... Hansen, E and Sengupta, S.: Bounding ** solutions ** ** of ** ** systems ** ** of ** ** equations ** using interval analysis BIT 21, 203–211 (1981) Neumaier, A.: Interval Methods for ** Systems ** ** of ** ** Equations ** Cambridge Univ Press, ... Fig Projection ** of ** a periodic Lorenz system Conclusion and perspectives We have presented a new method for ** enclosing ** the ** solutions ** ** of ** HDSs This method can prove the existence ** of ** such ** solutions ** (vide ... integrations on each ** of ** them as initial conditions 3 Rigorous enclosure ** of ** discrete change during a hybrid system simulation Hybrid dynamic ** systems ** (HDSs) are ** systems ** described by a mix ** of ** discrete and...

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... Annals ** of ** Mathematics, 160 (2004), 1141–1182 ** Isomonodromy ** ** transformations ** ** of ** ** linear ** ** systems ** ** of ** diﬀerence equations By Alexei Borodin Abstract We introduce and study **isomonodromy** ** transformations ** ** of ** ... solution ** of ** an associated ** isomonodromy ** problem for a ** linear ** system ** of ** diﬀerential equations with rational coeﬃcients The goal ** of ** this paper is to develop a general theory ** of ** **isomonodromy** ** transformations ** ... n Then there exists a unique formal ˆ solution ** of ** (1.1) ** of ** the form (1.2) with Y0 = I **ISOMONODROMY ** ** TRANSFORMATIONS ** 1149 Proof As in the proof ** of ** Proposition 1.1, we may assume that n = Comparing...

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... classes ** of ** ** nonlinear ** ** matrix ** ** equations ** (see [8-21]) In this study, we consider the following problem: Find (X1, X2, , Xm) Î (P(n))m solution to the following system ** of ** ** nonlinear ** ** matrix ** ** equations:** ... Duan, F: Positive defined solution ** of ** two kinds ** of ** ** nonlinear ** ** matrix ** ** equations ** Surv Math Appl 4, 179–190 (2009) Hasanov, V: Positive definite solutions ** of ** the ** matrix ** ** equations ** X ± A*X-q A = Q Linear ... Application ** of ** Mathematics in Engineering’24, Proceedings ** of ** the XXIV Summer School Sozopol’98.113–116 (1999) Liao, A, Yao, G, Duan, X: Thompson metric method for ** solving ** a class ** of ** ** nonlinear ** matrix...

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... doi:10.1186/1687-1847-2011-43 Cite this article as: Agarwal et al.: ** Existence ** ** results ** ** of ** ** Brezis-Browder ** ** type ** ** for ** ** systems ** ** of ** ** Fredholm ** ** integral ** equations Advances in Difference Equations 2011 2011:43 ... Triple solutions ** of ** constant sign ** for ** a system ** of ** ** Fredholm ** ** integral ** equations Cubo 6, 1–45 (2004) Agarwal, RP, O’Regan, D, Wong, PJY: Constant-sign solutions ** of ** a system ** of ** ** integral ** equations: ... Constant-sign solutions ** of ** a system ** of ** ** Fredholm ** ** integral ** equations Acta Appl Math 80, 57–94 (2004) Agarwal, RP, O’Regan, D, Wong, PJY: Eigenvalues ** of ** a system ** of ** ** Fredholm ** ** integral ** equations Math...

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... method ** of ** upper ** and ** lower solutions ** and ** the monotone iteration scheme to reaction-diﬀusion system ** with ** ** discontinuous ** coeﬃcients ** and ** ** continuous ** delays ** and ** use these methods ** and ** the results ** of ** 15, ... Pao, **Systems ** ** of ** ** parabolic ** ** equations ** ** with ** ** continuous ** ** and ** discrete delays,” Journal ** of ** Mathematical Analysis ** and ** Applications, vol 205, no 1, pp 157–185, 1997 C V Pao, “Convergence ** of ** solutions ** of ** ... ** with ** the use ** of ** Gronwall inequality Then, v ≤ u in DT , ** and ** the proof ** of ** part i ** of ** the lemma is completed The similar argument gives the proof ** of ** part ii ** of ** the lemma Advances in Diﬀerence Equations...

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... Computation, vol 188, no 1, pp 833–837, 2007 G Papaschinopoulos and C J Schinas, **On ** ** the ** behavior ** of ** ** the ** ** solutions ** ** of ** a system ** of ** two nonlinear diﬀerence equations,” Communications ** on ** Applied Nonlinear ... Communications ** on ** Applied Nonlinear Analysis, vol 8, no 1, pp 1–25, 2001 ¨ A Y Ozban, **On ** ** the ** positive ** solutions ** ** of ** ** the ** system ** of ** rational diﬀerence equations xn 1/yn−k , yn /xn−m yn−m−k ,” Journal ** of ** ... x0 , , x0 > 1, 2.20 then all ** solutions ** ** of ** 1.10 are positive k Proof We consider ** solutions ** ** of ** 1.10 with ** the ** initial values x0 , x0 , , x0 satisfying 2.20 If k mod , then from 1.10 and 2.20...

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... 2012, pp.667-686 669 1.4 ** Phase ** ** change ** ** material ** layers The addition ** of ** a ** phase ** ** change ** ** material ** (PCM) into the external wall ** of ** a building has been shown to reduce the amount ** of ** ** energy ** required to cool ... Handbook on Low **-Energy ** ** Buildings ** and District **-Energy ** ** Systems:** Fundamentals, Techniques and Examples Earthscan, London, 2006 [9] Salyer I O., Sircar A K., A Review ** of ** ** Phase ** ** Change ** Materials Research ... Thermal ** Energy ** Storage in Heating and Cooling Applications at the University ** of ** Dayton from 1982 to 1986 International Journal ** of ** Global ** Energy ** 1997, 9, 183-198 [10] Frank B., ** Using ** ** Phase ** ** Change ** Material...

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... Therefore, it is ** of ** great importance to control the cooling water temperature properly The mechanical equipment ** of ** a ** diesel ** ** power ** plant to be cooled includes: (1) Cylinder wall ** of ** M E and aux engines, ... The answer is ** of ** course "No", for too low a temperature will bring about a thermal stress ** of ** materials due to an abrupt drop ** of ** temperature, not to mention heat waste, since a ** diesel ** ** power ** plant ... positions, general ** engine ** oil may be safely taken The Cooling System Some mechanical equipment in a ** diesel ** ** power ** plant will turn out continuous heat during operation, part ** of ** which derives from...

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... the world ** of ** ** root ** ﬁnding 350 Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** for (i **=1;** i...

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... 1-800-8 **72-** 7 **423** (North America only),or send email to trade@cup.cam.ac.uk (outside North America) a x2 x3 b x1 d c f e 351 9.1 Bracketing ** and ** Bisection 3 **52 ** Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** ... known to be within an interval ** of ** size n , then after the next iteration it will be bracketed within an interval ** of ** size 354 Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** #include ... current best estimate ** of ** the ** root,** so that the two points continue to bracket the ** root ** (Figure 9 **.2.** 2) Mathematically, the secant method converges more rapidly near a ** root ** ** of ** a sufﬁciently continuous...

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... nrerror("Maximum number ** of ** iterations exceeded in rtflsp"); return 0.0; Never get here **35** 8 Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** Ridders’ Method f(x1 ) − 2f(x3 )eQ + f(x2 )e2Q = (9.2.2) ... 1-800-872-74 **23 ** (North America only),or send email to trade@cup.cam.ac.uk (outside North America) f(x) ** 35** 5 9.2 Secant Method, False Position Method, ** and ** Ridders’ Method f(x) ** 35** 6 Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ... READING: Ralston, A., ** and ** Rabinowitz, P 1978, A First Course in Numerical Analysis, 2nd ed (New York: McGraw-Hill), §8 **.3 ** Ostrowski, A.M 1966, Solutions ** of ** ** Equations ** ** and ** Systems ** of ** ** Equations,** 2nd ed...

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... 360 Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** x= [y − f(a)][y − f(b)]c [y − f(b)][y − f(c)]a + [f(c) − f(a)][f(c) ... contain a ** root ** Brent’s method combines ** root ** bracketing, bisection, ** and ** inverse quadratic interpolation to converge from the neighborhood ** of ** a zero crossing While the false position ** and ** secant ... taken as the next estimate ** of ** the ** root ** x ** Of ** course one must have contingency plans for what to if the ** root ** falls outside ** of ** the brackets Brent’s method takes care ** of ** all that If the three point...

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... Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** ** of ** the desired ** root ** But that means that in the neighborhood ** of ** an extremum there must be a tiny, perhaps distorted, copy ** of ** the basin ** of ** convergence ... Derivative f(x) 364 Chapter ** Root ** ** Finding ** ** and ** ** Nonlinear ** ** Sets ** ** of ** ** Equations ** f(x) Figure 9.4.3 Unfortunate case where Newton’s method enters a nonconvergent cycle This behavior is often encountered when ... 9 **.5 ** Roots ** of ** Polynomials 369 9 **.5 ** Roots ** of ** Polynomials Deﬂation ** of ** Polynomials When seeking several or all roots ** of ** a polynomial, the total effort can be signiﬁcantly reduced by the use ** of ** deﬂation...

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