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Resonances within Chaos
- Samuel Dalton
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1 1: Resonances and chaos 1 Resonances within Chaos G. Gallavotti 1,2, G. Gentile 3, A. Giuliani 3 1 Dip.to di Fisica, Univ. di Roma La Sapienza, 185 Roma - Italy 2 Dept. of Mathematics, Rutgers University, NJ USA 3 Dip.to di Matematica, Univ. di Roma Tre, 146 Roma - Italy Abstract: A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically. In chaotic systems synchronization phenomena, i.e. resonances, can occur: the simplest being motions asymptotically developing over a low dimension attractor which is visited in synchrony with a weak timeperiodic perturbing force. This is analogous to the synchronization ( phase locking ) occurring when an integrable system, perturbed by a periodic forcing, develops attracting periodic orbits with period being a simple fraction (1, 3/2, 2,...) of the forcing period. Formation of an attractor and existence of dissipation, i.e. of phase volume contraction, are concomitant. A chaotic system under a weak volume preserving periodic perturbation can have, instead, a very singular chaotic evolution, [1, 2], with dense orbits. A simple illustration of the resonance phenomenon in a chaotic system is exhibited here and exactly solved by deriving the shape of the attractor: which turns out to be a continuous surface with weak smoothness properties (being a strange attractor with an exponent of Hölder-continuity with a very small lower bound). The peculiarity of the class of systems treated is the possibility of determining analytically an attractor whose existence can be rather easily seen in simulations. 1 Resonances and chaos A chaotic system weakly interacting with a very regular system may generate a fully chaotic dynamics: ( ) as a basic example, consider the suspension flow of Arnold s 2 1 cat map A 2 = with a flat floor function (i.e. the flow on T 3 = [, 2π] where every point x T 2 of the base moves vertically with constant velocity until it reaches the flat floor, at which point it reappears on the base, at the location A 2 x) coupled with a clock, which moves at the same speed as the suspension flow. If observed at the times when the suspension flow hits the floor, the unperturbed
2 2: A simple example 2 dynamics takes the form of a linear discrete dynamical system A 3 : T 3 T 3, with 2 1 def A 3 = 1 1. Consider now a small perturbation of A 3 : it is remarkable that 1 in the case of volume preserving perturbations, some pathological phenomena can take place [1, 2]. Namely, there is an open set U of C 1 conservative perturbations of A 3 such that the following happens: the perturbed motion g U is ergodic with respect to the volume measure in T 3 and there exists a foliation of T 3 into C 2 curves l x that are invariant under g (i.e. gl x = l gx ); moreover, the central Lyapunov exponent along the leaves is positive on the set Ω of full three-dimensional measure where it is defined; the set Ω intersects every leaf at exactly k points, for some k > [1, 2]. Such results provide an interesting example of an absolutely singular foliation, in the sense of Katok [3]. The situation is destined to change substantially in the presence of friction: if we couple via a dissipative perturbation the suspension flow of A 2 with a clock, the phase between the two (that is arbitrary in the unperturbed case) might lock, making the motion fall onto a lower dimensional attractor, which would naturally be close to the union of k elements of a horizontal foliation of T 3. We can say, when this happens, that there is a resonance between the periodic forcing and the chaotic evolution on T 3 : and unlike the cases quite typical in generic perturbations of periodically forced integrable systems where the resonance may lead to the appearance of stable periodic orbits, in the presence of hyperbolicity and of small dissipation the forcing gives rise to a periodic strange attractor, i.e. to an attractor for the time evolution observed at times integer multiples of the forcing period, on which the dynamics is conjugate to a uniformly hyperbolic system. In this paper we provide examples of the above phenomenon: remark that in the non-dissipative case the perturbations discussed in [1, 2] can be in a set arbitrarily close to the unperturbed system and open in the C 1 topology (not containing the unperturbed system itself). Here we consider a class of analytic perturbations depending on a parameter ε and show that for any small ε the resonance occurs. The phenomenon is reminiscent of certain synchronization phenomena in chaotic systems [4] and the simple case considered below is, as far as we know, one of the first explicit examples of such phenomena that can be fully worked out analytically.
3 2: A simple example 3 2 A simple example Denoting by x = (x 1, x 2 ) a point of T 2, consider the evolution equation: ẋ = δ(z)(sx x) + εf(x, z, w), ẇ = 1 + εg(x, z, w), ż = 1, (2.1) with (x, w, z) T 2 T T and ε. Here δ is the 2π-periodic delta function, with the convention that t dt δ(t ) = 1 for all t >. Set f = to simplify as much as possible the problem. The map S could be any linear hyperbolic automorphism of T 2, in particular S = A 2. Then we can prove the following result. Theorem: Let S t g be the flow on T 4 associated with Eq.(2.1) with f = and g analytic. Let also γ (x, w) def = dt g(sx, t, w+t), γ 1 (x, w) def = dt g(sx, t, w+t), (2.2) w and suppose existence of w such that γ (x, w ) = and γ 1 (x, w ) = Γ <, independent of x, w. Then there are constants ε, C > such that for < ε < ε there exists a Hölder-continuous function W : T 2 T of exponent β Cε and the surface A def = {(x, W(x), ) : x T 2 } is invariant under the Poincaré map S 2π g ; the dynamics of S 2π g on A is conjugated to that of S on T 2, i.e. S 2π g (x, W(x), ) = (Sx, W(Sx), ). (2.3) Remarks. (1) It should be clear from the proof below that, for ε >, A is an attractor for Sg t with negative central Lyapunov exponent equal to εγ 2π (1+O(ε)), see concluding remarks in Section 7. Furthermore the function W is holomorphic in ε = ρe iα inside the domain which in polar coordinates is ρ(α) = ε cos α. (2) A simple explicit example of a function g satisfying the assumptions of the theorem with w = π and Γ = 1 is: g(x, z, w) = sin(w z) + sin (x 1 + w + z). (2.4)
4 3: The equation for the invariant manifold 4 (3) It would be interesting to estimate the positions of the poles of the power spectrum of the correlations of pairs of smooth observables in the sense of the chaotic resonances theory in [5]. The spectrum is meromorphic in a strip with poles off the real axis for a dense set of observables: the unperturbed system has poles at i log λ + + 2πk, k Z, if λ + is the largest eigenvalue of the matrix S; we expect the position of the poles closest to the origin to be modified by order ε. Notice that in the unperturbed system the spectrum is an entire function for all analytic observables and the poles really appear with non-zero residue for Hölder continuous functions (see Sec. 4.3 and Fig in [6]). Let us now turn to the proof of the theorem. The main ideas and the strategy of the proof are the following: (i) after having written the equation for the invariant manifold, we solve it recursively; (ii) the result of the recursion is conveniently expressed in terms of tree diagrams; (iii) these can be easily shown to give rise to a convergent expansion, provided that the large factors ε 1 produced under iterations by the small rate of contraction of phase space (of order O(ε)) is compensated by suitable cancellations, stemming from the condition that γ (x, w ) =. All these steps are discussed in detail in the following Sections 3 6. Finally, in Section 7, we add some comments on the assumptions made and on possible generalizations of our result. 3 The equation for the invariant manifold Let W(x) = w + U(x), x() = x and for < t 2π write w(t) = w + t + u(x, t), with u(x, + ) = U(x). Substituting into Eq.(2.1), for all < t 2π we find: Defining u(x, t) = εg(sx, w + t + u(x, t), t). (3.1) γ (x, t) = g(sx, w + t, t), γ 1 (x, t) = w g(sx, w + t, t), G(x, t, u) = g(sx, w + t + u, t) γ (x, t) u γ 1 (x, t), (3.2) Eq.(3.1) can be rewritten for all < t 2π as ( ) u(x, t) = εu(x, t)γ 1 (x, t) + ε γ (x, t) + G(x, t, u(x, t)), (3.3) with G(x, t, u) = p 2G p (x, t)u p. (3.4)
5 4: Recursion equations 5 Integrating from to t (, 2π], the equation for u(x, t) becomes where t u(x, t) = e εγ(x,t,) U(x) + ε dτ e εγ(x,t,τ)( ) γ (x, τ) + G(x, τ, u(x, τ)), (3.5) Γ(x, t, τ) = t τ dτ γ 1 (x, τ ). (3.6) By construction G vanishes to second order in u, hence, if δ is fixed once and for all, one has u(x,2π) = e Γε u(x,) + O(ε 2 ), so that u(x,2π) e Γε/2 u(x,), if δ u(x,) δ, (3.7) 2 provided ε is small enough. Therefore the region u δ is an attracting set for ε small (compared to δ). The condition of invariance for W(x) reads u(x,2π) = U(Sx), which gives U(Sx) e εγ U(x) = ε dτ e εγ(x,2π,τ)( ) γ (x, τ) + G(x, τ, u(x, τ)), (3.8) and hence U(x) = F(x) =ε e εγ(k 1) F(S k x), k=1 dτ e εγ(x,2π,τ)( ) γ (x, τ) + G(x, τ, u(x, τ)). (3.9) In order to solve the two coupled equations Eqs.(3.5)-(3.8), we find convenient to consider the two-parameters (µ, ε) equations t u(x, t) = e µγ(x,t,) U(x) + ε dτ e µγ(x,t,τ)( ) γ (x, τ) + G(x, τ, u(x, τ)), U(Sx) e µγ U(x) = ε dτ e µγ(x,2π,τ)( ) γ (x, τ) + G(x, τ, u(x, τ)), (3.1) first showing existence of a solution analytic in ε and Hölder-continuous in x, at fixed µ, and subsequently proving that µ can be taken to have values µ ε a little beyond ε. 4 Recursion equations Eq.(3.1) can be solved recursively as follows. Let
6 5: Tree expansion 6 u(x, t) = e µγ(x,t,) U(x) + ξ(x, t) (4.1) and write ξ(x, t) = εξ 1 (x, t) + ε 2 ξ 2 (x, t) + and U(x) = εu 1 (x) + ε 2 U 2 (x) +. Plugging the expansions into Eq.(3.1) and setting λ = e µγ, we find ξ 1 (x, t) = U 1 (x) = and, for n 3, ξ n (x, t) = t t k=1 dτ dτ e µγ(x,t,τ) γ (x, τ), ξ 2 (x, t) =, λ k 1 dτ e µγ(s kx,2π,τ) γ (S k x, τ), U 2 (x) =, U n (Sx) e µγ U n (x) = p=2 n 1,...,np 1 n np=n 1 dτ e µγ(x,t,τ) G p (x, τ) p i=1 (4.2) ( ) e µγ(x,τ,) U ni (x) + ξ ni (x, t), e µγ(x,2π,τ) G p (x, τ) (4.3) p=2 n 1,...,np 1 n np=n 1 p ( ) e µγ(x,τ,) U ni (x) + ξ ni (x, t), i=1 which give a recursive definition of ξ n, U n. Note that the second of Eq.(4.3) can be solved in a way analogous to Eq.(3.9), so that U n (x) = λ k 1 dτ k=1 p=2 p i=1 n 1,...,np 1 n np=n 1 e µγ(s k x,2π,τ) G p (S k x, τ) ( ) e µγ(s kx,τ,) U ni (S k x, τ) + ξ ni (S k x, τ). (4.4) For the incoming discussion, it is useful to note that by the analyticity of g, there exists a constant C such that G p (x, t) C p, eµγ(x,t,τ) C, (4.5) uniformly in x, t, τ. Moreover, if we consider the Fourier expansion G p (x, τ) = e iν x Ĝ p (ν, τ), e µγ(x,t,τ) = e iν x Γ(ν, t, τ), ν Z 2 ν Z 2 there exists κ >, such that uniformly in t, τ. (4.6) Ĝp(ν, τ) C e κ ν, Γ(ν, t, τ) C e κ ν, (4.7)
7 5: Tree expansion 7 5 Tree expansion The recursion for ξ n, U n can be conveniently represented graphically in terms of tree graphs. We start with some basic definitions. A connected graph G is a collection of points (nodes) and lines connecting all of them. We denote with V (G) and L(G) the set of nodes and the set of lines, respectively. A path between two nodes is the minimal subset of L(G) connecting the two nodes. A graph is planar if it can be drawn in a plane without graph lines crossing. A tree is a planar graph G containing no closed loops. One can consider a tree G with a single special node v : this introduces a natural partial ordering on the set of lines and nodes, and one can imagine that each line carries an arrow pointing toward the node v thus establishing a partial order on the tree. We can add an extra (oriented) line l exiting the special node v ; the added line l will be called the root line and the point r it enters (which is not a node) will be called the root of the tree. In this way we obtain a rooted tree θ defined by V (θ) = V (G) and L(θ) = L(G) l. Hence given two nodes v, w V (θ), it is v w (or w v) if w is on the path connecting v to the root line. A labeled tree is a rooted tree θ together with a label function defined on the sets L(θ) and V (θ). We shall call equivalent two rooted trees which can be transformed into each other by continuously deforming the lines in the plane in such a way that the latter do not cross each other (i.e. without destroying the graph structure). We can extend the notion of equivalence also to labeled trees, simply by considering equivalent two labeled trees if they can be transformed into each other in such a way that also the labels match. We can identify a line with the nodes it connects; given a line l = wv we say that l enters w and exits v, and we shall write also l = l v. Given two comparable nodes v and w, with v w, we denote with P(v, w) the path of lines connecting w to v, with v and w being included. For any node v v we denote by v v the node immediately following v, hence l v = v v, and we set v = r. Associate with the nodes and lines of any tree θ some labels, according to the following rules. With each node v we associate the labels (η v, k v ), where η v =, 1, while k v = if η v = and k v N (i.e. k v 1) if η v = 1; we call η v the type label of the node v. Furthermore we define k(v) = k v. (5.1) v P(v,v ) For each node there are p v entering lines. If p v = we say that v is an end-node. If p v > then p v 2. For p v 2 let s v be the number of nodes w with
8 5: Tree expansion 8 w = v such that η w = 1. Represent graphically the node v as a big white ball (white node) if η v = 1 and as a small black ball (black node) if η v =. Thus s v is the number of white nodes immediately preceding v. With each node v we associate a time variable τ v (, 2π], with τ v = t, a node factor F v = F v (x, τ v, τ v ) defined as { e µγ(s k(v) x,τ v,τ v) G F v = pv (S k(v) x, τ v )e µsvγ(s k(v) x,τ v,), η v =, (5.2) λ kv 1 e µγ(s k(v) x,2π,τ v) G pv (S k(v) x, τ v )e µsvγ(s k(v) x,τ v,), η v = 1, and an integral I v (η v ), with I v () = τv dτ v, I v (1) = dτ v. (5.3) With the definitions above, we denote by T n,ν,η the set of trees with n nodes and η v = η. Then one can check (for instance by induction) that U n (x) = Val(x; θ), ξ n (x, t) = Val(x; θ), θ T n,1 θ T n, Val(x; θ) = I v (η v )F v (x, τ v, τ v ), (5.4) v V (x;θ) where the integrals are understood to be performed by following the tree ordering (i.e. by starting from the end-nodes and moving toward the root). Note that in the formula for ξ n (x, t) in Eq.(5.4), the variable τ v = t plays no role, as I v (1) and F v (t, τ v ) in fact do not depend on t. For instance ˆξ 1 (ν, t) and Û1(ν) are represented graphically as in Figure 1. ξ 1 (x, t) = U 1 (x) = Figure 1. Graphical representation of ξ 1 (x, t) and U 1 (x). Since ξ 2, U 2 = the next simplest example is the representation of ξ 3, U 3. For instance, say, U 3 (x) is described in Figure 2. U 3 (x) = Figure 2. Graphical representation of U 3 (x). In a similar way we can represent graphically the other U n s or ξ n s. For example in Figure 3 we represent some contributions to U 5 (x): all the other contributions are obtained by replacing some white nodes with black nodes and vice
9 6: Convergence 9 versa, and possibly permuting the lines entering the nodes (the only node which must be necessarily white is the node v ). Figure 3. Graphical representation of some contributions to U 5 (x). In drawing the graphs in Figures 1 3 we have used that p v 2 whenever p v and that ξ 2 (x, t) and U 2 (x) vanish identically, as it follows from (4.2). 6 Convergence Given a tree ϑ T n,x,η, η {, 1}, let E(ϑ) be the number of its end-nodes, and let E (ϑ) and E 1 (ϑ) be the number of end-nodes of type and 1, respectively. Similarly, let N i (ϑ) be the number of internal vertices of ϑ (i.e. the number of vertices of ϑ with p v > ) and Nη(ϑ) i be the number of internal vertices of type η, with η =, 1. Note that, since p v 2 whenever p v, we have E(ϑ) (n+1)/2. A key remark is that, thanks to the condition that γ (x, w ) =, the contribution associated to every end-node v of type 1 is of order µ, dτ v λ kv 1 e µγ(s k(v) x,2π,τ v) γ (S k(v) x, τ v ) (const.)µ. (6.1) Using this cancellation and the bounds Eq.(4.5), we find that, for all n N and all ν Z 2, Val(x; θ) C1 n µ E 1(ϑ) λ kv 1, (6.2) v V (θ) ηv=1 for a suitable constant C 1, uniformly in x. Therefore, in order to obtain a bound on U n (x) we have to estimate the number of labeled trees in T n,1. For each node v with η v = 1 the corresponding sum over k v produces a factor C 2 µ 1. Finally the number of unlabelled trees with n nodes is bounded by C n 3, with C 3 = 4. By collecting together the bounds above we find U n (x) C n µ Ni 1 (ϑ), C = C 1 C 2 C 3. (6.3)
10 6: Convergence 1 Using N i 1 (ϑ) Ni (ϑ) = n E(ϑ) n (n + 1)/2, we find U n (x) C n µ (n 1)/2, (6.4) which yields a radius of convergence in ε given by ε = C 1 µ 1/2, hence we can take µ = ε. To study the regularity in x we need to get a similar upper bound for U n (x) U n (x ) x x β, β >. (6.5) We proceed as follows. Given a tree ϑ we introduce an arbitrary ordering of the nodes by setting V (ϑ) = {v 1,...,v V (ϑ) } and define Vp (ϑ) = {v 1,...,v p } and V p + = {v p+1,...,v V (ϑ) }, with the convention that V (ϑ) = V + V (ϑ) (ϑ) = and V V (ϑ) (ϑ) = V + (ϑ) = V (ϑ). Then we define Val ± p (x; ϑ) = I v (η v )F v (x, τ v, τ v ), (6.6) v V ± p (ϑ) with Val (x; ϑ) = Val+ V (ϑ) (x; ϑ) = 1, and write U n (x) U n (x ) = ( ) Val(x; ϑ) Val(x ; ϑ) = ϑ T n,1 ( I vp (η vp ) V (ϑ) p=1 ( ϑ T n,1 Val p 1 (x; ϑ)val+ p+1 (x ; ϑ) )) F vp (x, τ v p, τ vp ) F vp (x, τ v p, τ vp ). (6.7) Each summand in (6.7) can be studied as in the case β =, with the difference that the node factor is F v (x, τ v, τ v ) for v Vp 1 (ϑ), F v(x, τ v, τ v ) for v V p+1 + (ϑ) and F v (x, τ v, τ v ) F v (x, τ v, τ v ) for v = v p. Using Eqs.(5.2) and (4.6), we find that F v (x, τ v, τ v ) = e iν x ˆFv (ν, τ v, τ v ), ν Z 2 (6.8) ˆF v (ν, τ v, τ v ) λ (kv 1)δ ηv,1 C1 Cs v+2 e κ 2 Sk(v) ν, for suitable constants C, C 1, independent of τ v, τ v (in deriving the bound on the Fourier coefficients we used that F v (x, τ v, τ v ) depends on x through S k(v) x, see Eq.(5.2)). Therefore, F v (x, τ v, τ v ) F v (x, τ v, τ v ) x x β λ (kv 1)δ ηv,1 C1 Cs v+2 ν Z 2 ν β e κ 2 ν λ βk(v), (6.9)
11 7: Concluding remarks 11 where λ is the eigenvalue of the hyperbolic automorphism S with smallest absolute value; note that, if λ + is the other eigenvalue of S, we have λ = λ + 1, with λ + > 1. The factor λ βk(v) in Eq.(6.9) is bounded by v V (ϑ):η λ v=1 + βkv, so that U n (x) U n (x ) x x β n C n µ E 1(ϑ) λ kv 1 λ + βkv, (6.1) ϑ T n,1 v V (ϑ) ηv=1 for a suitable constant C. We must require that λ + β λ < 1, and in order for the sum k v 1 ( λ + β λ) kv to be still proportional to µ 1, we can take β = cµ, < c < Γ / log λ +, (6.11) which gives β = c ε for µ = ε. This concludes the proof of the theorem. 7 Concluding remarks Let us add a few comments on the role of the specific hypotheses in the theorem. The assumption that there is w such that dt g(x, t, w + t) is zero has been heavily used as well as the assumption that dt w g(x, t, w + t) = Γ, for Γ <. Both assumptions can be relaxed into (a) dt g(x, w + t, t) = εg(x), for some g(x), (b) dt w g(x, w + t, t) Γ, for Γ <, and the statement of the theorem remains valid (and its proof is essentially unchanged). Assumption (a) is strong and it does not allow for perturbations of the form εg because the ε-dependence has to involve higher powers of ε to satisfy (a) unless g(x) (as in the theorem proved here). It is unclear whether the results discussed in this paper would hold under the weaker assumptions that (a ) dt g(x, w + t, t) = g(x), with g(x) with average, (b ) dt w g(x, w + t, t) = g 1 (x), with g 1 (x) with negative average. Preliminary computations and numerical evidence suggest that the existence of an attractor A = {(x,, W(x))} for Sg 2π may still be true, possibly just for a.e.-x and with a non-smooth function W(x): in other words, a similar phaselocking phenomenon as the one proved in this paper may still take place, with A a fractal rather than a smooth surface.
12 7: References 12 It would be interesting to check that the central Lyapunov exponent in the theorem is also expressed by an expansion in tree graphs: the procedure should be the same illustrated in the theory of the tangent map for perturbations of the simple Anosov map (e.g., A 2 in Section 1), see proposition in [6]. Finally a natural conjecture is that the assumption f = in Eq.(2.1) can be eliminated as long as f is analytic. However, we do not have specific indications of what is the general structure of the attractor in this case. Acknowledgments. We gratefully acknowledge financial support from the Grant Sistemi dinamici, equazioni alle derivate parziali e meccanica statistica (28R7SKH2) (G.G., G.G. and A.G.) and from ERC Starting Grant CoMBoS (A.G.). A.G. thanks the Institute for Advanced Studies for hospitality during the completion of this work. References [1] M. Shub and A. Wilkinson. Pathological foliations and removable zero exponents. Inventiones Mathematicae, 139:495 58, 2. [2] D. Ruelle and A. Wilkinson. Absolutely singular dynamical foliations. Communications in Mathematical Physics, 219: , 21. [3] J. Milnor. Fubini foiled: Katok s paradoxical example in measure theory. Mathematical Intellegencer, 1:31 32, [4] S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, and C.S. Zhou. The synchronization of chaotic systems. Physics Reports, 366:1 11, 22. [5] D. Ruelle. Resonances of chaotic dynamical systems. Physical Review Letters, 56:45 47, [6] G. Gallavotti, F. Bonetto, and G. Gentile. Aspects of the ergodic, qualitative and statistical theory of motion. Springer Verlag, Berlin, 24.
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|Steve Blackburn <Steve.Blackb...@anu.edu.au>
|Re: Introduction, and a question
|Mon, 16 May 2005 10:12:34 GMT
Take a look at Quicksilver (no longer active). http://www.research.ibm.com/quicksilver/ "The Quicksilver project is exploring novel compilation models for Java. Our goals are to support deep analysis, aggressive optimization, testability and control over executables, all in the context of a fully compliant Java system. Our prototype is implemented within the Jalapeño compiler project." --Steve Christian Damsgaard wrote: > I brought up this idea with Lars Bak (HotSpot architect at Sun back > then) at a conference some years back when Sun introduced the HotSpot > VM. The argument back then was that a program mays not execute in the > same pattern every time and the optimization made previously may no > longer apply. > > Regards > Christian Damsgaard > > Brad Cox wrote: > >> Hello. I'm an old-timer with OO languages (Objective-C originator) >> but a newcomer to open source. I've just signed up to this list >> because Harmony sounds like something I could really get excited by. >> I'd welcome suggestions as to how to get started, traps to avoid, etc. >> >> I'll start by venturing what I suspect might be a naive question. >> Java is fast enough once it gets its legs beneath it, but the >> classloader is giving it a bad rap for speed. That's my impression, >> not measured fact. >> >> Has there been any consideration to stealing an old trick from >> Smalltalk/Lisp environments...a "restart" option that reloads the >> dynamic state saved by a previous execution, typically one that has >> just completed loading an app's classes but before run-specific >> instances were created? >> >> I seems too simple to not have been tried, particularly with such as >> Peter Deutch involved with the JIT compiler. > >
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The two industry bodies have strongly objected to two key issues of DTC, which include search and seizure provisions and 10% TDS on all payments
The national body for jewellery trade the All India Gems & Jewellery Trade Federation (GJF) and apex industry body Gems and Jewellery Industry (GJI) have opposed the proposed Direct Taxes Code (DTC), reports PTI.
Both the industry bodies have also made representations to the finance ministry to seek modifications in the DTC.
According to All India Gems & Jewellery Trade Federation chairman Vinod Hayagriv, "GJF strongly objects to two key issues of DTC, which include search and seizure provisions and 10% tax deducted at source (TDS) on all payments."
"GJF has more than 300,000 manufacturers, wholesalers and retail jewellers in India, which are already reeling under the effects of global recession. If our suggestions are not considered and necessary changes are not incorporated in the DTC, the proposed provisions will be highly detrimental to the operations of the assesses of the GJI and have the potential to adversely affect the very sustenance of such assesses," he added.
The seizure of such stock-in-trade of jewellery, bullion and precious stones would create great difficulties for the assesses of the GJI as it would result into cessation of their manufacturing operations resulting into loss of sales and break down of their entire business activity.
This is discrimination towards a single industry, such extreme measures are not applied in any other industry, so far. In case the amendments are not made in time, GJF shall call for a nationwide bandh (strike) and stall activities across the country, he said.
"We also strongly oppose deduction of 10% tax on all payments made for gold, diamonds, jewellery etc," former chairman All India Gems and Jewellery Trade Federation Ashok Minawala said.
Though this is the seventh oil discovery in the block, the company has yet not put a reserve estimate for any of the oil finds in the area
Reliance Industries (RIL) today said that it has made a seventh oil discovery in the Gujarat block, reports PTI.
The well, CB10A-N1 encountered hydrocarbon bearing zone between 1,388 and 1,403 metres below the earth in the block CB-ONN-2003/1 near Ahmedabad, the company said in a press statement in New Delhi.
"The well flowed at a rate of 410 barrels of oil per day," it said.
RIL, which has so far drilled 17 exploratory wells in the block, of which only six contained oil. The company has named the new discovery 'Dhirubhai-50'.
Though this is the seventh oil discovery in the block, the company has yet not put a reserve estimate for any of the oil finds in the area.
The company said it had notified the government and the Directorate General of Hydrocarbons (DGH) about the new find. "The potential commercial interest of the discovery is being ascertained through additional data gathering and analysis", added the company statement.
The block CB-ONN-2003/1 is located at a distance of about 130 km from Ahmedabad in Gujarat, in the Cambay basin. The block covers an area of 635-sq km in two parts—Part A and Part B.
RIL, as operator, holds 100% stake in the block. It had won the block in the fifth round of auction under the New Exploration Licensing Policy (NELP-V).
While the entire block was covered with 2D seismic, about 80% of the block area has 3D seismic coverage. Of the 17 exploratory wells drilled in the block by RIL, so far, 13 are located in Part-A and the remaining 4 in the Part B of the block.
Earlier on 11th June, RIL had informed of its sixth oil discovery in the Gujarat block. Based on acquired 3-D seismic data on this block, the company expects several more potential finds in the area.
How can you increase your chances of winning?
My previous book review (see: http://www.moneylife.in/article/78/6519.html) led me to attribute reason for my taking profits early, which meant smaller profits than I deserved, to lack of proper methodology. This book points me to another important aspect for it: hardwired psychological inclinations of risk aversion. It also answers why people, including me, ride loser stocks too long. Kiev is a psychiatrist who has written numerous books on related subjects. This book attempts to take another cut at the issue of successful trading by looking across a range of skill sets that are integral parts of the successful trader: a goal-oriented strategy, risk management, creative thinking, and a capacity for collaboration and leadership.
One question the book tries to answer is "How can you increase your chances of winning?" from a psychological perspective. The book explores the nature of investing and trading in terms of being a probabilistic field of endeavour and the kinds of traits and personality characteristics that must be developed to increase the likelihood of success. Kiev views the field of investing as 'sports betting' and that a trader can increase his/her odds of winning by learning to bet on high-probability bets. The approach that is imprinted throughout the book is to challenge oneself to be able to think originally and in terms of what is not immediately apparent. The "thinking outside the box" approach is about trusting your intuition and then developing the kind of research process that will support your hunch and not simply rely on conventional sources of information. It means investing in a lot of research to uncover expected value of a company that is beyond published reports. Traders can look for pricing discrepancy, disconnects, and other things that suggest that buying a company gives you a good shot at winning the bet in a reasonably well-defined time period, increasing your odds of winning.
Successful trading, Kiev asserts, requires an unusual and sometimes contradictory blend of intellectual and psychological abilities, including the willingness to take risks, but in a very controlled manner; the discipline to develop high-conviction trading ideas in the face of unpredictable markets and incomplete information, as well as a strong drive to win—but also accept failure. A person who is too cautious or a complete perfectionist is not a good candidate for portfolio management as much as someone who is too impulsive or an irrational risk-taker. At the end of the day, perseverance, experience, and drive serve to compensate for weakness in personality and natural talent. Kiev's views are supported and articulated with interviews from contemporary traders and portfolio managers. This covers numerous aspects such as: Intellect, Instinct and Guts; Goal Directedness; Ability to take risk; Importance of Ingenuity; Separating Emotions and Decisions; Nurturing team players; Directing Success. These are personality traits Kiev wants hedge fund managers to understand how to look for and choose the best person for a job from the pool of highly-talented individuals.
Some of the things covered in the book may already be known to you. Other things may look obvious and you may want to acquire that personality trait. By all means go for it. My belief is that our personality is somewhat hardwired. It is something based on all our life experiences and reactions to it that are stored in our subconscious. Most of the time how we behave comes from our subconscious. It is possible to reprogram it, but it will take time and effort. It will be foolish to expect that one can develop the right blend of risk-taking ability just by reading this or any other book. Take it in a positive approach as a new beginning in a right direction. Don't buy this book if you are a trader looking for anything other than psychological aspects to help you in trading.


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From the recipes to the friendly nature of the staff, just about every ingredient at Smokey Jack's BBQ has a family feel to it. The eatery sweetens the air at the corner of Royal Lane and MacArthur by seasoning and preparing barbecue favorites—ribs, brisket, pulled pork—right on site. But it also saves room on its menu for not-so-traditional items, such as stuffed potatoes and the Big Jack po' boy. On that, visitors choose to top either a hot link or smoked sausage with brisket, pulled pork, or chopped chicken. Those same visitors can also take advantage of complimentary beer, so long as they opt to dine-in, are of age, and aren't a wine cask.


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If you received an email notice about an unpaid toll, it is probably a fake. Learn more.
Order your E-ZPass Transponder or E-ZPass sticker for delivery today, and your transponder will usually arrive in less than a week.
Ohio is on the E-ZPass electronic toll collection network, so any transponder that displays the E-ZPass or IPass logo will be accepted in Ohio.
The E-ZPass can be purchased from vending machines at all Ohio Turnpike service plazas or ordered online.
Ohio offers both pre-paid and post-paid E-ZPass options for individuals and businesses. All options require you open an E-ZPass account where funds and payments may be managed.
The pre-paid option requires that you have money on your account and maintain money on account in order to pay for tolls as they are incurred.
The post-paid option may be of value for commuters or businesses that spend a minimum of $1,000 per year on tolls. This option does require a surety bond; however, for large fleets, the post-paid option may be of benefit. For interstate haulers, this could be quite useful for travel among other E-ZPass states.


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Monday, Gary Kubiak made good on his promise to address his future. Following the Denver Broncos 24-6 victory over the Oakland Raiders, Kubiak said that he would reveal his plans moving forward in a Monday presser.
He did that today, officially tendering his resignation as the Broncos head coach. In a statement released by the team, Kubiak reflected on the events and factors that led to his difficult decision.
"As I told our team last night, this is an extremely difficult decision to step down as head coach. I love to work and I love football, but ultimately the demands of the job are no longer a good fit for me.
"I gave everything I had to this team the last two seasons, but this year, in particular, has been tough on me. As hard as it is to leave this position, I know that it's the best thing for myself, my family and the Denver Broncos.
"I've been blessed to spend more than two decades with the Broncos working for Mr. Bowlen and a great organization from top to bottom. I'm forever grateful to this team, in particular John Elway and Joe Ellis, for giving me the opportunity to serve as its head coach. There are countless others to thank, including players, coaches, personnel staff, trainers, support staff and fans.
"Although we fell short of our goals this year, I'm proud of our teams these past two seasons. Helping to bring Mr. Bowlen, his family and this organization its third Super Bowl is something that will always be very special to me.
"I'm not sure what my future holds, but I know that I'll always consider myself a Bronco. This team is in good hands with a lot of outstanding people, and I expect great things ahead for the Denver Broncos."
In 10 seasons as a head coach in the NFL, Kubiak has a career record of 87-77 (.534). In two seasons as Denver's head coach, Kubiak went 21-11 (.656), won three playoff games, and a Super Bowl Championship.
Five Hot Threads On The MHH ForumsSchefter Elaborates On Kubiak Decision Who Should Broncos Target For Head Coach? Where Broncos Sit In Draft Order What Happened After The Bye? Free Agent Wish LIst
Including his two seasons as the head coach, Kubiak spent 22 years of his football life with the Denver Broncos — nine more as a quarterback (1983-91) and 11 as offensive coordinator (1995-2005). He was the offensive coordinator on Denver's back-to-back Super Bowl Championships (1997-98).
Hired as the 15th head coach of the Denver Broncos, Kubiak's 24 total wins were the second most in the NFL over that two-year span. No coach in team history had more wins in his first two years as head coach than Kubiak. With 24 victories, Kubiak tied Red Miller's previous mark from 1977-78.
Kubiak became just the fourth head coach in NFL history to lead his team to a World Championship in his first year, defeating the Carolina Panthers 24-10 in Super Bowl 50. His 15 total wins represents the most in team history for a coach in his first year.
Kubiak likes to use the word "special" to describe excellence. In that vein, it's clear how special Kubiak is and has been to the Denver Broncos.
Just as John Elway's hand has touched each of Denver's three Lombardi Trophies, so has Gary Kubiak's. Hats off to the one they call "Kube". And happy trails.
Chad Jensen is the Publisher of Mile High Huddle. You can find him on Twitter @ChadNJensen.
Follow Mile High Huddle on Twitter @MileHighHuddle and on Facebook.


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Curatorial Tour
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Accompany members of the Pulitzer's curatorial staff through the exhibition. Visitors will learn about the exhibition concept, central thematic elements, and cultural context of the works on display.
Past dates
- Occurred Saturday, January 5th, 2013 @ 1:30 pm – 2:30 pm
Shira Berkowitz


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1996 Ford Contour Problems
RepairPal has identified the most common problems with the 1996 Ford Contour based on complaints from actual vehicle owners. We'll tell you what the problem is and what it'll take to fix it.
1Known Problem
The Check Engine Light can illuminate with codes due to the lack of EGR (exhaust gas recirculation) flow caused. This is commonly a result of a clogged passage in the intake manifold. To correct this problem, the EGR valve has to be removed and the passage cleaned thoroughly. Partial restriction of this passage can cause smog test failures for the NOx emissions without causing a drivability symptom.


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Ancient Roman Recipes
Food fit for Emperors
There was a lot more to Ancient Roman food than exotic dishes served by slaves at orgies. Lavish feasts were commonplace among the rich, but ordinary people ate ordinary meals, not very different to what we eat today.
The Romans dined on roast pork in spicy sauces, snacked on cheese with dates and nuts, ate omelettes with mushrooms and enjoyed desserts of cheesecake and figs in custard.
Apicius, a popular Roman chef, produced an ancient cookbook which can still be used today allowing any of us to throw together a meal very much like that eaten by the ordinary people, the plebians of Rome. And, if you're feeling adventurous in the kitchen, you can also reproduce the more exotic offerings which once graced the table of Emperors.
Prepare an Ancient Roman Meal
You don't have to prepare and cook a Giraffe or a Flamingo to have an Ancient Roman meal, here are some simple recipes which are almost authentic.
I've made all of these dishes in my kitchen and can vouch for their simplicity. Anyway, who's going to argue about fish sauce?
An Ancient Roman Kitchen
From The Pompejanum, the reproduction of a Roman house, built in Aschaffenburg in 1840-1848 for King Ludwig I of Bavaria,. The Pompejanum (Pompeiianum) is now a Museum.
Roman Ingredients
Roman food was heavily reliant on fish sauce for its success. Wine, honey, vinegar, oil and fish sauce combined to create a balance of sweet-sour-salt.
Caroenum : Very sweet cooking wine, reduced to one-third its volume by boiling, and mixed with honey. You can add honey to a sweet wine or grape juice.
Defrutum : Thick fruit syrup, or a sort of Roman marmalade.
Garum : Fish Sauce. This was used to make foods salty in taste. You can substitute sauce from the Asian Supermarket. Nuoc Mam, Nam Pha.
Liquamen : is "any kind of culinary liquid, depending upon the occasion". It may be interpreted as brine or another word for light fish sauce. Use a pinch of salt in white wine if you have no fish sauce.
Pepper : For 'pepper', use nutmeg or allspice.
Want to cook a Dormouse?
From Apicius : 'Pound with pepper, caraway, cumin, bay leaves, dates, honey, vinegar, wine, liquamen and olive oil, then roast.'
A dormouse is hard to come by these days.so, in this recipe, I marinate chicken drumsticks overnight and call them dormouse (Gliris)
Cook Time
Prep Time: 20 min
Total Time: Marinate overnight
Serves: 2 - 4
- 8 Chicken drumsticks
- 1 cup plain all-purpose flour
- 2 teaspoons cumin seeds
- 2 teaspoons caraway seeds
- 2 teaspoons sweet paprika powder
- tablespoon honey
- 2 bay leaves
- A little vegetable oil
- Crush the cumin seeds using a mortar and pestle or equivalent
- Put the flour in a plastic bag with the crushed cumin, bay leaves, caraway and paprika..
- Lightly dab some vegetable oil on the drumsticks and toss them in the bag with the flour.
- Drop the honey into the bag. Give it a swirl around and leave the bag in the frig overnight so the flavours sink in.
- Place the drumsticks in a lightly oiled baking pan and bake for 20 - 30 mins, or until a skewer pushed into the thickest part releases only clear juice
Do you really want to cook a Dormouse?
In Ancient Roman times the dormouse was a delicacy, but these days it's one of the greatest threats to native British woodland.
After escaping from a private collection in the early 1900s, these rodents strip bark from trees, destroy fruit crops and, incidentally, chew through electrical wiring in homes.
It's listed as an invasive threat and no one would mind if you cooked a few.
Thynnus (Tuna)
I based this recipe on Patrick Faas' Around the Roman Table: Food and Feasting in Ancient Rome.
What the Romans called the Ingredients:
Ius in cordula assa : : piper, ligustcum, mentam, cepam, aceti modicum et oleum.
What we call the Ingredients:
sauce for roast tuna : : pepper, lovage, mint, onion, a little vinegar, and oil.
Cook Time
Prep Time: 5 minutes
Total Time: 5 minutes
Serves: Depending on the tuna steaks - one per person
- 2 large Tuna Steaks and ingredients for the vinaigrette- -
- 3 tablespoons strong vinegar
- 2 tablespoons garum (or vinegar mixed with a little anchovy paste)
- cup of olive oil
- 4 finely chopped shallots
- 1 teaspoon pepper
- 1 teaspoon lovage seeds (or celery seeds)
- bunch of fresh mint
- olives to garnish
- Brush your tuna fillets with oil, pepper and salt.
- Grill them on one side over a hot barbecue.
- Turn them and brush the roasted side with the vinaigrette. Repeat.
- Don't let tuna overcook, the flesh should be pink inside.
- Serve with the remains of the vinaigrette.
- Garnish with a few olives
Globuli (sweet fried curd cheese)
Curd Cheese?
Curd cheese is similar to cream cheese but with a lower fat content with a light flavour, colour and texture.
I use ricotta or sometimes bocconcini for this delightful sweet
Cook Time
Prep Time: 1 minute
Total Time: 1 minute
- Curd cheese, 500 g or about 1lb
- A cup of semolina
- honey
- olive oil
- Drain the the curd cheese. Use a sieve or colander, or let it hang in cheese cloth, or squash excess moisture out any way which suits you
- Mix with the semolina into a loose dough and let it sit for a few hours. (Have a sip of Vino Caroenum while you wait).
- With wet hands, form the mixture into dumplings.
- Quickly fry dumplings in olive oil for a few minutes.
- Drain and roll in honey.
Libum (Ancient Roman Cheesecake)
Libum was a sacrificial cake offered to the household spirits. The Romans ate it as well!
The following recipe is from Cato, the Consul, statesman and soldier, recorded in his book (instructions for running a farming property), De Agri Cultura. I'm sure he got the recipe from his Cook.
Cook Time
Prep Time: 5 minutes
Total Time: 45 minutes
- Half a cup of plain all-purpose flour
- One cup of ricotta cheese
- 1 egg, beaten
- bay leaves
- Half a cup of clear honey
- Sift the flour in a mixing bowl.
- Beat the cheese until soft, stir into the flour.
- Add the beaten egg to the flour/cheese mixture, forming a soft dough
- Divide the dough into four and shape each piece into a bun
- Place on a greased baking tray with a fresh bay leaf underneath.
- Heat the oven to 375F - 190C. Bake for 35 - 40 minutes until golden brown.
- Warm the honey, pour into a flat plate, place the buns on it to rest till the honey is absorbed
Isicia Omentata (Hamburgers)
Feed the Kids on Ancient Roman Food
Tell the kids they're going to have an Ancient Rome lunch.The food of gladiators, the food of emperors! Then serve them up ..
Pita bread with falafel and feta cheese
Chopped apples with yogurt and honey
They want meat? Make up some hamburgers - ( Isicia Omentata) - from the following recipe. Leave out the wine, go easy on the peppercorns, use a little water to moisten instead. Orange juice gives an exotic flavour..
Remember No tomato sauce. No ketchup
Cook Time
Prep Time: 10 minutes
Total Time: 20 minutes
Serves: a horde of children
- 500 g minced meat
- 1 french roll, soaked in white wine (or non-alcoholic cider)
- 1/2 tsp freshly ground pepper
- 50 ml Liquamen (or a little white wine with a pinch of salt - or orange juice)
- some pine nuts and green peppercorns
- a little Caroenum (optional)
- Baking foil
What's Caroenum?
Caroenum is a very sweet cooking wine, reduced to one-third its volume by boiling, and mixed with honey. Powerful stuff! You can substitute Marsala or Sweet Sherry, or add honey to grape juice
- Mix minced meat with the soaked french roll. Grind up the pine nuts and peppercorns, mix into the meat.
- Form small balls with your hands.. Put them in a little packet of foil and add a splash of Caroenum. Close the packet.
- Bake for 10 - 15 mins.
Kydonion syn Meliti - Quince with Honey, from Apicius
With quince boil it with honey and a little wine, after peeling off the skin; or remove the core and steep in honey, mold dough made from spelt around the whole quince, place in the embers and let the dough burn away completely; then this burnt layer is removed and so the whole quince is cooked and all the honey absorbed.
Ova Spongia ex Lacte
Eggs with Honey
Do you remember Ova Spongia ex Lacte from schooldays? Here's the full recipe from Apicius' De Re Coquinaria.
Ova spongia ex lacte: ova quattuor, lactis heminam, olei unciam in se dissolvis, ita ut unum corpus facias. in patellam subtilem adicies olei modicum, facies ut bulliat, et adicies impensam quam parasti. una parte cum fuerit coctum, in disco vertes, melle perfundis, piper adspargis et inferes.
Let's cook it!
Ova Spongia recipe
- 3 TBLsp honey
- 4 eggs
- 275 ml milk
- 25 g butter
- 1 TBLsp olive oil
- Good pinch of black pepper
- Beat together the eggs, milk and oil.
- Pour a little olive oil into a frying pan and heat. When this is sizzling add the omelette mixture.
- Agitate with a fork until the mix starts to solidify (this will make for a lighter omelette).
- When thoroughly cooked on one side turn the omelette over and cook on the other side. Fold in half and turn out onto a plate.
- Warm the honey and pour over the omelette. Fold this over once more and cut into thick slices.
- Sprinkle with black pepper and serve.
Allspice, Fructus Pimentae, with its pleasing clove-like aroma can be exchanged for the 'pepper' in many ancient Roman recipes.
It's a handy liitle spice, used by modern cooks for stews, sauces and for flavouring pickled vegetables.
Allspice takes its name from its aroma, which smells like a combination of spices, especially cinnamon, cloves, ginger and nutmeg. In much of the world, allspice is called pimento because the Spanish mistook the fruit for black pepper, which they called pimienta. (This is especially confusing since the Spanish had already called chillies pimientos).
What are these sauces? What's garum?
As they are with modern Romans, sauces and marinades were an essential element in ancient Roman cuisine.
One of the most popular was garum, a salty, pungent sauce made by fermenting fishgut, tails, heads, and other small whole fish in salt for several days out in the sun. Factories, salsamentarii, churned out massive amounts or you could make your own in the courtyard. It was really popular.
We don't need to use the original recipe, you can use a bit of Worcestershire sauce instead. Or buy a bottle of fish sauce from the Asian Supermarket - either Nuoc Mam or Nam Plah.
* Look for sauce of a light amber colour and the words nhi or thuong hang on the label. These terms indicate that the condiment came from the first extraction of liquid from the fermented fish. Grades of fish sauces are similar to that of olive oils. The first extraction is of the highest quality
Garum - Fish Sauce
Garum, as the Romans made it
Or why I buy my fish sauce at the Supermarket
From Gargilius Martialis, De medicina et de virtute herbarum
Use fatty fish, for example, sardines, and a well-sealed (pitched) container with a 26-35 quart capacity.
Add dried, aromatic herbs possessing a strong flavor, such as dill, coriander, fennel, celery, mint, oregano, and others, making a layer on the bottom of the container; then put down a layer of fish (if small, leave them whole, if large, use pieces) and over this, add a layer of salt two fingers high.
Repeat these layers until the container is filled. Let it rest for seven days in the sun. Then mix the sauce daily for 20 days. After that, it becomes a liquid.
If you want to try these instructions, best of luck to you! Please let me know how it went.
Reconstruction of a Roman Kitchen
A Taste of Ancient Rome
Giacosa gives us the original Latin text of several recipes from the ancient world, translates them into simple English and then gives us a list of ingredients which are available in our modern world to make these dishes.
Easily create ancient Roman recipes with ingredients of today.
A Roman Banquet
A medium menu
How can you can talk about the food of Ancient Rome without at least one mention of a banquet?
Here's one of the menus from Apicius for a medium- sized banquet.
It tells us a lot about the extent of Roman trade, for the ostrich and flamingo came from Africa, the dates from Judea, and the spices from throughout the Empire.
- Jellyfish and eggs
- Sow's udders stuffed with salted sea urchins
- Patina of brains cooked with milk and eggs
- Boiled tree fungi with peppered fish-fat sauce
- Sea urchins with spices, honey, oil, and egg sauce
Main Courses
- Fallow deer roasted with onion sauce, rue, Jericho dates, raisins, oil, and honey
- Boiled ostrich with sweet sauce
- Turtledove boiled in its feathers
- Roast Parrot
- Dormice stuffed with pork and pine kernels
- Ham boiled with figs and bay leaves, rubbed with honey, baked in pastry crust
- Flamingo boiled with dates
- Fricassee of roses with pastry
- Pitted dates stuffed with nuts and pine kernels, fried in honey
- Hot African sweet-wine cakes with honey
In the Words of a Roman
The Arbiter of Elegance
Gaius Petronius (27-66 ) was the advisor to the Emperor Nero in matters of luxury and extravagance. Petronius boasted an official title - arbiter elegantiae. As befitted his office, he slept days and partied nights.
Here's an account of a light supper which he attended in the course of his research into the good life :
""After a generous rubdown with oil, we put on dinner clothes. We were taken into the next room where we found three couches drawn up and a table, very luxuriously laid out, awaiting us.
We were invited to take our seats. Immediately, Egyptian slaves came in and poured ice water over our hands. The starters were served. On a large tray stood a donkey made of bronze. On its back were two baskets, one holding green olives, and the other black. On either side were dormice, dipped in honey and rolled in poppy seed. Nearby, on a silver grill, piping hot, lay small sausages.
As for wine, we were fairly swimming in it."
Fast Food of Ancient Rome
It wasn't all banquets
An Ancient Roman could also eat at a thermopolium, something like a small wine bar selling warmed wines and the ancient equivalent of fast food.
There were plenty of these hot food shops and taverna, places instantly recognisable to us as the handy corner shop blessed with a liquor license. A tradesman, sandal-seller or clerk would pick up some hot sausage, bread, cheese, dates and, of course, wine, on the way home.
Unless stated otherwise, photos are from
- Senior at Large — In a Sicilian Kitchen
La Cucina Siciliana
What do you think of Ancient Roman food?
Would you eat Ancient Roman food?
Fancy a Roman feast? While lying on the couch, you can leave a comment
© 2008 Susanna Duffy
Chalk a Message on the Kitchen Wall
Beautiful website lol
I like bikkies and cheese in my hair
I like ghoti tacos
I loike fesh
Being Italian, I love ricotta cheese, so that Libum sounds delicious! I'll be trying that soon (albeit minus the bay leave) and I'm really curious to see how it turns out - letting the "buns" soak up the honey seems like a great idea. Thank you!
I'm glad you found a substitute for the dormouse in the one recipe. Not sure I could eat one.
We have little chipmunks, maybe they would be good in that recipe.
These all look so fabulous! I think the Baked Dormouse might have to go on the menu this week!
Globuli sounds good and close to the Indian sweet Gulab Jamun, which happen to be one of my favorite dessert
I had no idea these old recipes were still accessible to us today. Even more surprising is that they can be prepared in modern kitchens. They don't look very complicated either. I am seriously going to try that chicken. It looks so delicious.
I like the look of the Ancient Roman Cheesecake. My daughter said she would dress up as a household spirit and accept the offering - all of it.
I think we'll have to find out how they cooked their jellyfish and eggs it sounds intriguing and there's certainly lots of jellyfish about.
I think it would be quite fun to host an Ancient Roman Feast for friends one day, certainly something different and we could feel like we were being quite cultural while stuffing our faces!!
interesting read and recipe
I love Italian and authentic Roman cuisine. Thanks for sharing these recipes. These will surely be added to my cookbook.
Thank you for the amazing recipes from Ancient Rome.
My husband and I been through so many trials with family deaths and his illness, that changed both of us. I became an unhappy and un appreciative wife. My husband left me for another woman. My relationship with the Lord was suffering. His leaving was the worst thing that ever happened to me. One day while I was going through the internet I saw a man called Dr. Ibolo, I contacted him he told me to have only trust, hope, faith and courage as he proceeds with my spell work, in 2days my lost husband came back.... And now we are one happy family and his sickness is no more and I got pregnant in few days and now we have a baby boy... Thanks to Dr. Ibolo, you can contact him on his email at (firstname.lastname@example.com) for help
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Thank you and be blessed
The history and food seem very interesting.
What a menu! I admit that some of it sounded good (not the dormouse...). Thanks for sharing these recipes!
What a fascinating read! We were just in Italy on vacation and visited Pompeii - I was fascinated by the stores that had that served hot food back in 710 b.c.
Excellent lens, can not wait to try cheesecake!
I love history and food, so this was a perfect combination. Your lens was featured on our G+ page today!


text: I was wondering if anyone has workplace safety programs? If you have a written handbook/ manual that you go by or what? Would just like to know more about it. Do you have daily, weekly, monthly meetings with employees. If anyone can help out, that would be greatly appreciated. Thank You


text:
State Codes and Statutes
Statutes > Missouri > T38 > C569 > 569_170
Burglary in the second degree.
569.170. 1. A person commits the crime of burglary in thesecond degree when he knowingly enters unlawfully or knowinglyremains unlawfully in a building or inhabitable structure for thepurpose of committing a crime therein.
2. Burglary in the second degree is a class C felony.
Effective 1-1-79
(1980) Trespass in the second degree is not a lesser included offense of burglary, as it does not require unlawful entering of a building. State v. Neighbors (A.), 613 S.W.2d 143.
(1980) Trespass in the first degree is lesser included offense of burglary in second degree, as every element of lesser offense is included in greater offense of burglary, and it is impossible to commit burglary without also committing trespass. State v. Neighbors (A.), 613 S.W.2d 143.
(1984) Crime of burglary requires proof of incursion into a building or inhabitable structure; an unlicensed entry upon open real property for whatever unlawful purpose does not constitute burglary. State v. Butler (Mo.App.), 665 S.W.2d 41.
(1984) An entry, however slight, by any part of the defendant's body is sufficient to establish the element of entry. State v. Sincup (Mo.App.), 674 S.W.2d 689.


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4mm Heart-Shaped Lab-Created Ruby Stud Earrings in 10K White Gold with CZ
Item# 18243857
A romantic surprise. These 4mm heart-shaped lab-created ruby earrings in 10K white gold feature round cubic zirconia accents. The earrings secure with friction back closures. Wish her a Happy Birthday in July with ruby birthstone jewelry.
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About the Book
Every morning is different, nature has his own way to
Features & Details
- Category Arts & Photography
Large Format Landscape, 13×11 in, 33×28 cm
200 Pages
- Publish Date Jan 03, 2012
- Tags Sun raise, morning lights, beautiful scenery clouds and lights
See More
About the Creator
Hernan Vanegas
Cancun Mexico
Colombian Hotelier Resident in Mexico, Cancun is my place, Photographer by hobby, love to travel, married two sons, having a great time traveling around Mexico I have the opportunity to expose some of my photo work in a collective colombian photographers exhibition in Barcelona Spain November 2013 and in Cartagena Colombia December 2013,Sttutgard Germany June 2014, Tijuana, Mexico July 2014.
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By Gary Thorne, Special for USA TODAY
Last Friday night in New York the Major League Baseball Players Alumni Association held its annual Legends for Youth Dinner.
The event raises money for youth baseball clinics that the organization holds, with many former players as instructors.
What brings hundreds to the dinner is the appearance of alumni members who sign autographs and interact with guests.
Hall of Famer Tom Seaver was presented with a lifetime achievement award. Orlando Cepeda, Association president Brooks Robinson, Al Leiter and Graig Nettles were among the attendees.
As master of ceremonies for the event for the past few years, I always hope the program will send the fans home longing for more. This year we invited a group of players on stage to ask questions of one another.
Sometimes it just works.
One of the former players on hand was Jim "Mudcat" Grant. Grant is one of just 13 African American pitchers to win at least 20 games in a season. He was the first to do so in 1965 with a 21-7 record for the Twins.
He has written a book, The Black Aces: Baseball's Only African-American Twenty-Game Winners, and speaks often on the proud history of African-Americans in the game and in society.
He pitched from 1958 to 1971 — times in which segregation still hung nastily in the forefront of our country.
He spoke of his days in the game with Baseball Prospectus in March of this year.
"It wasn't long after Jackie Robinson broke the color barrier, and Larry Doby (the first African-American to play in the American League) was my roommate, so I viewed myself as an African-American pitcher, and the only one who was a starter. … It was a time where you had to live in black hotels; when we were down in spring training, it was not being able to eat in restaurants — you had to read in a newspaper where you could go to eat. It was needing to wait for a black taxi, which would often take two hours because there weren't as many of them. So I was very aware of where I was. I was also aware that I was representing not only black athletes, but the entire African-American community. I was trying to help show America that we could live together, and that we could play together."
Grant wrote a poem about those days entitled Life, which included these verses:
Life is like a game of baseball,
You play it everyday.
It isn't just the breaks you get,
But the kind of game you play.
This game will not be easy,
There'll be trouble, there'll be strife.
To make the winning runs, my boy,
For this game is played on the field of life.
Fast forwarded to last Friday night when Grant took the stage with other former players to join in the player-to-player question period.
Each asked a question of the player seated to his left. Al Leiter turned to Grant and asked Grant's thoughts on the election of Barack Obama as president.
For a split-second, everything in the room stopped.
Then Grant began speaking.
"I thought back to the wonderful day in 1947 when Jackie Robinson came into the major leagues and a few months later when Larry Doby, who was my roommate in the minor leagues, came up. You couldn't help but think that baseball a long time ago showed America that we could play together, live together, worship together and really showed the world how we could change," Grant said.
"I cannot tell you how the last few days have affected my life."
Grant then leaned forward and looked to the last chair down the row to his left. There sat Brooks Robinson.
"He was from Little Rock," said Grant of Robinson, "and we watched him all the time."
Grant and his black teammates were waiting to see if the remnants of segregation and civil rights strife that had battered Little Rock would show up in the white star's actions.
"Oh, we watched him all right," said Grant.
Then Grant leaned more forward and looked directly at Robinson, who was looking back.
"Listen to me," said Grant, "Brooks Robinson is one of the best men you will ever meet. You could always talk to him. You could feel that this was a guy who was a fair man and didn't hold to the circumstances that happened back in those days. I want to say to Brooks, thank you very much."
In that moment, I was reminded of a poem.
It isn't just the breaks you get,
But the kind of game you play.
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Only a few years ago, making a website was not easy. If you had a friend or a relative that knew how, you could have one made. Otherwise, you had to pay someone to help you lay out your vision. Or, you could have done what I did, which is, learn HTML and CSS yourself, and make your own web pages. However, the problem with those old websites is, they didn't do anything. You can post articles and pictures, have a pretty color scheme. But all your site visitors could do was read. There was no interaction, no conversation. The web was just a bunch of pages of news and stories.
Well, it finally happened. I took a lot of chances over the years by not backing up my sites as much as I should have. This time, I paid the price and lost everything. The next thing I do will be to back up all my sites today. I have some sites with over 100 articles, hundreds of pictures, contacts, and paid links. That could really be a mess! In the meantime, I will have to start all over with this one.


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Jeri Brown
|jazz female vocalists vocal jazz jazz vocalist
|1980s 1990s 2000s
|allmusic image wikipedia
20 March 1952, St. Louis, Missouri, USA. Based in Nova Scotia, Canada, Brown is one of that countrys foremost contemporary jazz singing talents. Raised in St. Louis, she studied classical piano, percussion and vocals at the St. Louis Institute, before studying voice with Rosa Henderson of the Metropolitan Opera. During her 20s she sang with the St. Louis Symphony Orchestra and toured Europe. However, by now her interest in jazz had grown, sparked by conversations with her uncle, trumpeter Virgil Carter, who had at one time brought Miles Davis home to practise in the family basement. After her light opera tour of Europe in 1973, Brown moved to Chicago to work with Young-Holt Unlimited for a year. Subsequent work included stints with musicians such as Joe Lovano and Ernie Krivda. She made her solo debut in 1982 with Captain Bad for the Atlanta-based Antelope Records. One further album for the same label followed before her first release on her own Jongleur...