maxwell s equations in empty space

... Fuzzy Sets Syst 159, 730–738 (2008) doi:10.1016/j.fss.2007.07.011 Mirmostafee, AK, Moslehian, MS: Fuzzy versions of Hyers-Ulam-Rassias theorem Fuzzy Sets Syst 159, 720–729 (2008) doi:10.1016/j.fss.2007.09.016 ... doi:10.2969/ jmsj/00210064 Rassias, ThM: On the stability of the linear mapping in Banach spaces Proc Am Math Soc 72, 297–300 (1978) doi:10.1090 /S0 002-9939-1978-0507327-1 Bourgin, DG: Classes of transformations ... Trans Am Math Soc 347, 3111–3119 (1995) doi:10.2307/2154775 Hyers, DH, Isac, G, Rassias, ThM: Stability of Functional Equations in Several Variables Birkhäuser, Basel (1998) Hyers, DH, Isac,...

Ngày tải lên: 20/06/2014, 22:20

... Advances in Difference Equations which is actually a classical solution if x ∈ D A In the present paper, we investigate strong stability and asymptotical almost periodicity of the solutions For ... the assumption i implies the boundedness of S t Therefore, f t : S tx 2.38 is bounded and uniformly continuous on 0, ∞ In addition, the half-line spectrum set of f t is just the following set: ... is reflexive By assumption i , M is a closed subspace of X × Lp R , X Thus, Pettis s theorem shows that M is also reflexive Hence, in view of Lemma 1.3, we get b This completes the proof Corollary...

Ngày tải lên: 21/06/2014, 05:20

... and s ∈ 0, t \ e, denote by S t − s the adjoint operator of S t − s , then S t − s ∈ X ∗ , and φ S t − s G , wn s S∗ t − s φ G , wn s −→ S t − s φ G v∗ , w∗ s φ φ S t − s G v∗ , w∗ s , S t ... That is, assumption H1 is satisfied From iii , it is easy to see that assumption H2 is satisfied Therefore, the following result is deduced from Theorem 1.2 Theorem 3.1 If the assumptions i – iii ... evolution equations, ” Journal of Systems Science and Mathematical Sciences, vol 25, no 6, pp 720–728, 2005 Chinese 10 Y X Li, “Periodic solutions of semilinear evolution equations in Banach spaces,”...

Ngày tải lên: 21/06/2014, 07:20

... normed spaces, as in 22, 23, 27–29 Throughout this paper, Δ is the space of distribution functions, that is, the space of all mappings F : R ∪ {−∞, ∞} → 0, such that F is left-continuous and ... Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications, 34, Birkh¨ user, Basel, Switzerland, 1998 a 10 G Isac and Th M Rassias, “On the Hyers-Ulam ... Jensen functional equation,” Fuzzy Sets and Systems, vol 159, no 6, pp 730–738, 2008 25 A K Mirmostafaee and M S Moslehian, “Fuzzy versions of Hyers-Ulam-Rassias theorem,” Fuzzy Sets and Systems,...

Ngày tải lên: 22/06/2014, 02:20

... studied the oscillation of its solutions in the following sense: a solution ({xn }, { yn }) is oscillatory if both components are oscillatory With our definitions, the system is interpreted as ... of f being strongly monotone, that is, satisfying f (x) − f (y),x − y ≥ a x − y , perhaps in a directional sense Acknowledgments This research is partially supported by the Spanish (Grants MTM2007-60854 ... product, so that, by the Schauder fixed point theorem, T will have a fixed point in C if it is a compact operator, that is, if it is continuous and sends bounded sets onto relatively compact sets First,...

Ngày tải lên: 22/06/2014, 19:20

... Contents | 335 ENGINEERING ELECTROMAGNETICS 10.4 MAXWELL' S EQUATIONS IN INTEGRAL FORM The integral forms of Maxwell' s equations are usually easier to recognize in terms of the experimental laws from ... Á We should first look at the point form of Ampere 's circuital law as it applies to steady magnetic fields, rÂEˆÀ | v v This is discussed in several of the references listed in the Suggested ... always represents a theory Let us now collect the integral forms of Maxwell' s equations of the previous section Integrating (20) over a surface and applying Stokes' theorem, we obtain Faraday's...

Ngày tải lên: 07/08/2014, 20:23

... definitions of stabilities and show that these stabilities fit in with quasi-processes By using results in Section 2, we discuss the existence of almost periodic solutions for abstract almost periodic ... increasing interest in extending certain classical results to differential equations in Banach spaces In this book we will make an attempt to gather systematically certain recent results in this direction ... (s) |Mw emax{0,w}(t s) exp + σ 1.2.3 Mw L(r) dr ds s Equations with Infinite Delay As the phase space for equations with finite delay one usually takes the space of continuous functions This is...

Ngày tải lên: 29/10/2015, 12:32

... T(a s) g (s, B2 x (s) )ds+ −∞ , then T(a s) h (s, B3 x (s) ) dW (s) AT(t − s) f (s, B1 x (s) ) ds T(t − s) g (s, B2 x (s) )ds + a −∞ T(t − s) h (s, B3 x (s) ) dW (s) However, for t ≥ a, t T(t − s) h (s, B3 x (s) ) dW (s) a t = ... solutions to (1.1) Preliminaries In this section, we introduce some basic definitions, notations, lemmas, and technical results which are used in the sequel For more details on this section, we refer ... g (s, B2 x (s) ) − g (s, B2 y (s) ) ||2 ds −∞ ≤ e−δ(t s) (t − s) −α || g (s, B2 x (s) ) − g (s, B2 y (s) ) ||2 ds −∞ t 4M2 Lg α × e−δ(t s) (t − s) −α || g (s, B2 x (s) ) − g (s, B2 y (s) ) || ds −∞ t t e−δ(t s) ...

Ngày tải lên: 21/06/2014, 03:20

... where P is the metric We will show that D2 is best possible Example 2.5 Put E N , that is, E is a Hilbert space consisting of all the functions x from N into R satisfying k∈N |x k |2 < ∞ with inner ... following are satisfied NS1 For each t ≥ 0, T t is a nonexpansive mapping on C NS2 T s t T s ◦ T t for all s, t ≥ NS3 For each x ∈ C, the mapping t → T t x from 0, ∞ into C is strongly continuous ... approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces,” Nonlinear Analysis, vol 54, no 8, pp 1417–1426, 2003 L P Belluce and W A Kirk, “Nonexpansive mappings and...

Ngày tải lên: 21/06/2014, 20:20

... t S t x0 − g x dL α S t − s f s, x s ds , t S t x0 − g y α S t − s f s, y s ds t S t g x dL α S t − s f s, x s ds , t S t g y α S t − s f s, y s ds α ≤ dL S t g x t α , St g y dL S t − s f s, ... S t − s f s, x s ds o S t − s β−1 × x1 − g x − S T x0 − g x − T α S T − s f s, x s ds ds , t S t x0 − g y t S t − s f s, y s ds S t − s β−1 × x1 − g y − S T x0 − g y − T α S T − s f s, y s ds ... ds ds ≤ dL S t g x α t α , S tg y α dL S t − s f s, x s , S t − s f s, y s α ds t α dL S t − s β−1 g x , S t − s β−1 g y dL S t − s β−1 S T g x α ds t α , S t − s β−1 S T g y α ds t dL S t − s...

Ngày tải lên: 21/06/2014, 20:20

... distribution functions that is, the space of all mappings F : R ∪ {−∞, ∞} → 0, , such that F is leftcontinuous and nondecreasing on R, F 0 and F ∞ D is a subset of Δ consisting of all functions ... Progress in Nonlinear Differential Equations and Their Applications, Birkh¨ user, Boston, Mass, USA, 1998 a 10 G Isac and Th M Rassias, “On the Hyers-Ulam stability of ψ-additive mappings,” Journal ... generalized Hyers-Ulam-Rassias stability of different functional equations in random normed spaces has been recently studied in 24–29 Recently, Eshaghi Gordji et al 30 established the stability of...

Ngày tải lên: 22/06/2014, 02:20

... m-accretive mappings in Banach spaces By using the resolvent operator technique in , they constructed some new iterative algorithms for solving the nonlinear variational inclusions involving generalized ... Deng, “Nonlinear variational inclusions involving generalized maccretive mappings,” in Proceedings of the 9th Bellman Continuum International Workshop on Uncertain Systems and Soft Computing, pp ... implicit quasivariational inequalities for fuzzy mappings,” in Set Valued Mappings with Applications in Nonlinear Analysis, vol of Series in Mathematical Analysis and Applications, pp 63–77,...

Ngày tải lên: 22/06/2014, 02:20

... belong, should be as rich as possible, the case where Π coincides with the entire space X being the most desirable one It is of course natural to assume that Π⊆K , (3.62) because otherwise the assertion ... Then, A is K-subadditive (resp., K-superadditive) on the entire space X if = (resp., = −1) In both cases, operator (2.28) is positively homogeneous In some cases, the K-superadditivy and K-subadditivity ... wedge K The resulting theorem is somewhat strange due to the fact that the K-superadditive operators themselves are not typical representatives of the class of mappings T satisfying the symmetric...

Ngày tải lên: 22/06/2014, 18:20

... of difference equations defined on N with l∞ -phase space of sequences defined on N (see [9]) As a result, we have obtained a necessary and sufficient condition for difference equations to have an ... the operators T0 , T In particular, we will also get necessary and sufficient conditions for exponential dichotomy in Hilbert spaces and finite-dimensional spaces Moreover, using our characterization ... Exponential stability of dynamic equations on time scales, Advances in Difference Equations 2005 (2005), no 2, 133–144 [17] A Rodkina and H Schurz, Global asymptotic stability of solutions of cubic stochastic...

Ngày tải lên: 22/06/2014, 22:20

... families of nonexpansive mappings in [21] See also [20] In this paper, using the idea in [21], we prove Browder s type strong convergence theorems for in nite families of nonexpansive mappings without ... nonexpansive mappings is the set of fixed points of some single nonexpansive mapping; see Bruck [8] We also remark that we not use the notion of (invariant) mean Preliminaries Throughout this paper, ... following Lemma 2.4 Let {un } be a sequence in a Banach space E Assume that {un } has at most one cluster point, and every subsequence of {un } has a cluster point Then {un } converges Proof Since...

Ngày tải lên: 22/06/2014, 22:20

... is also equicontinuous, it follows from [8, Proposition 4.3 and Remarks 4.1] that u = supW exists in C(J,E), and there is an increasing sequence (un ) in W which converges pointwise strongly in ... equicontinuous subset of P Thus G satisfies the hypotheses of Lemma 2.2 Moreover, it is easy to verify that each solution of (3.1) in X belongs to P, and that Gu increases if c(u) or f (·,u) increases Thus ... it is easy to verify that each solution in Y belongs to P, and that Gu increases if c(u) decreases, or if d(u) or f (·,u) increases Thus the assertions follow from Lemmas 5.1 and 2.2 As a special...

Ngày tải lên: 23/06/2014, 00:20

... http://www.medsci.org Int J Med Sci 2010, Statistical Analysis Student t-test was used to assess the statistical significance in the data RESULTS Substitution I181M in B19 NS1 interferes with NS1-induced ... apoptosis observed in HepG2 cells expressing all B19 NS1 constructs showed continually increasing percentage of cells undergoing apoptosis starting at 24 hrs (Figure 2) At 48 hrs post-transduction ... substitution- carrying HepG2 cells resulted from a reduction in cells undergoing apoptosis We used the AnnexinV binding assay to assess apoptotic cell death in HepG2 cells The pattern of apoptosis...

Ngày tải lên: 26/10/2012, 09:32

... there is love and same tastes, which is a kind of representation of romanticism So she still rejects Darcy at the first time because his proposal seems to be a sacrifice to her by saying that she ... restraining her own passion She pursues happiness under the condition that she must obey the moral standards So, the author still arranges a happy marriage for her After all, it is Austen s view ... Design the study The assignment is divided into three main parts: Introduction: includes the rationale, method of the study and design of the study The discussion of the assignment consists of background...

Ngày tải lên: 10/04/2013, 21:34

Ngày tải lên: 22/11/2013, 09:16