applications of differential equations ppt

... is a solution of2.32, and according to one of the conditions of the lemma, admits estimate2.18 Therefore, estimate 2.31 is valid Trang 103 Proof of the main resultsProof of Theorem 1.1 ... functional differential equations and, particularly, for nonautonomous differential equations with deviated arguments, new sufficient conditions for the existence and uniqueness of a periodic solution ... original work is properly cited. 1 Statement of the main results 1.1 Statement of the problem Let n ≥ 2 be a natural number, ω > 0, L ω the space of ω-periodic and Lebesgue integrable on 0,

Ngày tải lên: 21/06/2014, 22:20

... compact subsets oft ≥0 for the solutionu(t;ε) of (1.1) and the solutionw(t) of (1.2) In this paper, we will continue these studies and investigate the convergence of deriva-tives of solutions for ... ap-proach,” Journal of Di fferential Equations, vol 70, no 1, pp 1–41, 1987. [2] J Liu, “A singular perturbation problem in integrodifferential equations,” Electronic Journal of Differential Equations, vol ... Stimulated by the work of Fattorini [1] and some models in physics, such as viscoelas-ticity, we studied in [4] the convergence of solutions of the problem (1.1) to solutions of the Cauchy problem

Ngày tải lên: 22/06/2014, 18:20

... Trang 1DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT NGUYEN TRUNG THANH Department of Mathematics, Hanoi University of Science Abstract In this note, we prove the almost periodicity of ... existence of periodic solutions to differential equation with piecewise constant argument In this note, we are concernded with differential equations with piecewise constant argument of the form ... 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, it has

Ngày tải lên: 11/03/2015, 07:57

... Notions of Admissibility 48 2.2.2 Admissibility for Abstract Ordinary Differential Equations 53 2.2.3 Higher Order Differential Equations 55 2.2.4 Abstract Functional Differential Equations ... verybeginning of this century The theory of almost periodic solutions has been de-veloped in connection with problems of differential equations, dynamical systems,stability theory and its applications ... fully nonlinearequations The conditions are given in terms of the dissipativeness of the equationsunder consideration In Chapter 3 we present the existence of almost periodic solutions of almost riodic

Ngày tải lên: 29/10/2015, 12:32

... Homogeneous systems of linear differential equations Trang 9Calculus 4c-39 Homogeneous systems of linear differential equations Example 1.3 Find that solution z1(t) = (x1, x2)T of (3) d dt  x1 ... 4c-35 I ntroduction Introduction Here we present a collection of examples of general systems of linear differential equations and some applications in Physics and the Technical Sciences The reader ... Trang 1Examples of Systems of Differential Equations Download free books at Trang 2Leif Mej lbr oExam ples of Syst em s of Differ ent ial Equat ions and Applicat

Ngày tải lên: 16/12/2017, 07:56

... extended to 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] Re-cently, ... 1Massera criterion for periodic solutionsof differential equations with piecewise constant argument N.T Thanh Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Viet ... criterion [12] was first introduced by Massera in 1950 to ordi-nary differential equations, saying that the linear differential equation of the form E-mail address: thanhnt79@vol.vnn.vn. 0022-247X/$

Ngày tải lên: 16/12/2017, 16:50

... the dimension of force can also be defined within this framework. H.P Langtangen and G.K Pedersen, Scaling of Differential Equations, derived unit, is the same as the dimension of mass times ... dimensions of [L] divided by [T], leading to the dimension of velocity as [LT^{-1}] This aligns with the definition of velocity, which is the ratio of distance ([L]) to time ([T]).In the analysis of ... difference having a dimension of [LT]⁻² Therefore, the general dimension of the derivative du/dt is the dimension of u divided by the dimension of t.Dimensions of common physical quantitiesDerived

Ngày tải lên: 27/05/2022, 10:30

... Topic2.NSFDmethodsforpartialdifferentialequations In recent years, the study of NSFD schemes for PDEs is also of interesttomany researchers(see[21–24,38,39]).Theclassesof equationsunder considerationarise inmany areas of ... ObjectivesandcontentsofthethesisThe aim of the thesis is to study NSFD methods for solving somedifferentialequationsarisinginfieldsofscienceandtechnology.Incasewhenqualitativeproper-tiesofthedifferentialmodelshavenotbeenestablishedcompletely,wewillperformqualitativeresearchbeforeproposingNSFDschemesandinvestigatingtheirproperties ... Inthisthesis,wehavesuccessfullydevelopedtheMickens’methodologytoconstructnonstandardfinitedifference(NSFD)methodsforsolvingsomeimportantclassesofdifferential equations arising in fields of scienceand technology The new contributionsareasfollows: 1 Proposing and analyzing NSFD schemes for some important classes of ential equations,

Ngày tải lên: 17/08/2023, 22:35

... collection of invariant sets contained in A R ∪ E ρ , as t → ∞. Proof The proof of I is equal to the proof of I of Theorem 3.2 If for some t0 ∈ 0, ∞,x t0φ, λ ∈ B R, then the proof of II ... limit-sets of solutions and also provide estimates of attracting sets and their basins of attraction Thus, it is important to consider the concept of derivative of a function along the solutions of2.1 ... possibility of studying the asymptotic behavior of solutions of differential equations without the explicit knowledge of solutions For this purpose, the invariance principle supposes the existence of a

Ngày tải lên: 10/11/2023, 18:15

... the linear differential equations on manifolds in which includes the external differential operators At research of such equations appear so named the small denominators, so such equations is ... bundle of manifolds X, C°(€) is the space of smooth differential forms and H*(€) is the Sobolev space of differential forms over X (see, [4]) By A we denote operator i(d+0), so-called natural differential ... Trang 1 Periodic solutions of some linear evolution systems of natural differential equations on 2-dimensional tore Dang Khanh Hoi* Department of General Education, Hoa Binh University,

Ngày tải lên: 14/03/2014, 13:20

... Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics, Harbin Institute of ... the number of basic frequencies of ˙x  ψx, t, x ∈ R, is the same as that of basic frequencies of its unique solution Trang 2The spectrum containment of almost periodic solution of equationxt ... inclusion just means that the minimal period of g1t is a multiple of the minimal period of g2t Some properties of basic frequencies the base of spectrum were discussed for almost periodic

Ngày tải lên: 21/06/2014, 20:20

... function Sketch of the proof First of all, by an equality similar to (3.32), we can prove t h a t (3.7) has no other solution except O(x) Then, by a proof similar to t h a t of Theorem 3.4, ... function 8 being the solution of (3.7) Conversely, if (X, ]I, Z) is a nodal solution of (3.1) with the repre- senting function 8 Then 8 is a solution of (3.7) Proof By Lemma 3.2, we can find ... non-uniqueness of the nodal solutions (and hence the non-uniqueness of the adapted solutions) to (3.1); and the number of the nodal solutions will be exactly the same as t h a t of the solutions

Ngày tải lên: 10/08/2014, 20:20

... vol 27, pp 505–535 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, the possibility of a stiff set of equations arises Stiffness occurs in ... THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations The values of y are ... scales of the independent variable on which the dependent variables are changing For example, consider the following set of equations[1]: u0= 998u + 1998v with boundary conditions By means of the

Ngày tải lên: 24/12/2013, 12:16

... according to visual perception of distance 112 Trang 23LIST OF FIGURES XIX6.17 Two examples of a pre–defined shape of a region–of–interest 1126.18 Region–of–interest mask with three quality ... analysis of medical and military signals, methods to solve boundary problems in differential equations, andregularization of inverse problems In opposition to hitherto common methods of signal ... A critical discussion of the region–of–interest coding of JPEG2000 concludes the investigation of still images Chapter 7contains our major contribution: the application of the wavelet transform

Ngày tải lên: 25/12/2013, 05:17

... and define the tip of each spoke as one engineering or science discipline: this book lays out the various applications of MCS with a goal of sparking innovative exercises of MCS across fields. Despite ... and Applications of Monte Carlo Simulations The distribution of the test statics V i1,i2 is known and the p-value of the two tail statistical test with... Resistance of Fibrin ... using the structure of an umbrella to define and exemplify the position of this book within the fields of science and engineering. Imagine that one can place MCS at the centerpoint of an umbrella

Ngày tải lên: 16/03/2014, 12:20

... and turnover of blood cells and immune system The high rate of regeneration of the liver, as compared to other tissues such as brain tissue, is due to prolifera-tion of two types of liver cells, ... in implantation of hepatic stem cells, or in implantation of hepatic cells obtained by differentia-tion of a different type of stem cell, such as mesenchy-mal stem cells Other applications, still ... in vitro, which offers a great potential in cell therapy for a very wide variety of liver diseases Histocompatible stem cell therapy Since one of the most important applications of cell therapy

Ngày tải lên: 18/06/2014, 16:20

... equations are more general than difference equations, differential equations, and differential equations with impulses The study of abstract measure differential equations was initiated by Sharma [1] ... differential equations There were some consideration on abstract measure delay differential equations [2] and perturbed abstract measure differential equations [4] However, to the best of authors’ ... measure functional differential equations In this article, we investigate the existence of solutions for perturbed abstract measure functional differential equations This is a problem of difficulty

Ngày tải lên: 18/06/2014, 22:20

... index of the numbers of soft bit value depending on the modulation scheme; k is the index into the 100 data subcarriers in an OFDM symbol Demapper Soft Bit ChannelEstimator Trang 24.2.2 Soft ... for TFC=1, BG=1 To avoid the cost of this CSI aided Viterbi decoder, the soft input of the decoding chain is obtained from the multiplication of the demodulation soft output R m and its corresponding ... imaginary part as a group of 4 soft bits, as described in (21)-(24) However, demapping performance can remain the same without using the factor of 10/5 The group of 4 soft bits applying two CSI

Ngày tải lên: 19/06/2014, 14:20

... Bit-Error-Rate (BER), for communication purposes and, in thecase of IR-UWB for ranging applications, to the estimation of the Time-of-Flight (ToF).The UWB channel is statistical, therefore determining ... environment,i.e indoor office, residential, industrial, outdoor, open outdoor, and for Line-Of-Sight (LOS) or Non Line-Of-Sight (NLOS) links IEE (2004) Also, the computation of ToF with TWRschemes ... of this block requires the definition of the complete packetexchange mechanism as well as detailed information on each single block of the receiver Trang 6Therefore, the complete development of

Ngày tải lên: 19/06/2014, 14:20

... 2004; Porcino & Hirt, 2003) One of the ‘killer’ applications of high-speed WPAN is wireless video area network (WVAN) that offers wireless transmission of high-definition videos (several Gbps) ... July 2008 by a group of international companies The main duties of the consortium include the development of the specification and compliance testing process, management of the certification ... have discussed the problem of UWB system performance in single-user and multi-user environments While there is a rich body of literature addressing this problem most of which has emerged recently,

Ngày tải lên: 19/06/2014, 14:20