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Hyperbolic Hemivariational Inequalities for Dynamic Viscoelastic Contact Problems
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DOI: 10.1007/s10659-012-9380-7
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- Kulig, A. J Elast (2013) 110: 1. doi:10.1007/s10659-012-9380-7
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The paper deals with second order nonlinear evolution inclusions and their applications. First, we study an evolution inclusion involving Volterra-type integral operator which is considered within the framework of an evolution triple of spaces. We provide a result on the unique solvability of the Cauchy problem for the inclusion. Next, we examine a dynamic frictional contact problem of viscoelasticity for materials with long memory and derive a weak formulation of the model in the form of a hemivariational inequality. Then, we embed the hemivariational inequality into a class of second order evolution inclusions involving Volterra-type integral operator and indicate how the result on evolution inclusion is applicable to the model of the contact problem. We conclude with examples of the subdifferential boundary conditions for different types of frictional contact.
KeywordsEvolution inclusion Pseudomonotone operator Volterra-type operator Multifunction Hyperbolic Contact problem Hemivariational inequality Viscoelasticity Clarke subdifferential
Mathematics Subject Classification35L90 35R70 45P05 47H04 47H05 74H20 74H25
1 Introduction
An important number of problems arising in Mechanics, Physics and Engineering Science lead to mathematical models expressed in terms of nonlinear inclusions and hemivariational inequalities. For this reason the mathematical literature dedicated to this field is extensive and the progress made in the last decades is impressive. It concerns both results on the existence, uniqueness, regularity and behavior of solutions for various classes of nonlinear inclusions as well as results on numerical approach of the solution for the corresponding problems.
Our study includes the modeling of a mechanical problem and its variational analysis. We derive the hemivariational inequality for the displacement field from nonconvex superpotentials through the generalized Clarke subdifferential. The novelty of the model is to deal with nonlinear elasticity and viscosity operators and to consider the coupling between two kinds of nonmonotone possibly multivalued boundary conditions which depend on the normal (respectively, tangential) components of both the displacement and velocity. We recall that the notion of hemivariational inequality is based on the generalized gradient of Clarke [6] and has been introduced in the early 1980s by Panagiotopoulos [33, 34]. We also note that the existence of solutions to the second order evolution inclusions as well as to the corresponding dynamic hemivariational inequalities has been studied, for instance, in Migórski [22, 23, 24, 25], Migórski and Ochal [27, 28] and Kulig [17, 18].
Finally, in order to illustrate the cross fertilization between rigorous mathematical description and Nonlinear Analysis on one hand, and modeling and applications on the other hand, we provide several examples of contact and friction subdifferential boundary conditions.
The paper is structured as follows. In Sect. 2 we recall some preliminary material. In Sect. 3 we describe the dynamic viscoelastic contact problem and present its classical and weak formulation. Next, we recall a result on the existence and uniqueness of solutions to the Cauchy problem for the second order nonlinear evolution inclusion involving a Volterra-type integral operator. We establish the link between a nonlinear evolution inclusion and the hemivariational inequality, and apply the aforementioned results to the viscoelastic contact problem with a memory term. The review of several examples of contact and friction subdifferential boundary conditions which illustrates the applicability of our results is provided in Sect. 4.
2 Preliminaries
In this section we recall the notation and basic definitions needed in the sequel.
Given a Banach space (X,∥⋅∥X), we use the symbol w-X to denote the space X endowed with the weak topology. The class of linear and bounded operators from X to X∗ is denoted by \(\mathcal{L}(X,X^{*})\). If U⊂X, then we have ∥U∥X=sup{∥x∥X:x∈U}. The duality between X and its dual is denoted by \(\langle\cdot,\cdot\rangle_{X^{*} \times X}\).
Given v∈H1 we denote its trace γv on Γ by v, where γ:H1(Γ;ℝd)→H1/2(Γ;ℝd)⊂L2(Γ;ℝd) is the trace map. Let n denote the outward unit normal vector to Γ. Since Γ is Lipschitz continuous, the normal vector is defined a.e. on Γ. For v∈H1/2(Γ;ℝd) we denote its normal and tangential components by vN=v⋅n and vT=v−vNn.
Let V be a separable Banach space. We identify H with its dual and we consider a Gelfand triple V⊂H⊂V∗ where all embeddings are compact, dense and continuous (see [7, 44]). We will need the following spaces \(\mathcal{V} = L^{2}(0,T;V)\) and \(\mathcal{W} = \{ w \in\mathcal{V} : w' \in\mathcal{V}^{*} \}\). The time derivative involved in the definition of \(\mathcal{W}\) is understood in the sense of vector valued distributions. It is well known that \(\mathcal{W}\) is a separable Banach space equipped with the norm \(\| v \|_{\mathcal{W}} = \|v\|_{\mathcal{V}} + \|v\|_{\mathcal{V}^{*}}\) and \(\mathcal{W} \subset\mathcal{V} \subset L^{2}(0,T;H) \subset {\mathcal{V}^{*}}\).
Let us recall some definitions needed in the next sections.
Measurable multifunction
Let (Ω,Σ) be a measurable space, \(\mathcal{X}\) be a separable Banach space and \(F \colon\Omega\to{2}^{\mathcal{X}}\). The multifunction F is said to be measurable if for every U⊂X open, we have F−(U)={ω∈Ω:F(ω)∩U≠∅}∈Σ.
Generalized directional derivative
Generalized gradient
Let X be a Banach space. The generalized gradient of a function h:X→ℝ at x∈X, denoted by ∂h(x), is a subset of a dual space X∗ given by \(\partial{h}(x) =\{ \zeta\in X^{*} \mid h^{0}(x; v) \ge\langle\zeta, v \rangle_{X^{*}\times X}\ \mbox{for all} \ v \in X \}\).
Regular function
A locally Lipschitz function h is called regular (in the sense of Clarke) at x∈X if for all v∈X the one-sided directional derivative h′(x;v) exists and satisfies h0(x;v)=h′(x;v) for all v∈X.
Finally we state results needed in a sequel whose proofs can be found in Kulig [18].
Lemma 1
- (i)
φ(⋅,y) is continuous for ally∈Y;
- (ii)
φ(x,⋅) is locally Lipschitz onYfor allx∈X;
- (iii)there is a constantc>0 such that for allη∈∂φ(x,y), we havewhere∂φdenotes the generalized gradient ofφ(x,⋅).$$\| \eta\|_{Y^*} \le c \bigl(1 + \| x \|_X + \| y\|_Y \bigr) \quad \mbox{\textit{for\ all}} \ x \in X, \ y \in Y,$$
Proposition 2
LetXbe a separable reflexive Banach space, 0<T<∞ andφ:(0,T)×X→ℝ be a function such thatφ(⋅,x) is measurable for allx∈Xandφ(t,⋅) is locally Lipschitz for allt∈(0,T). Then the multifunction (0,T)×X∋(t,x)↦∂φ(t,x)⊂X∗is measurable, where∂φdenotes the Clarke generalized gradient ofφ(t,⋅).
3 Dynamic Viscoelastic Contact Problem with Memory Term
In this section we present a short description of the modeled process, give its weak formulation which is a hyperbolic hemivariational inequality and obtain results on existence and uniqueness of weak solutions.
3.1 Physical Setting of the Problem
The physical setting and the process are as follows. The set Ω is occupied by a viscoelastic body in ℝd (d=2, 3 in applications) which is referred to as the reference configuration. We assume that Ω is a bounded domain with Lipschitz boundary Γ which is divided into three mutually disjoint measurable parts ΓD, ΓN and ΓC with m(ΓD)>0.
We study the process of evolution of the mechanical state in time interval [0,T], 0<T<∞. The system evolves in time as a result of applied volume forces and surface tractions. The description of this evolution is done by introducing a vector function u=u(x,t)=(u1(x,t),…,ud(x,t)) which describes the displacement at time t of a particle that has the position x=(x1,…,xd) in the reference configuration. We denote by σ=σ(x,t)=(σij(x,t)) the stress tensor and by ε(u)=(εij(u)) the linearized (small) strain tensor whose components are given by (a compatibility condition) \(\varepsilon_{ij} = \varepsilon_{ij}(u) = \frac{1}{2} (u_{i,j} + u_{j,i})\), where i, j=1,…,d. In cases where an index appears twice, we use the summation convention. We also put Q=Ω×(0,T).
3.2 Weak Formulation of the Problem
- \(\underline{H({\mathcal{A}})}\):
- The viscosity operator \({\mathcal{A}} \colon Q \times{ \mathbb {S}^{d}} \to{ \mathbb {S}^{d}}\) is such that
- (i)
\({\mathcal{A}}(\cdot,\cdot, \varepsilon)\) is measurable on Q for all \(\varepsilon\in{ \mathbb {S}^{d}}\);
- (ii)
\({\mathcal{A}}(x, t, \cdot)\) is continuous on \({\mathbb {S}^{d}}\) for a.e. (x,t)∈Q;
- (iii)
\(\| {\mathcal{A}}(x,t,\varepsilon) \|_{{\mathbb {S}^{d}}} \le {\widetilde{a_{1}}}(x,t) + {\widetilde{a_{2}}} \| \varepsilon\|_{{\mathbb {S}^{d}}}\) for all \(\varepsilon\in{ \mathbb {S}^{d}}\), a.e. (x,t)∈Q with \({\widetilde{a_{1}}} \in L^{2}(Q)\), \({\widetilde {a_{1}}}\), \({\widetilde{a_{2}}} \ge0\);
- (iv)
\(( {\mathcal{A}}(x, t, \varepsilon_{1}) - {\mathcal{A}} (x, t, \varepsilon_{2}) ): (\varepsilon_{1} - \varepsilon_{2}) \ge{\widetilde{a_{4}}}\| \varepsilon_{1} - \varepsilon_{2} \|^{2}_{\mathbb {S}^{d}}\) for all ε1, \(\varepsilon_{2} \in{ \mathbb {S}^{d}}\), a.e. (x,t)∈Q with \({\widetilde{a_{4}}} > 0\);
- (v)
\({\mathcal{A}}(x,t,\varepsilon) : \varepsilon\ge {\widetilde{a_{3}}} \| \varepsilon\|^{2}_{{\mathbb {S}^{d}}}\) for all \(\varepsilon\in{ \mathbb {S}^{d}}\), a.e. (x,t)∈Q with \({\widetilde{a_{3}}} > 0\).
- (i)
Remark 3
It should be remarked that the growth condition \(H({\mathcal{A}})\)(iii) excludes terms with power greater than one, but is satisfied within linearized viscoelasticity, and is satisfied by truncated operators, cf. [11, 41].
- \(\underline{H({\mathcal{B}})}\):
- The elasticity operator \({\mathcal{B}} \colon Q \times{ \mathbb {S}^{d}} \to{ \mathbb {S}^{d}}\) is such that
- (i)
\({\mathcal{B}}(\cdot,\cdot, \varepsilon)\) is measurable on Q for all ε∈Sd;
- (ii)
\(\| {\mathcal{B}}(x,t,\varepsilon) \|_{{\mathbb {S}^{d}}} \le {\widetilde{b_{1}}}(x,t) + {\widetilde{b_{2}}} \| \varepsilon\|_{{\mathbb {S}^{d}}}\) for all \(\varepsilon\in{ \mathbb {S}^{d}}\), a.e. (x,t)∈Q with \({\widetilde{b_{1}}} \in L^{2}(Q)\), \({\widetilde {b_{1}}}\), \({\widetilde{b_{2}}} \ge0\);
- (iii)
\(\| {\mathcal{B}}(x,t,\varepsilon_{1}) - {\mathcal{B}} (x,t,\varepsilon_{2})\|_{{\mathbb {S}^{d}}}\le L_{\mathcal{B}} \| \varepsilon_{1} - \varepsilon_{2} \|_{\mathbb {S}^{d}}\) for all ε1, \(\varepsilon_{2} \in{ \mathbb {S}^{d}}\), a.e. (x,t)∈Q with \(L_{\mathcal{B}} > 0\).
- (i)
Remark 4
If \({\mathcal{B}} (x, t, \cdot) \in{\mathcal{L}}(\mathbb {S}^{d}, \mathbb {S}^{d})\) for a.e. (x,t)∈Q, the conditions \(H({\mathcal{B}})\)(ii) and (iii) hold. Thus the hypothesis \(H({\mathcal{B}})\) is more general than the ones considered in [23, 24, 25, 26, 27, 32, 35] where the elasticity operator is assumed to be linear (which corresponds to the Hooke law).
- \(\underline{H({\mathcal{C}})}\):
The relaxation operator \({\mathcal{C}} \colon Q \times{ \mathbb {S}^{d}} \to{ \mathbb {S}^{d}}\) is of the form \({\mathcal{C}}(x,t,\varepsilon) = c(x,t) \varepsilon\) and c(x,t)={cijkl(x,t)} with cijkl=cjikl=clkij∈L∞(Q).
- \(\underline{H(f)}\):
f0∈L2(0,T;H), f1∈L2(0,T;L2(ΓN;ℝd)), u0∈V, u1∈H.
- \(\underline{H(j_{k})}\):
- The function jk:ΓC×(0,T)×(ℝd)2×ℝ→ℝ is such that
- (i)
jk(⋅,⋅,ζ,ρ,r) is measurable for all ζ, ρ∈ℝd, r∈ℝ,
jk(⋅,⋅,v(⋅),w(⋅),0)∈L1(ΓC×(0,T)) for all v, w∈L2(ΓC;ℝd);
- (ii)
jk(x,t,⋅,⋅,r) is continuous for all r∈ℝ, a.e. (x,t)∈ΓC×(0,T),
jk(x,t,ζ,ρ,⋅) is locally Lipschitz for all ζ, ρ∈ℝd, a.e. (x,t)∈ΓC×(0,T);
- (iii)
|∂jk(x,t,ζ,ρ,r)|≤ck0+ck1∥ζ∥+ck2∥ρ∥+ck3|r| for all ζ, ρ∈ℝd, r∈ℝ, a.e. (x,t)∈ΓC×(0,T) with ckj≥0, j=0, 1, 2, 3, where ∂jk denotes the Clarke subdifferential of jk(x,t,ζ,ρ,⋅);
- (iv)
\(j^{0}_{k} (x,t, \cdot, \cdot, \cdot; s)\) is upper semicontinuous on (ℝd)2×ℝ for all s∈ℝ, a.e. (x,t)∈ΓC×(0,T), where \(j^{0}_{k}\) denotes the generalized directional derivative of Clarke of jk(x,t,ζ,ρ,⋅) in the direction s.
- (i)
The functions jk for k=3, 4 satisfy the corresponding conditions with the last variable being in ℝd.
- \(\underline{H(j)_{reg}}\):
The functions jk for k=1,…,4 are such that for all ζ, ρ∈ℝd, a.e. (x,t)∈ΓC×(0,T), either all jk(x,t,ζ,ρ,⋅) are regular or all −jk(x,t,ζ,ρ,⋅) are regular for k=1,…,4.
The above hypotheses are realistic with respect to the physical data and the process modeling. We will see this in the specific examples of contact laws which are given in Sect. 4.
3.3 Evolution Inclusion for Hemivariational Inequality
In this section we state a result on the existence of solutions to second order evolution inclusions and apply it to an abstract hemivariational inequality. To this end, let Z=Hδ(Ω;ℝd), δ∈(1/2,1) and γ:Z→L2(ΓC;ℝd) be the trace operator. Let γ∗:L2(ΓC;ℝd)→Z∗ stand for the adjoint operator to γ.
Definition 5
- \(\underline{H(A)}\):
- The operator A:(0,T)×V→V∗ is such that
- (i)
A(⋅,v) is measurable on (0,T) for all v∈V;
- (ii)
A(t,⋅) is strongly monotone for a.e. t∈(0,T), i.e. there exists m1>0 such that 〈A(t,v)−A(t,u),v−u〉≥m1∥v−u∥2 for all u, v∈V, a.e. t∈(0,T);
- (iii)
\(\| A(t, v) \|_{V^{*}} \le a_{0}(t) + a_{1} \| v \|\) for all v∈V, a.e. t∈(0,T) with a0∈L2(0,T), a0≥0 and a1>0;
- (iv)
〈A(t,v),v〉≥α∥v∥2 for all v∈V, a.e. t∈(0,T) with α>0;
- (v)
A(t,⋅) is hemicontinuous for a.e. t∈(0,T).
- (i)
Remark 6
The hypothesis H(A) implies the operator A is pseudomonotone. Indeed, strong monotonicity clearly implies monotonicity which with hemicontinuity entails (cf. Proposition 27.6(a), p. 586, of Zeidler [44]) pseudomonotonicity. We also recall (cf. Remark 1.1.13 of [8]) that for monotone operators, demicontinuity and hemicontinuity are equivalent notions.
- \(\underline{H(B)}\):
- The operator B:(0,T)×V→V∗ is such that
- (i)
B(⋅,v) is measurable on (0,T) for all v∈V;
- (ii)
B(t,⋅) is Lipschitz continuous for a.e. t∈(0,T), i.e. \(\| B(t, u) - B(t, v) \|_{V^{*}} \le L_{B} \| u - v \|\) for all u, v∈V, a.e. t∈(0,T) with LB>0;
- (iii)
\(\| B(t, v) \|_{V^{*}} \le b_{0}(t) + b_{1} \| v \|\) for all v∈V, a.e. t∈(0,T) with b0∈L2(0,T) and b0, b1≥0.
- (i)
- \(\underline{H(C)}\):
The operator C satisfies \(C\in L^{2}(0,T; {\mathcal{L}}(V, V^{*}))\).
- \(\underline{H(F)}\):
- The multifunction \(F \colon(0,T) \times V \times V \to{\mathcal{P}}_{fc}(Z^{*})\) is such that
- (i)
F(⋅,u,v) is measurable on (0,T) for all u, v∈V;
- (ii)
F(t,⋅,⋅) is upper semicontinuous from V×V into w-Z∗ for a.e. t∈(0,T), where V×V is endowed with (Z×Z)-topology;
- (iii)
\(\| F(t, u, v) \|_{Z^{*}} \le d_{0}(t) + d_{1} \| u \| + d_{2} \| v \|\) for all u, v∈V, a.e. t∈(0,T) with d0∈L2(0,T) and d0, d1, d2≥0.
- (i)
- \(\underline{H(F)_{1}}\):
- The multifunction \(F \colon(0,T) \times V \times V \to{\mathcal{P}}_{fc}(Z^{*})\) satisfies H(F) and
- (iv)
\(\langle F(t, u_{1}, v_{1}) - F(t, u_{2}, v_{2}), v_{1} - v_{2} \rangle_{Z^{*}\times Z} \ge -m_{2} \|v_{1} - v_{2}\|^{2} - m_{3} \|v_{1} - v_{2}\| \|u_{1}-u_{2}\|\) for all ui, vi∈V, i=1, 2, a.e. t∈(0,T) with m2, m3≥0.
- (iv)
- \(\underline{(H_{0})}\):
\(f \in{\mathcal{V}}^{*}\), u0∈V, u1∈H.
- \(\underline{(H_{1})}\):
\(\alpha> 2 \sqrt{3} c_{e} (d_{1} T + d_{2})\), where ce>0 is the embedding constant of V into Z, i.e., ∥⋅∥Z≤ce∥⋅∥.
- \(\underline{(H_{2})}\):
\(m_{1} > m_{2} + \frac{1}{\sqrt{2}} m_{3}T\).
Theorem 7
Under the hypothesesH(A), H(B), H(C), H(F)1, (H0), (H1) and (H2), Problem\({\mathcal{P}}\)admits a unique solution.
For the proof, we refer to Theorem 8 of [19].
Lemma 8
Under the hypothesis\(H({\mathcal{A}})\), the operatorA:(0,T)×V→V∗defined by (9) satisfiesH(A) with\(a_{0}(t) = \sqrt{2} \| {\widetilde{a_{1}}} (t) \|_{L^{2}(\Omega)}\), \(a_{1} = \sqrt{2} {\widetilde{a_{2}}}\), \(\alpha= {\widetilde{a_{3}}}\), and\(m_{1} = {\widetilde{a_{4}}}\).
Lemma 9
Under the hypothesis\(H({\mathcal{B}})\), the operatorB:(0,T)×V→V∗defined by (10) satisfiesH(B) with\(L_{B} = L_{\mathcal{B}}\), \(b_{0}(t) = \sqrt{2} \| {\widetilde{b}}_{1}(t) \|_{L^{2}(\Omega)}\)and\(b_{1} = \sqrt{2} {\widetilde{b}}_{2}\).
Lemma 10
Under the hypothesis\(H({\mathcal{C}})\), the operatorCdefined by (11) satisfiesH(C).
- \(\underline{H(g)}\):
- The function g:ΓC×(0,T)×(ℝd)4→ℝ satisfies the following
- (i)
g(⋅,⋅,ζ,ρ,ξ,η) is measurable for all ζ, ρ, ξ, η∈ℝd,
g(⋅,⋅,v(⋅),w(⋅),0,0)∈L1(ΓC×(0,T)) for all v, w∈L2(ΓC;ℝd);
- (ii)
g(x,t,⋅,⋅,ξ,η) is continuous for all ξ, η∈ℝd, a.e. (x,t)∈ΓC×(0,T),
g(x,t,ζ,ρ,⋅,⋅) is locally Lipschitz for all ζ, ρ∈ℝd, a.e. (x,t)∈ΓC×(0,T);
- (iii)
\(\| \partial g (x, t,\zeta, \rho, \xi, \eta) \|_{(\mathbb{R}^{d})^{2}} \le c_{g0} + c_{g1} (\| \zeta\| + \| \xi\|) + c_{g2} (\| \rho\| + \|\eta\|)\) for all ζ, ρ, ξ, η∈ℝd, a.e. (x,t)∈ΓC×(0,T) with cg0, cg1, cg2≥0, where ∂g denotes the Clarke subdifferential of g(x,t,ζ,ρ,⋅,⋅);
- (iv)
g0(x,t,⋅,⋅,⋅,⋅;χ,σ) is upper semicontinuous on (ℝd)4 for a.e. (x,t)∈ΓC×(0,T) and all χ, σ∈ℝd where g0 denotes the generalized directional derivative of Clarke of g(x,t,ζ,ρ,⋅,⋅) in the direction (χ,σ).
- (i)
- \(\underline{H(g)_{reg}}\):
The function g:ΓC×(0,T)×(ℝd)4→ℝ is such that either g(x,t,ζ,ρ,⋅,⋅) or −g(x,t,ζ,ρ,⋅,⋅) is regular for all ζ,ρ∈ℝd, a.e. (x,t)∈ΓC×(0,T).
Lemma 11
If for k=1,…,k the functions −jk are regular in their last variables, then we proceed in the same way as above and deduce the regularity of −g(x,t,ζ,ρ,⋅,⋅) for (x,t)∈ΓC×(0,T) and ζ, ρ∈ℝd. We use the property (−g)0(x,t,ζ,ρ,ξ,η;χ,σ)=g0(x,t,ζ,ρ,ξ,η;−χ,−σ) for all ζ, ρ, ξ, η, χ, σ∈ℝd, a.e. (x,t)∈ΓC×(0,T) (cf. Proposition 2.1.1 of [6]), and again deduce (15).
- \(\underline{H(G)}\):
- The functional G:(0,T)×L2(ΓC;ℝd)4→ℝ is such that
- (i)
G(⋅,w,z,u,v) is measurable for all w, z, u, v∈L2(ΓC;ℝd),
G(⋅,w,z,0,0)∈L1(0,T) for all w, z∈L2(ΓC;ℝd);
- (ii)
G(t,w,z,⋅,⋅) is Lipschitz continuous on bounded subsets of L2(ΓC;ℝd)2 for all w, z∈L2(ΓC;ℝd), a.e. t∈(0,T);
- (iii)
\(\| \partial G (t, w, z, u, v) \|_{L^{2}(\Gamma_{C};\mathbb{R}^{d})^{2}} \le c_{G0} + c_{G1} (\| w \| + \| u \|) + c_{G2} (\| z \| + \| v \| )\) for all w, z, u, v∈L2(ΓC;ℝd), a.e. t∈(0,T) with cG0, cG1, cG2≥0, where ∂G denotes the Clarke subdifferential of G(t,w,z,⋅,⋅);
- (iv)For all w, z, u, v, \({\overline {u}}\), \({\overline {v}} \in L^{2}(\Gamma_{C};\mathbb{R}^{d})\), a.e. t∈(0,T), we havewhere G0 denotes the generalized directional derivative of G(t,w,z,⋅,⋅) at a point (u,v) in the direction \(({\overline {u}}, {\overline {v}})\);$$ G^0(t, w, z, u, v; {\overline {u}}, {\overline {v}}) = \int _{\Gamma_C} g^0 \bigl(x, t, w(x), z(x), u(x), v(x); {\overline {u}}(x), {\overline {v}}(x) \bigr) \,d\Gamma,$$(20)
- (v)
\(G^{0} (t, \cdot, \cdot, \cdot, \cdot; {\overline {u}}, {\overline {v}})\) is upper semicontinuous on L2(ΓC;ℝd)4 for all \({\overline {u}}, {\overline {v}} \in L^{2}(\Gamma_{C};\mathbb{R}^{d})\), a.e. t∈(0,T).
- (i)
- \(\underline{H(G)_{reg}}\):
The functional G:(0,T)×L2(ΓC;ℝd)4→ℝ is such that either G(t,w,z,⋅,⋅) or −G(t,w,z,⋅,⋅) is regular for all w, z∈L2(ΓC;ℝd), a.e. t∈(0,T).
Lemma 12
Under the hypothesesH(g) andH(g)reghold the functionalGdefined by (19) satisfiesH(G) with\(c_{G0} = c_{g0} \sqrt{5 m(\Gamma_{C})}\), \(c_{G1} = c_{g1} \sqrt{5}\), \(c_{G2} = c_{g2} \sqrt{5}\)andH(G)reg.
First, from H(g)(ii) and Lemma 1, it follows that g(x,t,⋅,⋅,⋅,⋅) is continuous on (ℝd)4 which together with H(g)(i) implies that g is a Carathéodory function. Hence (x,t)↦g(x,t,w(x),z(x),u(x),v(x)) is measurable for all w, z, u, v∈L2(ΓC;ℝd) and subsequently the integrand of (19) is a measurable function of x.
Before we establish the properties of the multifunction F given by (22), we need the following auxiliary lemma (cf. [18]).
Lemma 13
Let (Ω,Σ) be a measurable space, Y1, Y2be separable Banach spaces, \(A \in{\mathcal{L}}(Y_{1}, Y_{2})\)and let\(G \colon\Omega\to{\mathcal{P}}_{wkc}(Y_{1})\)be measurable. Then the multifunction\(F \colon\Omega\to{\mathcal{P}}_{wkc}(Y_{2})\)given byF(ω)=AG(ω) forω∈Ω is measurable.
Lemma 14
UnderH(G) andH(G)reg, the multifunction\(F \colon(0,T) \times V \times V \to2^{Z^{*}}\)defined by (22) satisfiesH(F) withd0(t)=cG0∥γ∥, d1=2cecG1∥γ∥2andd2=2cecG2∥γ∥2.
The fact that the mapping F has nonempty and convex values follows from the nonemptiness and convexity of values of the Clarke subdifferential of G (cf. Proposition 2.1.2 of [6]). Because the values of the subdifferential ∂G(t,w,z,⋅,⋅) are weakly closed subsets of L2(ΓC;ℝd), using H(G)1, we can also easily check that the mapping F has closed values in Z∗.
- \(\underline{H(j_{1})_{1}}\):
- j1:ΓC×(0,T)×(ℝd)2×ℝ→ℝ is such thatfor all ζ1, ζ2, ρ1, ρ2∈ℝd, r1, r2∈ℝ, a.e. (x,t)∈ΓC×(0,T) with a constant L1≥0.$$\bigl| \partial j_1 (x, t,\zeta_1, \rho_1,r_1) - \partial j_1 (x, t,\zeta_2,\rho_2, r_2)\bigr| \le L_1 \bigl( \| \zeta_1- \zeta_2 \| + \| \rho_1 - \rho_2 \| +|r_1 - r_2| \bigr)$$
- \(\underline{H(j_{2})_{1}}\):
- j2:ΓC×(0,T)×(ℝd)2×ℝ→ℝ is such that
- \(\underline{H(j_{3})_{1}}\):
- j3:ΓC×(0,T)×(ℝd)3→ℝ is such thatfor all ζ1, ζ2, ρ1, ρ2, θ1, θ2∈ℝd, a.e. (x,t)∈ΓC×(0,T) with a constant L3≥0.$$\bigl\| \partial j_3 (x, t,\zeta_1, \rho_1,\theta_1) - \partial j_3 (x, t,\zeta_2,\rho_2, \theta_2)\bigr\| \le L_3 \bigl( \|\zeta_1 - \zeta_2 \| + \| \rho_1 -\rho_2 \| + \| \theta_1 - \theta_2 \| \bigr)$$
- \(\underline{H(j_{4})_{1}}\):
- j4:ΓC×(0,T)×(ℝd)3→ℝ is such that
Remark 15
The hypothesis H(j2)1 (and H(j4)1) has been introduced and used earlier in [23] (under the name of relaxed monotonicity condition) in the case when j2 (and j4) does not depend on the variables ζ and ρ.
Lemma 16
It is clear that under the hypotheses, the condition H(j)reg holds. By Lemma 11 we know that the integrand g given by (14) satisfies H(g) and H(g)reg. Hence by Lemma 12, it follows that the functional G given by (19) satisfies H(G). Using Lemma 14, under H(G), we obtain that the multifunction F satisfies H(F).
In order to formulate and prove the results on the existence and uniqueness of solutions to the hemivariational inequality in Problem (HVI), we need the following two lemmas.
Lemma 17
Under hypotheses\(H({\mathcal{A}})\), \(H({\mathcal{B}})\), \(H({\mathcal{C}})\), H(f) andH(jk) fork=1,…,4, every solution of the Problem\(\mathcal{P}\)with the multivalued mapping of the form (22), withG:(0,T)×L2(ΓC;ℝd)4→ℝ of the form (19) and its integrandg:ΓC×(0,T)×(ℝd)4→ℝ given by (14), and the operatorsA, BandCdefined by (9), (10) and (11) respectively, is a solution to Problem (HVI).
Lemma 18
Assume the function definitions and hypotheses of Lemma 17. If eitherj1=j3=0 orj2=j4=0, thenuis a solution to Problem (HVI) if and only ifuis a solution to Problem\(\mathcal{P}\).
The case when j2=j4=0 can be treated in an analogous way. This completes the proof of the lemma. □
The following are the existence result for the hemivariational inequality in Problem (HVI) which are the direct conclusion from the lemmas above and Theorem 7.
Theorem 19
Theorem 20
Assume the hypotheses of Theorem 19. If, in addition, eitherj1=j3=0 orj2=j4=0, then the hemivariational inequality in Problem (HVI) admits a unique solution.
4 Applications to Viscoelastic Mechanical Problems
4.1 Prescribed Normal Stress and Nonmonotone Friction Laws
4.1.1 Nonmonotone Friction Independent of Slip and Slip Rate
4.1.2 Contact with Nonmonotone Normal Damped Response
4.2 Viscous Contact with Tresca's Friction Law
4.3 Other Nonmonotone Friction Contact Laws
We end this section with indications on specific applications of research on contact problems. It is of importance to provide various applications of the theoretical results to contact problems arising in real world. The applications concern the following areas.
Construction and exploitation of machines
The understanding of contact problems are extremely important in various branches of engineering such as structural foundations, bearings, metal forming processes, drilling problems, the simulation of car crashes, the car braking system, contact of train wheels with the rails, a shoe with the floor, machine tools, bearings, motors, turbines, cooling of electronic devices, joints in mechanical devices, ski lubricants, and many more, cf., e.g., Andrews et al. [4], Chau et al. [5], Kuttler and Shillor [20, 21], Rochdi et al. [37] and Sofonea and Matei [43].
The applications concerns the medical field of arthoplasty where bonding between the bone implant and the tissue is of considerable importance. Artificial implants of knee and hip prostheses (both cemented and cement-less) demonstrate that the adhesion is important at the bone-implant interface. These applications are related to contact modeling and design of biomechanical parts like human joints, implants or teeth, cf. Panagiotopoulos [34], Rojek and Telega [38], Rojek et al. [39], Shillor et al. [41] and Sofonea et al. [42].
Plate tectonics and earthquakes predictions
Results may be applicable to models with nonmonotone strain-stress laws in rock layers. Frictional contact between rocks are described by several models, cf. Dumont et al. [9], Ionescu et al. [12, 14], Ionescu and Nguyen [13], Ionescu and Paumier [15, 16] and Rabinowicz [36].
Medicine and biology
Results are applicable to nonmonotone semipermeable membranes and walls (biological and artificial), cf. Duvaut and Lions [10]. In particular, contact problems for piezoelectric materials will continue to play a decisive role in the field of ultrasonic transducers for imaging applications, e.g., medical imaging (sonogram), nondestructive testing and high power applications (medical treatment, sonochemistry and industrial processing), cf. Shillor et al. [41], Sofonea et al. [42].
Research partially supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Home > Archives > Nutrition Tips > Nutritious Berries
Nutritious Berries
Timeless Nutrition Tip
Berries pack quite a nutritional bang for your buck - they provide important amounts of vitamins, especially vitamin C, plenty of fiber, plus antioxidants and phytochemicals known to prevent certain diseases.
In regard to antioxidants, berries are on the top ten list and what better time of year to start incorporating more berries in your diet than summer? More berry-benefits include nutrients such as folate (folic acid), which helps prevent birth defects and may help reduce the risk of heart disease, stroke and colon cancer.
Berries can also help lower LDL cholesterol, a contributor to heart disease, stroke and atherosclerosis. Strawberries, and especially raspberries are high in ellagic acid, which has been shown to help reduce colon and cervical cancer and leukemia.
Fiber: Berries with edible skins also are a good source of fiber.
Some suggestions for adding more berries in your diet include adding strawberries to your cereal, snacking on raspberries, stirring blueberries into your yogurt and tossing blackberries in your dinner salad.
Berries & Fruit Jams
Make jam, jellies, pie fillings, desserts, ice cream toppings or fruit leather with strained berries. Simply process berries that have very small seeds. Remove stems and leaves. Rinse berries, drain well, then strain. Sweeten to taste.
Uh-Oh, Berry Stained Hands?
It is fun to pick your own berries, but your fingers can get stained from the berry juice. Soap and water isn't quite enough to clean those stains off. Try washing your hands with undiluted lemon juice, then wait a few minutes and wash with warm, soapy water. Repeat until your hands are stain-free.
Did you know?
The grapefruit, tomato and watermelon all fit the botanical definition of a berry.
Pledge of Allegiance Parfaits
1 cup strawberries, sliced
1 cup blueberries
2 cups vanilla lowfat yogurt
Fill the bottom of parfait glasses with strawberries. Add yogurt and blueberries, and then repeat layers in original order. Top with a flag decoration and serve. Per serving (Serves 2) : 4g protein, 1g fat, 450 mg calcium, 16.5g carbohydrates, 85 calories
Berry Frozen Yogurt
You will eat this because it is so refreshing and delicious - the fiber and anitoxidants are a bonus.
2-1/2 cups strawberries, sliced and frozen
2 cups blueberries, frozen
1/2 cup plus 2 tablespoons plain low fat yogurt
1 teaspoon fresh lemon juice
Place the frozen berries in the bowl of a food processor fitted with a steel blade. Process until smooth. Gradually add the yogurt and lemon juice and process until completely incorporated. Serve immediately or cover and freeze in individual portions for up to 2 weeks. If you freeze portions, let them sit at room temperature for 10 minutes before eating. Makes four servings.
Nutrition information per serving: Calories: 95; Calories from Fat: 10; Fat: 1.1g; Saturated Fat: 0g; Cholesterol: 2mg; Sodium: 28mg; Carbohydrates: 20.2g; Dietary Fiber: 3.5g; Protein: 3.2g
Watermelon and Berries Power Juice
This is a cleansing treat for the urinary tract and the liver. Also reduces inflammation in the body. Cranberries and blueberries line the cells of the urinary tract and bladder preventing harmful bacteria from anchoring to the cells. Blueberries also contain a powerful anti-inflammatory ingredient that is ten times stronger than aspirin (without the harmful side effects). Watermelon is one of the few foods that contain a potent nutraceutical called glutathione. Nutraceuticals are compounds found in food that have nutritional and medicinal properties. This super food greatly improves detoxification in the liver. This is a remarkable accomplishment that helps the body more effectively eliminate synthetic chemicals.
2 large slices of watermelon
1/2 cup blueberries
1/2 cup cranberries
Push all ingredients through a juicer. Serve over ice if desired.

subset: commoncrawl


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Austrian wants to bring more Personal Travellers on Board with "myHoliday"
• New design and new offers for personal travellers with Austrian myHoliday under the umbrella brand Austrian
• Austrian myHoliday should become the leisure time brand for the Austrians and attract an additional 150,000 passengers
• New in the flight programme: Palma, Palermo and Chios
Austrian Airlines is entering the personal travel segment effective immediately with a new branding and design: under the brand Austrian myHoliday individual private trips for different travel occasions can be booked in the future. There is a suitable offering to fit everyone. For example, City Breaks will be available for Singles, Beach Holidays for families and Luxury Holidays for the young at heart. Austrian Airlines also plans its own golf and ski trips, shopping trips, romantic breaks, spa holidays, adventure holidays, event breaks, all-inclusive holidays and winter sun holidays. Austrian myHoliday will be offered at competitive prices and should also reach the smart-buyers. Austrian myHoliday stands for an optimal price-performance ratio, excellent service with Austrian charm and cooking on board, and last but not least care-free travelling based on its worldwide service points. The various packages will now be successively launched in cooperation with different tour operators on the marketplace up until the summer.
Austrian Airlines also intends to position itself strongly in the incoming segment in the future, offering travel programs with tour operators. For example, there will be luxury packages to the Salzburg Festival, including the hotel in Salzburg and tickets to the festival.
Austrian Airlines anticipates 150,000 additional passengers in the first year of the new personalized travel offering. "With Austrian myHoliday we will more strongly exploit the strength of the Austrian brand nationally and internationally. Thus the charter business will be brought closer to the Austrian umbrella brand as an integrated part of Austrian Airlines", explains Austrian Airlines CCO Karsten Benz. "The objective is clear: Austrian myHoliday should become the leisure time brand of the Austrians." The new brand will be used for the summer flight schedule, which is valid as of May 1, 2013. In the future, Austrian Airlines in its role as a partner to tour operators will also offer an optimal price-performance ratio for tour operators and agencies as well as for customers. The offers can be booked on www.austrian.com.
New in the flight programme: Palma, Palermo and Chios
With 130 destinations, Austrian Airlines is the Austrian airline with the most flight destinations from and to Austria. As of May 17, 2013, Chicago will be added to the summer schedule with five flights per week. There will also be many interesting vacation destinations once again in the charter segment in the summer timetable. The focus will be on Italy and Greece. New destinations in the upcoming season are Palermo as of April 26, 2013, and Chios as of May 29, 2013, each with one flight per week. "We continue to be the undisputed market leader with 21 destinations in Greece", Karsten Benz adds. The offering of Austrian Airlines will also include Spain, Turkey, Great Britain and Egypt. Moreover, Palma has been added to the flight offering and will be served as of May 4, 2013 with three flights per week (in each case Thursday, Saturday and Sunday). "I have a good feeling that Palma will be a success, due to the fact that we see a great need here. With three flights per week we fulfill customer wishes to fly to Mallorca for both short and long trips. I am convinced that we will achieve good growth rates with it", Karsten Benz concludes.
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Alexandria Wedding from A. Dominick Events + Love Life ImagesWhen I first started checking out this Virginia wedding, there was something so romantic that I loved so much about it. I just couldn't put my finger on it. Yes, I loved the cake, the bridesmaids bouquets, the centerpieces, the
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You slap yourself in the face. This must still be part of the daydream.
"Sir? The wheel of--Sir?!" Demands the auctioneer, beginning to look rather concerned.
Not really caring, you continue to slap yourself in the face until the scene of the auction house fades and you find yourself at a beach in California. You're not entirely sure why you are at a beach in California, but you are sure that you are. Something--most likely the remains of one of the local sea monster's avian lunches (You know there's one of those too) is floating in the ocean nearby. That, you assume, must have been what led to the wheel-of-poultry daydream.
And that is when the day-nightmare (daymare?) ensues. Under the macabre floating feathers, a shadowy fishlike figure rises up. Oh dear, you think, That's the sea monster. As your fellow beachgoers run away screaming, you sit dumbly in the sand, wondering what you did to deserve this. The sea monster rises up out of the water (Perhaps it has lungs as well as gills), stares at you hungrily, opens its mouth, and says...


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Senate Votes To Roll Back Internet Privacy Rules Protecting User DataComcast, Verizon and other Internet service providers won't need permission to use or sell much of their customers' personal information.
Google's YouTube Losing Major Advertisers Upset With VideosAT&T, Verizon and several other major advertisers are suspending their campaigns on YouTube after discovering their brands have been appearing alongside videos promoting terrorism and other unsavory subjects.
Verizon Sought $925M Penalty For Yahoo's Lax SecurityVerizon demanded a $925 million discount on its acquisition of Yahoo's online services to help offset the damage from the biggest data breaches in internet history.
Yahoo Salvages Verizon Deal With $350 Million DiscountYahoo is taking a $350 million hit on its previously announced $4.8 billion sale to Verizon in a concession for security lapses that exposed personal information stored in more than 1 billion Yahoo user accounts.
Verizon Pulled Back To Unlimited Data GameVerizon, a longtime holdout, has joined other carriers in offering an unlimited data plan.
Yahoo To Change Name, CEO Mayer To Resign Under Verizon DealYahoo will adopt a new corporate identity and cut the size of its board in half if the proposed $4.8 billion sale of its digital services to Verizon Communications goes through.
Yahoo's Mega Breach Shows Just How Vulnerable Data IsThe revelation of Yahoo's latest hack underscores what many Americans have known for years: All those emails, photos and other personal files stored online can easily be stolen, and there's little anyone can do about it.
Another Yahoo Data Breach Rattles InvestorsYahoo shares slid Thursday on worries that Verizon will walk away or slash its $4.8 billion offer for the company's digital operations after another massive data breach.
Yahoo CEO Marissa Mayer Could Reap $44 Million If She Stays Until Verizon Sale Is CompletedYahoo CEO Marissa Mayer stands to collect a $44 million severance package if she leaves after Verizon completes its purchase of the once-mighty internet company.
Verizon Officially Buying Yahoo For $4.83 BillionVerizon is buying Yahoo for $4.83 billion, marking the end of an era for a company that once defined the internet.
Verizon Said To Have Bought Yahoo For Nearly $5 BillionThe deal is expected to be announced formally on Monday before markets open, according to multiple media reports.
Potential Bidding War For Yahoo Heating UpYahoo is one of the iconic brands of Silicon Valley, and still one of the most popular places for users on the web.


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Macedonia is not only a peaceful land of laidback rules, scented toilet paper, and void of pocket change; it is also a country with an epic flag and a complex history, dating back to the times of Alexander the Great. Part Balkan, part Mediterranean, with influences from Greek, Roman, and Ottoman history, Macedonia is the perfect combination of ancient sites and modern growth. However, Macedonia has only recently gained peaceful independence, so it is in need of helping hands to get it to its feet. Volunteer in Macedonia, Mother Teresa's birthplace, and you can explore the magnificent lakes, ancient towns, endless mountain peaks, and learn to "spread love everywhere you go."
Those who volunteer in Macedonia will fall in love with the beauty, the contrasting cultures, and the laidback vibes. Whether you want to lend a hand in a bustling city or explore the great outdoors, spend your free time admiring the contrasting architecture or relaxing at a cafe, you are sure to find a location that suits you in this jigsaw puzzle of modernity and ancient culture.
Skopje is the easygoing capital of Macedonia and hometown of Mother Teresa. While the city has an old-town feel with a Game-of-Thrones-worthy fortresses dating back to the fifth century, Skopje has also been under a massive construction spree. New statues, fountains, bridges, and museums pop up overnight, so almost every day you feel as if you're in a new city. In your free time, explore the lively Macedonian Square on the new side of town, or get lost for hours in Carsija, the old Turkish Bazaar. And don't leave Skopje without a visit to Tyrdina Kale Fortress, where you'll feel just like Khaleesi as you gaze out at a brilliant view of the city and river.
If you're the outdoorsy type, consider volunteering in Macedonia in Ohrid. This city is a prime destination for volunteer work in Macedonia, with rolling hills, medieval castles, and popular beaches to enjoy in your free time. During the summer months, the city and beaches are packed with tourists due to the famous summer festival. On the other hand, in the winter, volunteers can hit the alpine slopes around the region. Regardless of the season you choose for your volunteer program, you'll be able to take a break from English classes or construction sites to visit the 3-million-year-old Lake Ohrid, explore old Balkan villages, and meditate in medieval monasteries.
Despite its small size, Macedonia has more mountains than any country in the world. Bitola, another popular destination for volunteering in Macedonia, is located 660 meters high in the mountains. This city is known for its colorful townhouses, old Turkish mosques, chic cafes, and good-looking people. Bitola is more low-key, less touristy, and one of the most intriguing, livable cities in Macedonia. Volunteers usually appreciate its sophisticated feel and enjoy spending many afternoons on Sirok Sokak, the pedestrian-only street on the main promenade, sipping coffee and people watching.
Volunteer Programs in Macedonia
Macedonia is a fairly "new" region, only gaining its peaceful independence from Yugoslavia in the 1990s. The country's integration into the European Union has been slow, so despite its growing modernity, there are several areas that could benefit from international volunteer support.
More than 80,000 households in this small country lack long-term housing. While construction is on the rise, many of Macedonia's buildings are ancient, poorly-maintained, and some are even illegally-constructed. Construction projects are always in need of volunteers. You can work with a team to build better-constructed houses, repair and replace windows and doors, and help maximize energy efficiency, as "green" homes are in high demand.
Those who volunteer in Macedonia can also support the Syrian refugee crisis by becoming a medical volunteer. Due to the constant flow of refugees coming from Syria, Iraq, Afghanistan, and Africa into and through Macedonia to other European nations, the local health care system is strained. Hospitals are in constant need of medicine, vaccines, and medical supplies, and of course, volunteers who can deliver supplies or help care for refugees and children in hospitals.
Like many European countries, the demand for English speakers in the workforce is high, so volunteers can also serve as English teachers in Macedonia. Spend your time volunteering in Macedonia teaching conversational English to locals, while they introduce you to their own Macedonian dialect. Just be cautious when practicing around Bulgarians; they are convinced that Macedonians stole their language!
Costs & Affordability
While volunteering abroad will be an incredible experience, both for you and the people you are helping, most international volunteer programs cost quite a bit. Volunteer programs in Macedonia are no exception, as most require volunteers to pay an upfront program fee, which will be in addition to your flight there. Once you are on the ground, the price of volunteering in Macedonia will be well worth it though.
Volunteer program fees typically cover accommodation, meals, and transportation, as well as supplies for the duration of your volunteer work. While the initial cost of fees and flights can be high, reaching up to $2,000, the cost of living is very affordable in Macedonia. One Macedonian denar is equivalent to about 2 cents in the United States. Rent is cheap, a one bedroom apartment will only cost about $200 in Macedonia, and food and drinks cost next to nothing. Check out the local markets and you'll be able to fill grocery bags with fruit for only a couple dollars or less. Eat a meal out with new friends for $4 or hit the bars and socialize over $2 imported beers.
If the initial cost of getting there intimidates you, have no fear! Creating a FundMyTravel campaign can help you make your volunteer trip happen.
Accommodation & Visas
One of the coolest parts about becoming a volunteer in Macedonia is the accommodation provided by most programs. While shorter trips of a week or two accommodate volunteers in hotels, longer volunteer programs in Macedonia will often host volunteers in nearby monasteries. Typically, volunteers will be provided with meals as long as you BYO sleeping bag. Staying in a monastery can be a truly unique experience (like a homestay with monks), as you'll be staying in Byzantine masterpieces nestled in the hills.
Most volunteer programs in Macedonia are short term, lasting less than 90 days, so most volunteers don't need a visa; a valid passport and proof of your departure when you arrive at the airport. For more information on the visa process, or if you'd like to extend your trip, check out GoAbroad's Macedonian Embassy Directory.
Benefits & Challenges
Laidback culture. In Macedonia, they say anything goes. As a volunteer in Macedonia, you will experience a laidback lifestyle outside of your volunteer work. Sidewalks are filled with parked cars, smoking is permitted everywhere, and their colorful flag featuring a massively trippy sun mirrors the positive vibes of locals.
Finding a program. While Macedonia is in need of international volunteers, there are not many organized volunteer program opportunities. But if you do your research and find a program that suits you, you will no doubt have an incredible experience.
When most people think of volunteering abroad, they think of underdeveloped, third world countries where the homeless line the streets or live in slums; they don't think of majestic beauty, purple mountains, and medieval castles to go along with beautiful people. Despite the magnificent feel of the country, locals need your help all the same. Volunteering in Macedonia will have a truly unique experience, where you will play an essential role in teaching this country how to establish roots and it grows forward.


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Storm strength gales of up to 75mph, combined with heavy rain, could topple trees and cause structural damage to buildings, they say.
The unseasonably hot summer and mild autumn has caused many trees to keep leaves on their branches far longer than usual.
Experts fear the larger amounts of foliage will act like sails and make trees much more vulnerable to damage in high winds.
The strong gales will hit the South West Coast at around 9pm this evening and will move north-eastwards across the Midlands, northern England and Wales, bringing heavy rain throughout the night and into Saturday.
Temperatures are likely to be just above the seasonal norm of 9 or 10C (48-50F) but the wind chill factor will make it feel a little colder.
Although the wind and rain will continue through much of Saturday, Sunday is likely to be a much calmer and slightly warmer day with temperatures in some parts topping 13C (55F).
John Hammond, forecaster at the Met Office, said: 'We're expecting very strong winds and severe gales with speeds of up to 75 miles per hour affecting England and Wales this Saturday.
"There's scope for damage to trees and falling debris, when a lot of people will be out and about doing their Christmas shopping and going to events.
"The leaves are still on the trees after our warm weather, and the wind catches the branches more easily because the leaves act like a sail, so they could cause more damage.'
This year's conditions bear a striking resemblance to those preceding the storms of 1987.
Then there was a long hot summer too, with the dry conditions leading to tree roots loosening their hold.
And sudden rain in October – as there has been this year – softened the soil.
The onset of 115mph gales then brought down 15million trees, killed up to 20 people and led to insurance claims totalling £1.4billion.
Mr Hammond said that like most other months so far this year, November was also likely to be one of the warmest on record.
'We are on course for one of the warmest years on record,' he said.
'This summer we had a record breaking September and July and the continuation of winds coming from the south and south-west off a warm Atlantic is keeping temperatures above average.
"At the moment we're seeing temperatures of 10 to 12C (50-54F), so it's certainly mild. The average maximum temperatures for this time of year would be around 9 or 10C (48-50F), so we're above that by a few degrees.
"We're expecting temperatures to peak at 12 or 13C (54-55F) in London and the south-east.
"Overall, temperatures so far this month have been above average for November over the whole of the UK. Parts of Scotland and Northern Ireland have also been above average by one or two degrees.
"We've had shorter cold spells and we should see a mild end to the month as these warm winds continue."
The warmest November day ever recorded was in Prestatyn, Wales, on the November 4 1946, when temperatures reached 21.7C (71F).
- More about:
- Wales
- West Midlands


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... 105 acre gardens. Naturally, Avery and I felt right at home and exhibited our most bourgeois behavior while touring the place. We also learned it was the setting for the Keira Knightley Pride and Prejudice 2005 film. Here is a video summary slide show and a bunch of pictures from the ...
A Series of Peculiar Events
... about to step in when another one of the group dressed with his face painted like a kitty cat, ears on his head, and a velvet tail on his butt, grabbed the guys arm and told him "Step off, mate" and freed the girl. The drunken man mumbled something negative about us while we walked away. I was impressed by kitty cat man and surprised that didn't lead to a fight. All the bars we visited were named after animals and the last one ...
A weekend in Australia? Crazy!
... this but it makes the whole weekend even more worthwhile.
My return journey from Melbourne back to the UK on the Monday morning, the 4th May, will depart at 0915 on Virgin Australia flight VA679 and because of a long(ish) stopover/connection in Perth I will also be able to have lunch with friends if all goes to plan. I will then board my Etihad Airways flight EY487 to Abu Dhabi and then onto Manchester arriving on Tuesday morning at 0740 so ...
Journey of my life!
. Well Thursday 24th January has finally arrived and I am about to embark on the trip of a lifetime!!
Hugh and Tebs arrived at Midday to take me to Heathrow Airport, but first,off to meet Ashleigh and Willow for a farewell lunch. I'm sure going to miss them!!
Off we go to the airport, I'm feeling a mixture of excitement and apprehension, wondering just what I am about ...


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Can doctors use a pigs heart or a cows heart for a human heart transplant?
Let's think about size -- a cow's heart is simply too large to be placed in the existing spot in a human. It is true that a baboon's heart was placed in a baby, but she survived just one day with ...
Read More »
What is the disease called when your heart has uneven heart beats?
Its called arrhythmia....Here http://www.americanheart.org/presenter.j…http://www.americanheart.org/presenter.j…
I had seizure(sharp pain from the heart) is it due to asthma or is it the beginning of a heart attack?
Yes, it COULD and may be a sign of a potential heart attack or stroke. Note for any other bodily signs such as dizziness, blurred vision, impaired speech, etc. OR it may be a symptom called angina...
Read More »
""Personalised medicine is the next big thing in heart"". Is it a boon to heart ailment patients?
Well!!!!!!!!!Sure....It will be more than a boon!!!P.S:The link above is not working...May be this may help:http://timesofindia.indiatimes.com/city/…
Can a lot of anxiety and stress cause a heart attack in a person with a healthy heart?
I am the same exact way. I have been experiencing panic/anxiety attacks for a little more than a year. It is one of the scariest feelings in the world when you think something is wrong with your he...
Read More »


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Bistro Onion Burgers
Serving Size: 6
Prep Time:
Total Time:
1. Thoroughly mix the beef, soup mix and water. Shape the beef mixture into 6 (1/2-inch thick) burgers.
2. Cook the burgers in batches in a 10-inch skillet over medium-high heat until well browned on both sides, 10 minutes for medium or to desired doneness.
3. Serve the burgers on the rolls. Top with the lettuce and tomato.


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The Maryland fertilizer law will go into effect on Oct. 1. Below is a summary of some of the highlights.
Fertilizer Manufacturers and Distributors
Requires lawn fertilizer products sold in Maryland to include label directions to ensure that no more than 0.9 pound of total nitrogen is applied per 1,000 square feet; at least 20 percent of this nitrogen must be in a slow release form. The maximum amount of water soluble nitrogen in lawn fertilizer products applied per 1,000 square feet is capped at 0.7 pound. Effective October 1, 2013
Lawn Care Professionals
University of Maryland Extension (UME) is developing a training manual to prepare individuals to take the certification exam. Training classes will be available in 2013.
Individuals and companies hired to apply fertilizers must be certified by MDA or work under the direct supervision of an individual who is certified. MDA will offer fertilizer applicator certification exams beginning fall 2013 and will publish a list of certified professional fertilizer applicators on its website.
For the rest of the story, click here.


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Guest reviews of Cardamom Hotel and Apartment
Overall Rating
7.5 Good
Based on 20 reviews
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Putting you within a 10-minute drive of Royal Palace and Tuol Sleng Genocide Museum, Cardamom Hotel & Apartment features a rooftop terrace and offers an airport shuttle (available on request) for USD 12 per vehicle. The lobby lounge is a great place to grab a drink, and guests looking for a bite to eat can check out Mimosa Restaurant, which serves international cuisine and is open for breakfast, lunch, and dinner. Rooms offer up nice touches like fireplaces, premium bedding, and bathrobes.


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I'm running gnome and I have ALSA installed. I have enabled "start sound server" in gnome settings. Now I can listen music perfectly with xmms (selected alsa as output plugin), but when watching a movie with xine (tried starting it with xine -A alsa, xine -A esd, xine -A esound....) I can't hear any sound and after setting volume bar on max at xine, it usually goes back to 0 after few seconds.
Some other audio programs I tried says that can't find /dev/dsp, now it doesn't exists, I guess it should?
My sound card is Cmedia 8738.


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Clyde et al.,
Since AHS has a web site, is there any reason why matters of importance
that need a majority vote of the *membership* cannot be posted on the web
site, with yes or no vote, membership no. required and a deadline (strictly
adhered to) for registering a vote?? The only down side to that would be,
of course, excluding members who do not have a computer..This is not a
trivial downside..so maybe it's not such a "good thing."
But if the motion is sufficiently important to be voted on by the
membership, it should be written in advance...far enough in advance that it
could be included in the journal.
At 06:48 PM 9/4/99 EDT, you wrote:
>I could be wrong, but I forsee proxy voting will be permitted in the near
>future.I cannot imagine that the Board would be opposed to such.
>I should not be misunderstood to suggest that proxy voting should be allowed
>to interfere with orderly procedures.(Such as requiring that all members not
>in attendance be advised of a particular motion on the floor before a vote
>secured. E.G. , the somewhat archaic motion to accept the minutes of a Board
>Meeting without their being read.)
>I do think the local and regional societies could make things easier, if
>before a convention, the members, who are not attending an impending
>convention, give their proxies to an attending member.
>Also, the AHS should, well in advance of its annual meeting , inform all
>members of matters to be voted on.
>From what I have seen and heard, I gather that there is almost a unaimous
>view that proxy voting should generally be permitted. I'd like to hear any
>opposing view or views.
>Clyde Crockett
>To sign-off this list, send email to email@example.com with the
>message text UNSUBSCRIBE HOSTA-OPEN
To sign-off this list, send email to firstname.lastname@example.com with the
message text UNSUBSCRIBE HOSTA-OPEN


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Popular property highlights
Holiday Inn Mobile-Dwtn/Hist. District places you within a 10-minute stroll of popular attractions such as Gulf Coast Exploreum and Museum of Mobile. This 3-star hotel has 202 guestrooms and offers an outdoor pool, free in-room WiFi, and a fitness center. Located centrally in Mobile, it's also close to USS Alabama Battleship Memorial Park and National African American Archives and Museum.
In addition to a meal at the onsite restaurant, you can also enjoy a drink at the bar/lounge. Satisfy your hunger from the comfort of your room with room service. For your convenience, a cooked-to-order breakfast is served each morning for a fee.
All of Holiday Inn Mobile-Dwtn/Hist. District's 202 air-conditioned rooms provide microwaves, refrigerators, and minibars. Guests can expect TVs with cable channels, along with free WiFi and wired Internet. Bathrooms offer hair dryers and free toiletries, and pillowtop beds with pillow menus ensure a restful night. Other amenities include coffee makers, free newspapers, and free local calls.
At Holiday Inn Mobile-Dwtn/Hist. District, guests enjoy features like an outdoor pool, a fitness center, and free WiFi in public areas. Self parking is available for USD 8 per night. The front desk has multilingual staff standing by 24 hours a day to assist with dry cleaning/laundry and securing valuables. Additional amenities include 9 meeting rooms, conference space, and a business center.
Property features
- Walking distance to Gulf Coast Exploreum and Museum of Mobile
- Free WiFi and wired Internet in rooms and public areas
- Onsite dining
- Outdoor pool
HighlightsInformation missing or incorrect? Tell us!Opens in a new window
Holiday Inn Mobile-Dwtn/Hist. District
Hotel Amenities
Hotel Amenities
Holiday Inn Mobile-Dwtn/Hist. District features an outdoor pool and a fitness center. The hotel offers a restaurant. A bar/lounge is on site where guests can unwind with a drink. Public areas are equipped with complimentary wired and wireless Internet access.
Business-related amenities at this 3-star property consist of a business center and meeting rooms. Event facilities measuring 10000 square feet (929 square meters) include conference space. This business-friendly hotel also offers multilingual staff, gift shops/newsstands, and complimentary newspapers in the lobby. Parking is available onsite for a surcharge.
- Number of buildings/towers - 1
- Breakfast available (surcharge)
- Free WiFi
- Restaurant
- Conference space
- 24-hour front desk
- Total number of rooms - 202
- Safe-deposit box at front desk
- Porter/bellhop
- ATM/banking
- Laundry facilities
- Dry cleaning/laundry service
- Outdoor pool
- Fitness facilities
- Elevator/lift
- Number of floors - 16
- Bar/lounge
- Business center
- Free newspapers in lobby
- Gift shops or newsstand
- Free wired high-speed Internet
- Meeting rooms 9
- Multilingual staff
- Conference space size (feet) - 10000
- Conference space size (meters) - 929
- Self parking (surcharge)
Family Friendly Amenities
- Family Hotel
- Outdoor pool
- Free Wi-Fi
- Rollaway/extra beds available
- Laundry facilities
- Refrigerator
- Microwave
Available in all rooms: Free WiFi , Free wired high-speed Internet
Available in some public areas: Free WiFi , Free wired high-speed Internet
Self parking (surcharge)
Room Amenities
Holiday Inn Mobile-Dwtn/Hist. District offers 202 air-conditioned accommodations with minibars and safes. Beds feature pillowtop mattresses. A pillow menu is available. Premium cable television is provided. Guests can make use of the in-room refrigerators, microwaves, and coffee/tea makers. Bathrooms include complimentary toiletries and hair dryers.
Guests can surf the web using the complimentary wired and wireless Internet access. Business-friendly amenities include desks and complimentary newspapers, as well as phones; free local calls are provided (restrictions may apply). Housekeeping is provided daily.
- Free WiFi
- Free wired high-speed Internet
- Room service (limited hours)
- Connecting/adjoining rooms available
- Premium TV channels
- Air conditioning
- Free newspaper
- Phone
- Free local calls
- Refrigerator
- Minibar
- Coffee/tea maker
- Microwave
- Daily housekeeping
- Private bathroom
- Free toiletries
- Hair dryer
- Iron/ironing board
- In-room safe
- Television
- Desk
- Pillowtop mattress
- Rollaway/extra beds available
- Cribs/infant beds available
- Cable TV service
- Pillow menu
Where to Eat
Room service (during limited hours) is available.
Skyview Lounge - Onsite cocktail bar.
Onsite venue #2 - This restaurant specializes in American cuisine and serves breakfast and dinner.
Cooked-to-order breakfasts are available for a surcharge and are served each morning.
Nearby Things to Do
Recreational amenities at the hotel include an outdoor pool and a fitness center.
If you have requests for specific accessibility needs, please note them at check-out when you book your room.
- Accessible bathroom
- Roll-in shower
- In-room accessibility
Hotel Policies
Minimum check-in age is 21
Check-in time ends at midnight
Check-in time starts at 3 PM
Check-out time is 11 AM
Payment types
Children and extra beds
- Children are welcome.
- Rollaway/extra beds are available.
- Cribs (infant beds) are available.
- Pets not allowed
You need to know
Extra-person charges may apply and vary depending on property policy.
Government-issued photo identification and a credit card are required at check-in for incidental charges.
Special requests are subject to availability upon check-in and may incur additional charges. Special requests cannot be guaranteed.
Optional extras
- Self parking fee: USD 8 per night
Hotel Name
- Holiday Inn District Hotel Mobile-Dwtn/Hist.
- Holiday Inn Mobile-Dwtn/Hist. District
- Holiday Inn Mobile-Dwtn/Hist. District Hotel Mobile
- Holiday Inn Mobile-Dwtn/Hist. District Hotel
- Holiday Inn Mobile-Dwtn/Hist. District Mobile
We should mention
The property has connecting/adjoining rooms, which are subject to availability and can be requested by contacting the property using the number on the booking confirmation.


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I was just reading the Charlotte Hungerford Hospital Spring 2013 Health Matters news letter that came in the mail today. The newsletter has has wonderful colored pictures and reports. In the back of this newsletter there is a list of donations. I wish I saw the salaries of management printed What I can not understand is why the hospital would print and send by mail such a costly report. We are in a health care crisis in this country and valuable monies are being spent on wasteful newsletters that does nothing for health. Charlotte Hungerford Hospital is a for profit organization that has no local competitor. This very expensive public campaign is wasteful and unnecessary.
Clearly the Obama administration was well aware of the terrorist threat posed by the Tsarnaev brothers after being warned about them by a foreign government yet chose to ignore the obvious. Media reports indicate that the threat was so real and present that the FBI interviewed Tamerlan Tsarnaev two years ago yet did nothing about the danger in spite of links on his Face book to extreme International terrorist organizations and horrific videos of terrorist violence. Because these very dangerous brothers didn't fit the Obama narrative of terrorism no longer existing, savvy Americans now understand why the government failed to put them on the terrorist watch list with the end result being the deaths of three innocent victims and maiming of hundreds more. Others feel that Obama has been too busy plotting the confiscation of guns from honest law abiding Americans. Either way this represents a monumental national security failure of the Obama administration and brings new life to those who favor tight border control, selective immigration and the Second Amendment.
Re: The Sandy Hook Parents,
What I have seen is ordinary American citizens who have experienced an unbelieveable loss from a horrific event that many would like to believe could have been prevented if a better system of monitoring and control were in place.
With that belief, the Sandy Hook parents have taken to the media to tell the country what they think and feel.
Same as any parent would do in that terrible circumstance .
You need to give them a little slack there, they earned it.
Obama needs to use executive powers to ban all guns NOW!
Re: We Citizens
The gun issue is simple. Our Founding Fathers just got done fighting a war to liberate us from the tyranny in England. Fortunately they possessed enough foreknowledge to place the 2nd amendment in the Constitution, knowing they needed to allow this same opportunity for future citizens to protect themselves from an overpowerful tyrannical government.
There will be a day upon us when the people would have wished otherwise and will experience such travesty that people will say--"'they will say to the mountains, "Fall on us!" and to the hills, "Cover us!"


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Need an LH Test in Durham, NC? Simply order online 24/7 and get a fast, affordable LH Test at a lab near you (Find More Locations):
What is an LH Test?
The LH Test, also known as a Luteinizing Hormone test, is a lab test that measures the LH level in the body. The LH Test is used to help guide fertility decisions for people in Durham, NC.
How much does an LH Test cost?
Our LH Test price includes the doctor's order that you need to get tested in Durham, NC, all lab fees and taxes, and a pdf copy of your results. For current prices, CLICK HERE.
What does an LH Test report look like?
For an example of an LH Test sample report, please CLICK HERE.
We are delighted to offer the LH Test in Durham, NC.
LH Test in other cities near Durham, NC:Apex | Bahama | Butner | Carrboro | Cary | Chapel Hill | Creedmoor | Efland | Hillsborough | Hurdle Mills | Morrisville | Raleigh | Rougemont | Stem | Timberlake


text:
Royrituparna.com is a 1 year old domain.
It was registered by R Roy , who can be reached at . Registration details show that it was registered on 08 Jan 2016 through realtime register bv and will expire on 08 Jan 2017.
The site returns a status code of 200. It is being generated using WordPress 4.7.2. The site is being served through nginx.


text:
Create a free account to check out faster, store multiple shipping addresses, view and track your orders in your account, and much more.
Please enter your password to continue.
Sticky lip gloss is high up on our list of beauty pet peeves, right next to cakey concealer and smudgy mascara. One gust of wind, and your hair is stuck all over your lips. No thanks, we'll pass. We've become pretty picky about lip products, and these superlight, refreshing glosses make the cut. Created by the color pros at POP Beauty, they add a wash of sheer color and a high dose of shine, without that goopy, sticky feeling we all know too well.
I was nervous to try the gloss because it was a vibrant pink color in the tube, however when applied to the lips it was a nice pretty, natural looking pink (I will admit that my lips are naturally pretty pigmented). While it is a little sticky I don't mind it because I find that it helps the product last longer than glosses without a little tackiness. I like this product and would recommend it to friends.5
I got the color 'flowering fuschia' which is quite nice, indeed. I like the unique applicator, but it's taken a little getting used to. The gloss itself feels very nice, and has a slight tingle that I actually enjoy. But, despite claims, this product is sticky and my hair has gotten stuck to it! Wear this on ponytail days!3


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Produced back in January of 2013 and more works were added and taken away as a paint palette for my digital paint brush works until recently abandoned. Using my unique Amoxenyte Imitation Coral (extraterrestrial coral art)& GM digital pictures that were cataloged during the process of filling in orders, (making raw material) to ship to art collectors, museums, for the use in fish aquariums, HO Scale model arts, space odyssey modeling compounds) award trophy designs. Even for the production
and sales of GM through the internet, fotolog.net (Canadian), artist guild.com, country crafts, ebay.com.
Where thousands of images were taken at distances and of close ups to being cataloged on a day to day basis until I filled three to four cd's with all sorts of my own renderings and saved of works I sold and shipped, (while making my own invoices, hand crafted each box per sale, shipped on my own usually to save more money).
Then after so many years of advertising, speaking to thousands of individuals about the unique artwork I produced and invented in 84' to 94' and after, with over several other newer styles. I begin to cut down in late 2012 to learn how to use the digital paint brush art studio given to me by a Chinese Camera business I met up with through eBay.
Artwork went on board cd's sent out with orders with newer additional images on each (to go with purchased ones) the works were added before going out. So each collector would have a one of a kind.
{Yes other cd's exist}
galaxies galaxy orion's belt nebula disk solar system third rock big bang theory galaxy meteorite amoxenyte free webs canadian fotolog country crafts gallery camera camden campto camera's by camden ebay voice ebay staff worthless my ebay trust! 0 ebay tolerate! 0 ebay ignores me ebay will be closed if ebay is worthless then super stores wi wi-ll failwill fail ebay investigates0 ebay NOT MY friend retro pink emo chica black tea chinese rule of thumb artwork digital digital artwork paint brush cd artwork GM fe horse squid eats kingi.i
On October 25 2013 (sent by reddauug) at United States 9 Views
Nuevabetty On 26/10/2013
Que tengas un lindo sábado!
Peya067 On 26/10/2013
[email protected] ❥❥❥❥❥
Andreslomas2010 On 26/10/2013
Goldensilence90 On 25/10/2013
Buenas noches....
Gracias por tus visitas y firmas. Buen fin de semana!
Un besote y todo mi agradecimiento!
497 Photos
Grupo para subir lo más bello de la mar playas,costas calas,hoteles.todo lo referente del mar tambien barcos cruceros,fauna marina e historia.
Torrente de Amor Grupo. (amor ,poesia etc )
Fotolog sin fotos abstenerse de subir fotos, de lo contrario serán bloqueados,
la nueva administración no aceptara romper las reglas del grupo.
Este es un grupo fotolog, para que todos los aficionados de la gran fotografía,suban aquí su mejor trabajo.
Todo tipo de técnica fotográfica es bienvenida,siempre y cuando este adentro de las reglas de fotolog
This is a group photo for all fans of the big picture, upload your best work here.
All types of photographic techniques is welcome, as long as this in the rules of fotolog
Arte de la fotografía
Photograph Art


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"India continues to experience terrorist and insurgent activities which may affect US citizens directly or indirectly," the State Department said in its new worldwide travel alert for its citizens. "Anti-Western terrorist groups, some on the US government's list of designated Foreign Terrorist Organisations, are active in India, including Islamist extremist groups such as Harkat-ul-Jihad-i-Islami, Harakat ul-Mujahidin, Indian Mujahideen, Jaish-e-Mohammed, and Lashkar-e-Tayyiba," it said.
"Terrorists have targeted public places in India frequented by Westerners, including luxury and other hotels, trains, train stations, markets, cinemas, mosques and restaurants in large urban areas," the State Department said. US citizens are reminded to maintain a high level of vigilance and to take appropriate steps to increase their security awareness, the State Department said, adding that it remains concerned about the continued threat of terrorist attacks, demonstrations and other violent actions against US citizens and interests overseas.
"Current information suggests that al-Qaida, its affiliated organisations and other terrorist organisations continue to plan terrorist attacks against US interests in multiple regions, including Europe, Asia, Africa and the Middle East," the advisory said.


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UPDATED 05/13/2014: Welcome to our new series on "SEO Best Practices" in the CV3 environment. These posts will be tagged as SEO 101, SEO 201, and SEO 301 depending on how advanced they are. Please let us know what you think.
This post is about how to improve your CV3 site's "On-site ranking factors" by customizing your page titles, meta descriptions and urls. These are things you can do on your site to make your pages more search engine friendly.
Title Tags
In my opinion, optimizing your title tags is the single greatest "bang for your buck" in SEO. That does not mean that keywords in your title are sufficient to get you ranking for keyterms, but they are an element that is easy to change and which search engines look at to determine what your page is about. It is an eCommerce best practice to take the time to come up with keyword rich page titles for the different pages of your website.
- Title tags should be no longer than 60 characters in length and not contain commas. You can use pipes, dashes and colons ("|", "-", ":"), but not more than once.
- Try to write it like a catchy title to an article.
- Keywords in the title should only be relevant to what is on the page and include brand name only at the end.
- Never use keyword phrase more than once and try to keep it toward the front of the title.
Bad: Red Tomatoes | Buy Red Tomatoes | Red Tomatoes Online | Your Brand
Good: Red Cherry Tomatoes Large Selection | Tomato.com (This page would be about cherry tomatoes)
A great way to tell if Google likes your title is to look at the search results for that page. If your title matches the title in the search results then you are good. If it does match the search results that means that Google does not like your page title and has come up with its own title for that page.
(To see what your page looks like in search results type in to Google search "site: http://Your URL)
Meta Keywords
Meta Keywords have been retired and are no longer used by search engines. (leave them blank).
Meta Description
The meta description field is important. It is sometimes used on the engines' search results pages as the descriptor of the page that accompanies the clickable link. It is worthwhile to write a good meta description for your pages to help your search listings get more clicks. That is an important part of SEO often overlooked as people tend to focus on ranking alone.
- Limit your meta description to 140-155 characters.
- Try to use your keyword phrase in the description twice.
- Make sure that the description is relevant to what is on the page focusing on the product or service.
- Describe benefits of your product or service (marketing copy) this will increase click through rates.
Search Friendly URLs
Search friendly urls are urls that have words the search engine can read and understand. These urls can have keywords that tell the search engine that your page is about the keyword topic and therefore can help you rank for a keyword search in a way that a typical "dynamic url" can't.
Always use dashes as opposed to underscores between words. Search engines view dashes as a space, but if an underscore is used Search Engines view it as part of one word. Always use lowercase and never use spaces, commas, quotations, apostrophes, parenthesis or dollar signs.
This url is not friendly:
This url is friendly:
Bonus Tips:
Product Descriptions
This field is also important. You can use the same method you would for your meta descriptions. Include the search term for the product in the description. (You can use the Meta Description for your product description.)
Product Names
When coming up with a product title, try to keep it short but descriptive.
For example, if you sell brown high heel shoes:
You would not want to have the title as "brown shoes" or "high heel shoes" you want it to be "Brown High Heel Shoes". Better yet, include the brand if it's one shoppers would be searching for like "Gucci Brown High Heel Shoes"
Keep in mind if this page is exclusively focused on "Brown High Heel Shoes" this should also be a part of your page title, Meta description and Product description.
How to Edit Title Tags and Meta Tags in CommerceV3
In the left navigation go to "Marketing" then click on "Meta Tags".
Click on Default and you will see the edit Meta Tags interface:
You can fill in the Title Tag, Keyword and Description fields here.
Considerations for Title Tag
-Put your keywords first and any general info second, e.g. "Civil War Biographies – Rare Historical Books for Collectors", "French Revolution Books – Rare Historical Books for Collectors", etc
-Limit the title to 65 characters. Google will crop your title to the nearest full word.
-All titles should be typed in Title Case (or Proper Case)
Consideration for Meta Tags
Description- Depending on the page, you can either write 3-4 sentences about what the page is about (remember to use good keywords), or you can write out structured data, i.e. just the facts. I think this latter technique is especially good for product pages (see below).
Keywords- Pick 10-25 keywords or keyphrases and separate them with commas.
Category Pages and Product Pages:
CV3 does a great job of providing good page titles at the category and product level. By default, the page titles on category pages are simply the category name. In many cases this is a pretty good title. However, category names can be optimized for SEO by adding more keywords either before or after the category name. To do this, navigate to the Edit Category page in your CV3 admin (under Inventory in the left navigation) and then add your preferred page title in the "Meta Title" field in the Information section of the page.
The meta description and meta keywords fields are where you can edit your category page's meta tags. The general rules for these fields are the same as described in the section above. However, remember to reinforce the category's keyword themes in the meta fields.
For product pages, CV3 again does a fine job with titles. By default the page title for a product page will be [Category Name] –[Product Title]. That might be very good. However, sometimes you might want to do something different. For example, a bookstore might have the title of the book as the product title. It might be smart to make the page title include the Author's name as well since people often search by author. To change Titles and Metas for products in CV3 navigate to the Edit Product page and edit the fields under Product Display -> Product Display.
Page Templates
CommerceV3 allows you to specify a unique title, description, and set of keywords for each "top level" template. This allows you each static template to be given unique meta information to further increase SEO. Top level templates are those like "viewcart.tpl". Other templates, like _top.tpl, which are included within other templates will not have the custom meta information applied to the page.
To edit, navigate to your template list (Design -> Template Library), find and click the template, expand the Edit Meta Information section and Customize.
Note: CV3 also provides ways to write title and meta tags automatically according to a formula. This is beyond the scope of this blog post. If you are interested in this topic, let us know and we will write a subsequent post specifically on this.
How to Make Search Friendly URLs in CommerceV3
CommerceV3 makes it easy to make search friendly urls for your categories and products. To make a search friendly category url, navigate to the Edit Category page and, expand the Options section and type the name you want to use for pages in this category.
And it will show up like this:
For products, navigate to the Product, Expand Product Display -> Product Display and type the words you want to use in the url for the product.
And it will show up like this:
Note: You should not use spaces in the category or product url fields. Separate the words with dashes instead.
With a little effort on these three areas – titles, metas, and custom URLs, you will have a solid foundation for optimizing your CommerceV3 website for search. Look for upcoming posts on more SEO techniques in the coming weeks, including using Google Webmaster Tools, the different types of Ranking Factors that determine your search position and ways to build inbound links. As always, please let us know if this post has been helpful to you.


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Swimming by sea otters: adaptations for low energetic cost locomotion
- Accepted:
- Cite this article as:
- Williams, T.M. J. Comp. Physiol. (1989) 164: 815. doi:10.1007/BF00616753
- Citations
- 397 Downloads
- 1.
Sea otters used two distinct speed ranges that varied with swimming mode. Sustained surface swimming was limited to speeds less than 0.80 m/s, while sustained submerged swimming occurred over the range of 0.60 to 1.39 m/s.
- 2.
Rates of oxygen consumption (VO2) at the transition speed (0.80 m/s) were 41% lower for submerged swimming by sea otters in comparison to surface swimming.
- 3.
Total cost of transport for surface swimming sea otters, 12.56 joules/kg·sm, was more than 12 times the predicted value for a similarly-sized salmonid fish. Transport costs for submerged swimming at the same speed was only 7.33 times the predicted value.
- 4.
The allometric relationship for minimum cost of transport in surface swimming birds and mammals wasy=23.87x−0.15 wherey=cost of transport in joules/kg·m andx=body mass in kg. This regression loosely parallels the relationship for salmonid fish.
- 5.
Correlations between aquatic behavior, morphological specialization, and swimming energetics indicate that the development of swimming in mustelids involved transitions from fore-paw to hindpaw propulsion, and from surface to submerged swimming.


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CHassan's blog
What does the future hold?
Thu Jan 14, 2010 5:50 am
I dont know, what do you think I am, a fortuneteller or something? If I knew what the future held, dont you think I would be busy placing bets, buying stock, and moving to the next best place?
I can tell you I've not flown but twice since sometime in July. I can tell you I'll be doing everything I can to get out more often this year.
Demo Days looks to be a go again this year. I'd like to try one of race to goal comp. Several Ohio pilots have begun making plans to give a go in the sports class. I'm sure it would be a great time, but I may opt to hit some new sites. Then again, I'd kill for a local scooter tow sled run about now!
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Joined: 30 Jan 2008
Posts: 407
Location: Travelling The USA
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Posted: Thu Jan 14, 2010 6:33 am Post subject:
I feel for you in the lack of air time! Would you believe the last time I got to fly was in OH with you? The the "W"s have kept me grounded for the last year. Weather, Work, and Wife.............
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Joined: 27 Jul 2006
Posts: 4722
Location: Ohio
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Posted: Thu Jan 14, 2010 4:26 pm Post subject:
O!M!G! that was a long time ago!
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I found a photo of GOLDEN RUSSET on the Iris City website. Not a match.
I was assuming this iris was from the same era as INDIAN CHIEF (late
20s) until reading that browns were a more recent development. It does
resemble the photo of PRAIRIE SUNSET (1936) on The World of Iris website
except for the hafts.
Your guess that it's a relative or descendant sounds like a good one. I
will try a start of PS for comparison, & will check TWOI for more clues.
I wonder if PRAIRIE SUNSET is known to throw rebloomers...
Linda Mann east Tennessee USA zone 7/8
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photos archives: <http://www.hort.net/lists/iris-photos/>
online R&I <http://www.irisregister.com>
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TEENAGE keeper Daniel Bentley was the hero as Southend went through on
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Just good reminders
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Free Riley Bradshaw; Corvallis native ready to hit the court
MISSOULA, Mont. - As a senior at Corvallis High School, Riley Bradshaw had narrowed down his college basketball choices to either Utah State or Montana and while he initially chose Utah State, he quickly changed his mind and transferred to Missoula after only one semester.
"I knew I had this year of waiting, but it was worth it to me to get near family and friends and just to play here," recalls Bradshaw of his decision to transfer. "I knew I kind of wanted to come here and I felt like I kind of made a mistake."
It's been an extremely long wait for Bradshaw. After transferring from Utah State he's been forced to sit two full semesters due to NCAA rules. That means he hasn't played a game since his senior season at Corvallis, which was 22 months ago. But if all his grades can get finalized by game time on Friday, he could finally see the court against Montana Western.
"You know it is killing me, I can't wait to actually be out there on the floor," says the freshman guard. "You know I was actually hoping last week possibly, there was a little bit of hope for that."
"I know he's ready," says Montana junior guard Jordan Gregory. "He's one of my good friends. We live in the same apartment complex and we've been counting down the days for him so I'm really excited for him, he's been working really hard."
"We keep saying free Riley Bradshaw," added senior Kareem Jamar. "That's the slogan right now so we're happy for him and I can't wait for him to get out there, hopefully the teachers do all they can to get the grades up and get him out there."
'Free Riley Bradshaw' is not just about getting him off the bench; it's about adding another impact player to the Grizzly rotation.
"He makes the right passes. He makes the extra pass. He can shoot it and he can get in the paint," says Jamar.
"He's a guy that can make plays off the bounce, he can knock down shots, he can finish at the rim," says head coach Wayne Tinkle. "So that gives us another weapon out there on the perimeter."
The wait will also be over for Griz fans in the Missoula area who got to witness Bradshaw grow up on the hardwoods in Corvallis and now get to see him wear that maroon and silver for the Montana program.
"When Riley gets in, he's kind of a local legend," explained Gregory. "So once people see he's starting to get time there's going to be a lot more excitement."
"You would hope that with the Bradshaw clan and then all the folks down the Bitterroot that they might come and add to our attendance," says Tinkle.
"You got to root for a guy like that who comes in as a team guy and is still aggressive," added Jamar. "So we can't wait for him to be out there."
"I'm just going to be excited, might be a little nervous, who knows," responded Bradshaw about his upcoming Grizzly debut. "I mean I don't know what to expect really my first time stepping out on the court. I've tried to envision it but all I can say is I'm excited and I really can't wait."
If Bradshaw's semester transcript is not finalized in time for Friday's game against Montana Western, he would likely see his first minutes on the road at Idaho on December 28.