... 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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... behavior ** of ** polysilicate ** in ** controlling ** membrane ** ** fouling ** ** in ** three MBR ** systems ** (R1, R2, ** and ** R3) TMP was increased ** by ** ** membrane ** clogging ** and ** recovered ** by ** physical washing The concentrations ** of ** sole ... ** control ** ** of ** ** membrane ** ** fouling ** was more effective PSI effectively reduced biopolymer concentrations ** and ** ** membrane ** ** fouling ** ** in ** MBR The reduction ** of ** ** membrane ** ** fouling ** ** by ** PSI ** addition ** was caused ** by ** the ... 99-104 Mishima I ** and ** Nakajima J (2009) ** Control ** ** of ** ** Membrane ** ** fouling ** ** by ** ** Coagulant ** ** Addition ** ** in ** ** Membrane ** ** Bioreactor ** Process, Water Science ** and ** Technology, 59(7), 1255-1262 Nakajima J ** and ** Mishima I (2005)...

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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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... respect to ** the ** surrounding text **FIRST ** ** COURSE ** ** IN ** ** THE ** ** THEORY ** ** OF ** EQUATIONS ** BY ** ** LEONARD ** ** EUGENE ** ** DICKSON,** Ph.D CORRESPONDANT DE L’INSTITUT DE FRANCE PROFESSOR ** OF ** MATHEMATICS ** IN ** ** THE ** UNIVERSITY ** OF ** CHICAGO ... circle having as a diameter ** the ** line BQ joining ** the ** points B = (0, 1) and Q = (a, b) ** in ** Fig Then ** the ** abscissas ON and OM ** of ** ** the ** points B N ** of ** intersection ** of ** this circle with ** the ** O x-axis are ** the ** roots ... degree, ** in ** ** the ** coordinates ** of ** ** the ** general point on it Hence we are concerned with certain numbers, some being ** the ** coordinates ** of ** points, others being ** the ** coeﬃcients ** of ** ** equations, ** and still others...

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... to be valid ** in ** modelling many aspects ** of ** signal processing ** and ** transcriptional regulation Because ** of ** the rate ** of ** progress ** in ** systems ** biology,** it seems likely that a second edition ** of ** this book ... Chapter begins with 20 pages ** of ** elementary thermodynamics ** and ** enzymology, surely elementary for most readers, ** and ** ends with the same amount ** of ** text – a mere 20 pages – on metabolic control theory, which ... less likely to be familiar ** and ** is far more mathematically sophisticated Much ** of ** the account ** of ** ageing ** in ** chapter is devoted to the defective mitochondria theory – reasonably, ** in ** that one ** of ** the...

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... the ** solubilization ** ** of ** ** excess ** ** sludge ** ** by ** ** high ** ** speed ** ** rotary ** ** disk ** ** process ** This method is ** a ** kind ** of ** physical treatment The ** excess ** ** sludge ** from final sedimentation tank in wastewater treatment plant was ... 813-818 Hasegawa, S., Miura, M., Katsura, K (1997) ** Solubilization ** ** of ** organic sewage ** by ** thermophilic bacteria Journal ** of ** Japan Sewage Works Association, Vol.34, No.408, 76-82 Imaoka, T., Hatano, K., ... inorganic materials such as sand; 6) type ** of ** surface materials ** of ** ** disk ** ACKNOWLEDGMENT The authors wish to thank Mr Hirofumi NAGATA for his great cooperation and the TAKAHASHI Foundation for providing...

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... arrangements ** of ** flow third tank Figure Schematic diagram for ** improvement ** ** of ** ** water ** ** quality ** ** by ** ** removal ** ** of ** SS ** and ** ** biological ** ** filtration ** ** in ** ** closed ** ** water ** bodies a a: screw motor Ｍ b: ** biological ** carrier ... ** Water ** ** and ** Environment Technology, Vol.1, No.2, 2003 Conclusion The experiment on improving ** water ** ** quality ** was carried out ** by ** ** removal ** ** of ** SS ** and ** ** biological ** ** filtration ** ** in ** the ** closed ** ** water ** ** body,** Tokiwako ... ** closed ** ** water ** ** body,** Tokiwako Lake ** in ** Ube city The developed system is useful for ** improvement ** ** of ** ** water ** ** quality ** ** in ** ** closed ** ** water ** ** body ** Following results could be obtained from the experiment Micro-bubble...

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... tank and ** a ** microfiltration ** membrane ** as ** separation ** apparatus The aeration tank was made from Plexiglas ** with ** ** a ** working volume ** of ** liters Air was supplied to the aeration tank through diffusers at ** a ** ... quality, and kinetic parameters were also investigated PERMEATE COMPRESSED AIR INFLUENT AIR ** SLUDGE ** WASTE Fig Schematic Diagram ** of ** the ** Coupling ** ** of ** ** Activated ** ** Sludge ** ** Process ** and ** Membrane ** ** Separation ** ... Reactor Operation The ** sludge ** from ** activated ** ** sludge ** ** process ** was acclimatized ** by ** the ** textile ** ** wastewater ** in an aerobic batch tank without the ** membrane ** filtration unit Necessary amount ** of ** nitrogen and phosphorous...

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