, I think he’s done a really really nice job [knock knock knock], and he’ll keep it up.” James Ross got a lot of time last week. He was in there at the end. Was that specific to playing Northwestern because he might be a little faster? “No, it’s just playing different guys.” Desmond Morgan’s not banged up or anything? “No.” Northwestern used a lot of cutblocking. What can you do as a defense -- “You’ll never get cut if you put your helmet and your face on that guy’s face. So you teach technique and you talk about it and you teach it and you drill it. Now sometimes you ask to be cut because you’re not being aggressive enough. Sometimes you ask to be cut because you won’t put your face and bend your knees and everything you need to do to play a cut block.” Comment viewing options Why is Hoke so stingy with his comments re: Denard's legacy? I don't think a few statements like Mattison and Borges made about Denard's dedication, athleticism, career accolades, etc. would kill him, or his team-team-team mantra. Certainly the players (e.g., Roh) realize how important Denard has been. C'mon, Brady, show one of the most memorable Wolverines ever some love!! They all put in work, just like Denard. We all love Denard and everything he's done for the program, but he's no more important than the Senior who has spent 5 years on Scout team. I'm sure Denard will tell you the same thing. no more important than a guy on the Scout team? We will agree to disagree. and to others, i don't think you can blame a reporter for wanting to cover Denard before his last home game. That's not a bad guess as to what your readers want. You're looking for his coach to comment on the player's prodigious career... and the coach won't do it, even in a short soundbite. Hoke's drawing a too-strict line here. The thing I really enjoy about college sports is that the players are not payed according to their skill level, with the exception of walk-ons who for some reason participate with little chance to play and no tuition money. And they only get 4-5 years of time to participate in this unique bubble. Hoke completely embraces this position of near communism within the uniqueness of the college student athlete. And within that definition, all of the seniors are important on Senior day. What has Denard meant to this program and this team sport? He has meant as much as every other senior who shows up to practice and works hard and does what the coaches ask. So the reason Hoke doesn't give Denard any special privilege is because Denard is one of many student athletes. This is at the heart of Bo's message about the team the team the team. The message is not just that you are partipating as a team member, but also because you are not "playing for a contract". To Bo college provided the opportunity for the student athlete to play for the love of the game and the love of his teammates. When you bring money into that in a capitalistic way, and pay people according to talent, you destroy the entire incentive that The Team provides. It's the same belief that is behind the phrase, "the expectation for the position". While everyone wrings their hands about, "how will we replace Mike Martin", Hoke already knows how. By coaching up the next person in line. And every year there are about 20 new faces that need coaching up, and there are about 20 seniors who are trying to suck every last bit of enjoyment out of each day. These Seniors will "never play for a Team" again. Or as Bo put it in the middle of his speech; No man is more important than The Team. No coach is more important than The Team. The Team, The Team, The Team, and if we think that way, all of us, everything that you do, you take into consideration what effect does it have on my Team? Because you can go into professional football, you can go anywhere you want to play after you leave here. You will never play for a Team again. You'll play for a contract. You'll play for this. You'll play for that. You'll play for everything except the team, and think what a great thing it is to be a part of something that is, The Team. Ya, that is taking it too far. Denard >> scout team senior in terms of impact on michigan's football team. Perhaps, you meant to say...Denard = scout team senior in terms of effort and dedication to the program. Also, of course denard would say that even if it were untrue. I mean what is he supposed to say...I'm the guy who dump-trucked ncaa records so I'm more important. Because it's Team 133, not Team Denard. It's Senior Day, not Denard Day. Team 133 has 23 seniors, all of whom have their last game in the Big House on Saturday. They're all his sons and he's not playing favorites. I freaken love Hoke for being consistent with the idea of "the team, the team, the team." Even if he's just using it as an excuse to troll reporters. That writer has asked a question about Denard to every single person that has spoken at a press conference. I'm sure there are enough "Denard = awesome" quotes out there to write an article. Heck, Chengalis has already written her Rich Rod interview about Denard. Maybe it's just who he is...who knows what he tells those guys and how he feels behind closed doors. He may tell Denard that he's the single greatest player since Charles Woodson...but he may also feel that's between him and Denard and not for you (or us) to know. I really couldn't care less about how much information Hoke gives in his answers to questions as long as he wins. and won't have a "Circle of Trust" based on who the star players are. Hoke seems by all accounts to be fair and consistent and seems like he will resist the temptation to elevate one player above the others who are all putting in the work. The individual contributions on Saturday do not make a legacy. "Well, I think that's all part of everything when you have a bunch of football players. From the coaching standdpoint, I think we need to improve technique-wise, and that should take care of the football part of it." Another great exchange for someone to stick in front of a recuit's family to show Brady's mindset of each kid being like a son. It seems genuine and people who spend almost every day with him say it's really his perspective. He'll gush about Denard when the season is over and advocate for him to achieve Legend status. Until then, just 1 of his kids. I agree with you wholeheartedly. But I have to say that, sometimes, a person earns the right to be singled out and recognized above all the others. Just as Denard would want the focus to be on everyone (not on him), so too would his teammates want Denard to receive special recognition. Maybe Hoke is waiting for the end of the season but now seems like as good of a time as any (his assistant coaches see to agree). Nevertheless, everyone appreciates him and I'm sure he knows it. But he has always been singled out and given his due. By the media and the fans. Denard has earned the right and has been recognized above all others. I don't think its appropriate for the coach of the team to only focus on one player, whether that player is a heisman winner or a scout team guy. I agree with Raback above, Hoke is responsible for the entire team and needs to make sure each of the 23 seniors receives their due. The great Bo Schembechler once gave Andy Cannavino a special plaque for being "his greatest captain" after the 1980 team won Bo's first Rose Bowl. They sure as hell didn't do that for every captain. There's the value of a player, and then there's the player's VALUE. I don't see the harm in at least acknowledging what Denard's done for the past few years. The key word is "after." This team still has work to do. He may do something to acknowledge Denard's greatness or he may not. I think what is said between the two of them and the entire team is more important what his says to appease the masses. This is a Michigan nation problem, it happens on every board known to Michigan fans. It needs to be said because people seriously treat the guy like an infant child. I'll be at the game Saturday cheering my tail off for all of our seniors, and I will cheer a little harder when Denard's name is announced. I don't want to face a lecture about why Denards feelings may possibly get hurt. it wouldn't kill Hoke to say one or two things about Denard Robinson before his last game at Michigan Stadium. That's all. When a reporter asks about a guy who had a great game, Hoke usually doesn't say, "THEY ALL PLAYED A ROLE IN THAT GUY'S GREAT GAME, I WON'T TALK ABOUT ONE PARTICULAR GUY. THEY ALL WEAR THE HELMET." He usually comments on the specific player (albeit in his restrained way). Sometimes a guy stands out and deservers a little extra praise or reflection. Denard has stood out over four years, and reporter(s) are rightly asking Hoke to reflect. Just feels a little off key is all. EDIT: and this isn't about Denard's "feelings." Denard couldn't care less, I'm quite sure. This is for the fans who root for the team and want to hear what the coach thinks about the program's greatest player over the last four years on the eve of his last home game. Does Hoke really feel he's doing disservice to the other seniors if he comments on Denard?? I guess I'm missing something, but I will stop berating all of you now. Don't we probably already know what the coach would say he thinks about Denard, without it having to be a qoute for some guy to throw in a headline on some article he's writing? I think Denard is as great as the rest of us, but I enjoy reading the articles about the walk on tight end as much as some reinforced comment from the coach on a damn great player that we already know is a damn great player, without hearing again about how damn great he is, again... It's a team sport and I respect the hell out of Coach Hoke for digging in his heels are refusing to put Denard above the rest of the team and seniors just for some qoute. It reinforces the teamwork and work ethic of a team sport like no other for the coach to answer it the way he does in public. Behind the scenes, we and all the players can say all the "yea, but..." that we want; but you don't ask the dad who is favorite son is at the expense of the rest of the team. After the season, as others have pointed out there will be countless discussions about his historic place in UM not just for football but as an athlete, student, and citizen. I don't understand how Michigan fans can recite Bo's mantra ("The team, the team, the team.") and yet, at the same time, get upset over the coach not giving out enough praise for one particular player. The whole culture of this program revolves around the idea of the team over the individual. Is there any video of Funchess diving out of bounds? I had no idea until this presser. Good stuff! You can definitely picture it just by watching Devin play this season. He's always so innocently happy. Every touchdown is like his first no matter who scores. I can totally picture his 6'5 frame soaring to the sidelines as he tries to get off them field...and there being like 4-5 more seconds where he could've just walked. I do get a good chuckle out of how hard Hoke makes the reporters work for answers. And I get the not highlighting Denard above anyone else on Team 133. But what does everyone make of the 'non-answer' to the question about team culture compared to when Hoke was here before? Is it that Hoke doesn't really think about the culture he's trying to implement because it's just instinctive? Just wants to get out of the presser? Doesn't want to grade himself? I love the way Hoke leads and would love to hear more of his self-assessment of where he's at. not because he's uncomfortable up at a microphone but because he thinks that answering mind-numbingly repetitive and juvenile questions posed by comically unathletic-hard-pressed to do 25 girl pushups-donut-saturated doofuses who only care about getting some juicy controversial quote is a complete waste of his time. I don't blame him at all. This was my favorite moment of Hoke's presser. Hoke was dripping with contempt regarding his players getting cut block. “You’ll never get cut if you put your helmet and your face on that guy’s face. So you teach technique and you talk about it and you teach it and you drill it. Now sometimes you ask to be cut because you’re not being aggressive enough. Sometimes you ask to be cut because you won’t put your face and bend your knees and everything you need to do to play a cut block.”
Tag: being a mom With the rise of social media, the prevalence of judgment on other parents has reached epidemic proportions. A recent US study found that 90% of Moms and 85% of Dads feel judged by others, and nearly half of all parents feel judged almost all the time. According to Sunshine Coast business coach and mother of twins, Lauren Marie, this constant demand to conform to others’ rules not only undermines a parent’s wellbeing – it also stifles their ability to follow their dreams and create new financial opportunities for themselves and their families. A passionate entrepreneur with an unconventional pregnancy story, Lauren is concerned that most parents regulate many of their life choices in order to be seen as a “good parent”. As the expectations grow around them, new mothers and fathers begin to stifle their natural impulses, sacrifice their dreams and place more emphasis on society’s unwritten rules than on personal fulfillment. In doing so, Lauren believes that parents limit their actions – and therefore their possibilities for true happiness and financial wellbeing. “What if becoming a parent could allow you to create more, not less?” she suggests. “What if you are not expected to be ‘perfect’?” Lauren believes that children thrive in environments where their parents place emphasis on creativity, possibility and personal and financial fulfillment. “Your children will learn how to be and what to be based on what you be and do. When you choose more for you, they learn that it is ok for them to be more to.” With Lauren’s help, you can maintain balance, run a business and learn how to not sacrifice yourself. You can do one on one sessions with Lauren to get the tools you need to empower yourself to be the parent you truly want to be.
import React from 'react' import Enzyme, { shallow } from 'enzyme' import ColorPicker from './color_picker' import { HuePicker } from 'react-color' import Adapter from 'enzyme-adapter-react-16' Enzyme.configure({ adapter: new Adapter() }) describe('ColorPicker', () => { const ev = { target: { name: 'color', value: 10 } } it('<ColorPicker />', () => { shallow(<ColorPicker name='picker' color='' onChangeHandler={() => true} />) }) it('should start collapsed', () => { const wrapper = shallow(<ColorPicker name='picker' color='' onChangeHandler={() => true} />) expect(wrapper.find('button').length).toBe(1) expect(wrapper.find(HuePicker).length).toBe(0) }) it('should handle color change', () => { const instance = shallow(<ColorPicker name='picker' color='' onChangeHandler={() => true} />).instance() instance.handleColorChange(ev) }) it('should expand', () => { const wrapper = shallow(<ColorPicker name='picker' color='' onChangeHandler={() => true} />) wrapper.find('button').simulate('click') expect(wrapper.find('button').length).toBe(0) expect(wrapper.find(HuePicker).length).toBe(1) }) })
Product Id : DNP11636 Price : 1,395 Quantity : 8 Size : Total Amount : 11,160 Dispatch time : 1 - 2 Working days Note : + Shipping Charge You Can Download single image or bundled zip file (if there are multiple images) by clicking above "Download Image(s)" button. To extract/open all images from the zip file, a zip extractor software is needed. Links are given below if you don't have any similar software. Product color may Slightly vary due to specific monitor, the settings and the lighting AMIRAH PRESENTS AMIRAH VOL 16 AMIRAH PRESENTS AMIRAH VOL 16 Salwar Suit Wholesale Catalog 8 pcs AMIRAH PRESENTS AMIRAH VOL 16 Buy AMIRAH PRESENTS AMIRAH VOL 16 salwar Suit Catalog 8 pcs. Best & cheap Wholesale Prices. From Surat’s Online Wholesale Textile Market.AMIRAH PRESENTS AMIRAH VOL 16. AMIRAH PRESENTS AMIRAH VOL 16 Best designs and A grade goods. Designer Salwar suits have been the best comfortable and ethnic wear for women since many occasion outfits. Basically dress is divided, into parts three. Suit (Kurti) is the 1st section that covers the top body part. Salwar (Pajama) is the 2nd part that is worn below the suits (kurta) to cover the lower section of the body and Dupatta is the 3rd portion of the worn as a wrap according to dress design and the pattern. These three sections altogether can be designed by tailor in various methods to make an elegant & stylish outfit.Textilebazar.in has wide range of designer Salwar suits collection, you in the selected types of the Indian fashion traditional salwar kameez like AMIRAH PRESENTS AMIRAH VOL 16. Our online shopping portal return the latest modern fashion collection with every modify fashion and new style getting an instant position in our new arrival trendy stoke section. We have almost attires something for women wear. Indian Women ethnic wear is honestly stylish and fashionable for females. You can choose from wide range of designer dresses including, Patiala suits, Anarkali dresses, casual dress, Georgette suits and etc. Exhibit your superb style quotient at family events and festive function by online shopping for, salwar suits, prom dress, wedding bridal salwar kameez and more accessories with discount. Ladies wardrobe is any time relax the stabilize game when it arrive to having the best amount of traditional style and casual wear women clothing. Both the trends are equally attractive and beautiful their own excellence when it comes for family functions and more social events. If you are choosing to add to your regular apparels closet, shop online at Textilebazar.in for wide varieties of salwar kameez sets. You will search semi and full stitched salwar suits & unstitched dress that can be tailored and modify to your size outfits. Different Types of Modern Trendy Salwar Suits FashionAnarkali Salwar Suits,This designer anarkali salwar suits style is considered the best popular and superb in the market now a days. It gives beautiful royal look outfit. Basically, this dress is a frock type trend kurti is representing the Mughal time this type suit known as anarkaili kuti. The fabric very famous is net & chiffon. This type of suits becomes comfortable for occasions. They are definitely superb and beautiful. Anarkali suits are the most like among the females in India, especially for the wedding events and festivals. Anarkali salwar kameez is also the most wanted stylish dress for bridal wear among the Indian girls. Mostly Anarkali suit become Knee, Long and Full Length in size.Pakistani Salwar Kameez Style,The Pakistani dress trends are an inspiration now days and so the Indian designers are trying to make Pakistani salwar suit look beautiful the best this season. They look superb and new style and enhance the good looking of the women on wearing.Patiala Salwar Kameez,Patiala Salwar Kameez is a very India and international dress and it is the best suitable and comfortable provider stitched clothing. Patiala suit known as Punjabi salwar suits and is one of the best widely used these costumes, because this is easy to use & provides more relaxation to the wearer and is the best for use by ladies of all ages. The Patiala Punjabi suit is give heavy looks, so that this suit better for every women to keep them in style fashion. Short kameez shows the layer of Patiala & its beautiful looks. AMIRAH PRESENTS AMIRAH VOL 16 The most appreciated latest new version of Patiala salwar suit comes with small pleats which reproduce a kind of wrap.Bollywood Salwar Suits,Many Bollywood actresses including Priyanka, Deepika, Aishwarya and more have donned the salwar suit on a number of occasions & festivals. We bring to you a designer Bollywood Salwar suits collection of replica Anarkali suits and stylish glamorous worn by the glam women themselves. Choose and shop from a wide latest style variety of hues and new fashion depending on the memorable events, you are planning to buy for.Casual Salwar Suits,Casual salwar suits like to wear on a regular daily basis and office wear attires Textilebazar.in brings for you a casual salwar kameez latest new collection with the reasonable prices of work nor leaving the dress bare & yet not too more amount. Our online shopping portal gives you a huge range of colors & more patterns of styles which are best for casual daily wear and will help to you make a superb style.
Prevalence of frailty on clinical wards: description and implications. This paper describes the prevalence and frailty level of patients aged > or = 75 years upon admission to various clinical wards. The data collection took place on five clinical wards of different clinical specialisms: Geriatric Centre, traumatology, pulmonology/rheumatology, internal medicine and surgical medicine. The Groningen Frailty Indicator was used to assess the frailty of newly admitted patients. The presence of number and kind of the various frailty indicators was different for the clinical wards, because of clinical diagnose, age and gender. On the Geriatric Centre, almost all patients were indicated as frail. On the other wards, 50-80% of the patients were indicated as frail with most frailty indicators on the scale 'psychosocial'. The study show a high prevalence of frail elderly on some wards and gives an indication of the various needs for other disciplines within the framework of the care for frail elderly people.
I totally different take nothing about repairs, just trip reports, how you use your delica, etc Example today I loaded the chain saw and lined the back of the delica with a tarp. Grabbed my best bud (wheeler my dog) and went out and got a load of maple and cedar. Filled the delica up to the windows sorry no pics but the weather was great. The strangest load I've taken is a massive Christmas tree. Unfortunately we stuffed it in stump first and didn't wrap it (we were in a hurry). In case it isn't evident from that statement, the tree acted like one of those chinese finger locks. Luckily there was no damage but it sure took ages to unload. I've also used the van to haul drywall to the dump in place of my work truck. Unfortunately this left my black curtains covered in white dust. I installed new front and rear speakers. I had to get creative with the rear speaker mounting because I purchased 5.25" and the factory speakers were 6.5". No one had a size chart or application guide for my van. I cut the basket and magnet off the old speaker and used the "mounting ring" from it to sandwich the new speaker to the mount. I used a lid from a margarine container to fill the air gap between the hole and the speaker. Sounds great!! here are some pics: Last edited by R.Costa on Thu Jan 12, 2012 6:13 pm, edited 1 time in total. psilosin wrote: This thread is the same as the one already stickied. Merge merge merge! 1994delicaman wrote:I had the L400 packed with rc cars today. Woot. What kind of RC cars were you rocking? I've got a thing for collecting Tamiya RC cars. Read the title and the first description, I thought it would be a great idea to see what people do with there delicas. Doing this would also show why we love them and how diverse a group of people we are. Yeah I did read the first line but most responses ended up being the same as what the existing thread contains hence merge...or move those responses into the other thread so they stay distinct. Not too complicated and no reason for you to be a drama queen because people made off topic posting from what you envisioned by changing 'to' to 'with'. Also I am sorry to hear that your brain failed. legionnair wrote:Read the title and the first description, I thought it would be a great idea to see what people do with there delicas. Doing this would also show why we love them and how diverse a group of people we are. Ok ... what I did WITH my van ....... I picked up a bunch of 8' and 10' 2x6 from the lumberyard and boy was the L300 ever better for hauling compared to the L400. I was able to stack an armload of 8 footers between the seats and had to spin the pass seat around and stack e few 10 footers on the seat. Time for a roof rack.
package problem746 func minCostClimbingStairs(cost []int) int { for i := len(cost) - 3; i >= 0; i-- { cost[i] += myMin(cost[i+1], cost[i+2]) } return myMin(cost[0], cost[1]) } func myMin(a, b int) int { if a <= b { return a } return b }
Integration of digital, analog, radio frequency, photonic and other devices into a complex System-on-Chip (“SOC”) has been previously demonstrated. (See, e.g., Reference 1). Recently, for example, sensors, actuators and biochips are also being integrated, into these already powerful SOCs. SOC integration has been enabled by advances in mixed system integration and the increase in the wafer sizes (e.g., currently about 300 mm and projected to be 450 mm by 2018) (see, e.g., Reference 1), and it has also reduced the cost per chip of such SOCs. However, support for multiple capabilities, and mixed technologies, have increased the cost of owning an advanced foundry. For instance, the cost of owning a foundry will be approximately $5 billion in 2015. (See, e.g., Reference 2). Consequently, only advanced commercial foundries can now manufacture such high performance, mixed system, SOCs especially at the advanced technology nodes. (See, e.g., Reference 3). Absent the economies of scale, many of the design companies cannot afford to own and/or acquire expensive foundries, and have to outsource their fabrication process to one-stop-shop foundries. While the globalization of Integrated Circuits (“IC”) design flow has successfully ameliorated the design complexity and fabrication cost problems, it has led to several security vulnerabilities. If a design is fabricated in a foundry that may not be under the direct control of the fabless design house, attacks, such as reverse engineering, malicious circuit modification and Intellectual Property (“IP”) piracy can be possible. (See, e.g., Reference 3). For example, an attacker, anywhere in this design flow, can reverse engineer the functionality of an IC/IP, and then steal and claim ownership of the IP. An untrusted IC foundry can overbuild ICs and sell them illegally. Further, rogue elements in the foundry can insert malicious circuits (e.g., hardware Trojans) into the design without the designer's knowledge. (See, e.g., References 4 and 5). Because of these attacks and issues, the semiconductor industry loses tens of billions of dollars annually (see, e.g., Reference 6). This can also be because the designers have minimum control over their IP in this distributed design and fabrication flow. While hardware security and trust is a relatively recent concern, a somewhat similar, yet fundamentally different problem of manufacturing defects has been on the research agenda of VLSI test researchers for the last few decades. The attacks detailed above are man-made, intentional, and meant to be hidden, while manufacturing defects can be more natural and unintentional, hampering the use of existing defect testing techniques. However, many concepts in VLSI testing, such as, for example, justification and sensitization, can be adapted for application in the context of hardware security and trust. Inspired by the design enhancement approach (e.g., Design-for-Testability (“DfT”)) for better testability of manufacturing defects, strong Design-for-Trust (“DfTr”) solutions can be devised against these attacks, detecting and possibly preventing them. IC reverse engineering techniques can be broadly classified into two types: extraction of gate-level netlist from layout, and extraction of functional specification from gate-level netlist. Reverse engineering of an IC to extract a gate-level netlist has been proposed. (See, e.g., References 8 and 14). Procedures to extract a gate-level netlist from transistors have also been suggested. (See, e.g., Reference 15). For example, the DARPA IRIS program seeks to obtain the functional specification of a design by reverse engineering its gate-level netlist. Previous techniques can exploit structural isomorphism to extract the functionality of datapath units. (See, e.g., Reference 16). Other techniques have been used to reverse engineer the functionality of unknown units by performing behavioral matching against a library of components with known functionalities such as adders, counters, register files and subtracters. (See, e.g., Reference 17). Still other techniques have identified the functionality of unknown modules by performing a Boolean satisfiability analysis with a library of components with known functionalities. (See, e.g., Reference 18). Thus, it may be beneficial to provide an exemplary DfTr IC camouflaging technique, system, arrangement, computer accessible medium and method that can utilize fault activation, sensitization and masking, and which can overcome at least some of the deficiencies described herein above.
Microgranular promyelocytic leukemia: a multiparameter examination. Six cases of microgranular variant acute promyelocytic leukemia (M3v) were studied by use of a multiparameter approach including morphology, cytochemistry, flow cytochemistry, flow cytometry, cytogenetics, and gene rearrangement. Three of six cases demonstrated both myeloid and monocytoid associated surface markers by flow cytometry. One of six cases had strong alpha-naphthyl-butyrate esterase (alpha-NBE) activity in addition to myeloperoxidase activity. There was no correlation between percentage of positive monocytoid surface markers and intensity of cytoplasmic alpha-NBE activity. Four of six cases also had a T-cell-associated surface antigen. Further studies indicated that the T-cell markers appeared to be on the promyelocytes and that the T-B receptor gene was not rearranged. Similarly, cytogenetics studies indicated only one clonal abnormality t(15q+; 17q-). Whether these cases represent true "lineage infidelity" remains to be answered. Future important studies are needed on normal hematopoietic progenitor cells at early stages of development and childhood to study lineage-specific characteristics and to determine whether co-expression normally exists during early development.
Q: Getting 404 despite having defined "resources" in config/routes.rb I have this in my config/routes.rb resources :my_objects and I have app/controllers/my_objects_controller.rb def edit respond_to do \|format\| @my_object = MyObject.find(params[:id]) format.json { render :json => @my_object } end end But I get a 404 from my JQuery when I attempt to contact this URL (via GET) using http://localhost:3000/my_objects/edit/8 I have also tried http://localhost:3000/my_objects/edit?id=8 got still get a 404. What is the right URL I need to use to get data from my edit link? A: The RESTful routes created by resources follow this pattern: method path controller action --------------------------------------------------------- GET /my_objects #index POST /my_objects #create GET /my_objects/new #new GET /my_objects/:id/edit #edit GET /my_objects/:id #show PATCH\|PUT /my_objects/:id #update DELETE /my_objects/:id #destroy See: Rails Routing from the Outside In
click to enlarge University of Utah's own Daily Chronicle was posted on FailBlog today. Something tells me this wasn't a mistake.--- click to enlarge By the way, FailBlog, it would be nice if you created HTML anchors or individualized URLs for particular posts to your blog. It's a built-in feature of WordPress, which you are not using. That's such a... such a... what's the word I'm looking for? Update 5:07 p.m.: Whoop, FailBlog fail! Submitter seems to have missed the facing page. In the words of Paul Harvey, here's "the rest of the story." In the words of City Weekly managing editor Josh Loftin, "Wow! I don't even use that word!" click to enlarge Follow me on
Getty Images The Steelers host the Jaguars on Sunday, and as is customary Steelers coach Mike Tomlin made himself available for a conference call with the opposing city’s media. According to Tania Ganguli of the Florida Times-Union, Tomlin got irritated with questions regarding a 2007 playoff game between the two teams. The Jaguars won the game, making them the first team ever to win twice in Pittsburgh in the same season. And the game ended with a critical fourth-down draw play by former Jaguars quarterback David Garrard, during which the officials missed an obvious offensive holding call. Asked whether Tomlin complained to the league office, Tomlin said, “No.” Asked why he didn’t, he said, “Why would I?” Then, after it was explained that the call was critical to the outcome of the game, the fuse entered the bomb. “Guys, come on man. I’m not going to cry over four-year-old spilled milk. Anybody got any legitimate questions? Goll-lly,” Tomlin said. Per Ganguli, the reporters chuckled. Tomlin didn’t. “Guys, that was four years ago,” Tomlin then said. “I understand that might have been a big game in Jacksonville but that’s old news. Many of those guys are no longer here and definitely many of the guys that were in Jacksonville are no longer there. Anybody got any questions relative to this week?” After a few seconds, another reporter started to ask another question. But Tomlin hung up the phone. Perhaps the question for the Jacksonville media is whether they’ll complain to the league office, and if not why not?
Expression of renal aquaporins is down-regulated in children with congenital hydronephrosis. This study investigated mRNA and protein expression of four renal aquaporin isoforms [AQP1, 2, 3 and 4 (AQP1-4)] in congenital hydronephrotic kidneys (HK) due to pelviureteral junction obstruction and normal control kidneys. The expression of AQP1-4 was evaluated in 22 children (15 boys, seven girls, aged 58.9+/-54.3 months) using semi-quantitative reverse transcriptase-polymerase chain reaction (RT-PCR) techniques, immunoblotting and immunohistochemistry. Hydronephrosis was graded by ultrasound according to the Society for Fetal Urology. Both RT-PCR and immunoblotting showed significantly reduced mRNA and protein expression of AQP1-4 in grade IV compared with those in grade III HK and controls. Sequencing demonstrated 99% homology of AQP1-4 with those in GenBank. Positive immunoreactivity of AQP1 was found in plasma membranes of the proximal tubule, thin descending limb of Henle and descending vasa recta; AQP2 in the apical membrane of collecting duct principal cells; and AQP3 and 4 in the basolateral membrane of the same cells. In kidneys with grade IV hydronephrosis there was reduction in the protein abundance of all four AQP isoforms which was more pronounced compared with the protein abundance seen in kidneys with grade III hydronephrosis and control kidneys. The expression of AQP1-4 mRNA and protein abundance is reduced in proportion with the degree of hydronephrosis graded by ultrasound in human congenital HK.
/* * Copyright 2019 Advanced Micro Devices, Inc. * * Permission is hereby granted, free of charge, to any person obtaining a * copy of this software and associated documentation files (the "Software"), * to deal in the Software without restriction, including without limitation * the rights to use, copy, modify, merge, publish, distribute, sublicense, * and/or sell copies of the Software, and to permit persons to whom the * Software is furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL * THE COPYRIGHT HOLDER(S) OR AUTHOR(S) BE LIABLE FOR ANY CLAIM, DAMAGES OR * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR * OTHER DEALINGS IN THE SOFTWARE. * * Authors: AMD * / #include "hdcp.h" #define MIN(a, b) ((a) < (b) ? (a) : (b)) #define HDCP_I2C_ADDR 0x3a / 0x74 >> 1/ #define KSV_READ_SIZE 0xf / 0x6803b - 0x6802c / #define HDCP_MAX_AUX_TRANSACTION_SIZE 16 enum mod_hdcp_ddc_message_id { MOD_HDCP_MESSAGE_ID_INVALID = -1, / HDCP 1.4 / MOD_HDCP_MESSAGE_ID_READ_BKSV = 0, MOD_HDCP_MESSAGE_ID_READ_RI_R0, MOD_HDCP_MESSAGE_ID_WRITE_AKSV, MOD_HDCP_MESSAGE_ID_WRITE_AINFO, MOD_HDCP_MESSAGE_ID_WRITE_AN, MOD_HDCP_MESSAGE_ID_READ_VH_X, MOD_HDCP_MESSAGE_ID_READ_VH_0, MOD_HDCP_MESSAGE_ID_READ_VH_1, MOD_HDCP_MESSAGE_ID_READ_VH_2, MOD_HDCP_MESSAGE_ID_READ_VH_3, MOD_HDCP_MESSAGE_ID_READ_VH_4, MOD_HDCP_MESSAGE_ID_READ_BCAPS, MOD_HDCP_MESSAGE_ID_READ_BSTATUS, MOD_HDCP_MESSAGE_ID_READ_KSV_FIFO, MOD_HDCP_MESSAGE_ID_READ_BINFO, / HDCP 2.2 / MOD_HDCP_MESSAGE_ID_HDCP2VERSION, MOD_HDCP_MESSAGE_ID_RX_CAPS, MOD_HDCP_MESSAGE_ID_WRITE_AKE_INIT, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_CERT, MOD_HDCP_MESSAGE_ID_WRITE_AKE_NO_STORED_KM, MOD_HDCP_MESSAGE_ID_WRITE_AKE_STORED_KM, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_H_PRIME, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_PAIRING_INFO, MOD_HDCP_MESSAGE_ID_WRITE_LC_INIT, MOD_HDCP_MESSAGE_ID_READ_LC_SEND_L_PRIME, MOD_HDCP_MESSAGE_ID_WRITE_SKE_SEND_EKS, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST_PART2, MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_SEND_ACK, MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_STREAM_MANAGE, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_STREAM_READY, MOD_HDCP_MESSAGE_ID_READ_RXSTATUS, MOD_HDCP_MESSAGE_ID_WRITE_CONTENT_STREAM_TYPE, MOD_HDCP_MESSAGE_ID_MAX }; static const uint8_t hdcp_i2c_offsets[] = { [MOD_HDCP_MESSAGE_ID_READ_BKSV] = 0x0, [MOD_HDCP_MESSAGE_ID_READ_RI_R0] = 0x8, [MOD_HDCP_MESSAGE_ID_WRITE_AKSV] = 0x10, [MOD_HDCP_MESSAGE_ID_WRITE_AINFO] = 0x15, [MOD_HDCP_MESSAGE_ID_WRITE_AN] = 0x18, [MOD_HDCP_MESSAGE_ID_READ_VH_X] = 0x20, [MOD_HDCP_MESSAGE_ID_READ_VH_0] = 0x20, [MOD_HDCP_MESSAGE_ID_READ_VH_1] = 0x24, [MOD_HDCP_MESSAGE_ID_READ_VH_2] = 0x28, [MOD_HDCP_MESSAGE_ID_READ_VH_3] = 0x2C, [MOD_HDCP_MESSAGE_ID_READ_VH_4] = 0x30, [MOD_HDCP_MESSAGE_ID_READ_BCAPS] = 0x40, [MOD_HDCP_MESSAGE_ID_READ_BSTATUS] = 0x41, [MOD_HDCP_MESSAGE_ID_READ_KSV_FIFO] = 0x43, [MOD_HDCP_MESSAGE_ID_READ_BINFO] = 0xFF, [MOD_HDCP_MESSAGE_ID_HDCP2VERSION] = 0x50, [MOD_HDCP_MESSAGE_ID_WRITE_AKE_INIT] = 0x60, [MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_CERT] = 0x80, [MOD_HDCP_MESSAGE_ID_WRITE_AKE_NO_STORED_KM] = 0x60, [MOD_HDCP_MESSAGE_ID_WRITE_AKE_STORED_KM] = 0x60, [MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_H_PRIME] = 0x80, [MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_PAIRING_INFO] = 0x80, [MOD_HDCP_MESSAGE_ID_WRITE_LC_INIT] = 0x60, [MOD_HDCP_MESSAGE_ID_READ_LC_SEND_L_PRIME] = 0x80, [MOD_HDCP_MESSAGE_ID_WRITE_SKE_SEND_EKS] = 0x60, [MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST] = 0x80, [MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST_PART2] = 0x80, [MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_SEND_ACK] = 0x60, [MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_STREAM_MANAGE] = 0x60, [MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_STREAM_READY] = 0x80, [MOD_HDCP_MESSAGE_ID_READ_RXSTATUS] = 0x70, [MOD_HDCP_MESSAGE_ID_WRITE_CONTENT_STREAM_TYPE] = 0x0 }; static const uint32_t hdcp_dpcd_addrs[] = { [MOD_HDCP_MESSAGE_ID_READ_BKSV] = 0x68000, [MOD_HDCP_MESSAGE_ID_READ_RI_R0] = 0x68005, [MOD_HDCP_MESSAGE_ID_WRITE_AKSV] = 0x68007, [MOD_HDCP_MESSAGE_ID_WRITE_AINFO] = 0x6803B, [MOD_HDCP_MESSAGE_ID_WRITE_AN] = 0x6800c, [MOD_HDCP_MESSAGE_ID_READ_VH_X] = 0x68014, [MOD_HDCP_MESSAGE_ID_READ_VH_0] = 0x68014, [MOD_HDCP_MESSAGE_ID_READ_VH_1] = 0x68018, [MOD_HDCP_MESSAGE_ID_READ_VH_2] = 0x6801c, [MOD_HDCP_MESSAGE_ID_READ_VH_3] = 0x68020, [MOD_HDCP_MESSAGE_ID_READ_VH_4] = 0x68024, [MOD_HDCP_MESSAGE_ID_READ_BCAPS] = 0x68028, [MOD_HDCP_MESSAGE_ID_READ_BSTATUS] = 0x68029, [MOD_HDCP_MESSAGE_ID_READ_KSV_FIFO] = 0x6802c, [MOD_HDCP_MESSAGE_ID_READ_BINFO] = 0x6802a, [MOD_HDCP_MESSAGE_ID_RX_CAPS] = 0x6921d, [MOD_HDCP_MESSAGE_ID_WRITE_AKE_INIT] = 0x69000, [MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_CERT] = 0x6900b, [MOD_HDCP_MESSAGE_ID_WRITE_AKE_NO_STORED_KM] = 0x69220, [MOD_HDCP_MESSAGE_ID_WRITE_AKE_STORED_KM] = 0x692a0, [MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_H_PRIME] = 0x692c0, [MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_PAIRING_INFO] = 0x692e0, [MOD_HDCP_MESSAGE_ID_WRITE_LC_INIT] = 0x692f0, [MOD_HDCP_MESSAGE_ID_READ_LC_SEND_L_PRIME] = 0x692f8, [MOD_HDCP_MESSAGE_ID_WRITE_SKE_SEND_EKS] = 0x69318, [MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST] = 0x69330, [MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST_PART2] = 0x69340, [MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_SEND_ACK] = 0x693e0, [MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_STREAM_MANAGE] = 0x693f0, [MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_STREAM_READY] = 0x69473, [MOD_HDCP_MESSAGE_ID_READ_RXSTATUS] = 0x69493, [MOD_HDCP_MESSAGE_ID_WRITE_CONTENT_STREAM_TYPE] = 0x69494 }; static enum mod_hdcp_status read(struct mod_hdcp hdcp, enum mod_hdcp_ddc_message_id msg_id, uint8_t buf, uint32_t buf_len) { bool success = true; uint32_t cur_size = 0; uint32_t data_offset = 0; if (is_dp_hdcp(hdcp)) { while (buf_len > 0) { cur_size = MIN(buf_len, HDCP_MAX_AUX_TRANSACTION_SIZE); success = hdcp->config.ddc.funcs.read_dpcd(hdcp->config.ddc.handle, hdcp_dpcd_addrs[msg_id] + data_offset, buf + data_offset, cur_size); if (!success) break; buf_len -= cur_size; data_offset += cur_size; } } else { success = hdcp->config.ddc.funcs.read_i2c( hdcp->config.ddc.handle, HDCP_I2C_ADDR, hdcp_i2c_offsets[msg_id], buf, (uint32_t)buf_len); } return success ? MOD_HDCP_STATUS_SUCCESS : MOD_HDCP_STATUS_DDC_FAILURE; } static enum mod_hdcp_status read_repeatedly(struct mod_hdcp hdcp, enum mod_hdcp_ddc_message_id msg_id, uint8_t buf, uint32_t buf_len, uint8_t read_size) { enum mod_hdcp_status status = MOD_HDCP_STATUS_DDC_FAILURE; uint32_t cur_size = 0; uint32_t data_offset = 0; while (buf_len > 0) { cur_size = MIN(buf_len, read_size); status = read(hdcp, msg_id, buf + data_offset, cur_size); if (status != MOD_HDCP_STATUS_SUCCESS) break; buf_len -= cur_size; data_offset += cur_size; } return status; } static enum mod_hdcp_status write(struct mod_hdcp hdcp, enum mod_hdcp_ddc_message_id msg_id, uint8_t buf, uint32_t buf_len) { bool success = true; uint32_t cur_size = 0; uint32_t data_offset = 0; if (is_dp_hdcp(hdcp)) { while (buf_len > 0) { cur_size = MIN(buf_len, HDCP_MAX_AUX_TRANSACTION_SIZE); success = hdcp->config.ddc.funcs.write_dpcd( hdcp->config.ddc.handle, hdcp_dpcd_addrs[msg_id] + data_offset, buf + data_offset, cur_size); if (!success) break; buf_len -= cur_size; data_offset += cur_size; } } else { hdcp->buf[0] = hdcp_i2c_offsets[msg_id]; memmove(&hdcp->buf[1], buf, buf_len); success = hdcp->config.ddc.funcs.write_i2c( hdcp->config.ddc.handle, HDCP_I2C_ADDR, hdcp->buf, (uint32_t)(buf_len+1)); } return success ? MOD_HDCP_STATUS_SUCCESS : MOD_HDCP_STATUS_DDC_FAILURE; } enum mod_hdcp_status mod_hdcp_read_bksv(struct mod_hdcp hdcp) { return read(hdcp, MOD_HDCP_MESSAGE_ID_READ_BKSV, hdcp->auth.msg.hdcp1.bksv, sizeof(hdcp->auth.msg.hdcp1.bksv)); } enum mod_hdcp_status mod_hdcp_read_bcaps(struct mod_hdcp hdcp) { return read(hdcp, MOD_HDCP_MESSAGE_ID_READ_BCAPS, &hdcp->auth.msg.hdcp1.bcaps, sizeof(hdcp->auth.msg.hdcp1.bcaps)); } enum mod_hdcp_status mod_hdcp_read_bstatus(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_BSTATUS, (uint8_t )&hdcp->auth.msg.hdcp1.bstatus, 1); else status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_BSTATUS, (uint8_t )&hdcp->auth.msg.hdcp1.bstatus, sizeof(hdcp->auth.msg.hdcp1.bstatus)); return status; } enum mod_hdcp_status mod_hdcp_read_r0p(struct mod_hdcp hdcp) { return read(hdcp, MOD_HDCP_MESSAGE_ID_READ_RI_R0, (uint8_t )&hdcp->auth.msg.hdcp1.r0p, sizeof(hdcp->auth.msg.hdcp1.r0p)); } /* special case, reading repeatedly at the same address, don't use read() / enum mod_hdcp_status mod_hdcp_read_ksvlist(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = read_repeatedly(hdcp, MOD_HDCP_MESSAGE_ID_READ_KSV_FIFO, hdcp->auth.msg.hdcp1.ksvlist, hdcp->auth.msg.hdcp1.ksvlist_size, KSV_READ_SIZE); else status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_KSV_FIFO, (uint8_t )&hdcp->auth.msg.hdcp1.ksvlist, hdcp->auth.msg.hdcp1.ksvlist_size); return status; } enum mod_hdcp_status mod_hdcp_read_vp(struct mod_hdcp hdcp) { enum mod_hdcp_status status; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_VH_0, &hdcp->auth.msg.hdcp1.vp[0], 4); if (status != MOD_HDCP_STATUS_SUCCESS) goto out; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_VH_1, &hdcp->auth.msg.hdcp1.vp[4], 4); if (status != MOD_HDCP_STATUS_SUCCESS) goto out; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_VH_2, &hdcp->auth.msg.hdcp1.vp[8], 4); if (status != MOD_HDCP_STATUS_SUCCESS) goto out; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_VH_3, &hdcp->auth.msg.hdcp1.vp[12], 4); if (status != MOD_HDCP_STATUS_SUCCESS) goto out; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_VH_4, &hdcp->auth.msg.hdcp1.vp[16], 4); out: return status; } enum mod_hdcp_status mod_hdcp_read_binfo(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_BINFO, (uint8_t )&hdcp->auth.msg.hdcp1.binfo_dp, sizeof(hdcp->auth.msg.hdcp1.binfo_dp)); else status = MOD_HDCP_STATUS_INVALID_OPERATION; return status; } enum mod_hdcp_status mod_hdcp_write_aksv(struct mod_hdcp hdcp) { return write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKSV, hdcp->auth.msg.hdcp1.aksv, sizeof(hdcp->auth.msg.hdcp1.aksv)); } enum mod_hdcp_status mod_hdcp_write_ainfo(struct mod_hdcp hdcp) { return write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AINFO, &hdcp->auth.msg.hdcp1.ainfo, sizeof(hdcp->auth.msg.hdcp1.ainfo)); } enum mod_hdcp_status mod_hdcp_write_an(struct mod_hdcp hdcp) { return write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AN, hdcp->auth.msg.hdcp1.an, sizeof(hdcp->auth.msg.hdcp1.an)); } enum mod_hdcp_status mod_hdcp_read_hdcp2version(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = MOD_HDCP_STATUS_INVALID_OPERATION; else status = read(hdcp, MOD_HDCP_MESSAGE_ID_HDCP2VERSION, &hdcp->auth.msg.hdcp2.hdcp2version_hdmi, sizeof(hdcp->auth.msg.hdcp2.hdcp2version_hdmi)); return status; } enum mod_hdcp_status mod_hdcp_read_rxcaps(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (!is_dp_hdcp(hdcp)) status = MOD_HDCP_STATUS_INVALID_OPERATION; else status = read(hdcp, MOD_HDCP_MESSAGE_ID_RX_CAPS, hdcp->auth.msg.hdcp2.rxcaps_dp, sizeof(hdcp->auth.msg.hdcp2.rxcaps_dp)); return status; } enum mod_hdcp_status mod_hdcp_read_rxstatus(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_RXSTATUS, &hdcp->auth.msg.hdcp2.rxstatus_dp, 1); } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_RXSTATUS, (uint8_t )&hdcp->auth.msg.hdcp2.rxstatus, sizeof(hdcp->auth.msg.hdcp2.rxstatus)); } return status; } enum mod_hdcp_status mod_hdcp_read_ake_cert(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) { hdcp->auth.msg.hdcp2.ake_cert[0] = HDCP_2_2_AKE_SEND_CERT; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_CERT, hdcp->auth.msg.hdcp2.ake_cert+1, sizeof(hdcp->auth.msg.hdcp2.ake_cert)-1); } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_CERT, hdcp->auth.msg.hdcp2.ake_cert, sizeof(hdcp->auth.msg.hdcp2.ake_cert)); } return status; } enum mod_hdcp_status mod_hdcp_read_h_prime(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) { hdcp->auth.msg.hdcp2.ake_h_prime[0] = HDCP_2_2_AKE_SEND_HPRIME; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_H_PRIME, hdcp->auth.msg.hdcp2.ake_h_prime+1, sizeof(hdcp->auth.msg.hdcp2.ake_h_prime)-1); } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_H_PRIME, hdcp->auth.msg.hdcp2.ake_h_prime, sizeof(hdcp->auth.msg.hdcp2.ake_h_prime)); } return status; } enum mod_hdcp_status mod_hdcp_read_pairing_info(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) { hdcp->auth.msg.hdcp2.ake_pairing_info[0] = HDCP_2_2_AKE_SEND_PAIRING_INFO; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_PAIRING_INFO, hdcp->auth.msg.hdcp2.ake_pairing_info+1, sizeof(hdcp->auth.msg.hdcp2.ake_pairing_info)-1); } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_AKE_SEND_PAIRING_INFO, hdcp->auth.msg.hdcp2.ake_pairing_info, sizeof(hdcp->auth.msg.hdcp2.ake_pairing_info)); } return status; } enum mod_hdcp_status mod_hdcp_read_l_prime(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) { hdcp->auth.msg.hdcp2.lc_l_prime[0] = HDCP_2_2_LC_SEND_LPRIME; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_LC_SEND_L_PRIME, hdcp->auth.msg.hdcp2.lc_l_prime+1, sizeof(hdcp->auth.msg.hdcp2.lc_l_prime)-1); } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_LC_SEND_L_PRIME, hdcp->auth.msg.hdcp2.lc_l_prime, sizeof(hdcp->auth.msg.hdcp2.lc_l_prime)); } return status; } enum mod_hdcp_status mod_hdcp_read_rx_id_list(struct mod_hdcp hdcp) { enum mod_hdcp_status status = MOD_HDCP_STATUS_SUCCESS; if (is_dp_hdcp(hdcp)) { uint32_t device_count = 0; uint32_t rx_id_list_size = 0; uint32_t bytes_read = 0; hdcp->auth.msg.hdcp2.rx_id_list[0] = HDCP_2_2_REP_SEND_RECVID_LIST; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST, hdcp->auth.msg.hdcp2.rx_id_list+1, HDCP_MAX_AUX_TRANSACTION_SIZE); if (status == MOD_HDCP_STATUS_SUCCESS) { bytes_read = HDCP_MAX_AUX_TRANSACTION_SIZE; device_count = HDCP_2_2_DEV_COUNT_LO(hdcp->auth.msg.hdcp2.rx_id_list[2]) + (HDCP_2_2_DEV_COUNT_HI(hdcp->auth.msg.hdcp2.rx_id_list[1]) << 4); rx_id_list_size = MIN((21 + 5 * device_count), (sizeof(hdcp->auth.msg.hdcp2.rx_id_list) - 1)); status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST_PART2, hdcp->auth.msg.hdcp2.rx_id_list + 1 + bytes_read, (rx_id_list_size - 1) / HDCP_MAX_AUX_TRANSACTION_SIZE * HDCP_MAX_AUX_TRANSACTION_SIZE); } } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_SEND_RECEIVERID_LIST, hdcp->auth.msg.hdcp2.rx_id_list, hdcp->auth.msg.hdcp2.rx_id_list_size); } return status; } enum mod_hdcp_status mod_hdcp_read_stream_ready(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) { hdcp->auth.msg.hdcp2.repeater_auth_stream_ready[0] = HDCP_2_2_REP_STREAM_READY; status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_STREAM_READY, hdcp->auth.msg.hdcp2.repeater_auth_stream_ready+1, sizeof(hdcp->auth.msg.hdcp2.repeater_auth_stream_ready)-1); } else { status = read(hdcp, MOD_HDCP_MESSAGE_ID_READ_REPEATER_AUTH_STREAM_READY, hdcp->auth.msg.hdcp2.repeater_auth_stream_ready, sizeof(hdcp->auth.msg.hdcp2.repeater_auth_stream_ready)); } return status; } enum mod_hdcp_status mod_hdcp_write_ake_init(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKE_INIT, hdcp->auth.msg.hdcp2.ake_init+1, sizeof(hdcp->auth.msg.hdcp2.ake_init)-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKE_INIT, hdcp->auth.msg.hdcp2.ake_init, sizeof(hdcp->auth.msg.hdcp2.ake_init)); return status; } enum mod_hdcp_status mod_hdcp_write_no_stored_km(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKE_NO_STORED_KM, hdcp->auth.msg.hdcp2.ake_no_stored_km+1, sizeof(hdcp->auth.msg.hdcp2.ake_no_stored_km)-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKE_NO_STORED_KM, hdcp->auth.msg.hdcp2.ake_no_stored_km, sizeof(hdcp->auth.msg.hdcp2.ake_no_stored_km)); return status; } enum mod_hdcp_status mod_hdcp_write_stored_km(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKE_STORED_KM, hdcp->auth.msg.hdcp2.ake_stored_km+1, sizeof(hdcp->auth.msg.hdcp2.ake_stored_km)-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_AKE_STORED_KM, hdcp->auth.msg.hdcp2.ake_stored_km, sizeof(hdcp->auth.msg.hdcp2.ake_stored_km)); return status; } enum mod_hdcp_status mod_hdcp_write_lc_init(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_LC_INIT, hdcp->auth.msg.hdcp2.lc_init+1, sizeof(hdcp->auth.msg.hdcp2.lc_init)-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_LC_INIT, hdcp->auth.msg.hdcp2.lc_init, sizeof(hdcp->auth.msg.hdcp2.lc_init)); return status; } enum mod_hdcp_status mod_hdcp_write_eks(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_SKE_SEND_EKS, hdcp->auth.msg.hdcp2.ske_eks+1, sizeof(hdcp->auth.msg.hdcp2.ske_eks)-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_SKE_SEND_EKS, hdcp->auth.msg.hdcp2.ske_eks, sizeof(hdcp->auth.msg.hdcp2.ske_eks)); return status; } enum mod_hdcp_status mod_hdcp_write_repeater_auth_ack(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_SEND_ACK, hdcp->auth.msg.hdcp2.repeater_auth_ack+1, sizeof(hdcp->auth.msg.hdcp2.repeater_auth_ack)-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_SEND_ACK, hdcp->auth.msg.hdcp2.repeater_auth_ack, sizeof(hdcp->auth.msg.hdcp2.repeater_auth_ack)); return status; } enum mod_hdcp_status mod_hdcp_write_stream_manage(struct mod_hdcp hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_STREAM_MANAGE, hdcp->auth.msg.hdcp2.repeater_auth_stream_manage+1, hdcp->auth.msg.hdcp2.stream_manage_size-1); else status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_REPEATER_AUTH_STREAM_MANAGE, hdcp->auth.msg.hdcp2.repeater_auth_stream_manage, hdcp->auth.msg.hdcp2.stream_manage_size); return status; } enum mod_hdcp_status mod_hdcp_write_content_type(struct mod_hdcp *hdcp) { enum mod_hdcp_status status; if (is_dp_hdcp(hdcp)) status = write(hdcp, MOD_HDCP_MESSAGE_ID_WRITE_CONTENT_STREAM_TYPE, hdcp->auth.msg.hdcp2.content_stream_type_dp+1, sizeof(hdcp->auth.msg.hdcp2.content_stream_type_dp)-1); else status = MOD_HDCP_STATUS_INVALID_OPERATION; return status; }
Expiratory valves used for home devices: experimental and clinical comparison. A bench study followed by a clinical trial were performed to evaluate the mechanical characteristics of five (commercially available) expiratory valves used for home ventilators, as well as the potential clinical impact of differences between these valves. In the in vitro study, expiratory valve resistance was evaluated under unvarying conditions, whereas dynamic behaviour was evaluated by calculating the imposed expiratory work of breathing during a simulated breath generated by a lung model. Differences in resistance and imposed expiratory work of up to twofold and 150%, respectively, were found across valves. We then conducted a randomized crossover clinical study to compare the effects of the least resistive (Bennett) and most resistive expiratory valves (Peters) in 10 intubated patients receiving pressure support ventilation. There were no significant differences regarding blood gases or respiratory parameters except for the oesophageal pressure-time product (PTPoes), which was significantly increased by the Peters valve (236+/-113 cmH2O x s x min(-1) versus 194+/-90 cmH2O x s x min(-1)). An analysis of individual responses found that the Peters valve induced substantial increases in intrinsic positive end-expiratory pressure (PEEP), PTPoes, and expiratory activity in those patients with the greatest ventilatory demand. In conclusion, differences between home expiratory valve resistances may have a clinically relevant impact on the respiratory effort of patients with a high ventilatory demand.
Preview: Indians at Royals September 18, 2013\|Reuters SportsDirect Inc. Preview: Indians at Royals The Cleveland Indians are battling through every game as they attempt to chase down the Tampa Bay Rays and the Texas Rangers in the American League wild-card race. The Kansas City Royals, who host the Indians on Wednesday, are one of several teams nipping at Cleveland's heels in search of a postseason berth. The Royals and the Indians split the first two of the four-game set, leaving Cleveland a half-game back of a wild-card spot. Kansas City, which hosts Texas in a three-game series over the weekend, is running out of time to make up more ground and dropped 3 1/2 games behind the Rangers and Tampa Bay with Tuesday's 5-3 setback. The Royals, who took the series opener 7-1, owned a three-run lead Tuesday before the bullpen let the team down. The Indians are getting full use out of the expanded September rosters and used seven pitchers, one pinch hitter and three pinch runners in Tuesday's contest. Cleveland is limiting Salazar to around 80 pitches per start as it attempts to keep the rookie healthy and strong down the stretch. The 23-year-old is aiming for a sixth straight start allowing two or fewer earned runs, but is hoping to get past the fourth inning for the first time since Sept. 1. Salazar is making his first start against the division rivals and is 0-2 with a 2.35 ERA on the road. Chen had a string of three straight strong outings come to an end Friday, when he was reached for six runs (five earned) on seven hits over 4 1/3 innings in a loss at Detroit. The veteran swingman helped solidify the Kansas City rotation upon his promotion from the bullpen in late July and is 4-3 with a 3.44 ERA as a starter. Chen hasn't allowed an earned run in 12 1/3 total innings against Cleveland this season, including a six-inning start July 12 in which he surrendered only one hit. WALK-OFFS 1. The Indians will begin selling postseason tickets on Monday for a potential wild-card game and Division Series. 2. Kansas City 1B Eric Hosmer has hit safely in 18 of his last 20 games.
Fusion STRING allows inspection of the interaction evidence for any given network. Choose any of the viewers above (disabled if not applicable in your network). Nodes: Network nodes represent proteins splice isoforms or post-translational modifications are collapsed, i.e. each node represents all the proteins produced by a single, protein-coding gene locus. Node Color colored nodes:query proteins and first shell of interactors white nodes:second shell of interactors Node Content empty nodes:proteins of unknown 3D structure filled nodes:some 3D structure is known or predicted Edges: Edges represent protein-protein associations associations are meant to be specific and meaningful, i.e. proteins jointly contribute to a shared function; this does not necessarily mean they are physically binding each other. Known Interactions from curated databases experimentally determined Predicted Interactions gene neighborhood gene fusions gene co-occurrence Others textmining co-expression protein homology Your Input: Neighborhood Gene Fusion Cooccurence Coexpression Experiments Databases Textmining [Homology] Score Psed_3840 tRNA/rRNA methyltransferase SpoU (279 aa) Predicted Functional Partners: rplT 50S ribosomal protein L20; Binds directly to 23S ribosomal RNA and is necessary for the in vitro assembly process of the 50S ribosomal subunit. It is not involved in the protein synthesizing functions of that subunit (128 aa) 0.956 pheS Phenylalanyl-tRNA synthetase subunit alpha (366 aa) 0.887 pheT Phenylalanyl-tRNA synthetase subunit beta (846 aa) 0.865 rpmI 50S ribosomal protein L35 (64 aa) 0.804 Psed_3973 Ribonuclease II (474 aa) 0.767 infC Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins (250 aa) 0.729 Psed_5370 Hypothetical protein; Bifunctional enzyme that catalyzes the epimerization of the S- and R-forms of NAD(P)HX and the dehydration of the S-form of NAD(P)HX at the expense of ADP, which is converted to AMP. This allows the repair of both epimers of NAD(P)HX, a damaged form of NAD(P)H that is a result of enzymatic or heat-dependent hydration (480 aa) 0.696 rsmH Ribosomal RNA small subunit methyltransferase H; Specifically methylates the N4 position of cytidine in position 1402 (C1402) of 16S rRNA (326 aa) 0.651 Psed_6104 DNA repair protein RadA; DNA-dependent ATPase involved in processing of recombination intermediates, plays a role in repairing DNA breaks. Stimulates the branch migration of RecA-mediated strand transfer reactions, allowing the 3’ invading strand to extend heteroduplex DNA faster. Binds ssDNA in the presence of ADP but not other nucleotides, has ATPase activity that is stimulated by ssDNA and various branched DNA structures, but inhibited by SSB. Does not have RecA’s homology-searching function (434 aa) a tab-delimited file describing the names, domains and annotated functions of the network proteins Browse interactions in tabular form: node1 node2 node1 accession node2 accession node1 annotation node2 annotation score Psed_3840 Psed_3973 Psed_3840 Psed_3973 tRNA/rRNA methyltransferase SpoU Ribonuclease II 0.767 Psed_3840 Psed_5370 Psed_3840 Psed_5370 tRNA/rRNA methyltransferase SpoU Hypothetical protein; Bifunctional enzyme that catalyzes the epimerization of the S- and R-forms of NAD(P)HX and the dehydration of the S-form of NAD(P)HX at the expense of ADP, which is converted to AMP. This allows the repair of both epimers of NAD(P)HX, a damaged form of NAD(P)H that is a result of enzymatic or heat-dependent hydration 0.696 Psed_3840 Psed_6104 Psed_3840 Psed_6104 tRNA/rRNA methyltransferase SpoU DNA repair protein RadA; DNA-dependent ATPase involved in processing of recombination intermediates, plays a role in repairing DNA breaks. Stimulates the branch migration of RecA-mediated strand transfer reactions, allowing the 3’ invading strand to extend heteroduplex DNA faster. Binds ssDNA in the presence of ADP but not other nucleotides, has ATPase activity that is stimulated by ssDNA and various branched DNA structures, but inhibited by SSB. Does not have RecA’s homology-searching function 0.632 Psed_3840 infC Psed_3840 Psed_3843 tRNA/rRNA methyltransferase SpoU Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins 0.729 Psed_3840 pheS Psed_3840 Psed_3839 tRNA/rRNA methyltransferase SpoU Phenylalanyl-tRNA synthetase subunit alpha 0.887 Psed_3840 pheT Psed_3840 Psed_3838 tRNA/rRNA methyltransferase SpoU Phenylalanyl-tRNA synthetase subunit beta 0.865 Psed_3840 rplT Psed_3840 Psed_3841 tRNA/rRNA methyltransferase SpoU 50S ribosomal protein L20; Binds directly to 23S ribosomal RNA and is necessary for the in vitro assembly process of the 50S ribosomal subunit. It is not involved in the protein synthesizing functions of that subunit 0.956 Psed_3840 rpmI Psed_3840 Psed_3842 tRNA/rRNA methyltransferase SpoU 50S ribosomal protein L35 0.804 Psed_3840 rsmH Psed_3840 Psed_2799 tRNA/rRNA methyltransferase SpoU Ribosomal RNA small subunit methyltransferase H; Specifically methylates the N4 position of cytidine in position 1402 (C1402) of 16S rRNA 0.651 Psed_3840 thrS Psed_3840 Psed_3613 tRNA/rRNA methyltransferase SpoU threonyl-tRNA synthetase 0.627 Psed_3973 Psed_3840 Psed_3973 Psed_3840 Ribonuclease II tRNA/rRNA methyltransferase SpoU 0.767 Psed_3973 Psed_5370 Psed_3973 Psed_5370 Ribonuclease II Hypothetical protein; Bifunctional enzyme that catalyzes the epimerization of the S- and R-forms of NAD(P)HX and the dehydration of the S-form of NAD(P)HX at the expense of ADP, which is converted to AMP. This allows the repair of both epimers of NAD(P)HX, a damaged form of NAD(P)H that is a result of enzymatic or heat-dependent hydration 0.412 Psed_5370 Psed_3840 Psed_5370 Psed_3840 Hypothetical protein; Bifunctional enzyme that catalyzes the epimerization of the S- and R-forms of NAD(P)HX and the dehydration of the S-form of NAD(P)HX at the expense of ADP, which is converted to AMP. This allows the repair of both epimers of NAD(P)HX, a damaged form of NAD(P)H that is a result of enzymatic or heat-dependent hydration tRNA/rRNA methyltransferase SpoU 0.696 Psed_5370 Psed_3973 Psed_5370 Psed_3973 Hypothetical protein; Bifunctional enzyme that catalyzes the epimerization of the S- and R-forms of NAD(P)HX and the dehydration of the S-form of NAD(P)HX at the expense of ADP, which is converted to AMP. This allows the repair of both epimers of NAD(P)HX, a damaged form of NAD(P)H that is a result of enzymatic or heat-dependent hydration Ribonuclease II 0.412 Psed_6104 Psed_3840 Psed_6104 Psed_3840 DNA repair protein RadA; DNA-dependent ATPase involved in processing of recombination intermediates, plays a role in repairing DNA breaks. Stimulates the branch migration of RecA-mediated strand transfer reactions, allowing the 3’ invading strand to extend heteroduplex DNA faster. Binds ssDNA in the presence of ADP but not other nucleotides, has ATPase activity that is stimulated by ssDNA and various branched DNA structures, but inhibited by SSB. Does not have RecA’s homology-searching function tRNA/rRNA methyltransferase SpoU 0.632 infC Psed_3840 Psed_3843 Psed_3840 Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins tRNA/rRNA methyltransferase SpoU 0.729 infC pheS Psed_3843 Psed_3839 Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins Phenylalanyl-tRNA synthetase subunit alpha 0.828 infC pheT Psed_3843 Psed_3838 Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins Phenylalanyl-tRNA synthetase subunit beta 0.903 infC rplT Psed_3843 Psed_3841 Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins 50S ribosomal protein L20; Binds directly to 23S ribosomal RNA and is necessary for the in vitro assembly process of the 50S ribosomal subunit. It is not involved in the protein synthesizing functions of that subunit 0.984 infC rpmI Psed_3843 Psed_3842 Translation initiation factor IF-3; IF-3 binds to the 30S ribosomal subunit and shifts the equilibrum between 70S ribosomes and their 50S and 30S subunits in favor of the free subunits, thus enhancing the availability of 30S subunits on which protein synthesis initiation begins 50S ribosomal protein L35 0.939 page 1 of 3 Network Stats Network Stats analysis is still ongoing, please wait ... Functional enrichments in your networkNote: some enrichments may be expected here (why?) Enrichment analysis is still ongoing, please wait ... Statistical background For the above enrichment analysis, the following statistical background is assumed:
ENGINEERING DISASTERS BRAINSTORMERS (WT) RICHARD PRYOR: ICON AL CAPONE: ICON ENGINEERING DISASTERS Engineering has built our modern world. Everything from skyscrapers to roads and air travel exist because of advances in engineering. What happens when engineering goes horribly wrong? Engineering Disasters goes beyond the headlines to uncover what really happened in the most notorious engineering accidents. What caused an outdoor stage to collapse in Indiana, killing seven? How did a collection of classic Corvettes disappear right out of thin air? Why did a plane’s fuselage rip open in mid-flight? What was behind the collapse of a domed stadium? Each hour long episode combines expert and eyewitness interviews, state of the art graphics and dramatic ‘moment of disaster’ footage to tell the story behind the world’s most terrifying engineering disasters BRAINSTORMERS (WT) “BrainStormers” follows three Colorado-based backyard geniuses – a father, son and his friend – who are on a quest to build and test inventions that either fight bad weather or harness its power. From their homegrown workshop in Colorado, Poppy, Ryan and Bill test their ingenuity and tackle weather issues by recycling what some might consider junk. Every build is always filled with challenges, from creating a homemade mosquito trap or solar water heater to fixing a nearby town’s wind generator, and the road to success is filled with setbacks, revelations and a lot of fun. PRODUCED FOR: WEATHER CHANNEL RICHARD PRYOR: ICON Richard Pryor is cited as one of the greatest American comedians of all time, with a huge influence on comedy and this generation’s top comics. He was one of the first black men ever on television and pioneered a new brand of humor. On this episode of :ICON, we delve into the life and legacy of Richard Pryor, often using his own words, to show us his lasting affect on American comedy and culture. PRODUCED FOR: PBS AL CAPONE: ICON From his early days rising through the ranks of New York’s gangs, to his slow demise in the aftermath of the St. Valentine’s Day Massacre, Al Capone: Icon chronicles the complicated life of one of America’s favorite mob bosses. The special exposes Capone not only as a bootlegger, killer and gangster, but as the popular public figure who opened one of the nation’s first soup kitchens, fought for expiration dates on milk and wrote love songs to his wife from prison. It’s been more than 80 years since the height of Capone’s power, yet his impact is still felt. In addition to Capone’s history, Al Capone: Icon unveils his unexpected connections to modern-day organized crime, law enforcement, popular culture and even everyday life in Chicago.
"There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." The C3 collection is flying out the door. Make sure you stop by and check it out before it's sold out. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." The C3 collection is flying out the door. Make sure you stop by and check it out before it's sold out. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." While you're out looking for deals this weekend, don't forget to stop by The Android's Dungeon. We have lots of great books at low, low prices. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." We still have lots of great books that we need to list. Stop by this weekend and see what's new. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." We still have lots of great books that we need to list. Stop by and see what's new. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." We just listed a high-grade run of The Walking Dead issues 77-84 over on our IMAGE shelf. Stop by and check them out. Here are direct links to each issue: ONGOING:Listing High-Grade Marvels From A Recent 3,716 Book Collection Purchase. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." We just listed a high-grade run of The Walking Dead issues 77-84 over on our IMAGE shelf. Stop by and check them out. Here are direct links to each issue: ONGOING:Listing High-Grade Marvels From A Recent 3,716 Book Collection Purchase. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." We just listed a high-grade run of The Walking Dead issues 77-84 over on our IMAGE shelf. Stop by and check them out. Here are direct links to each issue: ONGOING:Listing High-Grade Marvels From A Recent 3,716 Book Collection Purchase. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." We just listed a high-grade run of The Walking Dead issues 77-84 over on our IMAGE shelf. Stop by and check them out. Here are direct links to each issue: ONGOING:Listing High-Grade Marvels From A Recent 3,716 Book Collection Purchase. "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." "There he goes. One of God's own prototypes. Some kind of high powered mutant never even considered for mass production. Too weird to live, and too rare to die." - Raoul Duke (Johnny Depp) from "Fear and Loathing in Las Vegas." Forum Jump Access You cannot post new topics in this forum. You cannot reply to topics in this forum. You cannot delete your posts in this forum. You cannot edit your posts in this forum. You cannot create polls in this forum. You cannot vote in polls in this forum.
Display devices like TFT-LCDs (thin film transistor liquid crystal displays) are used in laptop computers, and are also finding increasingly wider application in GSM (Global System for Mobile communications) telephones. In addition, other kinds of display devices instead of LCDs are being used in GSM telephones; for example, (polymer) LED display devices are being used. Apart from these types of displays, other display techniques, such as EWD devices suitable for flat plate displays are evolving. The electro-wetting functionality provides displays with excellent brightness and contrast, and relatively low power consumption compared to many other display technologies. Referring to FIG. 5, a top plan diagram of a sub-pixel unit of a related art EWD device is shown. The sub-pixel unit 100 is rectangular, and is defined by two opposite long side walls 101 and two opposite short side walls 102. The long side walls 101 and the short side walls 102 are connected end-to-end, and are made from hydrophobic interfacial materials. A thin film transistor element 121 is disposed at a corner of the sub-pixel unit 100. Another corner region of the sub-pixel unit 100 adjacent to the thin film transistor element 121 is defined as a first region 129. An area of the first region 129 is substantially two times an area of the thin film transistor element 121. A transparent electrode 122 is disposed in an entire area of the sub-pixel unit 100 except where the thin film transistor element 121 is located. A hydrophobic insulating layer (not shown), an oil layer (not shown), and a water layer (not shown) are positioned in that order on the thin film transistor element 121 and the transparent electrode 122. An area of the sub-pixel unit 100 is defined as X. The area of the thin film transistor element 121 is defined as Y. The oil layer has more affinity to the long side walls 101 than to the thin film transistor element 121, thus the oil layer in the first region 129 is not apt to move to the thin film transistor element 121. When the sub-pixel unit 100 works in an on state, the oil layer is displaced so that it covers only the first region 129, and therefore the first region 129 is not transparent. Accordingly, an aperture ratio of the sub-pixel unit 100 is substantially (X−3Y)/X. This aperture ratio is rather low. What is needed, therefore, is to provide an EWD device that can overcome the above-described deficiencies.
After a beautiful goal off of normally invisible Chris Kelly, the Bruins topped the Philadelphia Flyers 2-1 in regulation to bring our regular season record to 1-0-0. This win gives the Bruins a good bit of momentum going into tonight's tilt against the Detroit Red Wings in our first back to back series of the season. Overall, I am extremely happy with the performance I saw last night, especially considering we had lost arguably our best center and had a defense who were beginning to adjust to the loss of a main cog in the machine that is our defense. Although it's early, it could mean good things for this team in terms of recouping from the losses we suffered over the off-season. The first period saw some great offensive pressure and strong defensive play from the Bruins, which came to climax with a goal from Reilly Smith 10:39 into the period to put the Bruins up 1-0. Tuukka Rask, as always, was on point in net and was blocking the few shots the Flyers managed to get off on him like it was nothing. The second period definitely wasn't as satisfying as the first, with the Bruins getting off to a rocky start defensively. Zdeno Chara and Dougie Hamilton got stuck in the zone for over two minutes before an icing call freed them up long enough for Coach to call a time out and knock some sense into them. The Bruins also had to kill two penalties in the second period off of slashing call against Dennis Seidenberg and a tripping call on Loui Eriksson. Despite it all, the Bruins came out of the period unscathed. The third period is where things started to get interesting. 4:19 into the period the Bruins third period slump pattern seemed to have come back into existence as the Flyers tied it up at 1-1 of a goal from Sean Couturier. The Bruins once again had to kill off two penalties during the period after Saint Patrice got called for holding (the ref is going to hell for that call) and an elbowing call against Brad Marchand. However, in typical Bruins style, the Bruins were able to bang out the win with 1:51 seconds left off a goal from the elusive Chris Kelly. It is worth noting that, despite the fact that Kelly has literally been far from an asset for the Bruins, last night's goal earned him the first star in the game and the third star league wide behind Plekanec and Wingels. It literally blows my mind that he could even score a goal never mind that they would rank him that highly across the league. Bruins Positive 1. Smith's goal. My god was that a beauty. It was perfectly executed and definitely helped set the tone for the rest of the game. 2. Daniel Paille for playing his 500th NHL game. You go Piesy! 3. Bobby Robins first game. Despite all the feelings I have about Robins being on the team, you have to give the guy credit for finally making it into the big leagues at age 33. 4. Dougie Hamilton get scrappy. He needs to not fight because he's Dougie Hamilton, but I'm proud of him for stepping up. Bruins Negatives 1. Bobby Robins fight. As much as I of all people appreciate a good scrap, I'm so angry that Chia got rid of Thornton so the team could "move away from that style of hockey" only to bring in the guy who is literally the same as Thornton just a tad bit faster.
The Present Disclosure relates, generally, to optical fiber assemblies and, more particularly, to an optical fiber assembly having a ferrule carrier removable without the use of tools. Systems for interconnecting optical fibers typically utilize mating optical fiber connector or interconnect assemblies to facilitate handling and accurate positioning of the optical fibers. The individual optical fibers may be secured within a ferrule of each connector assembly, and the mating ferrules align the axis of each mating pair of optical fibers. The optical interfaces of the optical fibers sometimes become contaminated with dirt, dust and other debris such that the optical interfaces require cleaning. In some instances, it may be possible to clean the optical interfaces with the connectors in place. In other instances, it may be necessary to remove the optical fiber connectors from their operating environment to perform such a cleaning operation. Optical fiber connectors may be mounted on a substrate or board such as a backplane or daughter card through the use of screws and other mounting hardware. In addition, other components may be mounted on the substrate in close proximity to the connector. When removing an optical fiber connector from a substrate, such other components may interfere with access to the mounting hardware of the optical fiber connector or interfere with the ability of an operator to position a tool in the desired position to easily remove the mounting hardware that secures the optical fiber connector to the substrate. Such interference may substantially increase the difficulty and thus the time required to remove and replace optical fiber connectors mounted on a substrate. The foregoing background discussion is intended solely to aid the reader. It is not intended to limit the innovations described herein, nor to limit or expand the conventional state of the art, as discussed. Thus, the foregoing discussion should not be taken to indicate that any particular element of a conventional system is unsuitable for use with the innovations described herein, nor is it intended to indicate that any element is essential in implementing the innovations described herein. The implementations and application of the innovations described herein are defined by the appended Claims.
CREATE ACCOUNT FORGOT YOUR DETAILS? PakistanCriminalRecords.com is a free research resource being provided free of charge by managed by Background Check Pvt Ltd, one of the Asia's largest screening firms, to public for the awareness about the serious and organized crime in Pakistan. Charsadda: Son of former high court CJ shot dead Charsadda: Son of former high court CJ shot dead CHARSADDA: Son of former Peshawar High Courtchief justice, late Tallat Qayyum Qureshi, was killed when unidentified persons fired at him here at Sardaryab area Friday night. The deceased, Umer Tallat, 26, his brother Usman Tallat and a cousin had gone to Sardaryab, a recreational spot known for scores of food outlets, on the bank of River Kabul. The relatives accompanying him claimed that they stopped on a roadside on their way back to Peshawar from Sardaryab. “Four persons approached us and asked for a match box. When we told them that we did not have it, they started exchanging hot words with us and after that one of them opened fire,” said cousin of the deceased. The deceased was rushed to LadyReading Hospital in Peshawar but he expired on the way. The deceased had recently started practicing law. The attackers fled after the incident. The motive behind the incident was unclear as the family members claimed that they did not have enmity with anyone. The officials of the concerned Prang police station in Charssada came to know about the occurrence from the hospital and they rushed to Peshawar to get details of the incident. Justice Tallat Qayyum Qureshi passed away on Jan 18 due to cardiac ailments. He was appointed highcourt chief justice on Nov 3 when former CJ Tariq Pervez declined to take oath under the PCO.
Can molecular and cellular neuroprotection be translated into therapies for patients?: yes, but not the way we tried it before. The concept of neuroprotection is based on sound scientific data derived in preclinical studies. However, candidate neuroprotectants have never been successfully translated to patients. A review of past approaches to cellular and molecular neuroprotection, preclinical neuroprotection studies, and clinical approaches was undertaken. Although there is no evidence for fundamental barriers in biological principles that limit the translation of promising therapies to humans, ample evidence exists as to a lack of rigor in preclinical studies, obstacles posed by the complexities of acute ischemic stroke syndromes, and regulatory barriers. Alternative methods to translating stroke drugs may require trials in restricted stroke indications in well-defined patient populations. The translational gap between cellular and molecular neuroscience and patient therapy may be bridged by first developing therapies for narrow stroke indications. A single success may stimulate further research, funding, and a capacity to generalize initial results to broader stroke populations.
This outstanding and unique vintage metal art sign is created on enamel coated metal. The design is highly appealing and has a quality vintage look, which makes this piece of art stand out above the rest. This sign is perfect for a military recruiting office, home, office, game room, rec room, pubs, restaurants, kitchens, diners, just about anywhere! This sign measures approximately 12" x 12", features black and cream colors, has rustic edges, along with four pre-drilled holes. Ready to hang on the wall, or ready to frame!
History will judge Israel’s apologists the way Theresa May is now judged on apartheid South Africa. The UK Labour Party’s adoption of the International Holocaust Remembrance Alliance’s (IHRA) anti-Semitism code in full, including its list of 11 examples, means it now considers calling Israel “racist” a potentially racist act. But the reality is that since the foundation of Israel – beginning with David Ben-Gurion’s “Drive them out!” order to the Palmach in the 1948 Nakba – racial oppression of Palestinians has been the norm. As Palestinian freedom fighter Ahed Tamimi has observed, Israel is afraid of this truth being known. And by adopting the full IHRA definition, Labour is helping to stifle it. But we shouldn’t be surprised: UK politicians have a long and inglorious history of protecting states practising apartheid. Notably, they have never been held to account for their support for white rule in South Africa. We were reminded of this recently when Prime Minister Theresa May visited Robben Island, where Nelson Mandela and many other anti-apartheid activists were imprisoned for decades. When asked what she had done to hasten Mandela’s release and the end of minority rule in South Africa, she squirmed awkwardly, before claiming “what was important is what the United Kingdom did”. What the British government – and May’s Conservative Party – did was not only fail to support Mandela and the African National Congress (ANC) but actively support the apartheid South African regime for years. Following the 1970 UK election, Conservative Prime Minister Ted Heath pledged to end the arms embargo on South Africa and resume military equipment sales to the apartheid government. In the 1980s, Conservative Prime Minister Margaret Thatcher resisted global pressure to impose sanctions on South Africa and labelled the ANC “a terror organisation”. In the same era, an aspiring young politician – future Prime Minister David Cameron – went on an all-expenses-paid trip to South Africa courtesy of an anti-sanctions lobbying firm, while members of the Federation of Conservative Students went as far as wearing “Hang Nelson Mandela” stickers. The UK is as deeply complicit in Israel’s apartheid system as it was in South African apartheid, if not more so. Adoption of the IHRA’s definition of anti-Semitism by the Labour Party – and the Conservative government, nine months ago – is just the tip of the iceberg. From its historical role in smoothing a course for the ethnic cleansing of Palestine by issuing the Balfour Declaration to its contemporary arms sales to Israel, when it comes to Palestine the UK stays true to its colonial past. Israel is afforded impunity despite its multiple crimes, such as the killing of over 160 Palestinians in Gaza since the Great March of Return began. The UK seeks to protect Israel from accountability in global forums like the United Nations, for example by refusing to vote for an independent investigation into the killing of 60 Palestinians on May 14 this year, a massacre dubbed the “Palestinian Sharpeville” after the 1960 murder of 69 black protesters by South African apartheid security forces. Regardless of Israel’s long-standing disregard for international law and grave human rights violations, Britain even gifted it a royal stamp of approval in June when Prince William made a symbolic visit to the country, contravening seven decades of British policy against official royal visits to Israel. History is repeating itself. Just as the UK government shielded South African apartheid in the past, it is giving political, economic and military support to Israeli apartheid today. In 2017 alone, the UK government granted more than 289 million British pounds-worth ($375.3m) of licenses for the export of arms and military technology to Israel. But in the end, British support didn’t protect South African apartheid from the reach of justice and equality. Similarly, the IHRA won’t protect Israel’s ethnocracy. Palestinians and their allies will continue to name the racial oppression they face under Israel for what it is – a system of apartheid. And history is already beginning to repeat itself in another, more positive, sense. Just as a powerful global boycott movement helped make South Africa a pariah state – in the process making a vital contribution to ending apartheid – the Palestinian BDS campaign is following in its footsteps. The BDS movement understands that freedom, justice and equality will not be handed down from above by the very same politicians who have tolerated Israeli apartheid for so long. It can only be won by pushing from the grassroots up. Thirty years from now, British politicians will be asked what they did to end Israeli apartheid. And though the UK’s complicity will no doubt be similarly whitewashed, history will judge Israel’s apologists the way Theresa May is judged now on South Africa. The views expressed in this article are the author’s own and do not necessarily reflect Al Jazeera’s editorial stance.
Oxidative stress by Helicobacter pylori causes apoptosis through mitochondrial pathway in gastric epithelial cells. Helicobacter pylori is a gram negative bacterium that infects the human stomach of approximately half of the world's population. It produces oxidative stress, and mitochondria are one of the possible targets and the major intracellular source of free radicals. The present study was aimed at determining mitochondrial alterations in H. pylori-infected gastric epithelial cells and its relationship with oxidative stress, one of the recognized causes of apoptotic processes. Cells were treated with a strain of H. pylori for 24 h. Cellular oxidative burst, antioxidant defense analysis, mitochondrial alterations and apoptosis-related processes were measured. Our data provide evidence on how superoxide acts on mitochondria to initiate apoptotic pathways, with these changes occurring in the presence of mitochondrial depolarization and other morphological and functional changes. Treatment of infected cells with Vitamin E prevented increases in intracellular ROS and mitochondrial damage consistent with H. pylori inducing a mitochondrial ROS mediated programmed cell death pathway.
//------------------------------------------------------------------------------ // InstanceSymbols.cpp // Contains instance-related symbol definitions // // File is under the MIT license; see LICENSE for details //------------------------------------------------------------------------------ #include "slang/symbols/InstanceSymbols.h" #include "ParameterBuilder.h" #include "slang/binding/Expression.h" #include "slang/compilation/Compilation.h" #include "slang/compilation/Definition.h" #include "slang/diagnostics/DeclarationsDiags.h" #include "slang/diagnostics/LookupDiags.h" #include "slang/symbols/ASTSerializer.h" #include "slang/symbols/MemberSymbols.h" #include "slang/symbols/ParameterSymbols.h" #include "slang/symbols/PortSymbols.h" #include "slang/symbols/Type.h" #include "slang/symbols/VariableSymbols.h" #include "slang/syntax/AllSyntax.h" #include "slang/util/StackContainer.h" namespace { using namespace slang; class InstanceBuilder { public: InstanceBuilder(const BindContext& context, const InstanceCacheKey& cacheKeyBase, span<const ParameterSymbolBase* const> parameters, span<const AttributeInstanceSyntax* const> attributes) : compilation(context.getCompilation()), context(context), cacheKeyBase(cacheKeyBase), parameters(parameters), attributes(attributes) {} Symbol* create(const HierarchicalInstanceSyntax& syntax) { path.clear(); auto dims = syntax.dimensions; return recurse(syntax, dims.begin(), dims.end()); } private: using DimIterator = span<VariableDimensionSyntax>::iterator; Compilation& compilation; const BindContext& context; const InstanceCacheKey& cacheKeyBase; SmallVectorSized<int32_t, 4> path; span<const ParameterSymbolBase const> parameters; span<const AttributeInstanceSyntax* const> attributes; Symbol* createInstance(const HierarchicalInstanceSyntax& syntax) { // Find all port connections to interface instances so we can // extract their cache keys. auto& def = cacheKeyBase.getDefinition(); SmallVectorSized<const InstanceCacheKey, 8> ifaceKeys; InterfacePortSymbol::findInterfaceInstanceKeys(context.scope, def, syntax.connections, ifaceKeys); // Try to look up a cached instance using our own key to avoid redoing work. InstanceCacheKey cacheKey = cacheKeyBase; if (!ifaceKeys.empty()) cacheKey.setInterfacePortKeys(ifaceKeys.copy(compilation)); auto inst = compilation.emplace<InstanceSymbol>( compilation, syntax.name.valueText(), syntax.name.location(), cacheKey, parameters); inst->arrayPath = path.copy(compilation); inst->setSyntax(syntax); inst->setAttributes(context.scope, attributes); return inst; } Symbol recurse(const HierarchicalInstanceSyntax& syntax, DimIterator it, DimIterator end) { if (it == end) return createInstance(syntax); // Evaluate the dimensions of the array. If this fails for some reason, // make up an empty array so that we don't get further errors when // things try to reference this symbol. auto nameToken = syntax.name; auto dim = context.evalDimension(*it, / requireRange / true, / isPacked / false); if (!dim.isRange()) { return compilation.emplace<InstanceArraySymbol>( compilation, nameToken.valueText(), nameToken.location(), span<const Symbol const>{}, ConstantRange()); } ++it; ConstantRange range = dim.range; SmallVectorSized<const Symbol, 8> elements; for (int32_t i = range.lower(); i <= range.upper(); i++) { path.append(i); auto symbol = recurse(syntax, it, end); path.pop(); symbol->name = ""; elements.append(symbol); } auto result = compilation.emplace<InstanceArraySymbol>(compilation, nameToken.valueText(), nameToken.location(), elements.copy(compilation), range); for (auto element : elements) result->addMember(element); return result; } }; void createParams(Compilation& compilation, const Definition& definition, ParameterBuilder& paramBuilder, LookupLocation ll, SourceLocation instanceLoc, bool forceInvalidParams) { // Construct a temporary scope that has the right parent to house instance parameters // as we're evaluating them. We hold on to the initializer expressions and give them // to the instances later when we create them. struct TempInstance : public InstanceBodySymbol { TempInstance(Compilation& compilation, const Definition& definition) : InstanceBodySymbol(compilation, InstanceCacheKey(definition, {}, {})) { setParent(definition.scope); } }; auto& tempDef = compilation.emplace<TempInstance>(compilation, definition); // Need the imports here as well, since parameters may depend on them. for (auto import : definition.syntax.header->imports) tempDef.addMembers(import); paramBuilder.createParams(tempDef, ll, instanceLoc, forceInvalidParams, /* suppressErrors / false); } void createImplicitNets(const HierarchicalInstanceSyntax& instance, const BindContext& context, const NetType& netType, SmallSet<string_view, 8>& implicitNetNames, SmallVector<const Symbol>& results) { // If no default nettype is set, we don't create implicit nets. if (netType.isError()) return; for (auto conn : instance.connections) { const ExpressionSyntax* expr = nullptr; switch (conn->kind) { case SyntaxKind::OrderedPortConnection: expr = conn->as<OrderedPortConnectionSyntax>().expr; break; case SyntaxKind::NamedPortConnection: expr = conn->as<NamedPortConnectionSyntax>().expr; break; default: break; } if (!expr) continue; SmallVectorSized<Token, 8> implicitNets; Expression::findPotentiallyImplicitNets(expr, context, implicitNets); for (Token t : implicitNets) { if (implicitNetNames.emplace(t.valueText()).second) { auto& comp = context.getCompilation(); auto net = comp.emplace<NetSymbol>(t.valueText(), t.location(), netType); net->setType(comp.getLogicType()); results.append(net); } } } } } // namespace namespace slang { InstanceSymbol::InstanceSymbol(Compilation& compilation, string_view name, SourceLocation loc, const InstanceBodySymbol& body) : Symbol(SymbolKind::Instance, name, loc), body(body) { compilation.addInstance(this); } InstanceSymbol::InstanceSymbol(Compilation& compilation, string_view name, SourceLocation loc, const InstanceCacheKey& cacheKey, span<const ParameterSymbolBase* const> parameters) : InstanceSymbol(compilation, name, loc, InstanceBodySymbol::fromDefinition(compilation, cacheKey, parameters)) { } InstanceSymbol& InstanceSymbol::createDefault(Compilation& compilation, const Definition& definition) { return compilation.emplace<InstanceSymbol>( compilation, definition.name, definition.location, InstanceBodySymbol::fromDefinition(compilation, definition, / forceInvalidParams / false)); } InstanceSymbol& InstanceSymbol::createInvalid(Compilation& compilation, const Definition& definition) { // Give this instance an empty name so that it can't be referenced by name. return compilation.emplace<InstanceSymbol>( compilation, "", SourceLocation::NoLocation, InstanceBodySymbol::fromDefinition(compilation, definition, /* forceInvalidParams / true)); } void InstanceSymbol::fromSyntax(Compilation& compilation, const HierarchyInstantiationSyntax& syntax, LookupLocation location, const Scope& scope, SmallVector<const Symbol>& results) { auto definition = compilation.getDefinition(syntax.type.valueText(), scope); if (!definition) { scope.addDiag(diag::UnknownModule, syntax.type.range()) << syntax.type.valueText(); return; } ParameterBuilder paramBuilder(scope, definition->name, definition->parameters); if (syntax.parameters) paramBuilder.setAssignments(syntax.parameters); // Determine values for all parameters now so that they can be // shared between instances, and so that we can use them to create // a cache key to lookup any instance bodies that may already be // suitable for the new instances we're about to create. createParams(compilation, definition, paramBuilder, location, syntax.getFirstToken().location(), /* forceInvalidParams / false); BindContext context(scope, location); InstanceCacheKey cacheKey(definition, paramBuilder.paramValues.copy(compilation), paramBuilder.typeParams.copy(compilation)); InstanceBuilder builder(context, cacheKey, paramBuilder.paramSymbols, syntax.attributes); // We have to check each port connection expression for any names that can't be resolved, // which represent implicit nets that need to be created now. SmallSet<string_view, 8> implicitNetNames; auto& netType = scope.getDefaultNetType(); for (auto instanceSyntax : syntax.instances) { createImplicitNets(instanceSyntax, context, netType, implicitNetNames, results); results.append(builder.create(instanceSyntax)); } } static void getInstanceArrayDimensions(const InstanceArraySymbol& array, SmallVector<ConstantRange>& dimensions) { auto scope = array.getParentScope(); if (scope && scope->asSymbol().kind == SymbolKind::InstanceArray) getInstanceArrayDimensions(scope->asSymbol().as<InstanceArraySymbol>(), dimensions); dimensions.append(array.range); } const Definition& InstanceSymbol::getDefinition() const { return body.getDefinition(); } bool InstanceSymbol::isModule() const { return getDefinition().definitionKind == DefinitionKind::Module; } bool InstanceSymbol::isInterface() const { return getDefinition().definitionKind == DefinitionKind::Interface; } const PortConnection* InstanceSymbol::getPortConnection(const PortSymbol& port) const { resolvePortConnections(); auto it = connections->find(reinterpret_cast<uintptr_t>(&port)); if (it == connections->end()) return nullptr; return reinterpret_cast<const PortConnection>(it->second); } const PortConnection InstanceSymbol::getPortConnection(const InterfacePortSymbol& port) const { resolvePortConnections(); auto it = connections->find(reinterpret_cast<uintptr_t>(&port)); if (it == connections->end()) return nullptr; return reinterpret_cast<const PortConnection>(it->second); } void InstanceSymbol::resolvePortConnections() const { // Note: the order of operations here is very subtly important. // In order to resolve connections, we need to actually know our list of ports. // Asking the body for the list of ports requires fully elaborating the instance, // especially because of things like non-ansi port declarations which might be // deep in the body. That process of elaboration can actually depend back on the // port connections because of interface ports. // For example: // // interface I #(parameter int i) (); endinterface // module M(I iface, input logic [iface.i - 1 : 0] foo); // localparam int j = $bits(foo); // endmodule // // In order to resolve connections for an instance of M, we elaborate its body, // which then requires evaluating $bits(foo) which then depends on the connection // provided to `iface`. In the code, this translates to a reetrant call to this // function; the first time we call getPortList() on the body will call back in here. auto portList = body.getPortList(); if (connections) return; auto scope = getParentScope(); ASSERT(scope); connections = scope->getCompilation().allocPointerMap(); auto syntax = getSyntax(); if (!syntax) return; PortConnection::makeConnections( this, portList, syntax->as<HierarchicalInstanceSyntax>().connections, connections); } string_view InstanceSymbol::getArrayName() const { auto scope = getParentScope(); if (scope && scope->asSymbol().kind == SymbolKind::InstanceArray) return scope->asSymbol().as<InstanceArraySymbol>().getArrayName(); return name; } void InstanceSymbol::getArrayDimensions(SmallVector<ConstantRange>& dimensions) const { auto scope = getParentScope(); if (scope && scope->asSymbol().kind == SymbolKind::InstanceArray) getInstanceArrayDimensions(scope->asSymbol().as<InstanceArraySymbol>(), dimensions); } void InstanceSymbol::serializeTo(ASTSerializer& serializer) const { serializer.write("body", body); } InstanceBodySymbol::InstanceBodySymbol(Compilation& compilation, const InstanceCacheKey& cacheKey) : Symbol(SymbolKind::InstanceBody, cacheKey.getDefinition().name, cacheKey.getDefinition().location), Scope(compilation, this), cacheKey(cacheKey) { setParent(cacheKey.getDefinition().scope, cacheKey.getDefinition().indexInScope); } const InstanceBodySymbol& InstanceBodySymbol::fromDefinition(Compilation& compilation, const Definition& definition, bool forceInvalidParams) { // Create parameters with all default values set. ParameterBuilder paramBuilder(definition.scope, definition.name, definition.parameters); createParams(compilation, definition, paramBuilder, LookupLocation::max, definition.location, forceInvalidParams); return fromDefinition(compilation, InstanceCacheKey(definition, {}, {}), paramBuilder.paramSymbols); } const InstanceBodySymbol& InstanceBodySymbol::fromDefinition( Compilation& comp, const InstanceCacheKey& cacheKey, span<const ParameterSymbolBase const> parameters) { // If there's already a cached body for this key, return that instead of creating a new one. if (auto cached = comp.getInstanceCache().find(cacheKey)) return cached; auto& declSyntax = cacheKey.getDefinition().syntax; auto result = comp.emplace<InstanceBodySymbol>(comp, cacheKey); result->setSyntax(declSyntax); // Package imports from the header always come first. for (auto import : declSyntax.header->imports) result->addMembers(import); // Now add in all parameter ports. auto paramIt = parameters.begin(); while (paramIt != parameters.end()) { auto original = paramIt; if (!original->isPortParam()) break; if (original->symbol.kind == SymbolKind::Parameter) result->addMember(original->symbol.as<ParameterSymbol>().clone(comp)); else result->addMember(original->symbol.as<TypeParameterSymbol>().clone(comp)); paramIt++; } if (declSyntax.header->ports) result->addMembers(declSyntax.header->ports); // Finally add members from the body. for (auto member : declSyntax.members) { // If this is a parameter declaration, we should already have metadata for it in our // parameters list. The list is given in declaration order, so we should be be able to move // through them incrementally. if (member->kind != SyntaxKind::ParameterDeclarationStatement) { result->addMembers(member); } else { auto paramBase = member->as<ParameterDeclarationStatementSyntax>().parameter; if (paramBase->kind == SyntaxKind::ParameterDeclaration) { for (auto declarator : paramBase->as<ParameterDeclarationSyntax>().declarators) { ASSERT(paramIt != parameters.end()); auto& symbol = (paramIt)->symbol; ASSERT(declarator->name.valueText() == symbol.name); result->addMember(symbol.as<ParameterSymbol>().clone(comp)); paramIt++; } } else { for (auto declarator : paramBase->as<TypeParameterDeclarationSyntax>().declarators) { ASSERT(paramIt != parameters.end()); auto& symbol = (paramIt)->symbol; ASSERT(declarator->name.valueText() == symbol.name); result->addMember(symbol.as<TypeParameterSymbol>().clone(comp)); paramIt++; } } } } comp.getInstanceCache().insert(result); return result; } const Symbol InstanceBodySymbol::findPort(string_view portName) const { for (auto port : getPortList()) { if (port->name == portName) return port; } return nullptr; } void InstanceBodySymbol::serializeTo(ASTSerializer& serializer) const { serializer.write("definition", cacheKey.getDefinition().name); } string_view InstanceArraySymbol::getArrayName() const { auto scope = getParentScope(); if (scope && scope->asSymbol().kind == SymbolKind::InstanceArray) return scope->asSymbol().as<InstanceArraySymbol>().getArrayName(); return name; } void InstanceArraySymbol::serializeTo(ASTSerializer& serializer) const { serializer.write("range", range.toString()); } } // namespace slang
Bird flu precautions vital, seminar told By Suzanne Nam 30 June 2006 12:50 Thousands sick and dying in the streets, power and water barely functioning, even martial law; this bleak picture of the future is one the business community is becoming more willing to accept as a possibility if the H5N1 avian flu virus, commonly known as bird flu, mutates into a form easily transmitted among people. It is not a matter of if, just of when, where and how severe, said Dr Somrat Yindepit, safety, health and environment advisor to Esso (Thailand). While some are already making preparations, companies in Thailand need to devote more attention, and more resources, to planning for a potential avian flu pandemic, said government agencies and international organizations. Yesterday, government health officials, bird flu experts and hundreds of private sector representatives gathered for a seminar sponsored by the Thailand Center for Excellence in Life Sciences (TCELS), the Public Health Ministry, the World Health Organization and Assumption University to discuss ways companies can prepare for a worst-case scenario. Experts at yesterdays seminar told attendees to expect, and prepare for, serious business disruptions, absenteeism of up to 50 percent of the work force, travel restrictions, quarantines, loss of infrastructure and even civil unrest all of which could last for more than a year should bird flu become a human pandemic. An ill-prepared firm could be easily wiped out of business when a pandemic strikes, said a TCELS spokesman. The latest series of bird flu outbreaks began in Vietnam in December 2003 and has since spread throughout the globe. While infected birds have been found as far away as Britain, so far, most human victims have been in Asia. At least 22 people have been infected in Thailand, of whom 14 have died. The disease remains difficult for humans to catch. Although millions of birds have been infected, worldwide, only 228 people have been infected in the nearly three years it has been circulating. But viruses can mutate easily, and many have theorized that if bird flu does change into a virus transmissible between humans it will spark a global pandemic that could infect up to 40 percent of the worlds population and kill four percent, or more. Not all are as alarmist as Dr Somrat on whether bird flu will mutate. Many scientists, including those at the World Health Organization, instead characterize a bird flu pandemic as low probability but extremely high risk because of the virus high mortality rate. While the human toll would be catastrophic, the World Bank has estimated the possible toll on the global economy at US$1 trillion. The Asian Development Bank says the cost to the region could hit $282.7 billion in lost consumption, trade and investment. None of the experts at yesterdays conference offered a silver bullet that would allow companies to manage such a disaster, but all agreed that the private sector needs to do more to mitigate potential harm. Most preparation, according to companies such as Bangkok Bank and Thai Airways International, which made presentations at the seminar, involves crafting a plan of action and being prepared to implement it if necessary. Suraphon Israngura Na Ayutthaya, director of THAIs crisis management department, said the airline has even compiled an emergency operations manual, which he said the company is fully prepared to put into action.
[Update Mar 23 2020: Hello everyone. Here is some Buddhist meditation advice on dealing with anxiety during these uncertain times. Please check out an increasing number of live-streaming meditation classes at a Kadampa Center near you — learning to meditate or increasing your meditation practice will really help! Anyone can learn. All you need is somewhere to sit quietly for a while, and a wish to experience inner calm. Then just follow along.] Sometimes dubbed “the age of anxiety”, people are reportedly experiencing a lot of (di)stress in this modern age. Up to a third of the UK population, for example, will suffer from anxiety disorder or panic attacks at some point; and more people go to the doctor for anxiety in the UK than for the common cold. In the US, 40 million people are suffering from anxiety disorders, where anxiety is constant and overwhelming; and as for the occasional bout of panic, or the grumbling day-to-day unease, the number is probably closer to 300 million! I didn’t do a survey on the rest of the world, but I can’t imagine it’s much better. So, can you relate to any of these?: You’ve got a big meeting at work coming up where you have to give a presentation. You have to see your family and have a conflict with a family member who’ll be there. You know you’re going to run into your ex-girlfriend, who is with someone new whereas you are not. You see a police car in your rear view mirror, and you are a person of color. You have discovered a bump on your body and a quick Google search reveals that death is imminent. Your prostate is ten times larger than it should be. Your tent is leaking. You have to leave home soon because you are approaching adulthood but the future is scary. You are getting old and find yourself worrying about the smallest things that never used to bother you. Your co-worker is AWOL (again), leaving you with no support. You can’t understand why you don’t feel happier. You’ve eaten too much chocolate and have to go dress shopping with your mother, who is stick thin and always on at you about your weight. Your dog is sick. Your daughter is on drugs and possibly in trouble with the police. You can’t afford to leave a monotonous job even though your boss is a psychopath. You might be losing your Obamacare soon. You’ve read some very disturbing articles recently about the forces of darkness descending on our world. Your car has a rattle. You can’t make up your mind whether to (a) go grey gracefully or (b) go blonde. You’ve just spilled coffee all over your iPhone while writing this, with splashes landing on your keyboard (that one’s mine.) You’re going to die. Written down like this, does this seem like a list of anxiety-provoking situations?! Yet these are just snippets from the most recent conversations with the people around me. It makes me wonder, how much of our daily chit chat does revolve around things that make us anxious? Anyway, you may have more to add. And, while we have a mind to worry, the list is potentially endless for each of us. (At least we’re not alone?!) Dictionary.com defines anxiety as: Distress or uneasiness of mind caused by fear of danger or misfortune. It doesn’t matter whether fears or misfortunes are real or imagined, large or small — they all seem to consume us. With anxiety we can’t help overthinking, so there is no objective scale, you can’t number worries from 1 to 10 — worries never seem small because they each fill our mind. What does anxiety feel like? It can feel like we’re going mad, at its worst. We worry about everything and nothing. We feel out of control. The voice in our head is constant, we can’t stop it, it’s exhausting. We are on edge. Life is no fun. We can get no perspective even when we know we have things out of proportion and other people have it far worse. There was a swan, Angel, in the small pond behind my caravan last week in the Lake District. Beautiful to watch on the surface, gliding around like swans do – but she was all alone, recuperating from an attack that killed her mate; and I felt sad for her. And, looking at her legs, I was reminded of a description I read of anxiety: I smile gently while churning inside. I may seem calm. But if you could peer beneath the surface, you would see that I’m like a duck – paddling, paddling, paddling. What makes us anxious? There is always something to worry about if we have a tendency to worry: “What is there to worry about today?!” Did you wake up happy this morning?! Often when I ask people this question, they s ay they didn’t, not really. We are not even out of our warm cosy bed yet — nothing has happened! – and yet already we are feeling uneasy. So sometimes anxiety can be generalized, sort of random, lurking just below the surface of even the most uneventful day, with no specific cause. We usually cast around outside for something to blame for this feeling, “Must be because I have a presentation at work coming up in 3 weeks!” We can even lie there worrying that there is nothing to worry about, which must mean something horrendous is about to happen… At other times we feel anxiety about something in particular, such as in the list above. Luckily, although anxiety is a bad habit, all habits can be broken. What can we do about anxiety? Soooo, what is the secret of keeping it together in the face of worrying situations? Why and how do some people just seem to roll with the punches, while others are tormented by crippling anxiety at the merest glimpse of potential trouble? How do we rid ourselves of anxiety and connect with a more peaceful, balanced part of ourselves? First off, we need to start to experience some genuine peace of mind in which we can take refuge. Then we can gradually come to understand the causes of anxiety in more depth, learning tools to train in during our lives that will help us overcome this crippling emotion for good. Buddhist meditation can give us all of this. By the way, if you have concluded that meditation is not for you because you are just too distracted and worried to be able to concentrate, please know that pretty much everyone starts off too distracted and worried to concentrate. And this is exactly WHY we have to learn to meditate. Meditation is the medicine for distraction and distress. Not taking it is like saying: “I am too sad to be happy.” (Or as someone just said on Facebook “Actually, not meditating because it’s too hard is like saying “I’m too sad to take my Prozac.”) Our uncontrolled mind is in a state of apparent chaos, lurching from one chaotic situation to another; we feel caught in that small space. But if we can step back and see what is arising from a bigger place, we can realize the bigger story. We can step back and then CREATE the bigger story. So the first thing to do is to allow our mind to just settle, relax, and get bigger. Our mind is naturally peaceful, as explained here – our problem is that we keep shaking our mind up with uncontrolled thoughts, rather like a clear mountain lake being churned up by speedboats. Let the mind just settle through breathing meditation and we’ll discover that we already have peace, lucidity, and calm within. Worries fill our mind, so we need to empty our mind, for a while at least. Things feel less overwhelming in that space. We realize we can cope. We realize we can feel good. Anxiety, as they say, is a misuse of the imagination. We realize we can think differently. There are inner and outer problems, as explained here. I was thinking how each of those outer problems listed above requires different advice and solutions – the car may need to go to the mender, you may be able to enlist other people to help you with your work, your friends may have good suggestions on your hair, or you may be able to do something proactive to help prevent the forces of darkness from descending on our world. But internally, the advice is similar – control our mind and replace the anxious thoughts with helpful ones. Breathing meditation is increasingly popular because it really helps people relax. Even a small amount of time and effort can yield surprisingly big results. The breath may not be the most profound object, but this meditation teaches us something profound – that we don’t need to add peace from outside, it is already there inside us. If we allow our inner problems to temporarily subside by taking our attention away from them by single-pointed focus on the breath, our natural peace comes to the surface. And we can know that even if it is only a little bit of peace to begin with, (a) it feels so much better than anxiety and (b) there is plenty more where that came from. Phew. Plus we now have some space, control, and perspective to deal with the outer problems, as needs be. You can find out how to get started in a breathing meditation here. And there may be meditation classes in your area if you check this link. We’re out of space, so I’ll explain more next time. Meanwhile your comments are welcome. Related articles Don’t worry, be happy Getting perspective on hurt feelings Ever had self-loathing? How do I get rid of problems? How to avoid stress and burn-out at work Problem-free days Like this? Please share it: Facebook Twitter Reddit Print Email Pocket LinkedIn Tumblr Pinterest WhatsApp Skype Like this: Like Loading... Related
// Copyright (c) 2018 Uber Technologies, Inc. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. package image import ( "io/ioutil" "os" "testing" "github.com/uber/makisu/lib/log" "github.com/uber/makisu/lib/shell" "github.com/stretchr/testify/require" ) func TestDigestHexParsing(t testing.T) { require := require.New(t) digestStr := "sha256:123abc123" hex := Digest(digestStr).Hex() require.NotEqual(NewEmptyDigest(), hex) require.Equal("123abc123", hex) } func TestEmptyDigest(t testing.T) { require := require.New(t) tmpDir, err := ioutil.TempDir("/tmp", "makisu-digest-test") require.NoError(err) defer os.RemoveAll(tmpDir) targetPath := tmpDir + ".tar" err = shell.ExecCommand(log.Infof, log.Errorf, "", "", "tar", "cvf", targetPath, "--files-from", "/dev/null") require.NoError(err) defer os.Remove(targetPath) f, err := os.Open(targetPath) require.NoError(err) defer f.Close() equal, err := DigestEmptyTar.Equals(f) require.NoError(err) require.True(equal) f2, err := os.Open(targetPath) require.NoError(err) f2.Close() _, err = DigestEmptyTar.Equals(f2) require.Error(err) }
A New York Times piece by a diet specialist appears to have informed Trump’s idea to open up the country by Easter At the start of this week, as millions were following US government advice to combat the coronavirus pandemic by physical distancing and staying indoors, Donald Trump abruptly declared that people needed to soon return to work. Coronavirus US live: Pelosi says stimulus will pass but Congress is 'not doing enough' Read more “At a certain point we have to get open and we have to get moving. We don’t want to lose these companies. We don’t want to lose these workers,” Trump said at a White House press conference. Trump said this was going to happen “very soon”. The policy of returning to normal, nearly all epidemiologists warn, carries a threat of catastrophe: of allowing the virus to spread just as the measures proven to curb it are starting to work. So where did Trump’s U-turn come from? As frequently is the case with Trump’s political ideas, he seems to have been inspired – at least in part – by Fox News, and also by thinkpieces popular among conservatives, but often not written by epidemiologists. On Sunday, the Fox News host Steve Hilton railed against the idea of long-term social distancing. Hilton claimed “working Americans” will be “crushed” by an indefinite work shutdown. Hilton mused that there could be a situation where “the cure is worse than the disease”. Within hours, the Fox News message found its intended target. On Sunday evening Trump tweeted, mangling Hilton’s words slightly: “WE CANNOT LET THE CURE BE WORSE THAN THE PROBLEM ITSELF.” The idea of sending people back to work and restarting the economy had been floating around last weekend, propagated by two opinion pieces in particular. One was written on Medium. Another, published two days before the Hilton show, was an opinion piece by David Katz, a former director of the Yale-Griffin Prevention Research Center, which was published by the New York Times. Given the reach of the New York Times this piece, headlined Is Our Fight Against Coronavirus Worse Than the Disease?, attracted huge attention. In the piece, Katz argues that those over 60 and those who are immunologically compromised should be “preferentially protect[ed]”, with focused testing. “This focus on a much smaller portion of the population would allow most of society to return to life as usual and perhaps prevent vast segments of the economy from collapsing,” Katz wrote, adding that then children could return to school and adults return to their jobs. In time, people would develop immunity to the coronavirus, and in the meantime, damage to the economy would be minimized, Katz opined. But as many pointed out, Katz is not an epidemiologist. Instead, he specializes in nutrition advice, and has published a number of dietary books, including The Way to Eat, Cut Your Cholesterol and Stealth Health. Katz’s piece was shared widely among conservatives, including by Fox News host and informal Trump adviser Pete Hegseth. The article served as a handy tool for conservatives advancing the argument that the economy shouldn’t be sacrificed for coronavirus containment. A group of Yale epidemiologists swiftly wrote a letter to the Times, rebutting Katz’s piece. Others pointed out Katz’s lack of credentials and his links to big industry. He was once paid $3,500 an hour as an expert witness in a Chobani legal case to defend the sugar contained in its yoghurts. Katz has received hundreds of thousands of dollars from companies including Hershey’s, Kind Bars, the walnut industry and Quaker Oats. The science journalist Nina Teicholz has written about how in some cases, Katz wrote positive articles about those companies after receiving grants. “Dr Katz’s efforts on behalf of public health during this pandemic are uncompensated and born from a sense of duty and commitment to public health,” a spokeswoman for Katz told the Guardian. She pointed to a post Katz wrote on LinkedIn following the criticism, where he stresses how damage to the economy is also a massive public health issue. Yale itself went to lengths to distance itself from Katz. “David Katz is not academically affiliated with Yale and has not held an academic appointment here since 2016,” the university posted on Twitter. Gregg Gonsalves, an assistant professor of epidemiology at the Yale school of public health, said: “Yes, the elderly are at risk. But the ability to sequester safely for months on end, in the United States is untenable. We don’t have a social safety net that maybe continental European countries have.” He said: “The other thing is, low risk doesn’t mean no risk. We don’t know the natural history of the disease well enough to say: ‘Everybody under 65 is A-OK and ready to go back to work.’” Katz’s piece wasn’t the sole inspiration for Trump’s change of mind. The influential Fox News host Laura Ingraham and others eagerly shared a Medium article written by a tech worker named Aaron Ginn over the weekend, which advances some of the same ideas as Katz. Medium later took the article down after widespread criticism, including from experts in infectious diseases. The concept of trading off self-isolation for returning to normal to help the economy has also been pushed by Trump’s cabinet including, his economic adviser Larry Kudlow, who on Tuesday told reporters: “Public health includes economic health.” The arguments advanced by Katz and others, however, are a piece of a movement which could lead to Trump flip-flopping again on the seriousness of the coronavirus – which could be problematic for all.
Meri Aashiqui Tum Se Hi 21st October 2014 Written Episode Update Shanaila appreciates Pratik’s number. Daiwersh says he tells him the jokes. Pratik asks for Shanaila’s number but Daiwersh says he won’t send her. Shanaila stares at Daiwersh, then says she isn’t interested in his anymore. She tells him that her boy friend has arrived, and goes to the car. Pratik and Daiwersh were unable to see Chiraag, however. Amba welcomes Ritika and Mr. Javeri. She asks Ritika about her fast, Ritika looks at RV. Amba brings Dhoklay for Mr. Javeri which Ritika looks at RV takes Ritika to show her the house. The staff asks Ishika to go for engagement ceremony, but she says she has work left. Ritika thanks RV to save her, and says she isn’t used to telling lies. RV says she just have to hide the truth. The waiter brings RV a glass of juice, while Ritika takes immediately. RV laughs, and takes her into the room. He takes a plate from the waiter, and forbids him to tell his mother. He takes Ritika into the room. Ishaani stood with the study in the same room. He tells her to eat as much as she wants. She says she is hungry. He says he thought she would eat the plate as well. He says he won’t take any responsibility if they get caught. She asks would he leave him alone. He says that if he keeps siding her, she might get habitual about it. Ritika says that someone would think they are doing romance together here. Ishaani appears. Ritika says Hi, while RV scolds her for interfering in his private talk, and says she must have told them before that she was here. She was about to leave. He tells her that he needs the file early morning, she should complete it before leaving. Ishaani thinks where to work, and thinks about going to store-room where she used to work in childhood. Ritika says she didn’t know he is an angry boss as well. He asks is she thinking about changing his mind. She says he must tell him the whole story first. He says she is giving him surprises now. Ritaish and Chaitali come to engagement. Ritesh says they are uninvited guests her but Chaitali says it is her student’s house. Chaitali says she is going to give speech in English here as well. Amba repeats her speech in front of Chaitali. Chaitali asks her to say it without paper. Chaitali is worried to see Falguni and Baa coming there. Falguni says to Baa, that she must relax as they aren’t Amba’s guests. Baa says it is her own house. RV’s dad looks at Baa and Falguni, and thinks RV must have called them. Mr. Javeri tells him that he invited Ansa and Falguni, he hopes they don’t have any problem. He tells him that he was a good friend with Harshad, he thought about inviting his family and goes to meet him. Ritesh and Chaitali were shocked to see Baa and Falguni. He says he can’t show himself to Baa, or she will throw him out of the house. Baa tells Mr. Javeri that hadn’t he been his invitee, she would have never come here. Amba says whoever the invitee is, they are guests at their house. Mr. Javeri says that he wanted blessings for his children. Amba says that they must not leave without having dinner. Mr. Javeri goes with some guest. Amba says she is happy that they came here. She wants them to see who RV is marrying, and tells them not to put a bad eye on her daughter in law. She calls the waiter to take care of them. Baa goes to the temple to place a coin and some money in the temple. Falguni comes with her. Baa prays there, nostalgically. Chaitali comes across Baa, her head covered. Baa says Amba’s servants are just like her. Amba asks Chaitali if she is running watching Baa and Falguni, but she can’t leave until she is done with her speech. Ritika stood with Amba, she introduces her to them. Falguni thinks this is she, but where is Ranvir. Amba tells Ritika that she is Ishaani’s mom- the girl who works in RV’s office. Amba tells them that she and RV selected each other so soon, and tells them they are marrying in 4 days. Baa says Ishaani is also getting married in next four days. Ritika says poor girl, she is. Amba says she is really poor. Falguni says that her daughter is conscious about her work, and wants a simple marriage. Amba says they can’t afford a wealthy marriage. Baa asks does she want something else as well. Amba thinks she also wants to meet RV. Ishaani picks up her things, and thinks that she is done with her work now and must leave and maa and Baa must be waiting for her. She sits down again, thinking how do people fast, then thinks that now she will also fast for Chiraag. RV meets her in corridor. She tells him she mailed him the file and is leaving now. He says his mother wants his employees to attend the ceremony; she must stay and go after dinner. She says she is fasting, and can’t stay. He says she might not eat, but shall leave after the ceremony.
Countdown to Coverage: Last Call to Enroll in 2015, Avoid Fines The Health Insurance Marketplace open enrollment period for 2015 ends February 15, but there’s still time to sign up before the deadline. If you miss the deadline you will not be able to sign up for coverage until the fall, unless you have a qualifying life event. (Exception: enrollment in Texas Medicaid and CHIP for lower-income children and selected adults, as well as small business coverage, are available 365 days a year.) Remember, the Affordable Care Act requires citizens and lawfully residing immigrants to have health coverage – or minimal essential coverage – throughout the year. Individuals who are not covered for most of the year may face fines on next year’s tax return. For the 2014 tax year it has been estimated that 2 to 4 percent, or 3 to 6 million taxpayers, will face a fine. What are the fines for not having coverage in 2015? If you don’t have coverage in 2015, you’ll pay the higher of these two amounts: 2 percent of your yearly household income above the tax filing threshold ($10,150 for an individual). The maximum penalty is capped at the national average premium for a bronze plan. or $325 per adult ($162.50 per child; family maximum $975) To illustrate how the penalty is calculated, let’s take the example of a single adult whose modified adjusted gross income (MAGI) is $20,000. Percent of Income Penalty Flat Fee Penalty $20,000 - $10,150 = $9,850 x 2% = $197 $325 This individual would pay the higher of the two, the $325 flat-fee penalty. Who is exempt from the requirement to have insurance? Under certain circumstances, individuals are exempt from paying the fine for not having health insurance. For example, if your income is low enough that you do not need to file taxes or if you were without coverage for less than three months you are exempt. Individuals may also be exempt from paying the fine if they faced a hardship, including being homeless, filing for bankruptcy, or being determined ineligible for Medicaid (the “coverage gap”) because their state chose not expand coverage under the Affordable Care Act. I’m convinced. Health insurance good, fines bad. Now what? If you don’t have health insurance, go to Healthcare.gov and apply for coverage right now—you only have until February 15th. You can also get in-person application and enrollment help from local enrollment helpers. If you fall into the coverage gap and don’t have an affordable option for health coverage, Healthcare.gov can provide you information on exemptions from paying a penalty. All of the above information is in reference to the 2015 tax year. Look for upcoming posts on what you need to do on your 2014 tax return. At the Center for Public Policy Priorities, we believe in a Texas that offers everyone the chance to compete and succeed in life. We envision a Texas where everyone is healthy, well-educated, and financially secure. We want the best Texas - a proud state that sets the bar nationally by expanding opportunity for all. CPPP is an independent public policy organization that uses data and analysis to advocate for solutions that enable Texans of all backgrounds to reach their full potential. We dare Texas to be the best state for hard-working people and their families.
Robbins lemma In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter λ, and f is any function for which the expected value E(f(X)) exists, then Robbins introduced this proposition while developing empirical Bayes methods. References Category:Statistical theorems Category:Lemmas Category:Poisson distribution
Q: How to Write to a User.Config file through ConfigurationManager? I'm trying to persist user settings to a configuration file using ConfigurationManager. I want to scope these settings to the user only, because application changes can't be saved on Vista/Win 7 without admin privileges. This seems to get me the user's configuration, which appears to be saved here in Win 7 ([Drive]:\Users\[Username]\AppData\Local\[ApplicationName]\[AssemblyName][hash]\[Version\) Configuration config = ConfigurationManager.OpenExeConfiguration(ConfigurationUserLevel.PerUserRoamingAndLocal); Whenever I try to save any changes at all to this config I get this exception: InnerException: System.InvalidOperationException Message="ConfigurationSection properties cannot be edited when locked." Source="System.Configuration" StackTrace: at System.Configuration.SectionInformation.VerifyIsEditable() at System.Configuration.MgmtConfigurationRecord.GetConfigDefinitionUpdates(Boolean requireUpdates, ConfigurationSaveMode saveMode, Boolean forceSaveAll, ConfigDefinitionUpdates& definitionUpdates, ArrayList& configSourceUpdates) I have tried adding a custom ConfigurationSection to this config. I have tried adding to the AppSettingsSection. Whenever I call config.Save() it throws the exception above. Any ideas? I tried using the ApplicationSettingsBase class through the Project->Settings designer, but it doesn't appear that you can save custom types with this. I want similar functionality with the ability to save custom types. A: You need to set the SectionInformation.AllowExeDefinition value for the section: Configuration configuration = ConfigurationManager.OpenExeConfiguration(ConfigurationUserLevel.PerUserRoaming); UserSettings settings; if ((settings = (UserSettings)configuration.Sections[GENERAL_USER_SETTINGS]) == null) { settings = new UserSettings(); settings.SectionInformation.AllowExeDefinition = ConfigurationAllowExeDefinition.MachineToLocalUser; configuration.Sections.Add(GENERAL_USER_SETTINGS, settings); configuration.Save(); } The default value is ConfigurationAllowExeDefinition.MachineToApplication which allows only to place the section on machine.config and app.exe.config.
I usually make the sauce when I smoke a pork butt so to be honest a batch is almost gone by the time I rub out of pulled pork. I would think that with the amount of vinegar that is in the sauce you should be good for a couple three weeks. Uhhhh....I haven't been able to smoke as much as I would have liked this year (damned tornadoes), and still have a batch in my fridge from the Feb/March time frame. Guessing that's past its prime, eh? Doesn't smell bad. Yeah.. I would toss it if it was me. Costs like what to make another batch.. Costs like what to get sick..?? Not counting all the yacking. I store this sauce in the refrigerator for months. (Bringing up an old thread - saw this post when I looked up the recipe to cook some sauce...) You could be right but I do not want to recomend anything that might get some one sick. Just playing it safe._________________Chargriller Akorn WSM LIAR #100 _________________ Do not rely on a rabbits foot for luck, it did not work out too well for the rabbit...
My List Homes for sale near Bandera High School Good(Based on 2018 STAAR Data) 474 OLD SAN ANTONIO HWY, BANDERA, TX, 78003 Looking for real estate near Bandera High School? Use the list below to find your perfect home, investment, or rental property. Bandera High School is located at 474 OLD SAN ANTONIO HWY, BANDERA, TX, 78003. The school is part of the BANDERA ISD. To contact the school, call (830) 460-3898. The email address for the school is smenchaca@banderaisd.net. Don't see what you want? Try looking nearby in zip code 78003. You may also want to view Bandera High School in map search.
The fusion of enveloped viruses with their target cells is directed by the viral transmembrane glycoprotein. The first part of this protein to interact with the cellular membrane is called the fusion domain and is a conserved, largely hydrophobic, polymorphic sequence usually near the amino terminus. Site-directed mutagenesis has shown that the replacement of key residues in the fusion domain of influenza virus hemagglutinin (HA2) or HIV glycoprotein 41,000 (gp41) affect viral fusion. Synthetic peptides with the same sequences as these N-terminal regions, termed fusion peptides (FP), induce lipid mixing and lysis of liposomes and cell membranes. Although there is much information on the structure of viral FP, there is little understanding of the relationship of the intramembrane FP structures to their function. The principal objective of the proposed research is to determine the structural characteristics common to viral FP that are necessary for fusion competence. Using FP based on mutated viral sequences, we will seek correlations between their altered activity and membrane-bound structures. We will also further characterize the inhibition of FP by the C-helix (DP-178) or its fragments and we will assess the ability of FP to expand its conformational space to include the formation of amyloid suprastructures. Membrane-perturbing activities of FP and its variants will be screened with erythrocyte lysis and aggregation measured by the absorbance of released hemoglobin at 540nm and cell sizing with a Coulter Counter. Lipid mixing, leakage, and aggregation of synthetic large unilamellar vesicles induced by FP will be measured using fluorescence dequenching and light scattering assays. The conformation, orientation, and topography of fusion peptides in membranes or membrane mimmicking solvents will be examined by circular dichroism (CD), Fourier transform infrared (FTIR), electron spin resonance (ESR) spectroscopy and molecular modeling. Correlations will be sought between the structural models and the fusion activities and lipid perturbations induced by viral fusion peptides and variants.
Movement and gastroesophageal reflux in awake term infants with "near miss" SIDS, unrelated to apnea. Forty-five term infants who had a "near miss" for SIDS were studied with a continuous overnight polygraphic recording of endoesophageal pH, respiration, and ECG. Recordings were examined for occurrences of GER and for central apnea of 10 seconds or greater duration. There were 341 apneic events greater than or equal to 10 seconds recorded in 46 studies, with a mean of 7 +/- 7. In 91% of the infants, no apneas exceeded 15 seconds. Only 31 episodes of apnea greater than or equal to 10 seconds occurred during GER: in two of these episodes the apneic event was greater than or equal to 15 seconds. Twenty-four of the 31 apneas greater than or equal to 10 seconds during periods of pH less than 4 occurred in one infant. A total of 356 precipitous pH drops was recorded (mean 8.7 +/- 7.4). The pH drops occurred most frequently when the patient appeared to be awake (73%), and in 84% of events there was movement before and during the pH change. We conclude that the majority of these near miss SIDS infants had GER associated with movement during awake periods, without any temporal relationship to apnea. Although reflex apnea following GER may be seen in some term infants, this problem may be more significant for the immature infant.
Brief Intro! A Web Developer, Graphic Designer and a User Experience Architect, almost completed with Masters in Cloud Computing from University of Leicester, with four years of Industrial Experience from a Multinational Company's Research wing. I work on web technologies like HTML, CSS, JavaScript, jQuery and also during my free time, I create web applications in PHP & MySQL, or one of Classic ASP & Access, ASP.NET & MSSQL, J2EE & Oracle, and Ruby on Rails & PostgreSQL. I love working on Microsoft products as well as dedicating to the Open Source Community!
Envisioning a Politics of Coalition This book uses the Anglophone Caribbean as its site of critique to explore two important questions within development studies. First, to what extent has the United Nations' call to implement gender-mainstreaming projects resulted in the realization of gender equity for women within developing... Published October 14th 2013 by Routledge Simple Book Search Search for: Search by: Sort by: Date-range: Published Forthcoming All Advanced Book Search We suggest filling in as few fields as possible – this usually retrieves the best selection of search results.
% Generated by roxygen2: do not edit by hand % Please edit documentation in R/breaks-retired.R \name{trans_breaks} \alias{trans_breaks} \title{Pretty breaks on transformed scale} \usage{ trans_breaks(trans, inv, n = 5, ...) } \arguments{ \item{trans}{function of single variable, \code{x}, that given a numeric vector returns the transformed values} \item{inv}{inverse of the transformation function} \item{n}{desired number of ticks} \item{...}{other arguments passed on to pretty} } \description{ \Sexpr[results=rd, stage=render]{lifecycle::badge("retired")} These often do not produce very attractive breaks. } \examples{ trans_breaks("log10", function(x) 10 ^ x)(c(1, 1e6)) trans_breaks("sqrt", function(x) x ^ 2)(c(1, 100)) trans_breaks(function(x) 1 / x, function(x) 1 / x)(c(1, 100)) trans_breaks(function(x) -x, function(x) -x)(c(1, 100)) } \keyword{internal}
/* * Copyright 2002-2017 the original author or authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * https://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. / package org.springframework.web.bind.support; import org.springframework.lang.Nullable; import org.springframework.web.context.request.WebRequest; /* * Strategy interface for storing model attributes in a backend session. * * @author Juergen Hoeller * @since 2.5 * @see org.springframework.web.bind.annotation.SessionAttributes / public interface SessionAttributeStore { /* * Store the supplied attribute in the backend session. * <p>Can be called for new attributes as well as for existing attributes. * In the latter case, this signals that the attribute value may have been modified. * @param request the current request * @param attributeName the name of the attribute * @param attributeValue the attribute value to store / void storeAttribute(WebRequest request, String attributeName, Object attributeValue); /* * Retrieve the specified attribute from the backend session. * <p>This will typically be called with the expectation that the * attribute is already present, with an exception to be thrown * if this method returns {@code null}. * @param request the current request * @param attributeName the name of the attribute * @return the current attribute value, or {@code null} if none / @Nullable Object retrieveAttribute(WebRequest request, String attributeName); /* * Clean up the specified attribute in the backend session. * <p>Indicates that the attribute name will not be used anymore. * @param request the current request * @param attributeName the name of the attribute */ void cleanupAttribute(WebRequest request, String attributeName); }
INSIGHTS IAS REVISION PLAN FOR PRELIMS 2018 - DAILY REVISION TESTS Quiz-summary Information If you are wondering why these questions are posted, please refer to the detailed Timetable providedHERE. These questions serve TWO purposes: One to test your revision skills; Second is to give you a glimpse into topics that you might have missed during revision. If you score ow marks, please don’t feel bad. Revise more effectively and try to learn from mistakes. Wish you all the best. You have already completed the quiz before. Hence you can not start it again. Quiz is loading... You must sign in or sign up to start the quiz. You have to finish following quiz, to start this quiz: Results 0 of 20 questions answered correctly Your time: Time has elapsed You have reached 0 of 0 points, (0) Categories Not categorized0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Answered Review Question 1 of 20 1. Question 2 points Consider the following about girl’s education in India: Digital Gender Atlas for Advancing Girls’ Education has been made with the support of UNICEF Shagun portal has been specifically designed around the progress made around the atlas Which of the above statements is/are correct: a) 1 only b) 2 only c) Both 1 and 2 d) None of the above Correct Ans: A Digital Gender Atlas for Advancing Girls’ Education: Department of School Education and Literacy has prepared a Digital Gender Atlas for Advancing Girls’ Education in the country on its website. The tool, which has been developed with the support of UNICEF,(hence statement 1 is correct) will help identify low performing geographic pockets for girls, particularly from marginalized groups such as scheduled castes, schedule tribes and Muslims, on specific gender related education indicators. In order to plan and execute educational interventions, the purpose of the Gender Atlas is to help identify and ensure equitable education with a focus on vulnerable girls, including girls with disabilities. ShaGun portal – an Initiative to monitor the implementation of SSA: MHRD has developed a web portal called ShaGun (from the words Shaala and Gunvatta). (hence statement 2 is incorrect) Incorrect Ans: A Digital Gender Atlas for Advancing Girls’ Education: Department of School Education and Literacy has prepared a Digital Gender Atlas for Advancing Girls’ Education in the country on its website. The tool, which has been developed with the support of UNICEF,(hence statement 1 is correct) will help identify low performing geographic pockets for girls, particularly from marginalized groups such as scheduled castes, schedule tribes and Muslims, on specific gender related education indicators. In order to plan and execute educational interventions, the purpose of the Gender Atlas is to help identify and ensure equitable education with a focus on vulnerable girls, including girls with disabilities. ShaGun portal – an Initiative to monitor the implementation of SSA: MHRD has developed a web portal called ShaGun (from the words Shaala and Gunvatta). (hence statement 2 is incorrect) Question 2 of 20 2. Question 2 points Which of the following is NOT a sub-programme under Sarva Shiksha Abhiyaan a) Vidyanjali b) Pade Bharat Bade Bharat c) Rastriya aavishkar abhiyaan d) Atal Tinkering Labs Correct Ans: D Sub-Programmes under SSA a) The Padhe Bharat Badhe Bharat (PBBB), a sub-programme of the SSA, in classes I and II is focusing on foundational learning in early grades with an emphasis on reading, writing and comprehension and mathematics. b) The Rashtriya Aavishkar Abhiyan (RAA), also under the SSA, aims to motivate and engage children of the age group 6-18 years, in science, mathematics and technology by observation, experimentation, inference drawing and model building, through both inside and outside classroom activities. c) Vidyanjali, another sub-programme under SSA, was launched to enhance community and private sector involvement in Government run elementary schools across the country. d) ShaGun portal – an Initiative to monitor the implementation of SSA: MHRD has developed a web portal called ShaGun (from the words Shaala and Gunvatta) The Government of India has setup the Atal Innovation Mission (AIM) at NITI Aayog. Realizing the need to create scientific temper and cultivate the spirit of curiosity and innovation among young minds, AIM proposes to support the establishment of a network of Atal Tinkering Laboratories (ATL). ATL is a workspace where young minds can give shape to their ideas through hands-on do-it-yourself mode and learn innovation skills. a) The Padhe Bharat Badhe Bharat (PBBB), a sub-programme of the SSA, in classes I and II is focusing on foundational learning in early grades with an emphasis on reading, writing and comprehension and mathematics. b) The Rashtriya Aavishkar Abhiyan (RAA), also under the SSA, aims to motivate and engage children of the age group 6-18 years, in science, mathematics and technology by observation, experimentation, inference drawing and model building, through both inside and outside classroom activities. c) Vidyanjali, another sub-programme under SSA, was launched to enhance community and private sector involvement in Government run elementary schools across the country. d) ShaGun portal – an Initiative to monitor the implementation of SSA: MHRD has developed a web portal called ShaGun (from the words Shaala and Gunvatta) The Government of India has setup the Atal Innovation Mission (AIM) at NITI Aayog. Realizing the need to create scientific temper and cultivate the spirit of curiosity and innovation among young minds, AIM proposes to support the establishment of a network of Atal Tinkering Laboratories (ATL). ATL is a workspace where young minds can give shape to their ideas through hands-on do-it-yourself mode and learn innovation skills. 3. Question Shaala Siddhi is a tool to track School Standards and Evaluation Framework Shala Darpan is a monitoring school management systems to students, parents and communities Which of the above statements is/are correct: a) 1 only b) 2 only c) Both 1 and 2 d) None of the above Correct Ans: C Shaala Siddhi: School Standards and Evaluation Framework and its web portal was launched in 2015. It is a comprehensive instrument for school evaluation leading to school improvement. Developed by the National University of Educational Planning and Administration (NUEPA), it aims to enable schools to evaluate their performance in a more focused and strategic manner and facilitate them to make professional judgments for improvement. The programme’s objective is to establish an agreed set of standards and benchmarks for each school, by focussing on key performance domains and their core standards. (hence statement 1 is correct) Shala Darpan: The “Shaala Darpan Project” to cover all the 1099 Kendriya Vidyalayas was launched in June, 2015. The objective of this project is to provide services based on school management systems to students, parents and communities. Under school information services, the following list of services will be enabled i.e., school profile management, student profile management, employee information, student attendance, leave management, report cards, curriculum tracking custom, SMS alerts for parents / administrators on student and teacher attendance. (hence statement 2 is correct) Incorrect Ans: C Shaala Siddhi: School Standards and Evaluation Framework and its web portal was launched in 2015. It is a comprehensive instrument for school evaluation leading to school improvement. Developed by the National University of Educational Planning and Administration (NUEPA), it aims to enable schools to evaluate their performance in a more focused and strategic manner and facilitate them to make professional judgments for improvement. The programme’s objective is to establish an agreed set of standards and benchmarks for each school, by focussing on key performance domains and their core standards. (hence statement 1 is correct) Shala Darpan: The “Shaala Darpan Project” to cover all the 1099 Kendriya Vidyalayas was launched in June, 2015. The objective of this project is to provide services based on school management systems to students, parents and communities. Under school information services, the following list of services will be enabled i.e., school profile management, student profile management, employee information, student attendance, leave management, report cards, curriculum tracking custom, SMS alerts for parents / administrators on student and teacher attendance. (hence statement 2 is correct) Question 4 of 20 4. Question Ishan Uday– The UGC has launched a special scholarship scheme for students of north east region, Ishan Uday from the academic session 2014-15. The Scheme envisages grant of 10,000 scholarships to students from the region whose parental income is below 4.5 lakh per annum and would be provided scholarship ranging from ₹ 3,500 to ₹ 5,000 per month for studying at under graduate level in colleges/ universities of the country. Ishan Vikas – Academic Exposure for North Eastern Students The programme has been launched with a plan to bring selected college and school students from the north eastern states into close contact with IITs, NITs and IISERs during their vacation periods for academic exposure. Incorrect Ans: C Ishan Uday– The UGC has launched a special scholarship scheme for students of north east region, Ishan Uday from the academic session 2014-15. The Scheme envisages grant of 10,000 scholarships to students from the region whose parental income is below 4.5 lakh per annum and would be provided scholarship ranging from ₹ 3,500 to ₹ 5,000 per month for studying at under graduate level in colleges/ universities of the country. Ishan Vikas – Academic Exposure for North Eastern Students The programme has been launched with a plan to bring selected college and school students from the north eastern states into close contact with IITs, NITs and IISERs during their vacation periods for academic exposure. A managed or dirty float is a flexible exchange rate system in which the government or the country’s central bank may occasionally intervene in order to direct the country’s currency value into a certain direction. This is generally done in order to act as a buffer against economic shocks and hence soften its effect in the economy. A managed or dirty float is a flexible exchange rate system in which the government or the country’s central bank may occasionally intervene in order to direct the country’s currency value into a certain direction. This is generally done in order to act as a buffer against economic shocks and hence soften its effect in the economy. 6. Question IMF 2. Generally forbids the use of quantitative restrictions in trade. SAARC 3. Sanction of soft loans IDA 4. Promotes trade among South Asian Countries Codes: A B C D a) 1 2 3 4 b) 2 3 4 1 c) 2 1 4 3 d) 3 2 4 1 Correct Ans: C Incorrect Ans: C Question 7 of 20 7. Question 2 points The European Union has achieved all of the following, except a) Adopted a common fiscal policy for member nations b) Established a common system of agricultural price supports c) Disbanded all tariffs between its member countries d) Levied common tariffs on products imported from nonmembers Correct Ans: A It is often proposed that the European Union should adopt a form of fiscal union. Most member states of the EU participate in economic and monetary union (EMU), based on the euro currency, but most decisions about taxes and spending remain at the national level. Therefore, although the European Union has a monetary union, it does not have a fiscal union. Incorrect Ans: A It is often proposed that the European Union should adopt a form of fiscal union. Most member states of the EU participate in economic and monetary union (EMU), based on the euro currency, but most decisions about taxes and spending remain at the national level. Therefore, although the European Union has a monetary union, it does not have a fiscal union. Question 8 of 20 8. Question 2 points Which of the following are the role of Finance Commissions in India? To make recommendations on the distribution of tax proceeds between Centre and States. To make Recommendations on levying, removing or restructuring of taxes. To recommend Grants-in-aid under Article 275 of the Constitution To recommend plan and other grants under Article 282 of the Constitution Codes: a) 1 and 2 only b) 1 and 3 only c) 1, 3 and 4 only d) 1, 2, 3 and 4 Correct Ans: B Functions of Finance Commission Distribution of net proceeds of taxes between Center and the States, to be divided as per their respective contributions to the taxes. Determine factors governing Grants-in-Aid to the states and the magnitude of the same. To make recommendations to the president as to the measures needed to augment the Fund of a State to supplement the resources of the panchayats and municipalities in the state on the basis of the recommendations made by the finance commission of the state. Any other matter related to it by the president in the interest of sound finance. A finance commission is an autonomous body which is governed by the government of India. Incorrect Ans: B Functions of Finance Commission Distribution of net proceeds of taxes between Center and the States, to be divided as per their respective contributions to the taxes. Determine factors governing Grants-in-Aid to the states and the magnitude of the same. To make recommendations to the president as to the measures needed to augment the Fund of a State to supplement the resources of the panchayats and municipalities in the state on the basis of the recommendations made by the finance commission of the state. Any other matter related to it by the president in the interest of sound finance. A finance commission is an autonomous body which is governed by the government of India. Question 9 of 20 9. Question 2 points Margin requirement specified under which instruments of monetary policy? a) Variable Reserve Requirement b) Statutory Liquidity Requirement c) Selective Credit Controls d) Open Market Operations Correct Ans: C Selective credit control refers to qualitative method of credit control by the central bank. The method aims, unlike general or quantitative methods, at the regulation of credit taken for specific purposes or branches of economic activity. It aims at encouraging good credit, i.e., development credit while at the same time discouraging bad credit, i.e., speculative credit. PSL: priority sector lending DIRs: Differential interest rates Incorrect Ans: C Selective credit control refers to qualitative method of credit control by the central bank. The method aims, unlike general or quantitative methods, at the regulation of credit taken for specific purposes or branches of economic activity. It aims at encouraging good credit, i.e., development credit while at the same time discouraging bad credit, i.e., speculative credit. PSL: priority sector lending DIRs: Differential interest rates Question 10 of 20 10. Question 2 points About minimum support price, find out the correct combinations: If market price is higher, farmers will sell to the government. It ensures minimum assured price for the produce of the farmers. It helps in food security mission. This is highly rewarding to farmers because they earn huge profits on their produce. Codes: a) 1, 2 and 4 only b) 2, 3 and 4 only c) 2 and 4 only d) 2 and 3 only Correct Ans: D Minimum Support Price (MSP) is a form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices. The minimum support prices are announced by the Government of India at the beginning of the sowing season for certain crops on the basis of the recommendations of the Commission for Agricultural Costs and Prices (CACP). MSP is price fixed by Government of India to protect the producer – farmers – against excessive fall in price during bumper production years. The minimum support prices are a guarantee price for their produce from the Government. The major objectives are to support the farmers from distress sales and to procure food grains for public distribution. In case the market price for the commodity falls below the announced minimum price due to bumper production and glut in the market, government agencies purchase the entire quantity offered by the farmers at the announced minimum price and maintains public stocks. Incorrect Ans: D Minimum Support Price (MSP) is a form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices. The minimum support prices are announced by the Government of India at the beginning of the sowing season for certain crops on the basis of the recommendations of the Commission for Agricultural Costs and Prices (CACP). MSP is price fixed by Government of India to protect the producer – farmers – against excessive fall in price during bumper production years. The minimum support prices are a guarantee price for their produce from the Government. The major objectives are to support the farmers from distress sales and to procure food grains for public distribution. In case the market price for the commodity falls below the announced minimum price due to bumper production and glut in the market, government agencies purchase the entire quantity offered by the farmers at the announced minimum price and maintains public stocks. Question 11 of 20 11. Question 2 points Which of the followings have been important in growth of rice and wheat output in India after initiating green revolution programme? Changes in cropping pattern Improved yields Crop insurance Increased area under cultivation Codes: a) 2, 3 and 4 only b) 1, 2 and 4 only c) 1, 2 and 3 only d) 1, 3 and 4 only Correct Ans: B Crop insurance density still remains very low and Pradhan mantra Fasal Bima Yojana was launched to further crop insurance in India. Incorrect Ans: B Crop insurance density still remains very low and Pradhan mantra Fasal Bima Yojana was launched to further crop insurance in India. Question 12 of 20 12. Question 2 points Predatory pricing policy is designed to a) Drive competitors out of business b) Maximise profits c) Encourage entrants into the market d) Attain least cost output Correct Ans: A Predatory Pricing – the pricing of goods or services at such a low level that other firms cannot compete and are forced to leave the market. Incorrect Ans: A Predatory Pricing – the pricing of goods or services at such a low level that other firms cannot compete and are forced to leave the market. Question 13 of 20 13. Question 2 points Which of the following is correct about the ‘Hindu Growth Rate’? a) This is about economic growth of the Hindu population. b) Shows economic disparities among different social groups in India. c) Reflects low growth performance of the Indian economy during 1950-80. d) Hints at accelerated growth in India since 1980 Correct Ans: C The Hindu rate of growth is a term referring to the low annual growth rate of the planned economy of India before the liberalisation of 1991, which stagnated around 3.5% from 1950s to 1980s, while per capita income growth averaged 1.3%. It was a concept given by Prof. Raj Krishna Incorrect Ans: C The Hindu rate of growth is a term referring to the low annual growth rate of the planned economy of India before the liberalisation of 1991, which stagnated around 3.5% from 1950s to 1980s, while per capita income growth averaged 1.3%. It was a concept given by Prof. Raj Krishna Question 14 of 20 14. Question 2 points The idea of indicative planning was first adopted in which Five year Plan of India? India’s Eighth Plan was unique in the sense that it attempted to manage the transition from a centrally planned economy to a market-oriented economy without tearing the socio-cultural framework of the country, or to be more specific, our social commitments to the under- privileged sections. The Eighth Plan mentioned that planning would have to be reoriented so as to make it indicative. India’s Eighth Plan was unique in the sense that it attempted to manage the transition from a centrally planned economy to a market-oriented economy without tearing the socio-cultural framework of the country, or to be more specific, our social commitments to the under- privileged sections. The Eighth Plan mentioned that planning would have to be reoriented so as to make it indicative. Question 15 of 20 15. Question 2 points Consider the following statements: Phillips curve is an inverse relationship between the rate of unemployment and the rate of inflation in an economy Engel’s Law observes that as income rises the proportion of income spent on food falls even if the actual expenditure on food rises Which of the above statement is/are correct? a) 1 only b) 2 only c) 1 and 2 only d) None of the above Correct Ans: C The Phillips curve shows the relationship between unemployment and inflation in an economy. It states that inflation and unemployment have a stable and inverse relationship. The theory claims that with economic growth comes inflation, which in turn should lead to more jobs and less unemployment. (hence statement 1 is correct) Engel’s law is an observation in economics stating that as income rises, the proportion of income spent on food falls, even if absolute expenditure on food rises. In other words, the income elasticity of demand of food is between 0 and 1. The law was named after the statistician Ernst Engel (1821–1896). (hence statement 2 is correct) Incorrect Ans: C The Phillips curve shows the relationship between unemployment and inflation in an economy. It states that inflation and unemployment have a stable and inverse relationship. The theory claims that with economic growth comes inflation, which in turn should lead to more jobs and less unemployment. (hence statement 1 is correct) Engel’s law is an observation in economics stating that as income rises, the proportion of income spent on food falls, even if absolute expenditure on food rises. In other words, the income elasticity of demand of food is between 0 and 1. The law was named after the statistician Ernst Engel (1821–1896). (hence statement 2 is correct) Question 16 of 20 16. Question 2 points Hedging in the foreign exchange market refers to: a) An act of devaluation b) Covering a risk of fluctuations in the foreign exchange rates in future c) Not covering a risk of fluctuations in the foreign exchange rates in future d) An act of revaluation Correct Ans: B A hedge is an investment to reduce the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting position in a related security, such as a futures contract. Incorrect Ans: B A hedge is an investment to reduce the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting position in a related security, such as a futures contract. Question 17 of 20 17. Question 2 points Core inflation has been described as: a) Headline inflation − food inflation b) Headline inflation − (food inflation + fuel inflation) c) Headline inflation − fuel inflation d) Food inflation + Fuel inflation Correct Ans: B Core inflation is the change in costs of goods and services, but does not include those from the food and energy sectors. This measure of inflation excludes these items because their prices are much more volatile. Incorrect Ans: B Core inflation is the change in costs of goods and services, but does not include those from the food and energy sectors. This measure of inflation excludes these items because their prices are much more volatile. Question 18 of 20 18. Question 2 points Primary deficit is measured by: a) Fiscal deficit − interest payments b) Budget deficit − interest payments c) Budget deficit + total borrowings d) Total Revenue expenditure −total revenue receipts Correct Ans: A Primary deficit refers to difference between fiscal deficit of the current year and interest payments on the previous borrowings. Primary Deficit = Fiscal Deficit – Interest Payments. The total borrowing requirement of the government includes the interest commitments on accumulated debts. Incorrect Ans: A Primary deficit refers to difference between fiscal deficit of the current year and interest payments on the previous borrowings. Primary Deficit = Fiscal Deficit – Interest Payments. The total borrowing requirement of the government includes the interest commitments on accumulated debts. Question 19 of 20 19. Question 2 points Consider the following statements in relation to Gender Budgeting and answer from the code given below: ‘Gender analysis’ of the budget Preparing a separate budget for women Government of India adopted gender budgeting in 2005 – 06 Code: a) 1 and 2 only b) 1 and 3 only c) 2 and 3 only d) 1, 2 and 3 Correct Ans: B Gender Budgeting is a powerful tool for achieving gender mainstreaming so as to ensure that benefits of development reach women as much as men. It is not an accounting exercise but an ongoing process of keeping a gender perspective in policy/ programme formulation, its implementation and review. GB entails dissection of the Government budgets to establish its gender differential impacts and to ensure that gender commitments are translated in to budgetary commitments. Since 2005-06, the Expenditure Division of the Ministry of Finance has been issuing a note on Gender Budgeting as a part of the Budget Circular every year. This is compiled and incorporated in the form of Statement 20 as a part of the Expenditure Budget Document Volume 1 by the Expenditure Division of the Ministry of Finance. This GB Statement comprises two parts- Part A and Part B. Part A reflects Women Specific Schemes, i.e. those which have 100% allocation for women. Part B reflects Pro Women Schemes, i.e. those where at least 30% of the allocation is for women. Gender Budgeting is a powerful tool for achieving gender mainstreaming so as to ensure that benefits of development reach women as much as men. It is not an accounting exercise but an ongoing process of keeping a gender perspective in policy/ programme formulation, its implementation and review. GB entails dissection of the Government budgets to establish its gender differential impacts and to ensure that gender commitments are translated in to budgetary commitments. Since 2005-06, the Expenditure Division of the Ministry of Finance has been issuing a note on Gender Budgeting as a part of the Budget Circular every year. This is compiled and incorporated in the form of Statement 20 as a part of the Expenditure Budget Document Volume 1 by the Expenditure Division of the Ministry of Finance. This GB Statement comprises two parts- Part A and Part B. Part A reflects Women Specific Schemes, i.e. those which have 100% allocation for women. Part B reflects Pro Women Schemes, i.e. those where at least 30% of the allocation is for women. 20. Question Which organisation in India has been given the responsibility to monitor the progress of sustainable development goals? a) Reserve Bank of India b) Central Statistical Office c) NITI Aayog d) National Sample Survey office Correct Ans: C National Action on the SDGs in India NITI Aayog, the Government of India’s premier think tank, has been entrusted with the task of coordinating the SDGs. NITI Aayog has undertaken a mapping of schemes as they relate to the SDGs and their targets, and has identified lead and supporting ministries for each target. They have adopted a government-wide approach to sustainable development, emphasising the interconnected nature of the SDGs across economic, social and environmental pillars. States have been advised to undertake a similar mapping of their schemes, including centrally sponsored schemes. In addition, the Ministry of Statistics and Programme Implementation (MoSPI) has been leading discussions for developing national indicators for the SDGs. State governments are key to India’s progress on the SDG Agenda and several of them have already initiated action on implementing the SDGs. Incorrect Ans: C National Action on the SDGs in India NITI Aayog, the Government of India’s premier think tank, has been entrusted with the task of coordinating the SDGs. NITI Aayog has undertaken a mapping of schemes as they relate to the SDGs and their targets, and has identified lead and supporting ministries for each target. They have adopted a government-wide approach to sustainable development, emphasising the interconnected nature of the SDGs across economic, social and environmental pillars. States have been advised to undertake a similar mapping of their schemes, including centrally sponsored schemes. In addition, the Ministry of Statistics and Programme Implementation (MoSPI) has been leading discussions for developing national indicators for the SDGs. State governments are key to India’s progress on the SDG Agenda and several of them have already initiated action on implementing the SDGs.
Wales star Gareth Bale picked up the Welsh player of the year award earlier on in the week. The versatile attacker has notched six goals in Wales’ magnificent Euro 2016 qualification campaign, and has proved to be the world-class talent that he undoubtedly is. However, following Wales’ award ceremony, the £85-million Real Madrid ace claimed that Swansea skipper Ashley Williams should have been named Welsh player of the year after his rock-solid performances at the back. Bale said to the Daily Star, “It’s an honour to win any award, but I’m well aware that if it wasn’t for my team-mates I wouldn’t be picking up this award. “I voted for Ashley Williams because he has been a rock in defence throughout the whole campaign. “We’re a close-knit group, everyone encourages everybody else, but Ash is the leader of the pack and he helps make it stay that way and gets every player involved.” Williams, as well as Bale, has been instrumental for Wales’ Euro 2016 hopes and he’ll lead the Welsh out when they face Bosnia and Andorra in this weeks upcoming qualifiers. A win for Wales in Bosnia on Saturday will seal Euro qualification, meaning that we’ll then be seeing Wales in their first major competition since the 1958 World Cup. Swansea left-back Neil Taylor has also been a valuable asset for Wales’ defence in their rise into the top ten world rankings. Former-Swansea players Ben Davies and Jazz Richards also deserve a mention too after forming a fantastically resolute defensive unit. Now ahead of Saturday’s crucial game against Bosnia, Read Swansea would like to wish all of the Welsh squad a massive good luck! Together Stronger!
Raw Milk The consumer has been brainwashed for fifty years to avoid raw milk or alternately to trust only pasteurized milk.I grew up with this even though I drank fresh milk my entire childhood.The truth is that every farmer is fastidious over healthy cows and clean milking equipment.The consumer would be astonished to see the care maintained as a matter of course. The problem begins with the need to blend product in tankage and to transport it to a processing facility.Obviously a blended product hugely increases risk and pasteurization is designed to remove the risk.One cannot disagree with that protocol.In fact I personally want nothing to do with milk that must be days old at least by the time it arrives in my home, if it is not pasteurized.Recall that it is stored at the producer at least a couple of days even before shipping. Fresh milk directly from the producer will be from a known healthy herd with the personal guarantee of the owner and likely hours old simply because that will be the easiest way to sell it. The quality of the product will be hugely superior to anything you can imagine.In fact the best thing commercial milk has going for it is no one has ever tasted fresh milk. Fresh milk delivery has to be a same day proposition and the blending needs to be avoided.The customer can order directly from the herd.There is likely a viable business here with modern refrigeration. However, it is also time to rethink the whole process of milk handling and pasteurization.There are better ways that can surely be now perfected and plausibly applied at farm level. Using EM waves to knock out foreign bacteria is possible on small processing systems.So it may be possible to satisfy the health department with a neat technological fix. By the bye, If you have never drank raw milk, you are in for a treat. The difference is night and day. NEWMARKET, Ont. - Clutching a glass of raw milk, an emotional Michael Schmidt toasted what he called a victory for the local food movement Thursday after the Ontario dairy farmer was found not guilty of 19 charges related to selling unpasteurized milk. "People need to learn how to stand up even when it seems it's impossible to achieve change in our interpretation of the law," said Schmidt, who was often depicted by supporters as the small farmer fighting for consumer food rights against an established milk industry. In a legal battle that played out over three years, Schmidt fought to continue the operation of his 150-member raw milk co-operative in Durham, Ont., and defended himself against the charges for dispensing milk straight from the cow. Schmidt was charged under the Health Protection and Promotion Act and the Milk Act after an armed raid by about two dozen officers and government officials at his farm in 2006. While raw milk is legal to drink, it's illegal to sell in Canada. Officials consider it a health hazard. Under Schmidt's cow-share program each member of his co-operative owns a part of the cow. By owning the cow members were drinking milk from their own animal, he says. On Thursday, justice of the peace Paul Kowarsky ruled that Schmidt's method of distribution made the group exempt from the legislation. He also found the operation did not violate the province's milk-marketing or public-health regulations. Kowarsky said the Crown could not prove that Schmidt had tried to market the milk. It was made clear on signs at the farm and at the blue bus where Schmidt set up shop at a Vaughan, Ont., market that only members could purchase products made from raw milk, he added. "The undisputed evidence of the defendant is that there is no advertising or selling," said Kowarsky. The legislation was originally created to protect the vulnerable, but the cow-share members were not vulnerable and were cognizant of all concerns associated with drinking unpasteurized milk, he added. "They consume the milk at their own risk," said Kowarsky, adding the product had been thoroughly tested and was shown not to be contaminated. At trial, food scientists and health experts testified that mandatory pasteurization laws are needed to protect public health. Schmidt argued that government officials and food scientists could not guarantee the safety of any food, and suggested informed consumers should be able to buy raw milk if they want. At the culmination of the detailed verdict, Kowarsky said the cow-share program was a "legitimate and lawful" enterprise and called the case part of a "search for contemporary justice." A Ministry of Agriculture spokesman was not able to say if the ministry would be reviewing the Milk Act. "We're disappointed in the court's ruling," said Brent Ross. "The government will review the court's decision and determine next steps." Thrilled supporters, some wearing sweaters emblazoned on the back with "Team Raw Dairy," gasped and clapped as the justice of the peace handed down his verdict. The courtroom, packed with so many supporters that dozens were left standing, flocked to a teary-eyed Schmidt, as they flung their arms around him. "He's giving us all a chance for the small farmer to enter into private contracts such as cow-share or farm-share agreements where we can decide what we buy, eat and how we behave," said a jubilant Judith McGill, a cow-share member who has helped rally support for Schmidt. Outside of the court, two women poured and passed around creamy glasses of raw milk to people as children perched on signs reading "protect our food." During the verdict, Kowarsky also acknowledged the growing trend towards the local food movement, and said he found many cow-share programs existed around the world. This was a message not lost on Schmidt, who said the verdict had opened the door to new kind of conversation. "It was never a war. It was a Shakespearean drama," Schmidt said coyly. "We tried to get into a dialogue." Schmidt has not ruled out entering the political scene so he can push for the full legalization of raw milk. "Like (former prime minister Pierre Elliot) Trudeau said, the government has no business in the bedroom of the people, and here I say the government has no business in the stomach of the people either." For Allyson McMullen, Schmidt's win is also a win for consumer choice. "It's so much more about milk. It's about food. It's about us having the choice to put what we want in our bodies and I think that this is incredible," she said.
<%# Custom action. Available local variables: url icon html_options: custom html options -%> <%= link_to_if(action_if, content_tag(:span, '', :class => icon, :title => title), url, html_options) %>
A new flow cytometric pulse height analyzer offering microprocessor controlled data acquisition and statistical analysis. The instrument described is capable of storing up to 112 one parameter histograms (128 channels) or 16 one parameter and 3 two parameter histograms (64 X 64 channels). A low cost 10 Mhz oscilloscope displays the graphical and alphanumerical data. During data acquisition, the original pulses, an analogue rate meter and the growing histogram are displayed simultaneously on the screen. The instrument may be completely operated by an 18 element keyboard. The data processor allows calculation of integrals, mean values, standard deviations and coefficients of variation of operator selectable regions of the acquired histograms. Gaussian distributions determined by the statistical parameters may be compared directly with the measured distributions. Distribution curves can be normalized, shifted, added, subtracted or compared with artificial distributions which are generated by superimposition of distinct Gaussian curves. Exponentially fitted background curves can be subtracted from the measured histograms. A text line at the top of the screen displays the numerical values and explanatory remarks. The two parameter histograms may be rotated, observed from the sides or back and projected either on the x- or y-axes. The projections or selected lines or columns can be transferred to the one parameter range and treated statistically. Sequences of one parameter distributions may be transferred two parameter range and displayed as pseudo-two-parameter histograms.
Sierra Leone: From war to tourist paradise Weary of being a poster-child for an African war, Sierra Leone is working hard to lure back tourists, but for now getting to enjoy some of Africa's most beautiful scenery is not for the faint-hearted.Duration: 02:45
Q: Jquery console value not return any value? Hello every one i have small clarification in my project in my project console.log() function return no values. <script> $('#search-box<?=$x;?>').blur(function() { var val = $("#search-list<?=$x;?>").val(); $.ajax({ type: "POST", url: "searchlist.php", data:'amount='+$(this).val(), success: (data) => { console.log(data); var o_val = $("#unit_pricea<?=$x;?>").val(data); var number = $('#quantity<?=$x;?>').val(); console.log(o_val); } }); }); </script> here console.log(data); Values can display. var o_val = $("#unit_pricea<?=$x;?>").val(data); whenever i will assign the varible and showing that varible in console it is not working console.log(o_val); My Console Output is look like this console.log(data)----> 245 </br> var o_val = $("#unit_pricea<?=$x;?>").val(data); ---> n.fn.init [input#unit_pricea1.form-control.unit_pricea1, context: document, selector: "#unit_pricea1"] A: Whenever you set the value using $(selector).val(data), it returns the DOM selector instead of the value. If you want the value to be returned then you should use val(): $("#unit_pricea<?=$x;?>").val(data); var o_val = $("#unit_pricea<?=$x;?>").val(); console.log(o_val);
Saturday, March 2, 2013 Look, I'm not trying to insult Alan Cumming by saying he looks like he might be gay. I'm just saying that if Robert Downey Jr. were gay (again, not that there's anything wrong with that) he'd look exactly like Alan Cumming.
<?php /** * Locale data for 'dav_KE'. * * This file is automatically generated by yiic cldr command. * * Copyright © 1991-2013 Unicode, Inc. All rights reserved. * Distributed under the Terms of Use in http://www.unicode.org/copyright.html. * * @copyright 2008-2014 Yii Software LLC (http://www.yiiframework.com/license/) */ return array ( 'version' => '8245', 'numberSymbols' => array ( 'decimal' => '.', 'group' => ',', 'list' => ';', 'percentSign' => '%', 'plusSign' => '+', 'minusSign' => '-', 'exponential' => 'E', 'perMille' => '‰', 'infinity' => '∞', 'nan' => 'NaN', ), 'decimalFormat' => '#,##0.###', 'scientificFormat' => '#E0', 'percentFormat' => '#,##0%', 'currencyFormat' => '¤#,##0.00;(¤#,##0.00)', 'currencySymbols' => array ( 'AUD' => 'A$', 'BRL' => 'R$', 'CAD' => 'CA$', 'CNY' => 'CN¥', 'EUR' => '€', 'GBP' => '£', 'HKD' => 'HK$', 'ILS' => '₪', 'INR' => '₹', 'JPY' => 'JP¥', 'KRW' => '₩', 'MXN' => 'MX$', 'NZD' => 'NZ$', 'THB' => '฿', 'TWD' => 'NT$', 'USD' => 'US$', 'VND' => '₫', 'XAF' => 'FCFA', 'XCD' => 'EC$', 'XOF' => 'CFA', 'XPF' => 'CFPF', 'KES' => 'Ksh', ), 'monthNames' => array ( 'wide' => array ( 1 => 'Mori ghwa imbiri', 2 => 'Mori ghwa kawi', 3 => 'Mori ghwa kadadu', 4 => 'Mori ghwa kana', 5 => 'Mori ghwa kasanu', 6 => 'Mori ghwa karandadu', 7 => 'Mori ghwa mfungade', 8 => 'Mori ghwa wunyanya', 9 => 'Mori ghwa ikenda', 10 => 'Mori ghwa ikumi', 11 => 'Mori ghwa ikumi na imweri', 12 => 'Mori ghwa ikumi na iwi', ), 'abbreviated' => array ( 1 => 'Imb', 2 => 'Kaw', 3 => 'Kad', 4 => 'Kan', 5 => 'Kas', 6 => 'Kar', 7 => 'Mfu', 8 => 'Wun', 9 => 'Ike', 10 => 'Iku', 11 => 'Imw', 12 => 'Iwi', ), ), 'monthNamesSA' => array ( 'narrow' => array ( 1 => 'I', 2 => 'K', 3 => 'K', 4 => 'K', 5 => 'K', 6 => 'K', 7 => 'M', 8 => 'W', 9 => 'I', 10 => 'I', 11 => 'I', 12 => 'I', ), ), 'weekDayNames' => array ( 'wide' => array ( 0 => 'Ituku ja jumwa', 1 => 'Kuramuka jimweri', 2 => 'Kuramuka kawi', 3 => 'Kuramuka kadadu', 4 => 'Kuramuka kana', 5 => 'Kuramuka kasanu', 6 => 'Kifula nguwo', ), 'abbreviated' => array ( 0 => 'Jum', 1 => 'Jim', 2 => 'Kaw', 3 => 'Kad', 4 => 'Kan', 5 => 'Kas', 6 => 'Ngu', ), ), 'weekDayNamesSA' => array ( 'narrow' => array ( 0 => 'J', 1 => 'J', 2 => 'K', 3 => 'K', 4 => 'K', 5 => 'K', 6 => 'N', ), ), 'eraNames' => array ( 'abbreviated' => array ( 0 => 'KK', 1 => 'BK', ), 'wide' => array ( 0 => 'Kabla ya Kristo', 1 => 'Baada ya Kristo', ), 'narrow' => array ( 0 => 'KK', 1 => 'BK', ), ), 'dateFormats' => array ( 'full' => 'EEEE, d MMMM y', 'long' => 'd MMMM y', 'medium' => 'd MMM y', 'short' => 'dd/MM/y', ), 'timeFormats' => array ( 'full' => 'h:mm:ss a zzzz', 'long' => 'h:mm:ss a z', 'medium' => 'h:mm:ss a', 'short' => 'h:mm a', ), 'dateTimeFormat' => '{1} {0}', 'amName' => 'Luma lwa K', 'pmName' => 'luma lwa p', 'orientation' => 'ltr', 'languages' => array ( 'ak' => 'Kiakan', 'am' => 'Kiamhari', 'ar' => 'Kiarabu', 'be' => 'Kibelarusi', 'bg' => 'Kibulgaria', 'bn' => 'Kibangla', 'cs' => 'Kichecki', 'dav' => 'Kitaita', 'de' => 'Kijerumani', 'el' => 'Kigiriki', 'en' => 'Kingereza', 'es' => 'Kihispania', 'fa' => 'Kiajemi', 'fr' => 'Kifaransa', 'ha' => 'Kihausa', 'hi' => 'Kihindi', 'hu' => 'Kihungari', 'id' => 'Kiindonesia', 'ig' => 'Kiigbo', 'it' => 'Kiitaliano', 'ja' => 'Kijapani', 'jv' => 'Kijava', 'km' => 'Kikambodia', 'ko' => 'Kikorea', 'ms' => 'Kimalesia', 'my' => 'Kiburma', 'ne' => 'Kinepali', 'nl' => 'Kiholanzi', 'pa' => 'Kipunjabi', 'pl' => 'Kipolandi', 'pt' => 'Kireno', 'ro' => 'Kiromania', 'ru' => 'Kirusi', 'rw' => 'Kinyarwanda', 'so' => 'Kisomali', 'sv' => 'Kiswidi', 'ta' => 'Kitamil', 'th' => 'Kitailandi', 'tr' => 'Kituruki', 'uk' => 'Kiukrania', 'ur' => 'Kiurdu', 'vi' => 'Kivietinamu', 'yo' => 'Kiyoruba', 'zh' => 'Kichina', 'zu' => 'Kizulu', ), 'territories' => array ( 'ad' => 'Andora', 'ae' => 'Falme za Kiarabu', 'af' => 'Afuganistani', 'ag' => 'Antigua na Barbuda', 'ai' => 'Anguilla', 'al' => 'Albania', 'am' => 'Armenia', 'an' => 'Antili za Uholanzi', 'ao' => 'Angola', 'ar' => 'Ajentina', 'as' => 'Samoa ya Marekani', 'at' => 'Austria', 'au' => 'Australia', 'aw' => 'Aruba', 'az' => 'Azabajani', 'ba' => 'Bosnia na Hezegovina', 'bb' => 'Babadosi', 'bd' => 'Bangladeshi', 'be' => 'Ubelgiji', 'bf' => 'Bukinafaso', 'bg' => 'Bulgaria', 'bh' => 'Bahareni', 'bi' => 'Burundi', 'bj' => 'Benini', 'bm' => 'Bermuda', 'bn' => 'Brunei', 'bo' => 'Bolivia', 'br' => 'Brazili', 'bs' => 'Bahama', 'bt' => 'Butani', 'bw' => 'Botswana', 'by' => 'Belarusi', 'bz' => 'Belize', 'ca' => 'Kanada', 'cd' => 'Jamhuri ya Kidemokrasia ya Kongo', 'cf' => 'Jamhuri ya Afrika ya Kati', 'cg' => 'Kongo', 'ch' => 'Uswisi', 'ci' => 'Kodivaa', 'ck' => 'Visiwa vya Cook', 'cl' => 'Chile', 'cm' => 'Kameruni', 'cn' => 'China', 'co' => 'Kolombia', 'cr' => 'Kostarika', 'cu' => 'Kuba', 'cv' => 'Kepuvede', 'cy' => 'Kuprosi', 'cz' => 'Jamhuri ya Cheki', 'de' => 'Ujerumani', 'dj' => 'Jibuti', 'dk' => 'Denmaki', 'dm' => 'Dominika', 'do' => 'Jamhuri ya Dominika', 'dz' => 'Aljeria', 'ec' => 'Ekwado', 'ee' => 'Estonia', 'eg' => 'Misri', 'er' => 'Eritrea', 'es' => 'Hispania', 'et' => 'Uhabeshi', 'fi' => 'Ufini', 'fj' => 'Fiji', 'fk' => 'Visiwa vya Falkland', 'fm' => 'Mikronesia', 'fr' => 'Ufaransa', 'ga' => 'Gaboni', 'gb' => 'Uingereza', 'gd' => 'Grenada', 'ge' => 'Jojia', 'gf' => 'Gwiyana ya Ufaransa', 'gh' => 'Ghana', 'gi' => 'Jibralta', 'gl' => 'Grinlandi', 'gm' => 'Gambia', 'gn' => 'Gine', 'gp' => 'Gwadelupe', 'gq' => 'Ginekweta', 'gr' => 'Ugiriki', 'gt' => 'Gwatemala', 'gu' => 'Gwam', 'gw' => 'Ginebisau', 'gy' => 'Guyana', 'hn' => 'Hondurasi', 'hr' => 'Korasia', 'ht' => 'Haiti', 'hu' => 'Hungaria', 'id' => 'Indonesia', 'ie' => 'Ayalandi', 'il' => 'Israeli', 'in' => 'India', 'io' => 'Eneo la Uingereza katika Bahari Hindi', 'iq' => 'Iraki', 'ir' => 'Uajemi', 'is' => 'Aislandi', 'it' => 'Italia', 'jm' => 'Jamaika', 'jo' => 'Yordani', 'jp' => 'Japani', 'ke' => 'Kenya', 'kg' => 'Kirigizistani', 'kh' => 'Kambodia', 'ki' => 'Kiribati', 'km' => 'Komoro', 'kn' => 'Santakitzi na Nevis', 'kp' => 'Korea Kaskazini', 'kr' => 'Korea Kusini', 'kw' => 'Kuwaiti', 'ky' => 'Visiwa vya Kayman', 'kz' => 'Kazakistani', 'la' => 'Laosi', 'lb' => 'Lebanoni', 'lc' => 'Santalusia', 'li' => 'Lishenteni', 'lk' => 'Sirilanka', 'lr' => 'Liberia', 'ls' => 'Lesoto', 'lt' => 'Litwania', 'lu' => 'Lasembagi', 'lv' => 'Lativia', 'ly' => 'Libya', 'ma' => 'Moroko', 'mc' => 'Monako', 'md' => 'Moldova', 'mg' => 'Bukini', 'mh' => 'Visiwa vya Marshal', 'mk' => 'Masedonia', 'ml' => 'Mali', 'mm' => 'Myama', 'mn' => 'Mongolia', 'mp' => 'Visiwa vya Mariana vya Kaskazini', 'mq' => 'Martiniki', 'mr' => 'Moritania', 'ms' => 'Montserrati', 'mt' => 'Malta', 'mu' => 'Morisi', 'mv' => 'Modivu', 'mw' => 'Malawi', 'mx' => 'Meksiko', 'my' => 'Malesia', 'mz' => 'Msumbiji', 'na' => 'Namibia', 'nc' => 'Nyukaledonia', 'ne' => 'Nijeri', 'nf' => 'Kisiwa cha Norfok', 'ng' => 'Nijeria', 'ni' => 'Nikaragwa', 'nl' => 'Uholanzi', 'no' => 'Norwe', 'np' => 'Nepali', 'nr' => 'Nauru', 'nu' => 'Niue', 'nz' => 'Nyuzilandi', 'om' => 'Omani', 'pa' => 'Panama', 'pe' => 'Peru', 'pf' => 'Polinesia ya Ufaransa', 'pg' => 'Papua', 'ph' => 'Filipino', 'pk' => 'Pakistani', 'pl' => 'Polandi', 'pm' => 'Santapieri na Mikeloni', 'pn' => 'Pitkairni', 'pr' => 'Pwetoriko', 'ps' => 'Ukingo wa Magharibi na Ukanda wa Gaza wa Palestina', 'pt' => 'Ureno', 'pw' => 'Palau', 'py' => 'Paragwai', 'qa' => 'Katari', 're' => 'Riyunioni', 'ro' => 'Romania', 'ru' => 'Urusi', 'rw' => 'Rwanda', 'sa' => 'Saudi', 'sb' => 'Visiwa vya Solomon', 'sc' => 'Shelisheli', 'sd' => 'Sudani', 'se' => 'Uswidi', 'sg' => 'Singapoo', 'sh' => 'Santahelena', 'si' => 'Slovenia', 'sk' => 'Slovakia', 'sl' => 'Siera Leoni', 'sm' => 'Samarino', 'sn' => 'Senegali', 'so' => 'Somalia', 'sr' => 'Surinamu', 'st' => 'Sao Tome na Principe', 'sv' => 'Elsavado', 'sy' => 'Siria', 'sz' => 'Uswazi', 'tc' => 'Visiwa vya Turki na Kaiko', 'td' => 'Chadi', 'tg' => 'Togo', 'th' => 'Tailandi', 'tj' => 'Tajikistani', 'tk' => 'Tokelau', 'tl' => 'Timori ya Mashariki', 'tm' => 'Turukimenistani', 'tn' => 'Tunisia', 'to' => 'Tonga', 'tr' => 'Uturuki', 'tt' => 'Trinidad na Tobago', 'tv' => 'Tuvalu', 'tw' => 'Taiwani', 'tz' => 'Tanzania', 'ua' => 'Ukraini', 'ug' => 'Uganda', 'us' => 'Marekani', 'uy' => 'Urugwai', 'uz' => 'Uzibekistani', 'va' => 'Vatikani', 'vc' => 'Santavisenti na Grenadini', 've' => 'Venezuela', 'vg' => 'Visiwa vya Virgin vya Uingereza', 'vi' => 'Visiwa vya Virgin vya Marekani', 'vn' => 'Vietinamu', 'vu' => 'Vanuatu', 'wf' => 'Walis na Futuna', 'ws' => 'Samoa', 'ye' => 'Yemeni', 'yt' => 'Mayotte', 'za' => 'Afrika Kusini', 'zm' => 'Zambia', 'zw' => 'Zimbabwe', ), );
DAERA delivers new record for CAP payments The Department of Agriculture, Environment and Rural Affairs (DAERA) today announced that a record 98% of farmers in Northern Ireland have received a full or balance CAP payment in December 2018. The payments, totalling £91 million, were issued to 23,676 farm businesses. Since the completion of advance payments in early November 2018, the department has maintained its drive to maximise payment performance. A total of £281 million in CAP payments has been issued in 2018. This record number of payments, which builds on the achievements of last year (97%), has been made possible due to 100% of farmers submitting their Single Application online. Claims made online are faster, more secure and more accurate. Payments can only be made on fully verified claims. This year, 94% of farm businesses who had been subject to a land inspection have received their payment in December. This represents a 10% increase in the percentage of inspection cases paid in December 2017.
FOREWORD - selezionareI. INTRODUCTIONII. THE COLLABORATION BETWEEN THE RCC AND THE WCC - selez.III. ACTIVITIES OF THE JWG, 1991-1998 - selez.A. The unity of the church the goal and the way B. Common witness C. Ecumenical Formation IV. SOME OTHERS AREAS OF COLLABORATION - selez.V. PROSPECTS FOR THE FUTURE (1998-2005) - selez. APPENDIX A - selez. APPENDIX B - selez. APPENDIX C - selez. Appendix D FULL TEXT APPENDIX D ECUMENICAL FORMATION: ECUMENICAL REFLECTIONS AND SUGGESTIONS A STUDY DOCUMENT OF THE JOINT WORKING GROUP BETWEEN THE ROMAN CATHOLIC CHURCH AND THE WORLD COUNCIL OF CHURCHES Preface It is well accepted that there is an ecumenical imperative in the Gospel. However, there is also the indisputable fact that the goal of unity is far from realized. In that context of contradiction, the Joint Working Group (JWG) of the Roman Catholic Church and the World Council of Churches (WCC) decided in 1985 to focus on ecumenical formation as a contribution towards conscientizing people with regard to ecumenism. The minutes for that particular meeting of the JWG report: "It might aim at a more popular readership. The pamphlet should be parl of a wider process of promoting the idea of ecumenical formation. It should include an explanation of why ecumenical formation is a priority, along with documentation. Anything produced on ecumenical formation ought to be sub-titled ecumenical reflections and suggestions', to make clear there is no intention of giving directives in a field in which each church has its proper responsibility". The document is designed to be educational, aimed at stimulating on-going reflection as an integral part of a process of ecumenical formation. It is rooted in a conviction that there must be a deep spirituality at the heart of ecumenical formation. With these words, we are happy to recommend this document for study. 1. In his high priestly prayer Jesus prayed for all those who will believe in him, "that they may all be one; as you, Father, are in me and I am in you, may they also be in us, so that the world may believe that vou have sent me. The glory that you have given me I have given them, so that they may be one, as we are one" (Jn 17:21-22). The unity to which the followers of Jesus Christ are called is not something created by them. Rather, it is Christ's will for them that they manifest their unity, given in Christ, before the world so that the world may believe. It is a unity which is grounded in and reflects the communion which exists between the Father and the Son and the Holy Spirit. Thus the ecumenical imperative and the mission of, the Church are inextricably intertwined, and this for the sake of the salvation of all. The eschatological vision of the transformation and unity of humankind is the fundamental inspiration of ecumenical action. Disobedience to the Imperative 2. However, from very early in her history, the Church has suffered from tensions. The earliest Christian community in Corinth experienced tensions and factions (1 Cor 1:10-17). After the Councils of Ephesus (in 431) and Chalcedon (in 451), an important part of the Church in the East was no more in communion with the rest of the Church. In 1054 there was the great break between the Church of the East and the Church of the West. As if those were not enough, the Western Church was unhappily divided further at the time of the Reformation. Today we continue to have not only the persistence of those divisions but also new ones. Whatever the reasons, such divisions contradict the Lord's high priestly prayer and Paul considers such divisions sinful and appeals "that all of you be in agreement and that there be no divisions among you, but that you be united in the same mind and the same purpose" (1 Cor 1: 10). 3. Against that background, ecumenical formation is a matter of urgency because it is part of the struggle to overcome the divisions of Christians which are sinful and scandalous and challenge the credibility of the Church and her mission. Some Significant Responses to the Ecumenical Imperative 4. If there is a tragic history of disobedience to the ecumenical imperative, there is also heartwarming evidence that time and again the churches, conscious of their call to unity, have been challenged to confront the implications of their divisions. For instance, attempts at reconciliation between the East and the West have taken place in the 13th and 15th centuries. Also in the centuries that followed there were voices and efforts calling the churches away from divisions and enmity. At the beginning of this century the modern ecumenical history received significant impulses from the 1910 World Missionary Conference at Edinburgh. In 1920 the Ecumenical Patriarchate published an Encyclical proposing the establishment of a "koinonia of churches", in spite of the doctrinal differences between the churches. The Encyclical was an urgent and timely reminder that "world Christendom would be disobedient to the will of the Lord and Savior if it did not seek to manifest in the world the unity of the people of God and of the body of Christ". Around the same time Anglicans and Catholics engaged in theological dialogue at the Malines Conversations, and the first World Conferences on Life and Work (Stockholm 1925) and Faith and Order (Lausanne 1927) were held. 5. Another recall to the ecumenical imperative in modern times was the meeting held in 1948 at Amsterdam, at which the WCC was formally constituted. The theme of this meeting was very significant: "Man's Disorder and God's Design". The long process which culminated in the birth of the WCC represents a multilateral response to the ecumenical imperative, in which a renewed commitment to the Una Sancta (the one, holy, catholic and apostolic Church), and to making our own the prayer of Jesus that "Your will be done on earth as it is in heaven", were openly declared to be on the agenda of the churches. 6. A further important landmark on the ecumenical road was the announcement made by Pope John XXIII, on 25th January 1959, the feast of the conversion of St Paul, to convene the Catholic bishops for the Second Vatican Council, which Pope John XXIII opened in October 1962. This Council which has been highly significant for ecumenical advance definitely accelerated the possibilities for the Catholic Church to take part in the multilateral dialogue in Faith and Order, and to engage in a range of bilateral dialogues which are now an important expression of the one ecumenical scene. Various bilateral conversations between various churches attest to growing fruitful relations between churches and traditions which for centuries were at variance. 7. There have also been historic and symbolic actions which are very significant efforts to overcome the old divisions. For example, on the 7th of December 1965 Pope Paul VI and Patriarch Athenagoras, in solemn ceremonies in Rome and Constantinople, took steps to take away from the memory and the midst of the churches the sentences of excommunication which had been the immediate cause of the great schism between the Church of Rome and the Church of Constantinople in 1054. Moreover, the icon of the Apostles Peter and Andrew in embrace Peter being the patron of the Church of Rome and Andrew the patron of the Church of Constantinople presented by the Ecumenical Patriarch to the Pope, illustrates in graphic and religious form the reconciliation between the churches of the East and the West. The responses of many churches to the Faith and Order document on Baptism, Eucharist and Ministry, which was the result of multilateral ecumenical dialogue, is a further illustration of ecumenical advance. The Imperative, a Permanent Call 8. The foregoing historical moments in the life of the Church stand like promontories in the ecumenical landscape and attest to the fact that in spite of persisting divisions of which there is need for repentance, churches are experiencing a reawakening to the necessity of unity that stands in holy writ and in the Lord's will for the Church. Indeed many have observed that relationships between churches have radically changed from isolation and enmity to mutual respect, cooperation, dialogue, and between several churches from the Reformation also Eucharistic fellowship. The people of God are hearing anew the call "to lead a life worthy of the calling to which you have been called ... bearing with one another in love, making every effort to maintain the unity of the Spirit in the bond of peace" (Eph 4:1-3). These and other developments are steps towards that visible unity which is a koinonia given and expressed in the common confession of the one apostolic faith, mutual recognition and sharing of baptism, Eucharist and ministries, common prayer, witness and service in the world, and conciliar forms of deliberation and decision-making. IIEcumenical Formation: What Is Meant by It? 9. That for long periods we have been disobedient to the ecumenical imperative is a reminder that the spirit of ecumenism needs nurturing. Ecumenical formation is an on-going process of learning within the various local churches and world communions, aimed at informing and guiding people in the movement which inspired by the Holy Spirit seeks the visible unity of Christians. This pilgrimage towards unity enables mutual sharing and mutual critique through which we grow. Such an approach to unity thus involves at once rootedness in Christ and in one's tradition, while endeavoring to discover and participate in the richness of other Christian and human traditions. A Process of Exploration 10. Such a response to the ecumenical imperative demands patient, humble and persistent exploration, together with people of other traditions, of the pain of our situation of separation, taking us to both the depths of our divisions and the heights of our already existing unity in the Triune God, and of the unity we hope to attain. Thus ecumenical formation is also a process of education by which we seek to orient ourselves towards God, all Christians and indeed all human beings in a spirit of renewed faithfulness to our Christian mission. A Process of Learning 11. As a process of learning, ecumenical formation is concerned with engaging the experience, knowledge, skills, talents and the religious memory of the Christian community for mutual enrichment and reconciliation. The process may be initiated through formal courses on the history and main issues of ecumenism as well as be integrated into the curriculum at every level of the education in which the Church is involved. Ecumenical formation is meant to help set the tone and perspective of every instruction and, therefore, may demand a change in the orientation of our educational institutions, systems and curricula. 12. The language of formation and learning refers to some degree to a body of knowledge to be absorbed. That is important; but formation and learning require a certain bold openness to living ecumenically as well. In 1952 the 4th Faith and Order Conference took place in Lund, Sweden. The statement that came from it may be read as a representative text: "A faith in the one Church of Christ which is not implemented by acts of obedience is dead. There are truths about the nature of God and His Church which will remain for ever closed to us unless we act together in obedience to the unity which is already ours. We would, therefore, earnestly request our Churches to consider whether they are doing all they ought to do to manifest the oneness of the people of God. Should not our Churches ask themselves whether they are showing sufficient eagerness to enter into conversation with other Churches and whether they should not act together in all matters except those in which deep differences of conviction compel them to act separately? ... Obedience to God demands also that the Churches seek unity in their mission to the world". A Process for All 13. Thus in pursuit of the goal of Christian unity, ecumenical formation takes place not only in formal educational programs but also in the daily life of the Church and people. While the formation of the whole people of God is desired, indeed is a necessity, we also insist on the strategic importance of giving priority to the ecumenical formation of those who have special responsibility for ministry and leadership in the churches. To that extent, theologians, pastors, and others who bear responsibility in the Church, have both a particular need and responsibility for ecumenical formation. 14. The ecumenical formation of those with particular responsibility for forming and animating future church leaders, could involve the study of ecumenical history and documents resulting from the on-going bilateral and multilateral dialogues. In addition, ecumenical gatherings and organizations, particularly of scholars, can provide a useful climate for it. Exchange visits among seminary students in the course of their training may also help this process of deepening the appreciation of other traditions as well as their own. An Expression of Ecumenical Spirituality 15. It follows from the ecumenical imperative that the process of formation in ecumenism has to be undergirded by, and should indeed be an expression of ecumenical spirituality. It is spiritual in the sense that it should be open to the prayer of Jesus for unity and to the promptings of the Holy Spirit who reconciles and binds all Christians together. It is spiritual in yet another sense of leading to repentance for the past disobedience to the ecumenical imperative, which disobedience was manifested as contentiousness and hostility among Christians at every level. Having ecumenical spirituality in common prayer and other forms as the underpinning of ecumenical formation invites all to conversion and change of heart which is the very soul of the work for restoring unity. Furthermore, it is spiritual in the sense of seeking a renewed life-style which is characterized by sacrificial love, compassion, patience with one another and tolerance. The search for such life-style may include exposing students to the spiritual texts, prayers and songs of other churches with the goal and hope that such familiarity will contribute towards effecting change of heart and attitude towards others, which itself is a gift of the Holy Spirit. Such efforts will help deepen mutual trust, making it possible to learn together the positive aspects of each other's tradition, and thus live constructively with the awareness of the reality and pain of divisions. 16. Ecumenical formation is part of the process of building community in the one household of God which must be built on trust, centered on Jesus Christ the Lord and Savior. This demands a spirituality of trust which, among other things, helps to overcome the fear to be exposed to different traditions, for the sake of Christ. IIIEcumenical Formation: How to Realize It? Pedagogy, built on Communion 17. The renewed emphasis on understanding the Church as communion, like the image of the Church as the body of Christ, implies differentiation within the one body, which has nevertheless been created for unity. Thus the very dynamic of ecumenism is relational in character. We respond in faith and hope to God who relates to us first. God relates to us in love, commanding us to love one another (Mk 12:29-31). This response ought to be wholehearted'. Therefore, in order to help Christians to respond whole-heartedly to the ecumenical imperative, we must seek ways to relate the prayer of Jesus (Jn 17:20-24) to all our hearts and minds, to the affective as well as to the cognitive dimensions in them. Christians must be helped to understand that to love Jesus necessarily means to love everything Jesus prayed, lived, died and was raised for, namely "to gather into one the children of God who are scattered abroad" (Jn 11:52), the unity of his disciples as an effective sign of the unity of all peoples. 18. The koinonia or communion as the basic understanding of the Church demands attempting to develop common ecumenical perspectives on ecclesiology. Unity is not uniformity but a communion of rich diversity. Therefore, it is necessary to explore with others the limits of legitimate diversity. In this regard special cognizance must also be taken of the religious and socio-cultural context in which the process of ecumenical formation takes place. Where there is a predominant majority church, ecumenical sensitivity is all the more required. Going Out to Each and Every One 19. The effectiveness of Christian unity in the midst of a broken world ultimately depends on the work of God's Spirit who wishes each one of us to participate. God speaks to us today the words which were addressed to Adam and Eve, "where are you?" (Gn 3:9) as also the words to Cain, "where is your brother ... ?"(Gn 4:9). All Christians should become aware, and make each other aware, of who and where their sisters and brothers are and where they stand in regard to them, whether near or far (Ep 2:17). They should be helped to go out to meet them, to get involved with them. Involvement participation in the whole ecumenical formation process is crucial. 20. In a Christian response to God and the ecumenical imperative which comes from God, there is no such thing as "the few for the many". The response to the prayer of Jesus must be the response of each and every one. Therefore, the growth into an ecumenical mind and heart is essential for each and for all, and the introduction of, and care for, ecumenical formation are absolutely necessary at every level of the church community, church life, action and activities; at all educational levels (schools, colleges, universities; theological schools, seminaries, religious/monastic communities, pastoral and lay formation centers; Sunday liturgies, homilies and catechesis). Commitment to Learning in Community 21. While ecumenical formation must be an essential feature in every curriculum in theological training, care must be taken that it does not become something intended for individuals only. There must be commitment of learning in community. This has several components: (a) learning about, from and with others of different traditions; (b) praying for Christian unity, and wherever and whenever possible, together, as well as praying for one another; (c) offering common Christian witness by acting together; and (d) struggling together with the pain of our divisions. In this regard the participation of different institutions for theological education in common programs of formation is to be encouraged. Working ecumenically in joint projects becomes another important aspect of ecumenical must always be related to the search for Christian unity. 22. Seeking a renewed commitment for ecumenical formation does not imply to gloss over existing differences and to deny the specific profiles of our respective ecclesial traditions. But it may involve a common re-reading of our histories and especially of those events that led to divisions among Christians. It is not enough to regret that our histories have been tainted through the polemics of the past; ecumenical formation must endeavor to eliminate polemic and to further mutual understanding, reconciliation, and the healing of memories. No longer shall we be strangers to one another but members of the one household of God (Ep 2:19). Open to Other Religions 23. In this world, people are also divided along religious lines. Thus ecumenical formation must also address the matter of religious plurality and secularism, and inform about inter-religious dialogue which aims at deeper mutual understanding in the search for world community. It must be clear however that interreligious dialogue with other world religions such as Islam, Buddhism, Hinduism, etc. has goals that are specifically different from the goals of ecumenical dialogue among Christians. In giving serious attention to this important activity, Christians must carefully distinguish it from ecumenical dialogue. 24. That spirit of tolerance and dialogue must get to the pews and market places where people feel the strains of the different heritages which encounter each other. The faith that God is the Creator and Sustainer of all also requires Christians to do everything in their power to promote the cause of freedom, human rights, justice and peace everywhere, and thus actively to contribute to a renewed movement towards human solidarity in obedience to God's will. Using the Instruments of Communication 25. In today's search for unity there is a relatively new factor which must be taken seriously the scientific technological advances, particularly the communications revolution. The world has become a global village in which peoples, cultures and religions, and Christian denominations which were once far off are now next door one to another. The sense of the other' is being pressed on us and we need to relate to one another for mutual survival and peace. Thus the possibilities of mass communication can be an asset for communicating the ecumenical spirit. The media can be an extremely important resource for ecumenical formation, and the many possibilities which they offer to promote the ecumenical formation process should be made use of. However, the world of the media has its own logic and values; it is not an unambivalent resource. Critical caution must, therefore, be exercised in availing ourselves of the media for the ecumenical task. Conclusion: Ecumenical Formation and Common Witness 26. Ecumenism is not an option for the churches. In obedience to Christ and for the sake of the world the churches are called to be an effective sign of God's presence and compassion before all the nations. For the churches to come divided to a broken world is to undermine their credibility when they claim to have a ministry of universal unity and reconciliation. The ecumenical imperative must be heard and responded to everywhere. This response necessarily requires ecumenical formation which will help the people of God to render a common witness to all humankind by pointing to the vision of the new heaven and anew earth (Rev 21:1).
Q: How to paginate a native query in Doctrine 2? Doctrine 2 has the Doctrine\ORM\Tools\Pagination\Paginator class which can be used to paginate normal DQL queries. However if I pass it a native query, I get this error: Catchable fatal error: Argument 1 passed to Doctrine\ORM\Tools\Pagination\Paginator::cloneQuery() must be an instance of Doctrine\ORM\Query, instance of Doctrine\ORM\NativeQuery given I've tried removing the type-hinting from the paginator class in the cloneQuery method, but this just gives further errors because other bits of the paginator class expect methods found in Query that aren't in NativeQuery. Is there any easy way of paginating the native queries without needing to build a new paginator class or fetching every row from the database into an array? A: I made my own paginator adapter class compatible with Zend_Paginator. Probably won't be the most flexible since it relies on there being a " FROM " near the start of the query (see the count() method) but it's a relatively quick and easy fix. /** * Paginate native doctrine 2 queries / class NativePaginator implements Zend_Paginator_Adapter_Interface { /* * @var Doctrine\ORM\NativeQuery / protected $query; protected $count; /* * @param Doctrine\ORM\NativeQuery $query / public function __construct($query) { $this->query = $query; } /* * Returns the total number of rows in the result set. * * @return integer / public function count() { if(!$this->count) { //change to a count query by changing the bit before the FROM $sql = explode(' FROM ', $this->query->getSql()); $sql[0] = 'SELECT COUNT()'; $sql = implode(' FROM ', $sql); $db = $this->query->getEntityManager()->getConnection(); $this->count = (int) $db->fetchColumn($sql, $this->query->getParameters()); } return $this->count; } /** * Returns an collection of items for a page. * * @param integer $offset Page offset * @param integer $itemCountPerPage Number of items per page * @return array */ public function getItems($offset, $itemCountPerPage) { $cloneQuery = clone $this->query; $cloneQuery->setParameters($this->query->getParameters(), $this->query->getParameterTypes()); foreach($this->query->getHints() as $name => $value) { $cloneQuery->setHint($name, $value); } //add on limit and offset $sql = $cloneQuery->getSQL(); $sql .= " LIMIT $itemCountPerPage OFFSET $offset"; $cloneQuery->setSQL($sql); return $cloneQuery->getResult(); } }
Excerpt from Adam S. Miller, Letters to a Young Mormon (Provo, UT: Neal A. Maxwell for Religious Scholarship, 2014), 17-23. Used by Permission of the Neal A. Maxwell Institute. For FairMormon blog only. Not to be redistributed or copied. 3. Sin Dear S., Being a good person doesn’t mean you’re not a sinner. Sin goes deeper. Being good will save you a lot of trouble, but it won’t solve the problem of sin. Only God can do this. Fill your basket with good apples rather than bad ones, but, in the end, sin has as much to do with the basket as with the apples. Sin depends not just on your actions but on the story you use those actions to tell. Like everyone, you have a story you want your life to tell. You have your own way of doing things and your own way of thinking about things. But “my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts” (Isaiah 55:8–9). As the heavens are higher than the earth, God’s work in your life is bigger than the story you’d like that life to tell. His life is bigger than your plans, goals, or fears. To save your life, you’ll have to lay down your stories and, minute by minute, day by day, give your life back to him. Preferring your stories to his life is sin. Sin is endemic to the story you’re always telling yourself about yourself. This story shows up in that spool of judgmental chitchat—sometimes fair, sometimes foul—that, like an off-stage voice-over, endlessly loops in your head. This narration follows you around like a shadow. It mimes you, measures you, sometimes mocks you, and pretends, in its flat, black simplicity, to be the truth about you. This story is seductive. It seems so weightless and bulletproof and ideal. But as a shadow it hides as much as it reveals. You are not your shadow. No matter how carefully you line up the light, your body will never fit that profile. Sin is what happens when we choose our shadows over the lives that cast them. Life is full of stories, but life is not a story. God doesn’t love your story, he loves you. Your story, like everyone’s, is a bit of a Frankenstein. Without your hardly noticing or choosing, it gets sewn together, on the fly, out of whatever borrowed scraps are at hand. You may have borrowed a bit from your mother, a bit from a movie you liked, and a bit from a lesson at church. You may have stitched these pieces together with a comment overheard at lunch, a glossy image from a magazine, and a second-grade test score. Whatever sticks. More stuff is always getting added as other stuff is discarded. Your story’s projection of what you should be is always getting adjusted. Your idea of your shadow’s optimal shape gets tailored and tailored again. Like most people, you’ll lavish attention on this story until, almost unwittingly, it becomes your blueprint for how things ought to be. As you persist in measuring life against it, this Franken-bible of the self will become a substitute for God, an idol. This is sin. And this idolatrous story is all the more ironic when, as a true believer, you religiously assign God a starring role in your story as the one who, with some cajoling and obedience, can make things go the way you’ve plotted. But faith isn’t about getting God to play a more and more central part in your story. Faith is about sacrificing your story on his altar. Everyone knows that little blush of pleasure that comes when you feel like your life and your story match. And I’m sure you know the pinch of disappointment that follows when you feel like your life hasn’t measured up. These blushes and pinches tend to rule our daily lives. They push and pull and bully us from one plot point to the next. “Now I should be this,” we say, “now I should have this, now I should do this. . . .” Meanwhile, the pedestrian substance of life gets shuffled offstage in favor of epic shadows. Think about what it’s like when you buy a new shirt. You slip, hopeful, into the dressing room. Backed by doubled mirrors, you model it and ask, “Does this fit my story, does this match my shadow?” As a teenager, I never had much luck with this. In junior high, I grew fast, we didn’t have much money, and my clothes never seemed to fit. My sleeves were short and my pants were flooded. I was always yanking at my cuffs, trying to make them longer. Late one fall, my mother took me to buy a new coat. I picked a kind of knockoff ski jacket, bright blue and trimmed with red and green. We even bought it a size too big. When we got home, I put it on and went out for a long, cold walk along our empty country road. For a long time I walked back and forth, back and forth, on a half-mile stretch, imagining with great pleasure what a stranger might say if they saw me, what they might imagine about who I was or were I was going in that new jacket. I was buttoned up safe. The coat seemed like exactly the kind of prop I needed to tell myself a more convincing story. And a more convincing story seemed like exactly what I needed to better protect me. That coat was just one of the many, many stories in which I’ve tried to hide. But even if you can get a story to work for a while, you’ll still be afraid. And when it fails to meet the measure of life, as all stories do, you’ll feel ashamed and your shame and guilt will manifest once again in that familiar pinch of disappointment. Shame and guilt are life’s way of protesting against the constriction of the too-tight story you’re busy telling about it. The twist is that shame and guilt, manifest in this pinch, end up siding with your story and blaming life. Guilt doubles down on the self-important story you’re telling about yourself. Guilt is sin seen from the perspective of your sinfulness. Even if you feel guilty about how you’ve hurt others, that guilt remains problematic because your guilt is about you and about how you didn’t measure up to your story. Guilt recognizes your story’s poor fit and then still demands that life measure up. It recognizes that your shoes are too small and too tight and then blames your feet for their size. Repentance is not about shaving down your toes, it’s about taking off your shoes. Jesus is not asking you to tell a better story or live your story more successfully, he’s asking you to lose that story. “Those who find their life will lose it, and those who lose their life for my sake will find it” (Matthew 10:39). Hell is when your story succeeds, not when it fails. Your suffocating story is the problem, not the solution. Surrender it and find your life. Your story is heavy and hard to bear. “Come to me,” Jesus says, “all you that are weary and are carrying heavy burdens, and I will give you rest. Take my yoke upon you, and learn from me; for I am gentle and humble in heart, and you will find rest for your souls. For my yoke is easy, and my burden is light” (Matthew 11:28–30). Put down the millstone of your story and take up the yoke of life instead. You will find Jesus’ rest only in the work of caring for life. Let his life manifest itself in yours rather than trying to impose your story on the life he gives. Obedience is important but this isn’t just about obedience. For sinners like us, the problem is not just that sin follows when we break the law. The problem is that sin severs God’s law from life and then, rather than discarding it, cleverly repurposes it. In sin, the law, rather than rooting us in life, gets pressed into playing a leading role in the story you’re trying to tell. Maybe in your story the law plays the role of an accuser: “You can’t measure up, you’re worthless!” Or, maybe in your story the law plays the role of an admirer: “You’re so great, you keep the law, you do measure up!” But either way, reduced to the role of an extra in your story, the law kills you because it abets your preference for tidy stories over living bodies. Keeping the law doesn’t earn you heavenly merits and breaking the law doesn’t earn you hellish demerits. Both merits and demerits are about you. The purpose of the law is to point you away from yourself, free you from the self-obsessed burden of your own story, and center you on Christ. You don’t need to generate merit in order to be saved, you need instead to come unto Christ and “rely wholly upon the merits of him who is mighty to save” (2 Nephi 31:19). The law points wholly to Christ and his grace. Keeping the law is the work of relying on Christ’s merit, not the work of generating your own. This is still hard work, but it is work of an entirely different kind. When you sin, you sin not because you’ve failed to measure up to your story but because you’ve privileged your story in the first place. Privileging your story, you don’t treat others or yourself with the care life requires. By freeing you from your story, Christ frees you from your guilt. He saves you by revealing that even your own life was never about you. Bought-back and story-poor, Christ frees space in your head to pay attention to someone other than yourself. You don’t need rigid rules and expectations, you need Spirit. You need to be sensitive and responsive. Rather than filtering other people’s voices through the shame-making screen of your story, you must learn to be responsible for the work of caring for what you share with them. Jesus doesn’t want you to feel guilty, he wants you to be responsible. Your stories aren’t the truth, life is. And only the truth can set you free. Love, A.
Hello, thanks for looking at the contract we have with Sempra. Do you think we could have EOL add the rounding language and the correction to published prices as part of the product description for all power financial products? Would the correction to published prices language contradict the language already in the ISDA agreement? Let me know what you think. Thanks, Melissa From: Sara Shackleton on 04/26/2001 06:28 PM To: Melissa Ann Murphy/HOU/ECT@ECT cc: Subject: Sempra Energy Trading Melissa: I started with Sempra. It's one of the more unusual masters ( a "Master Master" covering both physical and financial) and it's not the typical "ECT Master". Further, it contains no rounding or correction to published prices provisions. We'll have to review these masters on a case by case basis. Sara Shackleton Enron North America Corp. 1400 Smith Street, EB 3801a Houston, Texas 77002 713-853-5620 (phone) 713-646-3490 (fax) sara.shackleton@enron.com
The impact of managed care on psychiatric hospitalizations and length of stay in Puerto Rico. The objective of this paper is to estimate the impact of managed care on psychiatric hospitalizations and length of stay of medically indigent residents in Puerto Rico. A quasi-experimental design and three waves of data from a random community sample were used. Results indicate that, after 2 years, managed care had minimal impact on the number of psychiatric hospitalizations; while the mean length of hospitalization decreased after implementation of managed care, this change was not significant. Based on the data in this study, the managed care initiative developed as part of health reform in Puerto Rico did not appear to affect rates of psychiatric hospitalization and produced only a nonsignificant reduction in the average length of psychiatric hospital stays. Additional research is needed to determine trends in mental health care provision in Puerto Rico based on more recent data.
A week is a long time in politics, they say, and that was especially true during the last seven days in New Brunswick. Last Tuesday, the Higgs government's reputation for making tough, politically risky decisions was at the forefront of the announcement of changes to small-town hospitals. If there was political flak, "we're going to do it anyway," Health Minister Ted Flemming declared. "A government has to govern. There's been enough studies, enough consultations, enough reviews, enough, enough, enough." The CEOs of the province's two health authorities were "fabulously qualified" to lead the reform along with their staffs and boards, he said, "to the point that New Brunswickers should be thankful and grateful that we have these people in New Brunswick." Fast forward to Premier Blaine Higgs's news conference on Monday, when he said that the plan was not as "ready to go" as the CEOs had said it was, and that its implementation was "not well-defined." "I did expect that they would have a greater ability to roll out the plan," he said of the CEOs, Karen McGrath at Horizon and Gilles Lanteigne at Vitalité. "I was disappointed that that was not the case. Anyone would be disappointed that we weren't able to roll this out seamlessly." Too many questions, few answers According to Higgs, too many questions came up in the intervening week that lacked answers. With six small-town emergency departments shutting down between midnight and 8 a.m. starting next month, would there be more advanced-care paramedics to accommodate the increase in patients travelling greater distances to city hospitals? Would there still be palliative care in those smaller hospitals? Were doctors spelled off from overnight shifts in the ER actually practising in those communities, allowing them to see more patients during the day, as the health authorities promised? Protests were held outside some of the affected hospitals, including the Sussex Health Centre, pictured above. (Graham Thompson/CBC) "Those questions should have been clear, answered, without any concern," Higgs said. But, he said, they weren't. And apparently they had not been asked by anyone in his government — a startling admission for a premier who emphasizes managerial competence and precise, measurable achievements. "I'm an engineer," Higgs told a business audience in Saint John last year. "I love Gantt charts," a kind of bar graph showing timelines and targets. "I love measurements. I love people to hold accountable: like 'Who owns this?' and 'When are you coming back with a report?' and 'what's that report going to look like?' and 'When are we going to see results,' so that we have a timeline." How, then, did no one ask the right questions about the health plan before it was released — especially given that versions of the plan have been floating around for more than a decade? Higgs acknowledged Monday he had not been shown a Gantt chart, "which I would normally see," for the health reforms. "I was assured it was all done," he said, "because we've been trying to do it for so long." He explained that as premier he wants to delegate decision-making to "people in their own divisions, to take responsibility for their everyday activities." In this case, though, it took a week of protests for Higgs to discover there was a lack of forethought about the spinoff effects on other parts of the system. Health reform plans aren't dead yet The resulting fallout took his minority government to the brink of a snap election call. It also cost him the only francophone MLA and minister he had, Robert Gauvin. He'll now lack that perspective in future caucus and cabinet deliberations. How, then, to go forward? "Doing nothing is not an option," Higgs said. "It's never been an option for me. Taking a step back is necessary." The plan isn't dead. "I don't know of another plan," Higgs said. It will be the basis for consultations the province will organize this spring — the consultations Flemming said a week ago were no longer necessary. That will include visits by Higgs himself to the six communities with affected hospitals. Rallies were planned for all six of the rural hospitals in opposition of the province's plan to close emergency rooms next month. (Philip Drost/CBC) But the premier added he'd be glad to hear alternatives that address the pressing issues that still need urgent solutions: not enough doctors and nurses to allow the system to care for an aging population. And how should people respond the next time he says he's standing firm on an unpopular policy and is willing to go into an election to ensure it goes ahead? "If I'm in a position again, which I hope to be, to say 'I have this plan to roll out, I have assurances we can do this,' maybe I'll ask more questions. But I do ask a lot of questions in any case, so I'm not sure how many more I would ask. "But I would expect for people to be accountable for delivering what they promise to deliver, and I have to rely on people to be able to do that." So, he said, he would stake his ground "on different issues going forward, on the basis that I believe in what the plan is, that it will be well executed," he said. "The concern here is that the implementation plan was just not well thought-out." For many who believed in Higgs — who were confident he was a non-politician willing to make the hard choices — that distinction was lost, the reversal particularly disappointing. "I truly thought he was stronger," Bob McVicar, a Saint John businessman and Conservative supporter, said in a social media post. "He just choked like the rest have in the past. I'm suddenly wondering what makes him different from Gallant." At the end of a critical week for Higgs and his government, that comparison — to the former Liberal premier he often accused of avoiding difficult decisions — may be the cruellest critique of all.
. ${distsharedir}/bhyve_nvme.conf # Default SQL scheme for DB local::bhyve_nvme #MYTABLE="bhyve_nvme" # MYCOL describe in bhyve_nvme.conf id="INTEGER PRIMARY KEY AUTOINCREMENT" devpath="text UNIQUE default 0" ram="integer default 0" maxq="integer default 0" ioslots="integer default 0" sectsz="integer default 0" ser="text default \"bhyve-CBSD-NVMe\"" CONSTRAINT="" INITDB=""
{ "images" : [ { "idiom" : "universal", "scale" : "1x" }, { "idiom" : "universal", "scale" : "2x" }, { "idiom" : "universal", "filename" : "bryan-minear-315773-unsplash.jpg", "scale" : "3x" } ], "info" : { "version" : 1, "author" : "xcode" } }
Mobile Access 2010 Six in ten Americans go online wirelessly using a laptop or cell phone; African-Americans and 18-29 year olds lead the way in the use of cell phone data applications, but older adults are gaining ground Summary of Findings Six in ten American adults are now wireless internet users, and mobile data applications have grown more popular over the last year. As of May 2010, 59% of all adult Americans go online wirelessly. Our definition of a wireless internet user includes the following activities: â€˘ Going online with a laptop using a wi-fi connection or mobile broadband card. Roughly half of all adults (47%) go online in this way, up from the 39% who did so at a similar point in 2009. â€˘ Use the internet, email or instant messaging on a cell phone. Two in five adults (40%) do at least one of these using a mobile device, an increase from the 32% of adults who did so in 2009. Taken together, 59% of American adults now go online wirelessly using either a laptop or cell phone, an increase over the 51% of Americans who did so at a similar point in 2009.1 Cell phone ownership has remained stable over the last year, but users are taking advantage of a much wider range of their phonesâ€™ capabilities compared with a similar point in 2009. Of the eight mobile data applications we asked about in both 2009 and 2010, all showed statistically significant year-to-year growth. The use of non-voice data applications has grown significantly over the last year The % of cell phone owners who use their phones to do the following 66 Take a picture 76 65 72 Send or receive text messages Play a game 27 34 Send or receive email 25 34 Access the internet Play music Send or receive instant messages Record a video 1 Because of changes in question wordings over time, our current wireless internet user definition is not directly comparable to any pre-2009 findings. page 2 This year we also asked for the first time about seven additional cell phone activities. Among all cell phone owners: • 54% have used their mobile device to send someone a photo or video • 23% have accessed a social networking site using their phone • 20% have used their phone to watch a video • 15% have posted a photo or video online • 11% have purchased a product using their phone • 11% have made a charitable donation by text message • 10% have used their mobile phone to access a status update service such as Twitter African-Americans and Latinos continue to outpace whites in their use of data applications on handheld devices. Continuing a trend we first identified in 2009, minority Americans lead the way when it comes to mobile access—especially mobile access using handheld devices. Nearly two-thirds of African-Americans (64%) and Latinos (63%) are wireless internet users, and minority Americans are significantly more likely to own a cell phone than their white counterparts (87% of blacks and Hispanics own a cell phone, compared with 80% of whites). Additionally, black and Latino cell phone owners take advantage of a much wider array of their phones’ data functions compared to white cell phone owners. It is important to note that our data for Hispanics represents English-speaking Hispanics only, as our survey did not provide a Spanish-language option. page 3 page 4 Young adults are heavily invested in the mobile web, although 30-49 year olds are gaining ground. Nine in ten 18-29 year olds own a cell phone, and these young cell owners are significantly more likely than those in other age groups to engage in all of the mobile data applications we asked about in our survey. Among 18-29 year old cell phone owners: • 95% send or receive text messages • 93% use their phone to take pictures • 81% send photos or videos to others • 65% access the internet on their mobile device • 64% play music on their phones • 60% use their phones to play games or record a video • 52% have used their phone to send or receive email • 48% have accessed a social networking site on their phone • 46% use instant messaging on their mobile device • 40% have watched a video on their phone • 33% have posted a photo or video online from their phone • 21% have used a status update service such as Twitter from their phone • 20% have purchased something using their mobile phone • 19% have made a charitable donation by text message Although young adults have the highest levels of mobile data application use among all age groups, utilization of these services is growing fast among 30-49 year olds. Compared with a similar point in 2009, cell owners ages 30-49 are significantly more likely to use a range of mobile data applications on a handheld device. The mobile data applications with the largest year-to-year increases among the 30-49 year old cohort include taking pictures (83% of 30-49 year old cell owners now do this, a 12-point increase from 2009); recording videos (39% do this, an 18-point increase from 2009); playing music (36% do this, a 15-point increase); using instant messaging (35% now do this, a 14-point increase); and accessing the internet (43% now do this, a 12-point increase compared with 2009). About the Survey This report is based on the findings of a daily tracking survey on Americans’ use of the Internet. The results in this report are based on data from telephone interviews conducted by Princeton Survey Research Associates International between April 29 and May 30, 2010, among a sample of 2,252 adults ages 18 and older, including 744 reached on a cell phone. Interviews were conducted in English. For results based on the total sample, one can say with 95% confidence that the error attributable to sampling and other random effects is plus or minus 2.4 percentage points. For results based cell phone owners (n=1,917), the margin of sampling error is plus or minus 2.7 percentage points. In addition to sampling error, question wording and practical difficulties in conducting telephone surveys may introduce some error or bias into the findings of opinion polls. page 5 Data about sending photos or videos to others using a cell phone and texting charitable donations are based on telephone interviews with a nationally representative sample of 1,009 adults living in the continental United States. Telephone interviews were conducted by landline (678) and cell phone (331, including 104 without a landline phone). The survey was conducted by Princeton Survey Research International (PSRAI). Interviews were done in English by Princeton Data Source from June 17-20, 2010. Statistical results are weighted to correct known demographic discrepancies. The margin of sampling error for the complete set of weighted data is Âą3.7 percentage points. page 6 Part One: The current state of wireless internet use As of May 2010, six in ten American adults (59%) are wireless internet users. Due to the quickly evolving nature of mobile technologies, our definition of a wireless internet user has changed several times since we began studying this topic; throughout this report, a wireless internet user is defined as someone who does one or more of the following: • Go online from a laptop using a wi-fi or mobile broadband internet connection. 86% of laptop owners go online in this way, which represents 47% of all American adults. • Use the internet, email or instant messaging from a cell phone. Half (49%) of cell phone owners do at least one of these on their mobile device, which works out to 40% of all adults. The 59% of American adults who do at least one of these activities represents an eight-point increase over the 51% of American adults who did so in our April 2009 wireless internet survey, and wireless access using both cell phones and laptops has grown significantly on a year-to-year basis.2 The remaining 41% of Americans includes those who are internet users but do not go online wirelessly (22%) as well as those who are not internet users (19%). Wireless internet use, 2009-2010 The % of all adults who do the following April 2009 39 51 47 Go online wirelessly with laptop May 2010 32 59 40 Go online wirelessly with cell phone Go online wirelessly from cell or laptop Source: Pew Research Center's Internet & American Life Project, April 29-May 30, 2010 Tracking Survey. N=2,252 adults 18 and older. Cell phone wireless users include those who use email on a cell phone; use the internet on a cell phone; or use instant messaging on a cell phone. 2 While our 2009 report on “Wireless Internet Use” found that 56% of Americans went online wirelessly, that figure included several access methods (such as using a wireless network with a desktop computer) that were not asked in this survey. The 51% number cited above represents only the proportion who went online wirelessly using a cell phone or laptop computer. Due to changes in question wording over time, 2009 is the only year with directly comparable data to our 2010 findings. page 7 Laptop computers and cell phones are the primary way Americans go online wirelessly. When we include other devices (such as mp3 players, e-book readers or tablet computers) in our definition of wireless internet usage, total usage increases by just one half of one percentage point. These other devices will be discussed individually in more detail in Part Three: Mobile access using laptops and other devices. This eight point year-to-year increase in wireless internet usage is reflected across a fairly broad range of demographic groups, with 18-29 year olds and those with a household income of less than $30,000 per year showing the greatest increases on a percentage point basis. Wireless internet usage remained flat for only a small number of groups, such as Latinos and those older than 50â€”although in contrast to older Americans, Latinos continue to have high overall rates of wireless adoption. In interpreting these figures, it is important to keep in mind that our survey did not provide a Spanish-language option so all data for Hispanics represents English-speaking Hispanics only.3 These higher rates of growth in wireless internet use by whites and African-Americans compared with Latinos are largely a function of laptop adoption. Rates of laptop ownership have grown dramatically among African-Americans in the last year (from 34% in 2009 to 51% in 2010) and moderately among whites (from 47% to 55%). By contrast, laptop ownership among English-speaking Latinos has remained flat over that time (54% of Latinos currently own a laptop computer, compared with 56% who did so in 2009). 3 Language proficiency has a strong association with technology useâ€”for more information on internet adoption and technology use among Latinos, see http://pewhispanic.org/reports/report.php?ReportID=119 page 8 page 9 Wireless internet users are evenly split between those who access the internet wirelessly using only one device (a total of 53% of wireless users go online using either a cell phone or a laptop, but not both) and those who do so using both a laptop and a mobile phone (47% of wireless users). Additionally, many wireless users take advantage of stationary technologies—70% of wireless internet users own a desktop computer, and 57% own a home gaming console such as an Xbox or PlayStation. The composition of the wireless population 59% of Americans go online wirelessly using a laptop or cell phone; this is how they access the mobile web Cell phone only 20% 47% Laptop only Cell phone and laptop 33% Source: Pew Research Center's Internet & American Life Project, April 29-May 30, 2010 Tracking Survey. N=2,252 adults 18 and older; n=1,238 based on wireless internet users. Cell phone wireless users include those who use email on a cell phone; use the internet on a cell phone; or use instant messaging on a cell phone. Several groups have relatively high rates of cell phone internet use. Some of these include: • African-Americans and Latinos – 18% of blacks and 16% of English-speaking Hispanics are cell-only wireless users, compared with 10% of whites. In total, roughly half of African-Americans (54%) and Hispanics (53%) go online from a mobile phone. • Young adults – 19% of 18-29 year olds are cell-only wireless users, compared with 13% of 30-49 year olds, 9% of 50-64 year olds and 5% of those ages 65 and older. In total, two-thirds of 18-29 year olds (65%) are cell phone internet users and 84% go online using either a cell phone or a laptop with a wireless internet connection. • Those with low levels of income and education – 17% of those earning less than $30,000 per year are cell-only wireless users, as are 20% of those who have not graduated from high school and 15% of those who have graduated high school but have not attended college. The affluent and well-educated have higher overall levels of wireless internet use due to their much higher rates of ownership and use of laptop computers. Seniors are currently the group with the lowest levels of wireless internet usage. Eight in ten seniors (those ages 65 and older) are either internet users who do not go online wirelessly (24%) or not online at all (56%). page 10 In the rest of this report, we will take a more detailed examination of wireless access using mobile phones (Part Two: Internet use and data applications using mobile phones) and laptop computers and other devices (Part Three: Mobile access using laptops and other devices). page 11 Part Two: Internet use and data applications using mobile phones The use of mobile data applications has grown dramatically over the last year, even as overall cell phone ownership has remained steady Eight in ten American adults (82%) currently own a cell phone of some kind, a figure that has remained fairly stable over the past year. Since a similar point in 2006, the proportion of Americans with a mobile phone has risen by nine percentage points. While overall mobile phone ownership has not grown over the last year, cell owners now take advantage of a much wider range of their phonesâ€™ capabilities. Compared to when we asked these questions in April 2009, mobile phone owners are significantly more likely to use their phones to take pictures (76% now do this, up from 66% in April 2009); send or receive text messages (72% vs. 65%); play games (34% vs. 27%); send or receive email (34% vs. 25%); access the internet (38% vs. 25%); play music (33% vs. 21%); send or receive instant messages (30% vs. 20%); and record a video (34% vs. 19%). The use of non-voice data applications has grown significantly over the last year The % of cell phone owners who use their phones to do the following 66 Take a picture 76 65 72 Send or receive text messages Play a game 27 34 Send or receive email 25 34 Access the internet Play music Send or receive instant messages Record a video Along with these eight activities, we also asked about seven additional cell phone data applications for the first time in our 2010 survey.4 Among all cell phone owners: • 54% have used their mobile device to send someone a photo or video • 23% have accessed a social networking site using their phone • 20% have used their phone to watch a video • 15% have posted a photo or video online • 11% have purchased a product using their phone • 11% have made a charitable donation by text message • 10% have used their mobile phone to access a status update service such as Twitter Young adults are much more likely than their elders to use mobile data applications, but cell phone access is becoming more prevalent among 30-49 year olds Picture-taking and texting are near-ubiquitous among young adult cell phone owners. Fully 95% of cellowning 18-29 year olds use the text messaging feature on their phones, and 93% use their mobile devices to take pictures. Since nine in ten young adults own a cell phone, that means that 85% of all 18-29 year olds text, and 83% take photos using a cell phone. Young adult cell phone owners are significantly more likely to do all of the other mobile data applications we asked about in our survey relative to older cell owners—often by fairly dramatic margins.5 4 Data about sending photos or videos to others and texting charitable donations were asked on a separate survey (see Methodology for more information) and are discussed individually in more detail later in this chapter. 5 For comparable data among teens, please see “Teens and Mobile Phones” (2010): http://pewinternet.org/Reports/2010/Teens-and-Mobile-Phones.aspx page 13 Although young adults are significantly more likely than all other age groups to use non-voice data applications on their mobile devices, these services are growing more popular among older adults (specifically, those ages 30-49). Compared with a similar point in 2009, cell owners ages 30-49 are significantly more likely to use their mobile phone to: â€˘ Take pictures (83% of cell owners ages 30-49 now do this, compared with 71% in April 2009) â€˘ Send or receive text messages (82% vs. 75%) page 14 • Access the internet (43% vs. 31%) • Record a video (39% vs. 21%) • Send or receive email (37% vs. 30%) • Play music (36% vs. 21%) • Send or receive instant messages (35% vs. 21%) Out of the eight mobile data activities we measured in both 2009 and 2010, playing games was the only one for which 30-49 year olds did not experience significant year-to-year growth—37% of cell owners ages 30-49 currently play games on a mobile phone, compared with the 32% who did so in 2009. Minority Americans continue to outpace whites in their use of cell phone data applications As we found in previous research on this topic,6 minority cell owners are significantly more likely than whites to use most non-voice data applications on their mobile devices. They also take advantage of a wider range of mobile phone features compared with whites. On average, white cell phone owners use 3.8 of the thirteen activities we measured, while black cell owners use an average of 5.4 and Englishspeaking Latinos use an average of 5.8 non-voice data applications. Additional mobile data applications â€“ sharing multimedia content and texting charitable donations In a separate survey, we asked about two additional mobile activitiesâ€”half of cell owners (54%) have used their mobile device to send a photo or video to someone else, and one in ten (11%) have made a charitable donation by text message. page 16 As with the other mobile data applications discussed above, both of these activities are particularly common among young cell owners and minority Americans (particularly Latinos). Fully 81% of cell owners ages 18-29 have used their phone to send a photo or video to someone else, significant higher the proportion of cell owners ages 30-49 (63%), 50-64 (40%) or 65+ (18%) who have done so. Young cell owners are also more likely than cell owners in other age groups to make a charitable donation using the text messaging feature on their phones (19% of cell owners ages 18-29 have done so, compared with 10% of 30-49 year olds, 8% of 50-64 year olds and just 4% of cell owners 65 and up). In terms of racial/ethnic comparisons, Latino cell phone owners are especially likely to do both of these activities using their mobile devices. Among cell owners, 70% of English-speaking Latinos have sent someone a photo or video (compared with 58% of African-Americans and 50% of whites) and 23% have made a charitable donation via text message (compared with 16% of African-Americans and 7% of whites). More than half of mobile web users go online from their phones on a daily basis In addition to being a growing proportion of the overall cell phone population, users of the mobile web now go online more frequently using their handheld devices than they did as recently as last year. More than half of all mobile internet users go online from their handheld devices on a daily basisâ€”43% do so several times a day, and 12% do so about once a day. At a similar point in 2009, just 24% of mobile internet users went online several times a day. More than half of cell phone internet users go online daily from their mobile device Frequency of cell phone internet use among those who go online from a cell phone (% of adult cell phone internet users) April 2009 43 39 37 25 24 12 Several times a day 15 12 About once a day 10 9 3-5 days a week 15 13 8 1-2 days a week Source: Pew Research Center's Internet & American Life Project, April 29-May 30, 2010 Tracking Survey. N=2,252 adults 18 and older; n=772 based on those who use a cell phone to access the internet. page 17 May 2010 September 2009 27 9 Every few weeks or less Among mobile internet users, frequency of use is highest among the affluent and well-educated, as well as Latinos. Among those who go online using a handheld device 55% of English-speaking Hispanics, 52% of college graduates and 56% of those with a household income of $75,000 or more per year use their cell phone to go online several times a day. Young adults are also intense mobile internet usersâ€”52% of those ages 18-29 who go online using a cell phone do so several times a day, and an additional 17% do so about once a dayâ€”although 43% of mobile web users ages 30-49 go online multiple times a day. page 18 Part Three: Mobile access using laptops and other devices Nearly as many Americans now own laptops as own desktops, and just under half of all adults use a laptop to go online wirelessly As of May 2010 55% of all American adults own a laptop computer. This is the first time since the Pew Internet Project began surveying laptop ownership that more than half of all adults own a laptop computer, and represents an eight percentage point increase since a similar point in 2009. Laptops are now nearly as common as desktop computers—62% of American adults now own a desktop computer, a figure that is relatively unchanged on a year-to-year basis and down slightly from the 68% of adults who owned a desktop computer in the spring of 2006. As we have found in previous research,7 18-29 year olds are one of the few groups more likely to own a laptop (70% of 18-29 year olds do so) than a desktop (61%), although 30-49 year olds are rapidly approaching that point as well (66% of 30-49 year olds own a desktop, compared with 63% who own a laptop computer). Desktop and laptop ownership, 2006-2010 The % of all adults who own a desktop or laptop computer 80% Desktop 60% Laptop 40% 20% 0% April 2006 Dec 2007 April 2008 April 2009 Sept 2009 Dec 2009 Jan 2010 May 2010 Source: Pew Research Center's Internet & American Life Project, April 29-May 30, 2010 Tracking Survey. N=2,252 adults 18 and older; n=1,238 based on wireless internet users. Cell phone wireless users include those who use email on a cell phone; use the internet on a cell phone; or use instant messaging on a cell phone. Not all laptop owners use their laptops to go online wirelessly, although the vast majority (86%) do so, using either a wi-fi or mobile broadband connection. That works out to 47% of all adults who use a lap7 See “Social Media and Young Adults” (2010), Part 2: http://pewinternet.org/Reports/2010/Social-Media-and-YoungAdults/Part-2/2-Computers.aspx?r=1 page 19 top to connect wirelessly to the internet. Both of these represent a statistically significant increase from what we found at a similar point in 2009. At that time, 82% of laptop owners (representing 39% of all adults) went online wirelessly using a laptop computer. Connecting via a wi-fi connection is by far the most common way laptop owners access the wireless internet. More than eight in ten laptop owners (84%) use wi-fi to go online, and one-quarter (23%) do so using mobile wireless broadband.8 There is some overlap between these two technologies, as around one in five laptop owners (22%) use both wi-fi and mobile wireless broadband to go online. Laptop ownership and mobile usage is most concentrated among the college educated, those younger than age 50 and those earning $50,000 or more per year. There are no major differences when it comes to race or ethnicityâ€”blacks and English-speaking Hispanics are just as likely as whites to own a laptop, and to access the internet on a laptop using a wireless connection. Notably, laptop ownership and usage among African Americans has grown significantly since 2009; half (51%) of all black adults now own a laptop computer, up from the 34% who said this in our April 2009 survey. 8 Note: because multiple responses were allowed, totals may sum to more than 100%. page 20 page 21 Most wireless laptop users go online from multiple locations Laptop owners utilize the portable nature and wireless capabilities of these devices to go online from a range of locations. Among those who use their laptop to go online wirelessly (using either a wi-fi or mobile broadband card) 86% do so at home, 37% do so at work, and 54% do so someplace other than home or work. Six in ten wireless laptop users (61%) go online from more than one of these locations, with two in five (20%) using their laptop to access the internet from all three locations (home, work and somewhere else). Overall, there are relatively few demographic differences among laptop owners when it comes to where they use their devices to access the internet. The primary differences relate to access at work. Among wireless laptop users: • 43% of those with some college experience go online using a laptop at work, compared with 22% of those with a high school degree or less. • 49% of those earning $75,000 or more per year go online using a laptop at work, compared with 30% of those earning less than $75,000 per year. • 41% of men go online using a laptop from work, compared with 32% of women. Mobile access using other devices Devices other than laptop computers and mobile phones also play into the wireless internet story, as 9% of American adults now go online using an mp3 player, e-book reader or tablet computer. However, these devices largely play a supporting role for Americans who already access the internet wirelessly using a laptop computer or cell phone. The addition of these devices to our wireless internet definition adds only one half of one percentage point to the overall wireless internet usage figure discussed above. Put another way, just 1% of Americans who do not go online wirelessly using a laptop computer or cell phone use some other type of mobile device to access the internet. By contrast, 15% of wireless internet users also use some other type of mobile device to go online in addition to a cell phone and/or wireless laptop. Mp3 players – Nearly half of all American adults (46%) own an mp3 player, and 16% of them use their handheld music players to go online. Not surprisingly, mp3 player ownership is strongly correlated with age: three-quarters (73%) of 18-29 year olds own this type of device, compared with 56% of 30-49 year olds, 33% of 50-64 year olds and just 7% of those ages 65 and older. Among mp3 player owners, men are slightly more likely than women to use their device to go online (19% vs. 14%), while internet use is also relatively high among 18-29 year olds (22% of mp3 owners in this age group use their player to access the internet). E-book readers – 4% of Americans own an e-book reader like a Kindle, and nearly half (46%) of these owners use their electronic book reader to access the internet. At the moment e-book readers are largely a luxury item owned primarily by the well-off and well-educated, as one in ten college graduates (9%) and 8% of those with an annual household income of $75,000 or more per year own an electronic book reader. The number of individuals in our survey who go online using e-book readers is too small for detailed demographic comparisons of internet use on this device. Game consoles – 42% of Americans own a game console like an Xbox or Play Station, and 29% of console owners use their gaming device to access the internet.9 Young adults are more likely than average 9 Note: we did not ask respondents to specify whether this internet access involved a wired or wireless network, so this page 22 to own a game console (62% of 18-29 year olds do so) as are parents (67%) and those ages 30-49 (56%). Although men and women are equally likely to own a gaming console, men are much more likely to use them to go online (38% of male console owners do so, compared with 20% of women). Additionally, nearly half of console owners ages 18-29 (45%) use their gaming to device to access the internet. Tablet computers â€“ This year for the first time we asked our respondents whether they owned a tablet PC such as an iPad, and 3% said that they do. Roughly six in ten of these individuals use their device to access the internet, although given the small number of tablet owners these findings are not reported in detail here. figure is not included in any of the wireless internet usage figures calculated in this report. page 23 Final Topline Spring Change Assessment Survey 2010 6/4/10 Data for April 29 – May 30, 2010 Princeton Survey Research Associates International for the Pew Research Center’s Internet & American Life Project Sample: n= 2,252 national adults, age 18 and older, including 744 cell phone interviews Interviewing dates: 04.29.10 – 05.30.10 Margin of error is plus or minus 2 percentage points for results based on Total [n=2,252] Margin of error is plus or minus 3 percentage points for results based on internet users [n=1,756] Margin of error is plus or minus 3 percentage points for results based on cell phone users [n=1,917] Q10 As I read the following list of items, please tell me if you happen to have each one, or not. Do you have… [INSERT ITEMS IN ORDER]? a. YES NO DON’T KNOW REFUSED Current 62 38 * * January 2010 59 58 62 64 65 65 68 41 42 37 36 34 35 32 0 * 0 * * * * * * * * ---- Current 55 45 * 0 January 2010 49 46 47 47 39 37 30 51 53 53 53 61 63 69 * * * * * * * A desktop computer December 2009 September 2009 April 2009 April 2008 Dec 2007 April 2006 b. A laptop computer or netbook1 December 2009 September 2009 April 2009 April 2008 Dec 2007 April 2006 1 Through January 2010, item wording was “A laptop computer [IF NECESSARY: includes a netbook].” Princeton Survey Research Associates International * * * * ---Q10 continued… 2 Q10 continued… Q10 As I read the following list of items, please tell me if you happen to have each one, or not. Do you have… [INSERT ITEMS IN ORDER]? c. YES NO DON’T KNOW REFUSED Current 82 18 * 0 January 20103 80 83 84 85 78 75 78 73 20 17 15 15 22 25 22 27 0 0 * * * * * * * * * * ----- 66 65 34 35 * * --- Current 4 96 * * September 2009 3 2 97 98 * * * * Current 46 54 * 0 September 2009 43 45 34 20 11 11 57 55 66 79 88 88 * * * * 1 1 A cell phone or a Blackberry or iPhone or other device that is also a cell phone2 December 2009 September 2009 April 2009 April 2008 Dec 2007 Sept 2007 April 2006 January 2005 4 November 23-30, 2004 d. An electronic book device or e-Book reader, such as a Kindle or Sony Digital Book April 2009 e. An iPod or other MP3 player5 April 2009 December 2007 April 2006 February 2005 January 2005 2 0 * ----Q10 continued… Prior to April 2009, item wording was “A cell phone.” From April 2009 thru December 2009, item wording was “A cell phone or a Blackberry or iPhone or other device that is also a cell phone.” Beginning December 2007, this item was not asked of the cell phone sample, but results shown here reflect Total combined Landline and cell phone sample. 3 In January 2010, item wording was “A cell phone or a Blackberry or iPhone or other handheld device that is also a cell phone.” 4 Through January 2005, question was not asked as part of a series. Question wording as follows: “Do you happen to have a cell phone, or not?” 5 Through February 2005, question was not asked as part of a series. Question wording as follows: “Do you have an iPod or other MP3 player that stores and plays music files, or do you not have one of these?” Princeton Survey Research Associates International 3 Q10 continued… Q10 As I read the following list of items, please tell me if you happen to have each one, or not. Do you have… [INSERT ITEMS IN ORDER]? f. YES NO DON’T KNOW REFUSED Current 42 58 * * September 2009 37 41 63 59 * * * * 3 97 * 0 A game console like Xbox or Play Station April 2009 g. A tablet computer like an iPad Current Q12 On your laptop computer or netbook, do you use [INSERT IN ORDER]?6 Based on internet users who have a laptop or netbook Mobile wireless broadband, such as an AirCard, to access the internet7 [IF NECESSARY: Wireless broadband is a longerrange wireless connection, offered by many telephone companies and others.] Q13 Thinking about when you access the internet wirelessly on your laptop or netbook – either using WiFi or mobile wireless broadband – do you ever do this [INSERT IN ORDER]? Based on internet users who use WiFi or mobile wireless broadband on their laptop or netbook 6 7 Prior to May 2010, question wording was “On your laptop computer, do you ever use [INSERT IN ORDER]?” Prior to January 2010, item wording was “Wireless broadband, such as an AirCard, to access the internet” Princeton Survey Research Associates International 4 a. YES NO DON’T KNOW REFUSED 86 13 1 0 91 9 * * Current 37 62 1 * September 2009 37 62 * * Current 54 46 * 0 September 2009 55 44 1 * At home Current [N=1,003] September 2009 [N=807] b. c. Q14 8 At work Someplace other than home or work Thinking now just about your cell phone… Please tell me if you ever use your cell phone to do any of the following things. Do you ever use your cell phone to [INSERT ITEMS; ALWAYS ASK a-b FIRST in order; RANDOMIZE c-h]?9 Based on cell phone users a. Current [N=1,917] January 2010 [N=1,891] December 2009 [N=1,919] September 2009 [N=1,868] April 2009 [N=1,818] December 2007 [N=1,704] b. January 2010 December 2009 September 2009 April 2009 December 2007 Take a picture Current d. NO DON’T KNOW REFUSED 34 30 29 27 25 19 66 70 70 73 75 81 0 0 * * * 0 0 0 * 0 0 -- 72 69 68 65 65 58 28 31 32 35 35 42 0 * * * * 0 0 0 0 0 0 -- 76 24 * * 33 27 21 17 67 73 79 83 0 0 * * 0 0 0 -- Send or receive text messages Current c. YES Send or receive email Play music Current September 2009 April 2009 December 2007 8 In September 2009, two separate series of questions were asked: one of internet users who use WiFi on their laptop [N=772] and one of internet users who use wireless broadband on their laptop [N=305]. Trend results shown here combine those two series for each item (home/work/other). 9 Prior to January 2010, question wording was “Please tell me if you ever use your cell phone or Blackberry or other device to do any of the following things. Do you ever use it to [INSERT ITEM]?” In January 2010, question wording was “Please tell me if you ever use your cell phone or Blackberry or other handheld device to do any of the following things. Do you ever use it to [INSERT ITEMS]?” For January 2010, December 2009, and September 2009, an answer category “Cell phone can’t do this” was available as a volunteered option; “No” percentages for those trends reflect combined “No” and “Cell phone can’t do this” results. Princeton Survey Research Associates International 5 e. Send or receive Instant Messages Current January 2010 December 2009 September 2009 April 2009 December 2007 f. Record a video Current April 2009 December 2007 30 29 31 27 20 17 69 70 68 72 79 83 1 1 1 1 * * 34 19 18 66 81 82 * 0 0 * 0 0 * * -0 0 -Q14 continued… Q14 continued… Q14 Thinking now just about your cell phone… Please tell me if you ever use your cell phone to do any of the following things. Do you ever use your cell phone to [INSERT ITEMS; ALWAYS ASK a-b FIRST in order; RANDOMIZE c-h]?10 Based on cell phone users g. Current April 2009 December 2007 h. Access the internet11 Current January 2010 December 2009 September 2009 April 2009 December 2007 WIRELESS YES NO DON’T KNOW REFUSED 34 27 27 66 73 73 * * 0 0 0 -- 38 34 32 29 25 19 62 66 67 71 74 81 0 0 * * * 0 0 0 0 0 * -- Play a game Wireless internet use12 WIRELESS INTERNET USER Current January 2010 December 2009 September 2009 April 2009 December 2008 59 53 55 54 56 43 INTERNET USER BUT NOT WIRELESS 22 24 24 25 23 30 ALL OTHERS 19 23 21 21 20 26 10 Prior to January 2010, question wording was “Please tell me if you ever use your cell phone or Blackberry or other device to do any of the following things. Do you ever use it to [INSERT ITEM]?” In January 2010, question wording was “Please tell me if you ever use your cell phone or Blackberry or other handheld device to do any of the following things. Do you ever use it to [INSERT ITEMS]?” For January 2010, December 2009, and September 2009, an answer category “Cell phone can’t do this” was available as a volunteered option; “No” percentages for those trends reflect combined “No” and “Cell phone can’t do this” results. 11 In December 2007, item wording was “Access the internet for news, weather, sports, or other information” 12 Definitions for wireless internet use may vary from survey to survey. Princeton Survey Research Associates International 6 November 2008 Q15 37 37 26 Using your cell phone, how often do you access the internet or email – several times a day, about once a day, 3-5 days a week, 1-2 days a week, every few weeks, less often or never? Based on those who use their cell phones to access the internet CURRENT % Q16 43 12 8 9 5 10 12 * * [n=779] Several times a day About once a day 3-5 days a week 1-2 days a week Every few weeks Less often Never Don’t know Refused SEPT 2009 APRIL 2009 37 15 9 13 7 11 7 * 0 [n=539] 24 12 10 15 12 14 13 0 0 [n=475] Thinking about other devices you own… Do you EVER access the internet or email using [INSERT IN ORDER]?13 YES NO DON’T KNOW REFUSED Current [N=97] 46 54 0 0 September 2009 [N=68] 35 63 2 0 April 2009 [N=44] 32 67 1 0 Current [N=929] 16 83 * 0 September 2009 [N=850] 15 85 * 0 April 2009 [N=846] 11 88 * 0 Current [N=815] 29 71 * 0 September 2009 [N=700] 23 77 * 0 April 2009 [N=742] 22 78 0 0 Item A: Based on e-Book users a. Your electronic Book device or e-Book Item B: Based on iPod or MP3 users b. An iPod or other MP3 player14 Item C: Based on game console users c. A game console like Xbox or Play Station15 Item D: Based on tablet computer users 13 September 2009 question wording was as follows: “Thinking about some of the electronic devices you have… Do you EVER access the internet using [INSERT IN ORDER]?” April 2009 question wording was as follows: “Thinking about these various devices… Do you EVER access the internet or email using [INSERT IN ORDER]? [If YES, ASK: Do you mostly do this at home, at work, or someplace other than home or work?].” Results for “Yes” reflect combined responses for “Mostly home,” “Mostly work,” “Mostly other,” and volunteered category “Combination of home/work/other.” 14 Through September 2009, item wording was “Your iPod or other MP3 player” 15 Through September 2009, item wording was “Your game console like Xbox or Play Station” Princeton Survey Research Associates International 7 d. A tablet computer like an iPad 59 Current [N=56] Q17 41 0 0 Do you ever use your cell phone toâ€Ś [INSERT ITEM; RANDOMIZE]? Based on those who use their cell phones to access the internet [N=779] YES, DO THIS NO, DO NOT DO THIS (VOL.) CELL PHONE CANâ€™T DO THIS DONâ€™T KNOW REFUSED a. Send a photo or video to someone 74 26 * 0 0 b. Post a photo or video online 31 68 1 0 0 c. Purchase a product, such as books, music, toys or clothing 22 78 * 0 0 d. Make a charitable donation by text message 10 89 0 * 0 e. Access a social networking site like MySpace, Facebook or LinkedIn.com 48 52 * * 0 f. Access Twitter or another service to share updates about yourself or to see updates about others 20 79 1 0 0 g. Watch a video 40 60 * 0 0 Methodology This report is based on the findings of a daily tracking survey on Americans' use of the Internet. The results in this report are based on data from telephone interviews conducted by Princeton Survey Research Associates International between April 29 and May 30, 2010, among a sample of 2,252 adults, age 18 and older. Interviews were conducted in English. For results based on the total sample, one can say with 95% confidence that the error attributable to sampling and other random effects is plus or minus 2.4 percentage points. For results based Internet users (n=1,756), the margin of sampling error is plus or minus 2.7 percentage points. In addition to sampling error, question wording and practical difficulties in conducting telephone surveys may introduce some error or bias into the findings of opinion polls. A combination of landline and cellular random digit dial (RDD) samples was used to represent all adults in the continental United States who have access to either a landline or cellular telephone. Both samples were provided by Survey Sampling International, LLC (SSI) according to PSRAI specifications. Numbers for the landline sample were selected with probabilities in proportion to their share of listed telephone households from active blocks (area code + exchange + two-digit block number) that contained three or more residential directory listings. The cellular sample was not list-assisted, but was drawn through a systematic sampling from dedicated wireless 100-blocks and shared service 100-blocks with no directory-listed landline numbers. New sample was released daily and was kept in the field for at least five days. The sample was released in replicates, which are representative subsamples of the larger population. This ensures that complete call procedures were followed for the entire sample. At least 7 attempts were made to complete an interview at a sampled telephone number. The calls were staggered over times of day and days of the week to maximize the chances of making contact with a potential respondent. Each number received at least one daytime call in an attempt to find someone available. For the landline sample, half of the time interviewers first asked to speak with the youngest adult male currently at home. If no male Princeton Survey Research Associates International 8 was at home at the time of the call, interviewers asked to speak with the youngest adult female. For the other half of the contacts interviewers first asked to speak with the youngest adult female currently at home. If no female was available, interviewers asked to speak with the youngest adult male at home. For the cellular sample, interviews were conducted with the person who answered the phone. Interviewers verified that the person was an adult and in a safe place before administering the survey. Cellular sample respondents were offered a post-paid cash incentive for their participation. All interviews completed on any given day were considered to be the final sample for that day. Non-response in telephone interviews produces some known biases in survey-derived estimates because participation tends to vary for different subgroups of the population, and these subgroups are likely to vary also on questions of substantive interest. In order to compensate for these known biases, the sample data are weighted in analysis. The demographic weighting parameters are derived from a special analysis of the most recently available Census Bureauâ€™s March 2009 Annual Social and Economic Supplement. This analysis produces population parameters for the demographic characteristics of adults age 18 or older. These parameters are then compared with the sample characteristics to construct sample weights. The weights are derived using an iterative technique that simultaneously balances the distribution of all weighting parameters. Princeton Survey Research Associates International 9 Following is the full disposition of all sampled telephone numbers: Table 1:Sample Disposition Landline 20,895 Cell 12,699 Total Numbers Dialed 1,160 982 12 8,886 1,675 8,180 39.1% 251 18 --4,906 176 7,348 57.9% Non-residential Computer/Fax Cell phone Other not working Additional projected not working Working numbers Working Rate The disposition reports all of the sampled telephone numbers ever dialed from the original telephone number samples. The response rate estimates the fraction of all eligible respondents in the sample that were ultimately interviewed. At PSRAI it is calculated by taking the product of three component rates: o o o Contact rate – the proportion of working numbers where a request for interview was made Cooperation rate – the proportion of contacted numbers where a consent for interview was at least initially obtained, versus those refused Completion rate – the proportion of initially cooperating and eligible interviews that were completed Thus the response rate for the landline sample was 21.8 percent. The response rate for the cellular sample was 19.3 percent.
Maajid Nawaz tracks down 'life-saver' after 25 years Published duration 18 September 2018 image copyright Quilliam image caption Maajid Nawaz as a teenager and today A political activist has tracked down an anonymous "hero" who was stabbed and beaten for defending him from a racist mob 25 years ago. Maajid Nawaz, a British-Pakistani born in Essex, was 15 when he was confronted by a group of skinheads armed with hammers and knives. A passer-by intervened but was attacked by the mob at a fair in Southend. Mr Nawaz, who is now a radio presenter for LBC, said he plans to meet up with the man on Thursday. The anti-extremism campaigner told the BBC: "I was on the verge of tears speaking to him. "He told me was a serving army officer at the time and was used to stepping in when he saw bad things happening all over the world, and he saw something wasn't right. "This is clearly a man used to doing he right thing out of a sense of duty." He said it led him to "segregate" himself from his "white friends" and when he was 16, Mr Nawaz joined the London-based Islamist group, Hizb ut-Tahri. He was imprisoned in Egypt for four years but released after being adopted by Amnesty International as a "prisoner of conscience". Mr Nawaz then renounced his extremist views and returned to the UK to launch a foundation to tackle extremism, Quilliam. The memory of the man who saved him played a key part in his transformation, he said. Mr Nawaz hopes to convince his "hero" to go public. "Everything this guy represents could help heal the divides in this country," he added.

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.