applications of differential equations in physics

... presentation of methods as well as results in the area In recent years, there has been an increasing interest in extending certain classical results to differential equations in Banach spaces In this ... abstract functional differential equations with infinite delay, there are three kinds of definitions of stabilities In Sections and 4, we prove some equivalence of these definitions of stabilities ... the case of almost periodic solutions of (linear and nonlinear) equations in Banach spaces To this end, in the first chapter we present introductions to the theory of semigroups of linear operators

Ngày tải lên: 29/10/2015, 12:32

... direction of an observer which is moving with the curve always facing forward in the direction of the tangent vector The binormal B is something like the flag in the back of sand dune buggy The set of ... always pointing in the direction of motion, whereas, the normal and binormal vectors point towards the directions in which the curve is tending to curve In particular, a complete description of how ... be a tangent vector in an open neighborhood U of a point p Ạ RỢ and let f be a CỎ function in U The directional derivative of f at the point p, in the direction of X, is defined by Vx(f)(p) =

Ngày tải lên: 27/03/2014, 11:52

... variationof-constants formula in the theory of linear ordinary differential equations So, we often call the representation formula obtained here the variation-ofconstants formula in the phase space Such ... is finite dimensional, the representation formula for functional differential equations has been established by Hale [5] in the case of finite delay and by Murakami [16] in the case of infinite ... references therein for more information of the theory of admissibility of function spaces with respect to linear equations in the bounded as well as the unbounded case In what follows, we shall investigate

Ngày tải lên: 17/12/2017, 16:49

... on different kinds of deterministic differential equations have been considerably investigated in lots of publications [5-15] because of its signifi- cance and applications in physics, mechanics, ... Advances in Difference Equations 2011, 2011:9 http://www.advancesindifferenceequations.com/content/2011/1/9 Page 7 of 12 Thus, using an estimate on Ito integral established in Ichikawa [26], we obtain ... Stochastic Equations in Infinite Dimensions Cambridge University Press, Cambridge; 1992 25 Pazy A: Semigroups of Linear Operators and Applications to Partial Equations In Applied Mathematical

Ngày tải lên: 21/06/2014, 03:20

... results Introduction Owing to the memory behavior cf., e.g., 1, of materials, many practical problems in engineering related to viscoelasticity or thermoviscoelasticity can be reduced to the following ... properties of linear Volterra integro-differential equations, ” Mathematical Models & Methods in Applied Sciences, vol 18, no 1, pp 21–45, 2008 L Pandolfi, “Riesz systems and controllability of heat equations ... Mathematics, Springer, Berlin, Germany, 1998 12 Advances in Difference Equations T Xiao and J Liang, “Laplace transforms and integrated, regularized semigroups in locally convex spaces,” Journal of Functional

Ngày tải lên: 21/06/2014, 05:20

... continuity of q in the semispace z > 6 Advances in Difference Equations Case β2 Recall that, since we are assuming that inequality 2.6 holds, we have β1 α2 / In this case, the forbidden set of ... be to give a description of the dynamics of the system in terms of the eigenvalues of the associated matrix A given in 2.2 We begin with the following result concerning 2-periodic solutions ... stability of fixed points in some of the cases Recall that a fixed point of our system x∗ , y∗ always verifies y∗ λ for some real eigenvalue λ of the matrix A We will say in such case that the fixed point

Ngày tải lên: 21/06/2014, 05:20

... Andrzej Szulkin We discuss on the generalized Ulam-Hyers stability for functional equations in a single variable, including the nonlinear functional equations, the linear functional equations, ... in any medium, provided the original work is properly cited. 1. Introduction and preliminaries The study of functional equations stability originated from a question of Ulam 1940 concern- ing ... existence of a mapping c : G → Y such that the following hold. i c is a fixed point of J,thatis, w ◦c ◦ ηxcxhx, ∀x ∈ G. E w,η  The mapping c is the unique fixed point of J in the set

Ngày tải lên: 22/06/2014, 06:20

... inequality (2.3) implies The following definition, which is a modified version of one introduced in [3], provides a kind of the strict inequality in X Definition 2.5 Let H be a linear manifold in ... = in the topology of X Since (2.21) can be rewritten in the form of the inclusion βm f − x, βm f + x ⊂ K, (2.22) taking into account the closedness of K and passing to the limit as m → +∞ in ... assertions of the statements of Sections and involving the linear manifold H become trivial when (2.9) is violated, and we thus not deal with this case in the proofs Proof of Theorem 3.1 In view of Remark

Ngày tải lên: 22/06/2014, 18:20

... family of dichotomy projections {Pn }n∈N satisfying kerP0 = Z (ii) TZ : lZ → l p is invertible p Proof We first note that the following proof is inspired by the proof of [14, ... Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol 840, Springer, Berlin, 1981 [8] N T Huy, Exponential dichotomy of evolution equations and admissibility of ... dichotomy of evolution equations on the. .. Stability of the notion of dichotomy of linear impulsive differential equations in a Banach space, Italian Journal of Pure and

Ngày tải lên: 22/06/2014, 22:20

... equicontinuous subset of P, then U is relatively well-order complete in P in the sense that all well-ordered and inversely well-ordered chains of U have supremums and in? ??mums in P. Proof. (a) In both cases ... exists in C(J,E), and there is an increasing sequence (u n )inW which converges pointwise strongly in case (A) and weakly in the case (B) to u. Moreover, in both cases,   u(t)   ≤ liminf n→∞ ... definition (2.1)ofP. If W is an inversely well-ordered chain in U,then−W is a well-ordered chain in −U. The above proof ensures that v = sup(−W) exists in C(J,E) and belongs to P.Thus, inf W =−v exists

Ngày tải lên: 23/06/2014, 00:20

... amino acids) or CotB∆105 (275 amino acids) or CotC (66 amino acids) as carrier proteins (all in blue). The three 27-amino-acids repeats of full lenght CotB and the part of them remaining in ... t12) of storage at room temperature were examined by dot blotting of extracted spore coat proteins. Concentrations of purified TTFC (in nanograms) and of coat proteins (in micrograms) are indicated. ... differentiation of a growing cell into a dormant spore little is known about the mecha- nisms of protein incorporation into the coat, the nature of structural components forming the most external part of

Ngày tải lên: 11/08/2014, 00:22

... novel statistical procedure Detecting differential splicing is presented that uses probe-level information on Affymetrix exon arrays to detect differential splicing. ... detection of differential splicing in Affymetrix exon array studies Essi Laajala*, Tero Aittokallio*†, Riitta Lahesmaa* and Laura L Elo*† Addresses: *Turku Centre for Biotechnology, University of Turku ... University of Turku and Åbo Akademi University, Turku, FI-20521, Finland †Department of Mathematics, University of Turku, Turku, FI-20014, Finland Correspondence: Laura L Elo Email: laliel@utu.fi Published:

Ngày tải lên: 14/08/2014, 21:20

... Massera in 1950 to ordinary differential equations, saying that the linear differential equation of the form b= Alt)e(t) + f(t), Trang 2 [1], to OFDE with advance and delay in [5, 11, 12], to abstract ... (inclusion length) such that every interval {a,a +) contains at least one point of E Let f be a continuous function from R to X Recall also that f is said to be almost periodic (in the sense of ... Equation” , Springer-Verlag, 1974 4) T Furumochi, T Naito and Nguyen Van Minh, Boundedness and almost pe- riodicity of solutions of partial fictional! differential equations, J Differential Equations

Ngày tải lên: 11/03/2015, 07:57

... movement of the sample in the separation channel through eddy flow during sample injection and separation via the “floating sample loading” scheme. In principle, diffusion at intersecting channels ... the EOF Since the driving force of EOF is uniformly distributed along the capillary internal wall; EOF can provide a plug-like flow profile in contrast with the parabolic flow profile ... molecules of proteins are made of L- amino acids, which are carboxylic acids with an amino group at its α-position Amino acids can form polymers as a result of the amino group of one amino

Ngày tải lên: 11/09/2015, 14:27

... between coating and metal, resulting in the formation of a defined, homogeneous, thin, but dense layer of metallic oxide (Fe2O3 on iron or steel) This kind of self-protecting mechanism ... of Conducting Polymer Inhibitors on Pitting Corrosion of. .. number of electrons in the polymer chain remains unchanged, involves protonating all heteroatoms in polymer, namely nitrogen ... formation of this kind of ion is more accentuated in an acidic medium where one can expect the occurrence of protonic doping of the polymer. This is supported by the emeraldine salt coatings on

Ngày tải lên: 16/09/2015, 15:55

... Thus, changing point of view, instead of looking for a weak solution of (6.4) we may, equivalently, look for a minimizer of (6.5) However there is a drawback It turns out that the minimum problem ... obviously easier Indeed, in this vector space (thinking of R as the scalar field) we may introduce an inner product given by (u, v)1 = ∇u · ∇v Ω with the same properties of an inner product in Rn Then, ... functions f is integrable if and only if |f| is integrable All the functions Riemann integrable in a set A are Lebesgue integrable as well An interesting example of non integrable function in (0, +∞)

Ngày tải lên: 18/05/2017, 15:31

... characterization of the exponential dichotomy (obtained in [8]) of evolution equations in admissible function spaces to construct the structures of solutions in mild forms, which belong to some certain classes ... methods in [9] to the case of partial functional differential equations (PFDE) The main difficulties that we face when passing to the case of PFDE are the following two features: Firstly, since the ... (3.5)) in such a way that it allows to combine the exponential dichotomy of the linear part of Eq (1.1) with the existence and uniqueness of its bounded solutions in the case of ϕ -Lipschitz nonlinear

Ngày tải lên: 16/12/2017, 03:22

... 4c-3 Contents Cont ent s Introduction Homogeneous systems of linear dierential equations Inhomogeneous systems of linear dierential equations 44 Examples of applications in Physics 62 Stability 72 ... Transfer functions 88 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies and new markets provide ... solution of the homogeneous system of equations is given by x y = c1 cosh t sinh t + c2 sinh t cosh t , c1 , c2 arbitrære Due to the linearity, the complete solution of the inhomogeneous system of differential

Ngày tải lên: 16/12/2017, 07:56

... ordinary functional differential equations (OFDE) of delay type in [2], to OFDE with advance and delay in [4,10,11], to abstract functional differential equations in [20] Recently, it has been extended ... existence of periodic solutions to Eq (1.1) via the so-called Massera criterion Massera criterion [12] was first introduced by Massera in 1950 to ordinary differential equations, saying that the linear ... solutions of evolution equations in [13–16] For a more complete introduction to this topic we refer the reader to any introduction of these papers and counterexamples for almost periodic equations in

Ngày tải lên: 16/12/2017, 16:50

... considering the weights of different metrics, there may be other three directions of interest to us in combining technical and business interestingness Fuzzy weighting of individual interestingness ... describe applications, including interesting knowledge on how domain-specific knowledge was incorporated in the development of the DM solution and issues involved in the integration of this solution in ... pattern interestingness development in data mining We roughly categorize the initial work into the following efforts: • studying interestingness metrics highlighting the significance and evaluation of

Ngày tải lên: 23/10/2019, 16:11