Let (* ) u,, du + q(x, t) u = 0 in D x [0, T], where D c R3 is a bounded domain with a smooth boundary dD, T> d, d: =diam D, q(x, I) E C( [O, 2’1, L”(D)). Suppose that for every (**) ~I,+~=f(x, l)EC’(dDx [0, T]), the value u*,;,:= h(s, t) is known, where N is the outer normal to dD, u solves (* ) and ( ** ) and satisfies the initial conditions u = U, = 0 at I = 0. Then q(x, I) is uniquely deter...

Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...

Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...

having briefly been reviewed the historical process of changing the formulae for determining the times of islamic prayers, two newly found formulae and a new rule for establishing the times of prayers would be discussed. these matters have been exploited from four texts, still preserved as manuscript: (1) siyyid ¾?y? al-d?n sh?shtar?’s ¼ad b?b dar macrifa al-a½??rl?b, (2) b?r?n?’s ’ist?c?b f? c...

Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüfer (i.e, its integral closure is a Prüfer domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content cD(g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with cD(g) v = D. Using these facts, the...

let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr&amp;quot;{u}fer domains and um$t$ domains in terms of dimension ine...

due to some difficulties during seismic data acquisition, like natural obstacles (high voltage electricity cable, bad coupling of geophones with the ground) some of the traces cannot be recorded. since bad traces make the final stack unclear, usually bad traces go mute while processing. the final image of the earth’s crust is highly dependent of the quality and resolution of acquired data and m...

Let u t = ∇ 2 u − q(x)u := Lu in D × [0, ∞), where D ⊂ R 3 is a bounded domain with a smooth connected boundary S, and q(x) ∈ L 2 (S) is a real-valued function. is the outer normal to S, one can find q(x) uniquely. A similar result is obtained for the heat equation u t = Lu := ∇ · (a∇u). These results are based on new versions of Property C.