... immunocomplexes were then probed with the furin polyclonal antibody (Fig 9A) No furin was immunoprecipitated with MT1-MMP in bbHT1080 cells transfected with pCDNA 3.1 Zeo+ alone (Fig 9A, lane 1) or expressing ... complex between these two proteins (Fig 9B) We next tested whether expression of the EGFP-furin chimera could exert a dominant negative effect on proMT1-MMP processing by disrupting the complex between ... containing mgÆmL)1 BSA Beads were washed with lysis buffer and mixed with the protein extracts for h at °C under constant rotation Beads were washed three times for 15 with lysis buffer and resuspended...
... determined mixture component number Word hard interest line serve Context window size 15 25 all 15 25 all 15 25 all 15 25 all Model orderwith χ2 2 2 4 5 3 3 Model orderwith f req 3 4 6 4 4 3 context ... second order context vectors: to select better feature words in contexts to construct better second order context vectors enabling better feature selection Since the sense associated with a word’s ... to construct its second order context vector by summing the vectors of contextual words, then let the feature selection procedure start to work on these second order contextual vectors to select...
... meters of water annually withdrawn from its domestic water sources Even Egypt, with water self-sufficiency high on the political agenda and with a total water withdrawal within the country of 65 ... next section reviews a number of developments that urge for global arrangements in order to cope with local problems of water scarcity, flooding and pollution The third section includes an explorative ... interlinked with how the global economy works and is therefore a true global problem Water pollution is intertwined with the global economic system to such an extent that it cannot be dealt with independently...
... one hand and Unix scripting languages like Bourne Shell and awk on the other Perl’s first major proponents were Unix system administrators, people familiar with C and with Unix scripting languages; ... tagged texts unchanged These texts will be inserted into the list of labeled texts that are passed to the element function call for the element that is one level up; compare this with the final example ... $header_text = join '', @keeper_text; return $header_text; } Or we could write it more compactly: sub extract_headers { my $tree = shift; TEAM LinG 32 Recursion and Callbacks my @tagged_texts...
... you want to have with (or better yet, through) the computer For example, in a Web chat room, should the context of the expression—that is, the posture of the user—accompany the text of the chat? ... advantages Without a computer, you can connect a button being pressed to a light turning on With a computer, you can make the relationship between the button and the light more complex For example, ... 254 Controlling Motors 255 Controlling DC Motors and Gearhead Motors 255 Controlling RC Servos 259 Controlling Stepper...
... mapping t0 +L x ∈ S −→ I (x) = x( s) ds t0 attains its maximum and its minimum, that is, there exist x , x ∈ S such that I (x ) = max{I (x) : x ∈ S}, I (x ) = min{I (x) : x ∈ S} (6) Now, if x ∈ S is ... is such that x ≥ x on I then we have I (x) ≥ I (x ) and, by (6), I (x) ≤ I (x ) So we conclude that I (x) = I (x ) which, along withx ≥ x , implies that x = x on I Hence x is a maximal element ... implies x = x whenever x is a solution to (1) and x ∈ Y We say that x is the least (respectively, the greatest) solution of (1) in Y if x ≤ x (respectively, x ≥ x) for any other solution x ∈...
... ˜ ˜ ˜ + x2 + y1 x2 + x1 y2 + x1 − 2˜ y2 − 2y1 − y2 − y1 y2 − x1 x2 x ˜ ˜ ˜ y1 − x + x − y2 + + y − x ˜ ˜ ≤ −α y1 − x1 + y2 − x2 c q ∗ D+ V(t, y where α > depends on the order q ˜ ˜ − x) ≤ −αV(t, ... R(t, x, y) of (4.2 (a)) is ˜ ˜2 x1 − y1 + y2 + x2 − 2˜ y2 x ˜ ˜ ˜ ˜ ˜ x − y + y x + x1 y − y y − xx ˜ R(t, x, y) = for t ≥ τ0 ˜ ˜ ˜ ˜ Let us choose the Lyapunov function as V(t, y − x) = ||y − x| | ... fractional order vector differential system with the order q in Caputo’s sense for t ≥ τ0, τ0 Î ℝ as follows c ˜ Dq x = c Dq x ˜ c Dq x ˜ ˜ ˜ x1 (τ0 ) x = 01 ˜ ˜ x2 (τ0 ) x0 2 = −˜ + 2˜ y2 + 2y1 xx ˜...
... : X ∩ Dom L → Y, Lx(t) = x (t), x ∈ X ∩ Dom L, for Nx(t) = f (t, x( t), x (t)) + e(t), for x ∈ X, N : X → Y, respectively, where ⎧ ⎨ Dom L = x ∈ W 2,1 [0, T]Ì , x (0) = 0, x( T) = ⎩ T σ ⎫ ⎬ x (s) ... every x1 such that |x1 | ≤ r, |f (t, x1 , x2 )| ≤ ar Let the Banach space X = C [0, T]Ì with the norm | |x| | = max{| |x| | ∞ , | |x Δ || ∞ }, where | |x| |∞ = supt∈[0,T]Ì |x( t)| Let L1oc [0, T]T = {x : x| [s,t]T ... xn, x0 Î E ⊂ X satisfy ||xn - x0 || ® 0, (n ® ∞); thus, there exists M > such that ||xn|| ≤ M for any n ≥ One has that ||Nxn − Nx0 ||∞ = sup |Nxn − Nx0 | = sup |f (t, xn (t), xn (t)) − f (t, x0 ...
... get xi (t) = Iα {fi (t, x1 (t), , xn (t)) + gi (t, x1 (t − r1 ), , xn (t − rn ))}, i = 1, 2, , n (4) Now let F : X ® X, defined by Fxi = Iα {fi (t, x1 (t), , xn (t)) + gi (t, x1 (t ... x1 (t), , xn (t)) + gi (t, x1 (t − r1 ), , xn (t − rn ) dt Integrating both sides, we obtain t I1−α xi (t) − I1−α xi (t)|t=0 = {fi (t, x1 (t), , xn (t)) + gi (t, x1 (t − r1 ), , xn ... is stable if for any ε > 0, there exists δ > such that for any two solutions x( t) = (x1 (t), x2 (t), , xn(t))’ ˜ ˜ ˜ x and x( t) = (˜ (t), x2 (t), , xn (t)) with the initial conditions (2)-(3)...
... WT Xk = span{ek }, Yk = ⊕k Xj , Zk = ⊕∞ Xj j=1 j=k (2:2) Lemma 2.13 [19] Let X be a reflexive infinite Banach space, j Î C1 (X, ℝ) is an even functional with the (C) condition and j(0) = If X ... there exist positive constants μ >p+ and Q > such that lim sup |x| →+∞ F(t, x) ≤Q |x| μ uniformly for a.e t Î [0, T]; (B3) there exists μ’ >p+ and Q’ > such that lim inf |x| →+∞ F(t, x) ≥Q |x| μ uniformly ... 3.1 Let F(t, x) satisfies the condition (A’), and suppose the following conditions hold: (B1) there exist b >p+ and r > such that βF(t, x) ≤ (∇F(t, x) , x) for a.e t Î [0, T] and all |x| ≥ r in ℝN;...
... linking theorem of the existence of critical levels for a functional Let X be an Hilbert space, Y ⊂ X, r >0 and e Î X\ Y , e ≠ Set: Bρ (Y) = {x ∈ Y : xX ≤ ρ}, Sρ (Y) = {x ∈ Y : xX = ρ}, ρ (e, Y) = ... X1 0, R >0 and e Î X1 , e ≠ such that r < R and sup F < Sρ (X1 ) inf F; R (e ,X2 ) (c) −∞ < a = inf R (e ,X2 ) F; (d) (P.S.)c holds for any c Î [a, b], where b = supBρ (X1 ... σe + v X σe + v X ≤ ρ}, = ρ} ∪ {v : v ∈ Y, v X ≤ ρ} THEOREM 3.1 ("A Variation of Linking”) Let × be an Hilbert space, which is topological direct sum of the subspaces X1 and X2 Let F Î C1 (X, R)...
... | |x| |, x ∈ K, | |x| | = R (b) ||Ax|| ≤ | |x| |, x ∈ K, | |x| | = r; ||Ax|| ≥ | |x| |, x ∈ K, | |x| | = R Then, A has a fixed point x Î Kr, R such that r ≤ | |x| | ≤ R Preliminaries To establish the existence ... s)dτ f (s, x( s))ds em (x) dxds + t em (x) dx t f (s, x( s)) em(s) t em (x) dx em (x) dxds s em (x) dx g(τ )G(τ , s)dτ f (s, x( s))ds, t we get (Tx) (t) = λ m(t) − e c −λ t s e−m(s) f (s, x( s)) 0 em(t) ... em(t) c(1 − σ ) em (x) dxds + e−m(s) f (s, x( s)) t em (x) dxds s g(τ )G(τ , s)dτ f (s, x( s))ds, (Tx) (t) = m (t)(Tx) (t) − λf (t, x( t)) Therefore, −(Tx) (t) + m (t)(Tx) (t) = λf (t, x( t)), t ∈ (0,...
... F(t, x) − F(t, 0) = (∇F(t, sx), x) ds for all x Î ℝN and a.e t Î [0, T] By (S1) and Lemma 2.1, one has F(t, x) − F(t, 0) ≤ (f (t)h(|sx|) + g(t), x) ds ≤ f (t)[h( |x| ) + C] |x| + g(t) |x| ≤ f (t)[ε |x| ... [1-13] cannot be applied Example 4.2 Consider the function F(t, x) = |x| 2 T − t ln (100+ |x| 2 ) + A(t) |x| − ω2 |x| 2 + ω2 + T − t 2 + B(t), |x| 4 − |x| > 1, + T − t |x| 6 , |x| ≤ 1, 4ω where A(t), B(t) ... HT Example 4.3 Consider the function F(t, x) = T − t ln(100 + |x| 2 ) We observe that |∇F(t, x) | ≤ 2 |x| ≤2 T−t , T−t 100 + |x| 2 which means ∇F(t, x) is bounded, moreover, one has T F(t, x) dt...
... applications of integer order differential equations with deviated arguments, we refer the reader to the references [39-45] As far as we know, fractional order differential equations with deviated arguments ... problem for second order differential equations with an advanced argument Nonlinear Anal 2006, 65:2013-2023 Jankowski T: Positive solutions for fourth -order differential equations with deviating ... fractional integral of order a is defined as t (α) α I f (t) = (t − s)α−1 f (s)ds, α > 0, provided the integral exists Definition 2.3 The Riemann-Liouville fractional derivative of order a for a function...
... lim supt → ∞ x t and lim inft → ∞ x t x2 Clearly x2 ≤ x1 From the definition of z t , we find that x1 px2 ≤ ≤ x2 px1 ; hence x1 ≤ x2 and x1 x2 This completes proof of the theorem Remark 2.10 ... Examples In this section, we illustrate the obtained results with the following examples Example 3.1 Consider the second order delay dynamic equation x t x δ t t2 ΔΔ √ λ1 x t 3/2 t λ2 5/3 √ x ... second order neutral delay dynamic equation with mixed nonlinearities of the form: r t ut Δ q t |x τ t |α−1 x τ t n qi t |x τi t |αi −1 x τi t 0, 1.6 i where T is a time scale, t ∈ T and u t | x t...