class: center, middle # Computing Conley Indices and Connection Matrices for Spaces of Braids .center[ ![:scale 50%](./images//ATDD2018.png) ] Shaun Harker Rutgers University Joint work with Kelly Spendlove and Konstantin Mischaikow --- # Abstract The Conley-Morse approach to dynamics considers a Morse graph -- the Hasse diagram of a flow-defined partial order of isolating neighborhoods -- labelled with an invariant called Conley index. Nontrivial Conley indices indicate non-empty invariant sets. Additional information, taking the form of a connection matrix, relates the Conley indices between isolating neighborhoods. We exhibit the Conley-Morse approach to dynamical systems, along with connection matrix theory, on a computational example due to Ghrist, Van Den Berg, and Vandervorst where one can prove solution forcing results for a class of parabolic PDEs by applying Conley-Morse theory to systems of disentangling braids. --- # Talk Outline 1. An example: Braid Spaces for Parabolic Partial Differential Equations 2. Homology 3. Lattices of Reachable Sets 4. Lattices of Representable Attracting Blocks 5. Conley-Morse Graphs 6. Connection Matrices 7. Computations --- class: center, middle # Part 1.  Consider the evolution of functions $u : \mathbb{Z} \to \mathbb{R}$ satisfying $$\frac{d u\_i}{dt} = f\_i (u\_{i-1}, u\_i, u\_{i+1}).$$ This is a _discrete parabolic differential equation_. We are interested in studying the behavior of period $P$ functions (i.e. $u_{i+P} = u_i$) which evolve according to this rule. Given knowledge of a few stationary solutions with periods that are integer multiples of $P$, we can make rigorous statements (i.e. prove _forcing theorems_) about the dynamics of this system. --- ## Braid Diagrams A complicated braid diagram with $P = 6$ with 3 stationary solutions, two of period $6$ and one with period $12$: .center[ ![:scale 50%](./images//6DBraidDiagram.png) (Example from Ghrist '06) ] --- ## Comparison Principle A relative braid diagram with $P = 2$ with 4 stationary solutions of period 2, with a _free strand_ $u$ pictured in yellow: .left-column[ ![:scale 130%](./images//2DBraidDiagram.png) (Example from Ghrist '06) ] .right-column[ * _Lap number_: # positive crossings * Idea: Parabolic PDEs are smoothing * Example: heat equation. * Hence, lap number never increases ] --- ## Relative Braid Complex .left-column[ ![:scale 130%](./images//2DBraidDiagram.png) (Figure from Ghrist '06) ] .right-column[.left[![:scale 130%](./images//2DRelativeBraidComplex.png)]] --- ## A Dynamical Theorem There _must_ be invariant dynamics inside of the yellow relative braid class, since it has the Conley index of a hyperbolic fixed point: .center[![](./images/2DYellowBraidClass.png)] --- ## Computing Lap Numbers for Domains Why stop there? .center[ ![:scale 70%](./images/2DRelativeBraidLapNumbers.png) ] --- ## Directed Graph Goal: Make a directed graph which has an edge between any two adjacent domains for which we cannot prove transversality on the closure of the codimension-1 wall between them. To this end, we: .right-column[ * Make edges both ways when lap numbers are the same * Make edges one way when lap number decreases * "Censor" the collapsed braids by connecting all surrounding domains in all ways ] .left-column[ ![:scale 150%](./images/2DRelativeBraidGraph.png) ] --- ## Morse Decompositions, Conley Index, and Connection Matrices There is an entire structure here. The machinery we explore in this talk will be * Morse Decompositions, * Conley Index, and * Connection Matrices. --- ## Morse Decomposition * Roughly speaking: make "black boxes" around all complicated dynamics * We give a partial order on the "black boxes" which respects the flow * Computationally, this corresponds to a strongly connected components calculation: .left-column[ ![:scale 110%](./images/2DStronglyConnectedComponents.png) ] .right-column[ ![:scale 80%](./images/2DMorseGraph.png) ] --- ## Conley Index * Each Morse graph node is associated to an _isolating neighborhood_. * We can construct a _Conley index pair_ for these isolating neighborhoods. * The rough idea is it is the isolating neighborhood modulo its exit set. * We can handle homology of pairs via "excision" (i.e. remove the exit set cells) * Thus, in our setting, Conley index pairs are just subcomplexes: .center[![:scale 50%](./images/2DIndexSubcomplexes.png)] --- ## Conley-Morse Graph .center[![:scale 80%](./images/2DConleyIndex.png)] --- ## Connection Matrix .center[![:scale 80%](./images/2DConnectionMatrixVisualization.png)] --- class: center, middle # Part 2. Homology .left[ * Cell Complexes * Cycles and Boundaries * Homology * Collapses * Homology via Sequences of Collapses * Generators via Reversing Sequence of Collapses ] --- ## Cell Complexes General idea: * Given: a finite set of cells $\mathcal{X}_k$ for dimensions $k = 0, 1, \cdots, d$. * Given: a _face relationship $<$ _ between $\mathcal{X}\_k$ and $\mathcal{X}\_{k+1}$ * Define: $\mathcal{C}\_k := 2^{\mathcal{X}\_k}$ is the set of _$k$-chains_, i.e. sets of $k$-cells. * Define: $ + : \mathcal{C}\_k \times \mathcal{C}\_k $ via _symmetric difference of sets_. * Define: For $\sigma \in \mathcal{X}\_k$ define $\partial\_k \\{\sigma\\} = \\{ \tau \in \mathcal{X}\_{k-1} : \tau < \sigma\\}$ * Define: Extend $\partial\_k$ to $\partial\_k : \mathcal{C}\_k \to \mathcal{C}\_{k-1}$ via linearity. * Requirement: $\partial\_{k} \circ \partial\_{k+1} = 0$. More generally we can axiomatize _chain complexes_ directly: * $\mathcal{C}\_k $ is a finite dimensional vector space over $\mathbb{F}\_2$ for $k = 0, 1, \cdots, d.$ * $\partial\_{k+1} : \; \mathcal{C}\_{k+1} \to \mathcal{C}\_k$ for $k = 0, 1, \cdots, d-1.$ * $\partial\_k \circ \partial\_{k+1} = 0 $ --- ![:scale 100%](./images/CellComplex1.png) **Definition.** Define $\partial\_{k+1}:\; \mathcal{C}\_{k+1} \to \, \mathcal{C}\_k$ to be the unique linear map satisfying $\partial\_{k+1} \\{\sigma\\} = (\text{boundary of }\sigma)$ for all $k = 0,1,\cdots,d-1$, and all $\sigma \in \mathcal{X}\_{k+1}$. --- ![:scale 100%](./images/CellComplex2.png) --- ## Cycles and Boundaries ![:scale 90%](./images/CyclesAndBoundaries.png) * Cycles are chains with zero boundary, i.e. $\partial c = 0$, $Z\_k = \text{ker }\partial_k$. * Boundaries are chains in the image of $\partial$, i.e. $B\_k = \text{im }\partial_{k+1}$. * The assumption that $\partial\_{k}\circ\partial\_{k+1} = 0$ is equivalent to the statement that all boundaries are cycles. (That's why this is the right algebraization of the idea.) --- ## Homology .left-column[![:scale 150%](./images/ChainDeformation.png)] .right-column[ * Cycles modulo Boundaries * Choose a minimal set of cycles (called _generators_) such that every cycle is the sum of generators and a boundary * The number of $k$-dimensional generators required is called the $k$th _Betti number_. * The list of Betti numbers is called the _Homology_. ] --- ## Collapses Given a cell complex, there is a way of making a _reduced complex_ that has the same homology. We do this via a _collapse_: .center[![:scale 50%](./images/SingleCollapse.png)] Procedure: * Pick any two cells $K$ and $Q$ such that $Q$ is a face of $K$. * Remove $K$ and $Q$ from the complex * For all $K'$ such that $Q$ was a face of $K'$, we add to the boundary of $K'$ the boundary of $K$. * The new complex has the same homology. * Moreover, there is a way to translate chains between the original complex and the reduced complex via so-called _chain equivalences_. --- ## Homology via Sequences of Collapses .center[![:scale 90%](./images/SequenceOfCollapses.png)] * Make sequence of collapses until no longer possible. * Then read off the Betti numbers by counting cells of each dimension. --- ## Generators via Reversing the Sequence of Collapses .center[![:scale 90%](./images/ReverseSequenceOfCollapses.png)] * To get generators we need to "lift" back to the original complex * The proof that a collapse yields a complex with the same homology gives us a pair of chain equivalences that allows us to do this * Note: the lifted generators are not uniquely defined, but depend on the sequence of collapses --- class: center, middle # Part 3. Lattices of Reachable Sets .left[ * Reachable Sets in Directed Graphs * Intersection and Union of Reachable Sets * Birkhoff's Representation Theorem * Strongly Connected Components ] --- ## Reachable Sets in Directed Graphs .center[![:scale 80%](./images/ReachableSets.png)] * A _reachable set_ $R$ is a collection of vertices in a directed graph which do not admit any out-edges outside of the collection, i.e. $R$ such that $u \to v$ and $u \in R$ implies $v \in R$. --- ## Intersection and Union of Reachable Sets .center[![:scale 80%](./images/ReachableSets.png)] * **Proposition.** The intersection of reachable sets is again a reachable set. * **Proposition.** The union of reachable sets is again a reachable set. * This means reachable sets have a finite distributive lattice structure. --- ## Birkhoff's Representation Theorem .center[![:scale 80%](./images/ReachableSets.png)] * Representing finite distribute lattices computationally is best not done directly. * It suffices to store a partially ordered set of "join-irreducible" lattice elements. * The lattice can be recovered as the down-sets of this poset, with meet and join being intersection and union of down-sets. --- ## Strongly Connected Components .center[ ![:scale 80%](./images/PosetOfStronglyConnectedComponents.png) ] * Strongly connected components (equivalence classes of vertices under the mutual-reachability relation) correspond to join-irreducible reachable sets. They are partially ordered by reachability. --- class: center, middle # Part 4. Lattices of Representable Attracting Blocks .left[ * Flows * Compact Global Attractor * Transversality Graph * Representable Sets * Attracting Blocks * Representable Attracting Blocks * Lattice of Representable Attracting Blocks * Reachable sets of Transversality Graphs Correspond to Attracting Blocks ] --- ## Flows .center[ ![:scale 50%](./images/Flow.png) (Figure from Wikipedia) ] * We restrict our attention to dynamical systems governed by flows on $\mathbb{R^n}$. * Flows express dynamics by telling us how a point in phase space moves as time progresses * A flow is a continuous function $\phi : X \times \mathbb{R} \to X$ such that * $\phi(\phi(x,t),s) = \phi(x,s+t)$ * $\phi(x, 0) = x$ * _Phase portraits_ are useful in conveying qualitative information about the flow by sketching flow lines. --- ## Compact Global Attractor .center[ ![:scale 50%](./images/CompactGlobalAttractor.png) (Figure not from Wikipedia) ] * We will also restrict our attention to cases where there is a _compact global attractor_. * This is ensured if there exists a compact set $N \subset \mathbb{R}^n$ such that for all $x \in \mathbb{R}^n$, there exists $T > 0$ such that $\phi(x,[T, \infty)) \subset N$. * In this case the global attractor is given by $A = Inv(N,f)$. --- ## Transversality Graph .center[![:scale 40%](./images/GlobalAttractorInCubicalComplex.png)] * Our setting consists of: * A flow on $\mathbb{R}^d$ with a global attractor interior to a bounded rectangle $R \subset \mathbb{R}^d$ * A decomposition of $R$ into a cubical complex In this setting, a _transversality graph_ is a directed graph on $d$-cells such that every edge $u \to v$ is between a pair of adjacent $d$-cells (in the sense that $u$ and $v$ share a $(d-1)$-dimensional face $w$), and for every pair of adjacent $d$-cells $u$ and $v$, there is an edge $u \to v$ unless the flow is transverse to $\text{cl }w$ in the direction from $v$ to $u$. --- ## Transversality Graph: Example .center[![:scale 60%](./images/2DRelativeBraidGraph.png)] --- ## Representable Sets .center[![:scale 50%](./images/RepresentableSet.png)] * A set is _representable_ if it can be written as a union of cells. --- ## Attracting Blocks .center[![:scale 50%](./images/AttractingBlock.png)] * A compact set $A$ is an _attracting block_ if $\phi(A,t) \subset \text{int }A$ for all $t > 0$. --- ## Representable Attracting Blocks .center[![:scale 50%](./images/RepresentableAttractingBlock.png)] * A _representable attracting block_ is a representable set that is also an attracting block. --- ## Lattice of Representable Attracting Blocks .left-column[![:scale 140%](./images/LatticeOfAttractingBlocks.png)] .right-column[ * **Proposition.** The intersection of attracting blocks is again an attracting block * **Proposition.** The union of attracting blocks is again an attracting block * Given a finite set of attracting blocks, we can grind out all possible unions and intersections * This gives a _finite distributive lattice_, with meet and join corresponding to intersection and union, respectively. ] --- ## Reachable sets of Transversality Graphs Correspond to Attracting Blocks .left-column[![:scale 90%](./images/TransversalityLattice.png)] .right-column[ * **Proposition.** Reachable sets of a transversality graph correspond to representable attracting blocks. * **Theorem:** Given a transversality graph, computing the poset of strongly connected components yields the Birkhoff representation of a lattice of representable attracting blocks for the underlying dynamical system. ] --- class: center, middle # Part 5. Conley-Morse Graph .left[ * Morse Graph * Attracting Block and Exit Block for a Morse Node * Isolating Neighborhoods and Conley Indices * Conley Index via Excision * Conley-Morse Graph ] --- ## Morse Graph .left-column[ ![:scale 100%](./images/2DMorseGraph.png) ] .right-column[ * The Hasse diagram of the poset $P$ of join-irreducible representable attracting blocks is called the _Morse Graph_. * Call the vertices of the poset $P$ _Morse nodes_. ] --- ## Attracting Block and Exit Block for a Morse Node .left-column[ ![:scale 90%](./images/MorseNodeAttractingBlock.png) ![:scale 90%](./images/MorseNodeExitBlock.png) ] .right-column[ * Denote by $N\_p$ the attracting block corresponding to a Morse node. Call this the _attracting block for the Morse node_. * **Proposition.** A join-irreducible element $p$ of a lattice $\mathcal{P}$ has a unique predecessor. * Denote by $L\_p$ the attracting block corresponding to the unique predecessor (in the lattice) of the Morse node. Call this the _exit block for the Morse node_. ] --- ## Isolating Neighborhoods and Conley Indices ![:scale 25%](./images/MorseNodeIsolatingNeighborhood.png) ![:scale 25%](./images/2DIndexSubcomplexes.png) For each Morse node $p \in P$, define: * _Combinatorial Morse Set_: $M\_p := \text{cl }(N\_p \setminus L\_p)$. * _Conley Index Pair_: $I\_p := (N\_p, L\_p)$. We have: * **Proposition.** Combinatorial Morse sets are isolating neighborhoods, i.e. $\text{Inv}(M\_p) \subset \text{int }M\_p$. * **Proposition.** The collection $\text{Inv}(M\_p)$ partialled order via $P$ is a _Morse Decomposition_ of the dynamical system. * **Proposition.** $I\_p$ is a Conley Index pair for $M\_p$ --- # Conley Index via Excision .right-column[![:scale 90%](./images/2DIndexSubcomplexes.png)] .left-column[ To compute $H\_*(N\_p, L\_p)$: * Consider $N\_p \setminus L\_p$. * This gives an _index subcomplex_ * Compute homology of each index subcomplex ] --- ## Conley-Morse Graph .center[ ![:scale 70%](./images/2DConleyIndex.png) ] Annotating each node of the Morse Graph with $H\_*(N\_p, L\_p)$ results in a _Conley-Morse Graph_. --- .left-column[ ![:scale 180%](./images/ConleyIndexInterpretation.png) ] .right-column[ .right[ ## Interpreting the Conley Index Occam's razor approach to Conley Index: What is the simplest dynamics giving rise to this index? This gives us rough intuition as to what is going on. ] ] --- class: center, middle # Part 6. Connection Matrix .left[ * Connection Matrix Overview * Visualizing the Connection Matrix ] --- ## Connection Matrix Overview .left-column[.center[![:scale 50%](./images/2DConleyMorseGraph.png)]] .right-column[.left[ * How do the Conley Indices of Morse nodes relate? * Strategy: collapse complex under rule not to collapse pairs in different index subcomplexes * The boundary map of the resulting complex is called a _connection matrix_. * It gives the relationship we sought * We can lift chains from the reduced complex to the original to visualize it ]] --- ## Visualizing the Connection Matrix .center[![:scale 80%](./images/2DConnectionMatrixVisualization.png)] --- class: center, middle # Part 7. Computation .left[ * 2D Braids Example, Lap Number Computation * 2D Braids Example * 3D Braids Example * Visualizing Connection Matrix in 3D Braids Example ] --- .scroll-box[ ## 2D Braids Example, Lap Number Computation * We can compute a lap number for each domain on a computer: ```python from Braids import * diagram = BraidDiagram([ [1,3,1], [2,1,2], [3,4,3],[4,2,4]]) ``` We can ask it to draw a picture of the diagram: ```python diagram ``` ![png](./images/2DCodeBraidDiagram.png) First we compute the complex: ```python braid_complex, braid_graph = BraidComplex(diagram) ``` Next, we extract a list of 2-cells (domains) from the complex: ```python domains = [ cell for cell in braid_complex if cell.dimension() == 2 ] ``` Now loop through each domain and call a `lap` function which the `BraidDiagram` class supports: ```python lap_numbers = [] for cell in domains: lap_numbers.append(str(cell) + "\t\t" + str(diagram.lap(cell))) ``` Now sort the answers (to get them in a nice order) and print them out line by line: ```python print('\n'.join(sorted(lap_numbers))) ``` ```python (-inf,1)x(-inf,1) 0 (-inf,1)x(1,2) 1 (-inf,1)x(2,3) 2 (-inf,1)x(3,4) 3 (-inf,1)x(4,inf) 4 (1,2)x(-inf,1) 1 (1,2)x(1,2) 2 (1,2)x(2,3) 3 (1,2)x(3,4) 2 (1,2)x(4,inf) 3 (2,3)x(-inf,1) 2 (2,3)x(1,2) 1 (2,3)x(2,3) 2 (2,3)x(3,4) 1 (2,3)x(4,inf) 2 (3,4)x(-inf,1) 3 (3,4)x(1,2) 2 (3,4)x(2,3) 3 (3,4)x(3,4) 2 (3,4)x(4,inf) 1 (4,inf)x(-inf,1) 4 (4,inf)x(1,2) 3 (4,inf)x(2,3) 2 (4,inf)x(3,4) 1 (4,inf)x(4,inf) 0 ``` ] --- .scroll-box[ ## 2D Braids Example ```python from Braids import * from ConleyMorseFibration import * diagram = BraidDiagram([ [1,3,1], [2,1,2], [3,4,3],[4,2,4]]) braid_complex, braid_graph = BraidComplex(diagram) fibration = ConleyMorseFibration(braid_complex, braid_graph) fibration ``` ![:scale 25%](./images/2DConleyMorseFibration1.svg) ```python from ConnectionFibration import * connection_fibration, (phi, psi) = ConnectionFibration(fibration) connection_fibration ``` ![:scale 25%](./images/2DConleyMorseFibration2.svg) ```python bd = lambda cell : connection_fibration.complex().boundary(cell) C = connection_fibration.complex().cells() print("Connection Matrix Data") print("======================") for d in [2,1,0]: print(" Boundaries of " + str(d) + "-cells in Connection Fibration:") print(" " + str({ c : bd(c) for c in C if c.dimension() == d})) ``` ```python Connection Matrix Data ====================== Boundaries of 2-cells in Connection Fibration: {} Boundaries of 1-cells in Connection Fibration: {((2, 3), (3, 3)): (1)*[{-inf}x{inf}]+(-1)*[{4}x{1}]} Boundaries of 0-cells in Connection Fibration: {((4, 4), (1, 1)): 0, ((-inf, -inf), (inf, inf)): 0} ``` ] --- .scroll-box[ ## 3D Braids Example ```python from Braids import * from ConleyMorseFibration import * from ConnectionFibration import * diagram = BraidDiagram([ [1,4,1,4], [2,2,2,2], [3,3,3,3], [4,1,4,1]]) diagram ``` ![png](./images/3DConleyMorseFibration1.png) ```python (complex, discrete_flow) = BraidComplex(diagram) fibration = ConleyMorseFibration(complex, discrete_flow) fibration ``` ![:scale 90%](./images/3DConleyMorseFibration2.svg) ```python connection_fibration, (phi,psi) = ConnectionFibration(fibration) connection_fibration ``` ![:scale 90%](./images/3DConleyMorseFibration3.svg) ## Accessing the connection matrix data To see that what we have computed is more than a Conley-Morse graph we compute the connection matrix entries: ```python bd = lambda cell : connection_fibration.complex().boundary(cell) C = connection_fibration.complex().cells() print("Connection Matrix Data") print("======================") for d in [2,1,0]: print(" Boundaries of " + str(d) + "-cells in Connection Fibration:") print(" " + str({ c : bd(c) for c in C if c.dimension() == d})) ``` ```python Connection Matrix Data ====================== Boundaries of 2-cells in Connection Fibration: {((2, 2), (1, 2), (2, 3)): (1)*[(2,3)x{3}x{2}]} Boundaries of 1-cells in Connection Fibration: {((2, 3), (3, 3), (2, 2)): 0} Boundaries of 0-cells in Connection Fibration: {((1, 1), (2, 2), (3, 3)): 0} ``` ## Lifting the generators back to the original complex The cells in the connection fibration correspond directly to original cells in the complex. However, we can also lift these cells back up to the original complex through the sequence of chain equivalences provided by the sequence of strict equivalencies. This corresponds to Franzosa's chain complex braid morphism. ```python print('\n\n'.join([ "psi(" + str(ElementaryChain(c)) + ") = " + str(psi(ElementaryChain(c))) for c in C])) ``` ```python psi((1)*[{1}x{2}x{3}]) = (1)*[{1}x{2}x{3}] psi((1)*[{2}x(1,2)x(2,3)]) = (1)*[(2,3)x{1}x(2,3)]+(1)*[{2}x(1,2)x(2,3)]+(1)*[(2,3)x(1,2)x{3}]+(-1)*[(2,3)x(1,2)x{2}]+(1)*[{3}x(1,2)x(2,3)]+(-1)*[{2}x(2,3)x(2,3)]+(-1)*[(2,3)x(2,3)x{2}] psi((1)*[(2,3)x{3}x{2}]) = (1)*[(2,3)x{3}x{2}]+(1)*[{2}x{3}x(2,3)]+(-1)*[{2}x(2,3)x{3}]+(-1)*[{3}x{2}x(2,3)]+(1)*[(2,3)x{2}x{3}]+(1)*[{3}x(2,3)x{2}] ``` ```python from CubicalVisualizer import * original_complex_cells = [ cell for critical in C for cell in psi(ElementaryChain(critical))] CubicalVisualizer(original_complex_cells) ``` ] --- ## Visualizing Connection Matrix in 3D Braids Example ![:scale 100%](./images/3DCubicalVisualizer.png) --- class: center, middle ## Thank you


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SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, $ LDZ, J1, INFO ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL WANTQ, WANTZ INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, N * .. * .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), $ Z( LDZ, * ) * .. * * Purpose * ======= * * CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) * in an upper triangular matrix pair (A, B) by an unitary equivalence * transformation. * * (A, B) must be in generalized Schur canonical form, that is, A and * B are both upper triangular. * * Optionally, the matrices Q and Z of generalized Schur vectors are * updated. * * Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' * Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' * * * Arguments * ========= * * WANTQ (input) LOGICAL * .TRUE. : update the left transformation matrix Q; * .FALSE.: do not update Q. * * WANTZ (input) LOGICAL * .TRUE. : update the right transformation matrix Z; * .FALSE.: do not update Z. * * N (input) INTEGER * The order of the matrices A and B. N >= 0. * * A (input/output) COMPLEX arrays, dimensions (LDA,N) * On entry, the matrix A in the pair (A, B). * On exit, the updated matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * B (input/output) COMPLEX arrays, dimensions (LDB,N) * On entry, the matrix B in the pair (A, B). * On exit, the updated matrix B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * Q (input/output) COMPLEX array, dimension (LDZ,N) * If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, * the updated matrix Q. * Not referenced if WANTQ = .FALSE.. * * LDQ (input) INTEGER * The leading dimension of the array Q. LDQ >= 1; * If WANTQ = .TRUE., LDQ >= N. * * Z (input/output) COMPLEX array, dimension (LDZ,N) * If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, * the updated matrix Z. * Not referenced if WANTZ = .FALSE.. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1; * If WANTZ = .TRUE., LDZ >= N. * * J1 (input) INTEGER * The index to the first block (A11, B11). * * INFO (output) INTEGER * =0: Successful exit. * =1: The transformed matrix pair (A, B) would be too far * from generalized Schur form; the problem is ill- * conditioned. * * * Further Details * =============== * * Based on contributions by * Bo Kagstrom and Peter Poromaa, Department of Computing Science, * Umea University, S-901 87 Umea, Sweden. * * In the current code both weak and strong stability tests are * performed. The user can omit the strong stability test by changing * the internal logical parameter WANDS to .FALSE.. See ref. [2] for * details. * * [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the * Generalized Real Schur Form of a Regular Matrix Pair (A, B), in * M.S. Moonen et al (eds), Linear Algebra for Large Scale and * Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. * * [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified * Eigenvalues of a Regular Matrix Pair (A, B) and Condition * Estimation: Theory, Algorithms and Software, Report UMINF-94.04, * Department of Computing Science, Umea University, S-901 87 Umea, * Sweden, 1994. Also as LAPACK Working Note 87. To appear in * Numerical Algorithms, 1996. * * ===================================================================== * * .. Parameters .. COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), $ CONE = ( 1.0E+0, 0.0E+0 ) ) REAL TEN PARAMETER ( TEN = 10.0E+0 ) INTEGER LDST PARAMETER ( LDST = 2 ) LOGICAL WANDS PARAMETER ( WANDS = .TRUE. ) * .. * .. Local Scalars .. LOGICAL STRONG, WEAK INTEGER I, M REAL CQ, CZ, EPS, SA, SB, SCALE, SMLNUM, SS, SUM, $ THRESH, WS COMPLEX CDUM, F, G, SQ, SZ * .. * .. Local Arrays .. COMPLEX S( LDST, LDST ), T( LDST, LDST ), WORK( 8 ) * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL CLACPY, CLARTG, CLASSQ, CROT * .. * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, MAX, REAL, SQRT * .. * .. Executable Statements .. * INFO = 0 * * Quick return if possible * IF( N.LE.1 ) $ RETURN * M = LDST WEAK = .FALSE. STRONG = .FALSE. * * Make a local copy of selected block in (A, B) * CALL CLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST ) CALL CLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST ) * * Compute the threshold for testing the acceptance of swapping. * EPS = SLAMCH( 'P' ) SMLNUM = SLAMCH( 'S' ) / EPS SCALE = REAL( CZERO ) SUM = REAL( CONE ) CALL CLACPY( 'Full', M, M, S, LDST, WORK, M ) CALL CLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M ) CALL CLASSQ( 2*M*M, WORK, 1, SCALE, SUM ) SA = SCALE*SQRT( SUM ) THRESH = MAX( TEN*EPS*SA, SMLNUM ) * * Compute unitary QL and RQ that swap 1-by-1 and 1-by-1 blocks * using Givens rotations and perform the swap tentatively. * F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 ) G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 ) SA = ABS( S( 2, 2 ) ) SB = ABS( T( 2, 2 ) ) CALL CLARTG( G, F, CZ, SZ, CDUM ) SZ = -SZ CALL CROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, CZ, CONJG( SZ ) ) CALL CROT( 2, T( 1, 1 ), 1, T( 1, 2 ), 1, CZ, CONJG( SZ ) ) IF( SA.GE.SB ) THEN CALL CLARTG( S( 1, 1 ), S( 2, 1 ), CQ, SQ, CDUM ) ELSE CALL CLARTG( T( 1, 1 ), T( 2, 1 ), CQ, SQ, CDUM ) END IF CALL CROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, CQ, SQ ) CALL CROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, CQ, SQ ) * * Weak stability test: |S21| + |T21| <= O(EPS F-norm((S, T))) * WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) ) WEAK = WS.LE.THRESH IF( .NOT.WEAK ) $ GO TO 20 * IF( WANDS ) THEN * * Strong stability test: * F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A, B))) * CALL CLACPY( 'Full', M, M, S, LDST, WORK, M ) CALL CLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M ) CALL CROT( 2, WORK, 1, WORK( 3 ), 1, CZ, -CONJG( SZ ) ) CALL CROT( 2, WORK( 5 ), 1, WORK( 7 ), 1, CZ, -CONJG( SZ ) ) CALL CROT( 2, WORK, 2, WORK( 2 ), 2, CQ, -SQ ) CALL CROT( 2, WORK( 5 ), 2, WORK( 6 ), 2, CQ, -SQ ) DO 10 I = 1, 2 WORK( I ) = WORK( I ) - A( J1+I-1, J1 ) WORK( I+2 ) = WORK( I+2 ) - A( J1+I-1, J1+1 ) WORK( I+4 ) = WORK( I+4 ) - B( J1+I-1, J1 ) WORK( I+6 ) = WORK( I+6 ) - B( J1+I-1, J1+1 ) 10 CONTINUE SCALE = REAL( CZERO ) SUM = REAL( CONE ) CALL CLASSQ( 2*M*M, WORK, 1, SCALE, SUM ) SS = SCALE*SQRT( SUM ) STRONG = SS.LE.THRESH IF( .NOT.STRONG ) $ GO TO 20 END IF * * If the swap is accepted ("weakly" and "strongly"), apply the * equivalence transformations to the original matrix pair (A,B) * CALL CROT( J1+1, A( 1, J1 ), 1, A( 1, J1+1 ), 1, CZ, CONJG( SZ ) ) CALL CROT( J1+1, B( 1, J1 ), 1, B( 1, J1+1 ), 1, CZ, CONJG( SZ ) ) CALL CROT( N-J1+1, A( J1, J1 ), LDA, A( J1+1, J1 ), LDA, CQ, SQ ) CALL CROT( N-J1+1, B( J1, J1 ), LDB, B( J1+1, J1 ), LDB, CQ, SQ ) * * Set N1 by N2 (2,1) blocks to 0 * A( J1+1, J1 ) = CZERO B( J1+1, J1 ) = CZERO * * Accumulate transformations into Q and Z if requested. * IF( WANTZ ) $ CALL CROT( N, Z( 1, J1 ), 1, Z( 1, J1+1 ), 1, CZ, CONJG( SZ ) ) IF( WANTQ ) $ CALL CROT( N, Q( 1, J1 ), 1, Q( 1, J1+1 ), 1, CQ, CONJG( SQ ) ) * * Exit with INFO = 0 if swap was successfully performed. * RETURN * * Exit with INFO = 1 if swap was rejected. * 20 CONTINUE INFO = 1 RETURN * * End of CTGEX2 * END


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‘We fought for result,’ says Jürgen Klopp after win against Crystal Palace – video
by SNTVJürgen Klopp said Liverpool were ‘ready to fight for the result’ after his Premier League leaders escaped Crystal Palace with a dramatic 2-1 victory on Saturday. 'Could we have played better? Yes. We are not out there to break records. We are out there to get the best result over the full season,' Klopp said.


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greetings-route
Index
EIP
Tested
Time (ms)
Properties
0
from
10
{uri=direct:greetings}
24
setBody
1
{constant=Hello from Cloud Cuckoo Camel Land!}
25
to
5
{uri=file:target/output}


2 Thessalonians 2:11
And for this cause God shall send them strong delusion, that they should believe a lie:


there is nothing here yet. I barely configured the server.
while we develop this puppy, why don't you watch FGSquared stream some games?


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Instructions: c = clear screen t = save as training data s = push training data to server g = get training data from server


GOD'S ARMY (PG)
Written, Produced, & Directed by Richard Dutcher Originally Released: March 10, 2000
Reviewed by E. Benjamin Kelsey
* * ½ (out of four)
Jehovah Witnesses' notoriety as the Avon Ladies of religion, ever-ready to knock on your door and offer up a magazine chock full of things you definitely need, has been the source of many jokes on television and in movies for years. Less often, though sometimes more mean-spiritedly, the same has been done about the other door-to-door salesmen of faith, the LDS - aka Mormon - missionaries.
Now writer/producer/director Richard Dutcher is serving his own mission - to change the stereotype of Mormon missionaries, and Mormonism in general, by giving us a movie from their point of view. No, not a documentary or a church promotional video, but an actual movie, in theaters, popcorn and all.
Such a feat may sound like a pet project for any steadfast believer who's used to seeing the extent of Mormon cinema as ORGAZMO and Mormon-filmmaker Neil LaBute's anything-but-religious films, IN THE COMPANY OF MEN and YOUR FRIENDS & NEIGHBORS. But instead of jumping on an immediate soapbox and creating a purely self-serving and self-redeeming film, Dutcher has produced GOD'S ARMY, a surprisingly intimate yet humble film that remains as objective as possible, coming from the eyes, mind, words, and heart of a true believer.
GOD'S ARMY tells the story of Elder Brandon Allen (Matthew Brown), a young man just arrived from Kansas to serve a mission in Los Angeles for the LDS church. "You're not in Kansas anymore, Elder," a welcoming missionary greets him. Trite, but true, something any one of us might have said in the same situation. One day in L.A. definitely holds a whirlwind of experiences for a naive 19-year-old.
Immediately, Elder Allen is introduced to his new companion, Elder Dalton. At the ripe old age of 29, Elder Dalton (played by Dutcher) is the oldest serving missionary in the district, someone the lot of 19 and 20 year old missionaries affectionately refer to as "Pops". As we quickly learn, Pops is the stalwart missionary, eager to get the job done, no questions asked. In fact, even as Elder Allen carries his luggage back to an apartment he's yet to see but will be living in for some considerable time, Pops is stopping and knocking on doors, asking anyone who'll give him the chance if they'd like to hear a brief message.
It's all a bit overwhelming for Elder Allen, who's internally dealing with the issues of a family falling apart back home - a mother who's asked for her name to be taken off the records of the Church, a stepfather about to go to prison. The culture shock - not of being thrust into L.A. from a dinko town in eastern Kansas, but of suddenly being a messenger who lives, sleeps, and breaths religion - is more than a bit jarring. Awestruck by Pops' ability to assert himself towards complete strangers at their own homes, Elder Allen responds, "I could never do that." Without flinching, the no-nonsense Pops tells him, "Yes, you can. You get the next one."
The first day on the job seems too much for Elder Allen, and that night, he finds himself in a bus station, ready to forget the mission and serve his own well-being. Some reverse psychology from Elder Dalton brings him back, but the battle for self-conviction is already underway.
GOD'S ARMY isn't so much about missionary work as it is about attaining a testimony of personal convictions one's never been forced to question before. That being the underlying theme, it's a bit disappointing that the message comes off so wearily in the end. It seems Dutcher wanted to touch base on every key belief, misconception, and stereotype the Mormon church carries, an effort all too time consuming to leave room for character development. Even if Dutcher's overall motive was only to give America a glimpse of what Mormonism is truly about, doing this by way of character study would only have accentuated his cause.
For example, far too often than not, Dutcher puts all emphasis on the events surrounding the missionaries, rather than on how these events are affecting them. The elements of storyline and character are kept too far separated, the focus constantly switching between them. While Dutcher engages himself in a checklist of things Mormons might face while serving a mission, characters are allowed to become subscripts to subplots - and underdeveloped ones at that.
Ironically, it is within these weaker alleys that the most powerful material is awaiting realization. In particular, what could be the most promising aspect of the film concerns a fellow missionary's vehement interest in anti-Mormon literature. Michael Buster undeniably gives the strongest and most professional performance of the group as Elder Kinegar, a missionary whose faith is crumbling under the weight of constantly fueled doubt. What could've served as the film's most poignant device for both believers and non-believers is suppressed so as not to intrude on the above said checklist.
Often, too much leeway is given to tick off the "this and that"'s that should, could, and would only work had they been combined with an examination of a young man's psychology. Instead of demonstrating how Elder Allen views the events on his mission, Dutcher seems assured that merely presenting the two in the same scene will allow the audience to "figure it out", leaving us to guess and internally decide how the young man is being affected.
Still, Dutcher must be applauded for his objectiveness. With a subject as touchy as religion, making a film about your own faith is perhaps the riskiest venture one could take. Seeming presumptuous, even pompous, could be a near guarantee in the hands of a relatively inexperienced filmmaker/screenwriter who's examining their own beliefs. GOD'S ARMY isn't 100% success in that department. A miracle healing in the film is sure to seem highly brazen to some non-Mormons. Yet, at the same time, Dutcher willingly and unbiasedly brings up attributes of the religion that have remained highly controversial and repellent to outsiders for years. And non-Mormons are never presented as wayward souls in need of salvation only Mormons can provide.  And with that, the scene ends. Dutcher doesn't give his valiant Mormon a brilliant explanation to reply with. The conversation is over. The non-Mormon finishes on top. It's a sincerely appreciated gesture.
On the plus side for believers, in a relative way, Dutcher uses his discreet abilities to delicately debunk several untruths often associated with the Church. The fact that Mormons are Christians who read the Bible is humbly clarified during a scene of scripture study. The fact that Mormon missionaries are not paid for their two years of service is confirmed during a modest "get-to-know-you" conversation between Elder Allen and Elder Dalton. Whether the script is on the defense or offense for Mormon beliefs, Dutcher is careful not to paint the Church through bias eyes that forgive and forget any "flaws" the faith may have.
In the acting department, Matthew Brown shows a definite competency for portraying the timid observer; an unsettled outsider who must be thinking a great deal more than they are saying. While Brown is meant to be the main star, the center of the film, if one can be had, is definitely Dutcher's Elder Dalton. He's the mentor, the example, the teacher. In this role, Dutcher does fairly well, but his character seems a bit too impassioned despite his tenacity. It's the smaller actors who outshine the leads hands down when given the chance. The aforementioned Buster, DeSean Terry, and even the nearly missed Jeff Kelly are all impressive as fellow missionaries, and luckily, Dutcher has given the first two semi-substantial parts. The one overall flaw among the actors - not one of them can pass a convincing laugh to save their soul.
All in all, GOD'S ARMY may work best as a curiosity piece. The target audience is unclear. If it's Mormons, there are plenty of moments where identifiableness becomes monotony of things they already know. If it's non-Mormons, there is plenty of humor Dutcher probably doesn't even expect them to get. Yet for all the moments he leaves the non-believers on the back burner, its obvious he's trying his best to appear genuine to both sides, no matter what the scene. Either audience should at least find a buzzing curiousity as to how the LDS faith is first being presented onscreen (in a serious manner). And both audiences may come away a bit surprised, even pleased, with the results.
March 10, 2000
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{{hasChild? 'Destroy' : 'Create'}} child component by clicking below button and observe console log. It will log each lifecycle hooks when they called.


--- layout: home ---
Fast and easy to use Java <> JSON library.
Genson API is designed to be easy to use, it handles for you all the databinding stuff, streaming, etc.
Highly modular architecture and configurable via the GensonBuilder.
Full support of generic types, polymorphic types and immutable objects that don't provide a default constructor.


DOMDocument
has a doctype
attribute whose value is either null
or a DOMDocumentType
object.
More...
Public Member Functions | |
Destructor | |
| virtual | ~DOMDocumentType () |
| Destructor. | |
Functions introduced in DOM Level 1 | |
| virtual const XMLCh * | getName () const =0 |
The name of DTD; i.e., the name immediately following the DOCTYPE keyword. | |
| virtual DOMNamedNodeMap * | getEntities () const =0 |
A DOMNamedNodeMap containing the general entities, both external and internal, declared in the DTD. | |
| virtual DOMNamedNodeMap * | getNotations () const =0 |
A DOMNamedNodeMap containing the notations declared in the DTD. | |
Functions introduced in DOM Level 2. | |
| virtual const XMLCh * | getPublicId () const =0 |
| Get the public identifier of the external subset. | |
| virtual const XMLCh * | getSystemId () const =0 |
| Get the system identifier of the external subset. | |
| virtual const XMLCh * | getInternalSubset () const =0 |
The internal subset as a string, or null if there is none. | |
Protected Member Functions | |
Hidden constructors | |
| DOMDocumentType () |
DOMDocument
has a doctype
attribute whose value is either null
or a DOMDocumentType
object.
The DOMDocumentType
interface in the DOM Core provides an interface to the list of entities that are defined for the document, and little else because the effect of namespaces and the various XML schema efforts on DTD representation are not clearly understood as of this writing.
The DOM Level 2 doesn't support editing DOMDocumentType
nodes.
See also the Document Object Model (DOM) Level 2 Core Specification.
| DOMDocumentType::DOMDocumentType | ( | ) | [protected] |
| virtual DOMDocumentType::~DOMDocumentType | ( | ) | [virtual] |
Destructor.
| virtual const XMLCh* DOMDocumentType::getName | ( | ) | const [pure virtual] |
The name of DTD; i.e., the name immediately following the DOCTYPE
keyword.
| virtual DOMNamedNodeMap* DOMDocumentType::getEntities | ( | ) | const [pure virtual] |
A DOMNamedNodeMap
containing the general entities, both external and internal, declared in the DTD.
Parameter entities are not contained. Duplicates are discarded. For example in: <!DOCTYPE
the interface provides access to
ex SYSTEM "ex.dtd" [ <!ENTITY foo "foo"> <!ENTITY bar
"bar"> <!ENTITY bar "bar2"> <!ENTITY % baz "baz">
]> <ex/>
foo
and the first declaration of bar
but not the second declaration of bar
or baz
. Every node in this map also implements the DOMEntity
interface.
The DOM Level 2 does not support editing entities, therefore entities
cannot be altered in any way.
| virtual DOMNamedNodeMap* DOMDocumentType::getNotations | ( | ) | const [pure virtual] |
A DOMNamedNodeMap
containing the notations declared in the DTD.
Duplicates are discarded. Every node in this map also implements the DOMNotation
interface.
The DOM Level 2 does not support editing notations, therefore notations
cannot be altered in any way.
| virtual const XMLCh* DOMDocumentType::getPublicId | ( | ) | const [pure virtual] |
Get the public identifier of the external subset.
| virtual const XMLCh* DOMDocumentType::getSystemId | ( | ) | const [pure virtual] |
Get the system identifier of the external subset.
| virtual const XMLCh* DOMDocumentType::getInternalSubset | ( | ) | const [pure virtual] |
The internal subset as a string, or null
if there is none.
This is does not contain the delimiting square brackets.The actual content returned depends on how much information is available to the implementation. This may vary depending on various parameters, including the XML processor used to build the document.


Steam Local Content Server
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RT @confreaks: New Video! #rubyconf @rubyconf - Profiling Ruby: Finding 10x Gains In RSpec and CRuby by @xshay http://www.confreaks.com/videos/2860-rubyconf2013-profiling-ruby-finding-10x-gains-in-rspec-and-cruby
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IN THE HIGH COURT OF KERALA AT ERNAKULAM PRESENT: THE HONOURABLE MR.JUSTICE P.N.RAVINDRAN TUESDAY, THE 18TH DAY OF FEBRUARY 2014/29TH MAGHA, 1935 WP(C).No. 4810 of 2014 (A) --------------------------- PETITIONER : -------------------------- JEEJA RANI, W/O.BIJU,AGED 28 YEARS, ORUCHENNIVILLA HOUSE, ALAKODE P.O., TALIPARAMBA TALUK, KANNUR DT. BY ADV. SRI.P.NARAYANAN RESPONDENT(S): ---------------------------- 1. M.R.BALAKRISHNAN,S/O.RAMAKRISHNAN, MANGATTU HOUSE, ALAKODE P.O., TALIPARAMBA TALUK, KANNUR DT. PIN-670 141 2. THE SECRETARY,ALAKODE GRAMA PANCHAYATH, ALAKODE P.O., KANNUR DT. PIN-670 141 3.  EXHIBIT-P2: COPY OF THE COMMUNICATION DATED 26.9.2012 ISSUED BY THE 2ND RESPONDENT. EXHIBIT-P3: COPY OF THE SALE DEED NO.2777/1994 OF ALAKODE SRO. EXHIBIT-P4: COPY OF THE DOCUMENT NO.2364/1/2005 OF ALAKODE SRO. EXHIBIT-P5: COPY OF THE COMPLAINT DATED 30.7.2012 SUBMITTED BY THE PETITIONER TO THE DISTRICT COLLECTOR. EXHIBIT-P6: COPY OF THE COMMUNICATION DATED 27.9.2012 ISSUED BY THE 3RD RESPONDENT TO THE 1ST RESPONDENT. EXHIBIT-P7: COPY OF ORDER DATED 22.5.2013 IN W.P.C.30244/2013. EXHIBIT-P8: COPY OF THE SKETCH PLAN SUBMITTED BY THE 1ST RESPONDENT BEFORE THE 3RD RESPONDENT ALONG WITH THE APPLICATION FOR CONSENT TO OPERATE. EXHIBIT-P9: COPY OF THE AFFIDAVIT SUBMITTED BY THE 1ST RESPONDENT ALONG WITH THE APPLICATION FOR CONSENT TO OPERATE, BEFORE THE 3RD RESPONDENT. EXHIBIT-P10: COPY OF THE COMMON JUDGMENT IN W.P. 30244/2012 AND W.P.17793/2013 DATED 4.9.2013. EXHIBIT-P11: COPY OF THE COMMUNICATION NO.A5/5357/2013 DATED 8.11.2013 AND THE DECISION NO.118/2013 DATED 31.10.2013 ISSUED BY THE 2ND RESPONDENT. EXHIBIT-P12: COPY OF THE STATEMENT DATED 30.10.2013 SUBMITTED BY THE PETITIONER BEFORE THE 3RD RESPONDENT. EXHIBIT-P13: COPY OF THE APPLICATION DATED 23.1.2013 SUBMITTED BY THE PETITIONER. EXHIBIT-P14: COPY OF THE COMMUNICATION NO.PCB/KNR/RI ACT/151/2005 DATED 16.1.2014 ISSUED BY THE 3RD RESPONDENT. EXHIBIT-P15: COPY OF THE CONSENT TO OPERATE DATED 4.12.2013 ISSUED BY THE 3RD RESPONDENT TO THE 1ST RESPONDENT. RESPONDENT(S)' EXHIBITS: NIL /TRUE COPY/ sts P.A.TO.JUDGE P.N.RAVINDRAN, J. --------------------------- W.P.(C) No.4810 of 2014 -------------------------- Dated this the 18th day of February, 2014 J U D G M E N T
Ext.P15 consent to operate issued by the Environmental Engineer, Kerala State Pollution Control Board, District Office, Kannur under section 25 of the Air (Prevention & Control of Pollution) Act, 1981 and the Environment (Protection) Act, 1986 to the first respondent herein, is under challenge in this writ petition filed under Article 226 of the Constitution of India by a neighbouring resident.
2. Section 31(1) of the Air (Prevention and Control of Pollution) Act, 1981, stipulates that any person aggrieved by an order made by the State Board under this Act may, within thirty days from the date on which the order is communicated to him, prefer an appeal to the appellate authority constituted by the State Government. Though the period of limitation prescribed for filing an appeal is 30 days from he date of the order, the appellate authority is empowered to condone the delay if sufficient cause is shown. Under section 31B of the Act, a further appeal lies to the National Green Tribunal established under section 3 of the National Green Tribunal Act, 2010. The petitioner has thus got an appellate remedy before the appellate authority W.P.(C) No.4810/2014 2 constituted by the State Government and a further appeal to the National Green Tribunal. In such circumstances, I am of the opinion that the petitioner should invoke the alternate remedies available to her instead of invoking the jurisdiction of this Court under Article 226 of the Constitution of India.
I accordingly decline jurisdiction and dismiss the writ petition leaving open the petitioner's contentions and reserving liberty with her to challenge Ext.P15 in other appropriate proceedings.
P.N.RAVINDRAN, (JUDGE) vps


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Dearest In Christ, It is with Heavy Heart i am reaching you regarding the death of my late client. I am Barrister Robert Beaud, the legal adviser to late MR. MIKE & CAROL HALL, a very Wealthy Couple that lived here in the United Kingdom, before their recent Death on the 26th of December during the Tsunami disaster last year (2004).http://news.bbc.co.uk/1/hi/england/bristol/4153821.stm) these couple served God as very dedicated Christians,they so dedicated their life to God but they had no child till they died. They acquired a lot of landed properties like lands, Stocks/Bond,house properties, etc. As their legal adviser, before their death, the husband Mr. Mike & Carol Hall instructed me to write his WILL because they had no child, they dedicated their wealth to God. According to the WILL, their assets should be given out to a ministry for the work of God. As their legal adviser, all the documents for the assets that are deposited with the security company are in my care. He gave me the authority to give out the funds to the Ministries for the work of God. As instructed by MR. MIKE HALL before his death. As a matter of fact the total amount of money that is contained in the two trunk Boxes is $10,000,000.00 ,They did not want the management of the Security Company to know the content of the consignments, therefore they registered the content of the consignments as Gold Bars. Now, the security company believes that what They deposited with them were Gold Bars. As a born again Christian,I have been reading my bible and I have to do what is lawful and right in the sight of God by giving out the fund to the chosen ministry for the purpose of God's work as instructed by the owner before his death.After my fasting and prayers Today, I asked God to make his choice and direct me to an honest Christian or the chosen ministry that deserves this fund by his Grace. I then came across your address on the Internet as I was browsing through a Christian site.I appeal to you for the fund to be used wisely for things that will glorify the name of God. I have just notified the Security Company where they deposited the consignments that contained the fund, that I am moving the consignment abroad, and the security company is awaiting my authority to move the consignment out of the shores of my country. Dear child of zion, if you know that you will use this fund honestly and wisely for things that will glorify God's name, then do contact me with the above mentioned information via<EMAIL_ADDRESS>Your prompt response will be highly appreciated. Yours in Christ. Barrister Robert Beaud.


18649 - Improvements Log
18649 Fall 2015
Group 12 - Tom Eliot (tke), Shepard Emerson (semerson), Daniel Gorziglia (dgorzigl), Daniel Haddox (dhaddox)
For each submission, you should
update this log with a list of ideas or suggestions you have for
improving the project. This could include identifying bugs in the
project handouts or documentation, identifying parts of the project
that were unclear or confusing, and offering ideas for new features for
the simulator. If you have no suggestions or issues for a
particular project, add an entry that says "no suggestions" or
something similar.
Project 1
Project 2
Project 3
Project 4
Project 5
Project 6
- discovered the utilities files after writing our own functions; it would have been nice if these were clearly pointed out.
Project 7
Project 8
- It is unclear how the tasks in this project need to be split up. It says: "Additionally, each team member must EITHER do a design activity (secnarios/sequence diagrams/requirements) OR a test activity. (It is OK for someone to do both.) Each team member must satisfy the minimum stated per-member requirements." The min_reqs spreadsheet has rows for design tasks, and in previous projects it was explicitly stated that a row didn't need an entry for every team member. We interpreted this as it being OK for a member to participate in only testing and not design tasks, but it is not 100% clear to us that this is the intention.
Project 9
Project 10
Project 11
Project 12
Project 13
Overall Project Comments
- Assign the runtime requirements monitors to be due earlier. This could even be as early as the design phase, or as late as when the code for that controller is due. They were as helpful if not more helpful than the unit / integration tests at working out bugs early on in the controller design. We didn't take them as seriously as we should have early enough.


The Computer Fraud and Abuse Act needs to be fixed. Here is another sentence about this to introduce people to the idea.
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Fix the CFAA is supported by


Fantasy Island
Home
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Culture
Main content section
Main infomation section


‘Tesla gets 1.46 lakh orders for Cybertruck’ Says Elon Musk
San Francisco: Despite a chaotic launch and broken glass, Tesla has received 146,000 orders for its electric pickup called “Cybertruck” that starts from $39,900.
“146k cybertruck orders so far, with 42% choosing dual, 41% tri & 17% single motor,” Elon Musk said in a tweet on Saturday. He referred to three different versions available: single-motor rear-wheel-drive, dual-motor all-wheel-drive and tri-motor all-wheel drive.
The Tesla CEO Elon Musk added that the orders have come with no advertising and no paid endorsement.
In total, Tesla has reportedly received deposits worth $14.6 million in just two days after unveiling “Cybertruck”. The truck will come in three versions with 250 miles, 300 miles and 500 miles of range, respectively. The base version of the truck starts at $39,900, while the prices for the top end Tri Motor All-Wheel-Drive version of the Cybertruck start at $69,900. The most expensive version of the truck, the Tri Motor AWDrive will be able to carry 3,500 pounds, tow up to 14,000 pounds and go from zero to 60 in 2.9 seconds.
It comes with six seats and features armoured glass and ultra-strong panels that are made of the same alloys found on spacecraft. Production of the tri-motor variant of the cybertruck is expected to begin in late 2022, Tesla said. (IANS)
Also Read: Why SpaceX CEO Elon Musk Suddenly Gone Offline Without Reason?
Also Watch: Kokrajhar operations against illegal timber smugglers, seized valuable logs from Chirang & Kokrajhar


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setBalance(float)
- Method in class de.ralleytn.simple.audio.
AbstractAudio
setBalance(float)
- Method in interface de.ralleytn.simple.audio.
Audio
Sets the balance.
setFramePosition(long)
- Method in interface de.ralleytn.simple.audio.
Audio
Sets the position at which the audio should play.
setFramePosition(long)
- Method in class de.ralleytn.simple.audio.
BufferedAudio
setFramePosition(long)
- Method in class de.ralleytn.simple.audio.
StreamedAudio
setLoop(boolean)
- Method in class de.ralleytn.simple.audio.
Playlist
Sets whether the
Playlist
should restart once it reached the end or not.
setMute(boolean)
- Method in class de.ralleytn.simple.audio.
AbstractAudio
setMute(boolean)
- Method in interface de.ralleytn.simple.audio.
Playable
Sets wherever the
Playable
should be muted or not.
setMute(boolean)
- Method in class de.ralleytn.simple.audio.
Playlist
setPosition(long)
- Method in interface de.ralleytn.simple.audio.
Audio
Sets the position at which the audio should play.
setPosition(long)
- Method in class de.ralleytn.simple.audio.
BufferedAudio
setPosition(long)
- Method in class de.ralleytn.simple.audio.
StreamedAudio
setShuffle(boolean)
- Method in class de.ralleytn.simple.audio.
Playlist
Sets whether the next track to play should be picked randomly or not.
setTrack(int)
- Method in class de.ralleytn.simple.audio.
Playlist
setVolume(float)
- Method in class de.ralleytn.simple.audio.
AbstractAudio
setVolume(float)
- Method in interface de.ralleytn.simple.audio.
Playable
Sets the volume.
setVolume(float)
- Method in class de.ralleytn.simple.audio.
Playlist
start(File)
- Method in class de.ralleytn.simple.audio.
Recorder
Starts the recording and writes the data in the given file.
start(OutputStream)
- Method in class de.ralleytn.simple.audio.
Recorder
Starts the recording and writes the data on the given output stream.
stop()
- Method in class de.ralleytn.simple.audio.
BufferedAudio
stop()
- Method in interface de.ralleytn.simple.audio.
Playable
Stops the
Playable
.
stop()
- Method in class de.ralleytn.simple.audio.
Playlist
stop()
- Method in class de.ralleytn.simple.audio.
Recorder
Stops the recording.
stop()
- Method in class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio
- Class in
de.ralleytn.simple.audio
Never loads the entire audio data into the RAM.
StreamedAudio(String)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(File)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(Path)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(String, String)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(File, String)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(Path, String)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(URL)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
StreamedAudio(URI)
- Constructor for class de.ralleytn.simple.audio.
StreamedAudio
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@* * Copyright 2020 HM Revenue & Customs * * 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. *@ @(title: String, text: String, linkUrl: String = "", linkGaAction: String = "", linkGaLabel: String = "", dismissText: String = "", dismissUrl: String = "", dismissGaAction: String = "", dismissGaLabel: String = "")(implicit messages: Messages)


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| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Object coins.simd.SimdOpt
Class for SIMD level optimization
| Field Summary | |
static int |
MAX_SIMD_PARALLEL
Maximum size of elements in SIMD Parallel instructions |
boolean |
messageFlag
Flag of printing out trace informations |
| Constructor Summary | |
SimdOpt(Function f)
Constructs a SimdOpt object and initialize bopList,boneList and simdReg. |
| Method Summary | |
java.util.Vector |
allocateSimdReg(java.util.Vector in)
Allocate SIMD registers. |
java.util.Vector |
combineSimd(java.util.Vector in)
Combines SIMD instructions. |
java.util.Vector |
decompose(java.util.Vector in)
Decomposes DAG into basic operations(bop). |
boolean |
defined(Symbol var,
LirNode inst)
Tests if a symbol is defined in an instruction. |
java.util.Vector |
invoke(BiList live,
java.util.Vector in,
ReplaceRegNames rrn)
Invokes methods for SIMD optimization. |
java.util.Vector |
liveReg(java.util.Vector in)
Calculate live registers. |
java.util.Vector |
liveReg(java.util.Vector in,
java.util.Vector live)
|
java.util.Vector |
restrictInst(java.util.Vector in)
Applies constraints for instructions and registers. |
boolean |
used(Symbol var,
LirNode inst)
Tests if a symbol is used in an instruction (LirNode). |
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Field Detail |
public static final int MAX_SIMD_PARALLEL
public boolean messageFlag
| Constructor Detail |
public SimdOpt(Function f)
f
- Function| Method Detail |
public java.util.Vector invoke(BiList live, java.util.Vector in, ReplaceRegNames rrn) throws SimdOptException
live
- ImList,which has liveness information.in
- Vector,which contains LIR instructions as elements.rrn
- ReplaceRegNames, which replaces and has info. of replaced regs
SimdOptException
public java.util.Vector decompose(java.util.Vector in) throws SimdOptException
in
- Vector,which contains DAGs as its elements.
SimdOptException
public java.util.Vector combineSimd(java.util.Vector in) throws SimdOptException
in
- Vector, which contains LirNodes as its elements.
SimdOptException
public java.util.Vector restrictInst(java.util.Vector in) throws SimdOptException
in
- Vector, which contains combined instructions(LirNodes).
SimdOptException
public java.util.Vector allocateSimdReg(java.util.Vector in) throws SimdOptException
in
- Vector, which contains SIMD instructions (LirNodes).
SimdOptException
public java.util.Vector liveReg(java.util.Vector in)
in
- Vector, which contains instruction (LirNodes).
public java.util.Vector liveReg(java.util.Vector in, java.util.Vector live)
public boolean defined(Symbol var, LirNode inst)
var
- Symbolinst
- LirNode
public boolean used(Symbol var, LirNode inst)
var
- Symbol which is checked.inst
- LirNode which represents an instruction.
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