... the efforts of the subcommissions of the ICS and other stratigraphic and regional experts A Geologic TimeScale 201 At thetime of this writing, a major comprehensive update of the Geologic Time ... I I I I numerical ages for the geologic timescale These methods and discussion of uncertainties are summarized in A Geologic TimeScale 2004 and other publications The ages of events and stage ... events, their relationships to international divisions of geologic time, and their estimated numerical ages On-screen display and production of user-tailored time- scale cham is provided by the Timescale...
... calculating thetime difference xi (t ) between each clock and the average timescaleThe value xi (t ) can be calculated from thetime difference X ij (t ) between the clocks, the epoch t0 at which the ... hi is thetime of clock i, and TA is the average timeThe average timescale is theoretically defined as follows: N TA0(t ) = ∑ wi (t ) hi (t ), i =1 N ∑ w (t ) = i i =1 (1) Here, i is the index ... establishing the average timescale of VMI with three clocks is described and the conclusion is section V Timescale algorithm general Hereinafter, time is discussed in reference to "ideal time, " referring...
... arbitrarily, then substituting T with t in (13) yields the desired inequality (3) Remark 2.1: Since T is an arbitrary time scale, then if we take T for some peculiar cases in Theorem 2.1, then we ... ≤ n , 0 then u(n) ≤ {G−1 [G(a(n)) + b(n) n−1 f (s)]} p , n ∈ Z0 s=n0 In Theorem 2.1, if we change the conditions for a, b, ωp; then, we can obtain another bound for the function u(t) Theorem ... doi:10.1016/S0898-1221(01)00135-3 Bohner, M, Matthews, T: The Grüss inequality on time scales Commun Math Anal 3(1), 1–8 (2007) Ngô, QA: Some mean value theorems for integrals on time scales Appl Math Comput 213,...
... C1 – C3 in Theorem 4.2 are satisfied for the above specified functions and parameters Therefore, in the light of Theorem 4.2, we conclude that the dynamic equation on the specified time scales uΔ ... point theorem and the five functionals fixed point theorem are adopted in the arguments It is valuable to mention that the writing form of the ending point of the interval on time scales should be ... establish the following result on the existence of at least three solutions in the boundary value problems 1.9 and 1.10 Theorem 4.2 Suppose that the hypotheses H1 – H3 are all fulfilled Assume that there...
... βi u θi u i They established a corresponding iterative scheme for the problem by using the monotone iterative technique All the above works were done under the assumption that the nonlinear ... nonnegative on time scales Therefore, it is a natural problem to consider the existence of positive solution for higher order p-Laplacian equations with sign changing nonlinearity on time scales This ... ∈ ∂DK Then the following results hold If Ax ≤ x , x ∈ ∂DK , then iK A, DK If there exists x0 ∈ K \ {0} such that x / Ax iK A, DK λx0 for all x ∈ ∂DK and all λ > 0, then and iK A, UK 0, then A...
... are derived from thetimescale T as follows If T has a left-scattered maximum t1 , then Tk T − t1 , otherwise Tk T If T has a right-scattered minimum t2 , then Tk T − t2 , otherwise Tk T Definition ... to discuss these problems Many difficulties occur when we deal with them For example, basic tools from calculus such as Fermat’s theorem, Rolle’s theorem, and the intermediate value theorem may ... that there is a large number of functions that satisfy the conditions of Theorem 3.3 In addition, the conditions of Theorem 3.3 are also easy to check Acknowledgments This work is sponsored by the...
... closed subintervals of an arbitrary time scale, and to 12 for a broad introduction to dynamic equations on time scales Definition 1.1 u is said to be a solution in the sense of distributions to P ... 1 · ϕσ s Δs 0, 2.17 and the proof is therefore complete Propositions 2.3 and 2.4 lead to the following sufficient condition for the existence of at least one solution in the sense of distributions ... compact support on a, b T We denote as · C D the norm in C D , that is, the supremum norm On the other hand, we consider the first-order Sobolev spaces HΔ D : H H0,Δ D : v : D −→ R : v ∈ AC D ,...
... of thetimescale T3 , which is then restricted to thetimescale T1 , but the necessary conditions (3.4) and (3.5) are stated in terms the original timescale T3 and Tκ , Tκ In this case, the ... general time scales, there are certain difficulties with this basic formulation These difficulties can be avoided by some additional conditions on the structure of thetime scale, but we show that these ... formulation of the problem avoids the difficulties The difficulties just mentioned concern the basic formulation of the linear operator formed from the left-hand side of (1.1), together with the boundary...
... preserved, we get the statement 8 Hille-Nehari theorems on time scales Similarly as for Theorem 3.1, there is a corollary of Theorem 3.3 where the condition M∗ = M ∗ leads to the existence of ... those in Theorem 4.1 can obvi∞ ously be established also in the case when a 1/r(s)Δs < ∞ Then they involve the expression Ꮽ(t) For the proof we use Theorem 3.3 and the counterpart—in the sense ... See [12], which is the initiating paper of the time- scale theory written by Hilger, and the monographs [2, 3] by Bohner and Peterson containing a lot of information on time- scale calculus We will...
... (1.5) The proofs rely on the a priori bounds on solutions of Section and the nonlinear alternative The following theorem gives the existence of solutions to the Dirichlet BVP on time scales Theorem ... operator by the Arzela-Ascoli theorem Therefore, Theorem 1.8 is applicable to T and T must have a fixed point Hence the BVP has a solution This concludes the proof The following theorem gives the existence ... a ≤ t ≤ b} The jump operators σ and ρ allow the classification of points in a timescale in the following way: if σ(t) > t, then call the point t right-scattered; while if ρ(t) < t, then we call...
... for the duration of the command, refer to the file named after the ‘‘>’’ For example: ls ordinarily lists, on the typewriter, the names of the files in the current directory The command: ls >there ... file called there and places the listing there Thus the argument >there means ‘‘place output on there.’’ On the other hand: ed ordinarily enters the editor, which takes requests from the user via ... Implementation of the shell The outline of the operation of the shell can now be understood Most of the time, the shell is waiting for the user to type a command When the newline character ending the line...
... that the cluster arrival rate implies the parameter for the intercluster arrival times and the ray arrival rate refers to the parameter for the intracluster arrival times The distributions of these ... described by the Poisson distribution of (2.4) The inter-ray arrival times, τkl , are dependent on thetime of the first arrival in the cluster Tl In the Saleh-Valenzuela model, the first cluster time ... with time Their model proposes that both of these decaying patterns are exponential with time, and are controlled by two time constants: Γ, the cluster arrival decay time constant, and γ, the...
... to understand the hydrgeological setting and the related geological controls of the hot groundwater reservoirs, which is the scope of this study This will help exploring the geothermal water, ... in the marine environment These geothermal sources are well known to the fishermen along the Lebanese coastal zone They are clearly identified in three localities as follows: - Along the southern ... studying thegeological maps for the volcanic rocks as basalt, since the majority of the geothermal waters occur in contact with hot rocks In this study, the applicable approaches to identify geothermal...
... the original time under study In short, an idea or conclusion is reached from observing one time period; then the thesis is applied to data from another time, either before or after the test or ... averaged the 1980s and the 1990s to continue the same procedure used by Gould on the earlier data The pattern holds, telling us there is consistency to the concept What we see is that in the card ... much the same thing: Prices bottomed early in the year, followed by a summer run-up, a pullback in the fall of the year (the seven year buy zone), and then another two-year bull market The 1907...
... the original time under study In short, an idea or conclusion is reached from observing one time period; then the thesis is applied to data from another time, either before or after the test or ... averaged the 1980s and the 1990s to continue the same procedure used by Gould on the earlier data The pattern holds, telling us there is consistency to the concept What we see is that in the card ... much the same thing: Prices bottomed early in the year, followed by a summer run-up, a pullback in the fall of the year (the seven year buy zone), and then another two-year bull market The 1907...
... of thetime spent in carrying the mails on the chief routes throughout the country Although the speed fixed by the Government for the postboys was seven miles an hour in the summer months, the ... feet forward in the street; on the east side being another building answerable thereto." These premises served as the Post Office for the long period of 118 years The first half of the present Bristol ... to the Right Hon Wm Pitt, representing the great benefits received from the plan, and requesting a continuance of the same, together with the extension of the same plan to other parts of the...
... To get in, they climbed up the back of the rear workman, walked across the cabinet, and scaled down the front of the leading man They went up the stairs to the fifteenth floor Here they crawled ... placed the nails, one by one, in the line The distance left to cover was less than six inches! He lined up the last few nails Then both men were sinking back on their heels, as they saw there ... relief For a long time he was too busy with the dog to bother about the sobbing noises Apparently the dog failed to hear them, for he gave no sign Miller scratched him behind the ear "What shall...
... between their accept and submit times Nonetheless, the times ought to be better estimates as they are taken over larger samples The average speed for the HNG postings seems to be slower than the ... perhaps the most widely used metric in the MT community The x-axis measures the number of sentence translation pairs in the training data The VG curves are cut off at the point at which the stopping ... there’s thetime required to examine each word and translate them in some sense (even if not one-to-one) and then there is an extra significant overhead time to put it all together and synthesize...