applications of differential equations in real life

... nicepresentation 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 infinitedelay, there are three kinds of definitions of stabilities In Sections 3 and 4, we provesome 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 introduc-tions to the theory of semigroups of linear operators

Ngày tải lên: 29/10/2015, 12:32

... is a life-threatening systemic response to infection, leading to death in 34% to 65% of patients [1-5] It is common in patients requiring inten-sive care in France, where more than 10% of admitted ... applying a quality of life coefficient of 0.6, patients in the pre-license phase gained 3.68 ± 4.32 QALYs and those in the post-license phase gained 4.01 ± 4.40 QALYs, result-ing in a difference of ... as in a trial setting or (more likely) to selection of patients with no serious risk for bleeding in real-life clinical practice It is also worth noting that the reduction in 28-day mortality in

Ngày tải lên: 13/08/2014, 08:20

... admissibility of some spaces of functions whose spectra are contained in a closed subset of the real line © 2002 Elsevier Science Key Words: functional differential equations; phase space; variation-of-constants ... variation-of-constants formula in the theory of linear ordinary differential equations So, we often call the representation formula obtained here the variation-of-constants 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

Ngày tải lên: 17/12/2017, 16:49

... the following Volterra equation: ut  Aut  t 0 at − sAusds, t ≥ 0, u0  x 1.1 in a Banach space X, with A being the infinitesimal generator of a C0-semigroup Tt defined on X, ... examples are given to illustrate our results 1 Introduction Owing to the memory behavior cf., e.g., 1, 2 of materials, many practical problems in engineering related to viscoelasticity or thermoviscoelasticity ... ∩ iR is countable. Proof Since the first coordinate of2.5 is the unique solution of 1.1, it is easy to see that the strong stability and asymptotic almost periodicity of1.1 follows from

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, ... existence of a mapping c : G → Y such that the following hold. i c is a fixed point of J, that is, The mapping c is the unique fixed point of J in the set This says that c is the unique mapping verifying ... and we obtain the exis-tence of a mapping c : G → Y such that the following hold. i c is a fixed point of J, that is, c x  Fx, c The mapping c is the unique fixed point of J in the set

Ngày tải lên: 22/06/2014, 06:20

... uK0, then inequality (2.3) implies The following definition, which is a modified version of one introduced in [3], vides a kind of the strict inequality inX. pro-Definition 2.5 Let H be a linear ... the interior of the abovementioned cone in L ∞[0, 1] is empty The proofs of the results of this paper rely upon properties of a certain nonlinear tional associated with the wedgeK and a certain ... (2.29) is nonlinear 3 Mutual comparability of solutions of ( 1.1 ) The aim of this section is to establish certain conditions under which each two solutions of (1.1) lying in a certain linear manifold

Ngày tải lên: 22/06/2014, 18:20

... solvability of (1.2) inl∞spaces of sequences defined onN In the present paper, we will characterize the exponential dichotomy of (1.1) by the solvability of (1.2) in l p spaces (1≤ p < ∞) of sequences ... n belonging to a relevant sequence space (1.3) In the infinite-dimensional case, in order to characterize the exponential dichotomy of (1.1) defined onN, beside the surjectiveness of the operatorT, ... spaceX, we investigate the characterization of exponential dichotomy of the difference equations vn+1 = A n v n We characterize the exponential dichotomy of difference equations in terms of the exis-tence

Ngày tải lên: 22/06/2014, 22:20

... differential equations and the initial or boundary conditions may con-tain discontinuous nonlinearities; (5) problems on unbounded intervals; (6) finite and infinite systems of initial and boundary value ... that all well-ordered and inversely well-ordered chains of U have supremums and infimums in P. Proof (a) In both cases (A) and (B), the mapping x → x+is continuous inE and  x+ ≤  x for eachx ... definition (2.1) ofP. IfW is an inversely well-ordered chain in U, then − W is a well-ordered chain in − U. The above proof ensures thatv =sup(−W) exists in C(J, E) and belongs to P Thus, infW

Ngày tải lên: 23/06/2014, 00:20

... C-terminal half formedby three 27 amino acid-repeats rich in serine, lysine and glutamine residues Serine residues account for over 50% of the CotB C-terminal half The lysine residues in the ... (380 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 CotB∆105 ... 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 the

Ngày tải lên: 11/08/2014, 00:22

... exons in the complex colon cancer study, demonstrating its high potential also in real biomedical applications We focused here mainly on the rankings of the exons, since in practice the ranking ... generated from a single gene by selectively join-ing together exons of a primary transcript in different pat-terns (see, for example, [1] for a review) Thus, instead of coding a single protein, the same ... detection of differential splicing is the complexity of the splicing process Several types of splicing events have been observed, such as exon inclusion/exclusion, alteration of exon length, intron

Ngày tải lên: 14/08/2014, 21:20

... extended to ordinary functional ditferential equations (OFDE) of delay type in Trang 2[1], to OFDE with advance and delay in [5, 11, 12], to abstract functional differentia equations in [22] Recently, ... introduced by Massera in 1950 to ordinary differential equations, saying that the linear differential equation of the form b= Alt)e(t) + f(t), where A, f is continuous, periodic with the same period ... evolution equations in (15, 16, 17, 18] For a more complete introduction to thi topic we refer the reader to any introduction of these papers and counterexample for almost periodic equations in [7,

Ngày tải lên: 11/03/2015, 07:57

... identical to that in the reservoirs (except in the case of isoelectricfocusing) At the beginning of a common run, a small amount of sample is introduced (by pressure or electrical field) into the buffer-filled ... offenders and the appraisal of the consanguinity Amino acids, peptides and proteins Proteins are very important to life, the complex molecules of proteins are made of L- amino acids, which are carboxylic ... possibilities of applying hydrophobic compounds as terminating ions Since the miniaturization has received considerable attention in the recent development of CE The use of microfabrication techniques

Ngày tải lên: 11/09/2015, 14:27

... 32.6.1 Applying Semi-infinite Linear Diffusion on a Planar Electrode 2.6.3 Applying Semi-infinite Linear Diffusion on a Planar Electrode 2.7 Derivation of a Model for the Passivation of Metals ... unacceptability of chromates Trang 39c) Costd) Practicality on application of the coating in terms of handling and storage Section 2.10 Conducting Polymer Coatings Industrial treatment of carbon steel ... found that in acidic solution, polarisation of stainless steel in the passive potential region will result in selective dissolution of iron, leaving chromium in the passive film Whereas in basic

Ngày tải lên: 16/09/2015, 15:55

... bring into play the energy In fact, the total potential energy is proportional to E (v) = Ω |∇v|2dx /0 1 internal elastic energy − Ω fv dx /0 1 Thus, changing point of view, instead of looking ... space likeRn, where life is obviously easier Indeed, in this vector space (thinking ofR as the scalar field) we may introduce an inner product given by (u, v)1= 0 Having defined the inner product (·, ... for Symmetric BilinearForms Lin-6.1 Motivations The main purpose in the previous chapters has been to introduce part of the basicand classical theory of some important equations of mathematical

Ngày tải lên: 18/05/2017, 15:31

... 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 of admissible spaces ... (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 ofϕ-Lipschitz nonlinear ... defined in Definition 2.3below We will extend the 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

Ngày tải lên: 16/12/2017, 03:22

... ContentsCont ent s Introduction 5 6 44 62 72 88 www.sylvania.com We do not reinvent the wheel we reinvent light. Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies ... t  − sinh t cosh t  = −  t + 1 − sinh t t − cosh t  , t ∈ R Homogeneous systems of linear differential equations Trang 9Calculus 4c-39 Homogeneous systems of linear differential equations ... everyone of the vectors (2)  cosh t sinh t  ,  sinh t cosh t  ,  et et  ,  2et 2et  , is a solution of (1) 2) Are the vectors in (2) linearly dependent or linearly independent? 3) How many linearly

Ngày tải lên: 16/12/2017, 07:56

... structural buildings Several problems developed owing to a lack of understanding of the FRP material, mainly arising from insufficient knowledge of its in-service properties relating to durability ... bridge enclosures and fairings • bridge decks • external reinforcement rehabilitation and retrofitting to RC structures (including FRP confining of concrete columns) • external reinforcement rehabilitation and retrofitting ... followed by the involvement of interested civil engineering consultants undertaking industrial research and the utilisation of the structural material in practice The application of advanced polymer

Ngày tải lên: 05/04/2018, 15:53

... solu- tions of a delay differential equation, while in the second example, we will obtain the bound of the solutions of an integral equation. For the sake of proving the global existence of solutions of ... validity of the present integral inequalities. 2 Main results In the rest of the paper we denote the set of real numbers as R,andR + =[0,∞)isa subset of R. Dom(f)andIm(f) denote the definition domain ... Zheng and Feng: Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations. Journal of Inequalities and Applications 2011 2011:20. Submit...

Ngày tải lên: 21/06/2014, 01:20

... an indication of the meaning of words. They also have a fixed spelling. Because morphemes are represented in spelling, many word that is seemed to have an unpredictable or irregular spelling ... time and scope, we have introduced some features of English morpheme system as well as its importance in learning English in general and spelling, developing vocabulary in particular. It’s also ... mạnh mẽ: strong → powerful • rực → rực rỡ: flaring → blazing The reduplication decreasing intensity: • nhẹ → nhè nhẹ: soft → mild (less) • xinh → xinh xinh: pretty → cute • đỏ → đo đỏ: red → reddish •...

Ngày tải lên: 08/04/2013, 09:31

... expression in (16), bearing in mind that when k =0the total is just N 2 , the number of terms in the sum over j and l. Random Matrices and Number Theory 5 APPLICATIONS OF RANDOM MATRICES IN PHYSICS ing. ... and enjoy rapidly growing list of applications in seem- ingly disconnected disciplines of physics and mathematics. A few recent, randomly ordered, examples of emergence of the Random Matrix Theory ... connection between the Riemann zeros and the primes. In outline, the proof involves computing the pair correlation function of the derivative of N(T ). Using the explicit formula (5), this pair correlation function...

Ngày tải lên: 22/03/2014, 09:20