Using a more accurate effective Hamiltonian governig the time evolution in the particle–antiparticle subspace of states than the one obtained within the Lee–Oehme–Yang approach we show that in the case of particles created at the instant t = t0 only the masses of a stable particle and its antiparticle are the same at all t ≥ t0 in a CPT invariant system, whereas the masses of an unstable partic...

where T is a time scale unbounded above, the variable delays k, : [t0,∞)T → T are nondecreasing with k(t), (t) < t for all t ∈ [t0,∞)T such that limt→∞ k(t), (t)=∞. The coefficient functions p,q : T→R are right-dense continuous with p bounded and q ≥ 0. To clarify some notation, take −1(t) := sup{s : (s) ≤ t}, −(n+1)(t)= −1( −n(t)) for t ∈ [ (t0),∞)T, and n+1(t) = ( n(t)) for t ∈ [ −3(t0),∞)T. ...

It is known that the solution to a Cauchy problem of linear differential equations: x′(t) = A(t)x(t), with x(t0) = x0, can be presented by the matrix exponential as exp( ∫ t t0 A(s) ds)x0, if the commutativity condition for the coefficient matrix A(t) holds: [ ∫ t t0 A(s) ds, A(t) ] = 0. A natural question is whether this is true without the commutativity condition. To give a definite answer to...

Let L(t) represent the equation x1 + x2 + · · · + xt−1 = xt. For k > 1, 0 6 i 6 k − 1, and ti > 3, the generalized Schur number S(k; t0, t1, . . . , tk−1) is the least positive integer m such that for every k-colouring of {1, 2, . . . ,m}, there exists an i ∈ {0, 1, . . . , k − 1} such that there exists a solution to L(ti) that is monochromatic in colour i. In this paper, we report twenty-six p...

We obtain sufficient conditions for oscillation of all solutions of the neutral impulsive difference equation with continuous variable Δτ(y(t) +P(t)y(t−mτ)) +Q(t)y(t− lτ)= 0, t ≥ t0− τ, t = tk, y(tk + τ)− y(tk)= bk y(tk), k ∈N(1), where Δτ denotes the forward difference operator, that is, Δτz(t)= z(t+ τ)− z(t), P(t)∈ C([t0− τ,∞),R ),Q(t)∈ C([t0− τ,∞),(0,∞)),m, l are positive integers, τ > 0 and...

Proof (of Lemma 2). Assume that S `C t t0. By definition we get that S `C t. If (CANCEL) was used to derive S `C t t0 then t has the form t1 :t2 :t3 and t0 has the form t1 :t3, and furthermore we know that S t1 ! S0 t2 ! S0. It follows immediately that S `C t1:t3, and hence that S `C t0 and finalC(S, t) = finalC(S, t 0), as required. On the other hand, if (SWAP) was used to derive S `C t t0 the...

BACKGROUND Anthracyclines are agents with a wellknown cardiotoxicity. The study sought to evaluate the hemodynamic response to an anthracycline using realtime continuous-wave (CW)-Doppler ultrasound cardiac output monitoring (USCOM) and echocardiography in combination with serum biomarkers. METHODS 50 patients (26 male, 24 female, median age 59 years) suffering from various types of cancer re...

Let X be a scalar diffusion process with drift coefficient pointing towards the origin, i.e. X is mean-reverting. We denote by X∗ the corresponding running maximum, T0 the first time X hits the level zero. Given an increasing and convex loss function , we consider the following optimal stopping problem: inf0≤θ≤T0 E[ (X ∗ T0 −Xθ)], over all stopping times θ with values in [0, T0]. For the quadra...