... derived only once or several times depending ** on ** ** the ** approach used ** in ** ** the ** ** inverse ** ** problem ** and has been discussed ** in ** ** the ** corresponding ** review ** ** on ** ** solving ** ** the ** forward ** problem ** [2] Then, ** in ** conjunction ... Introducing Anatomo-Functional Priors ** in ** ** the ** ** EEG/** MEG ** Inverse ** ** Problem ** IEEE Transactions ** on ** Biomedical Engineering 1997, 44(5):374-385 Pascual-Marqui RD: ** Review ** of Methods for ** Solving ** ** the ** ** EEG ** ** Inverse ** ... that ** in ** addition to ** source ** localization, LORETA provides ** source ** orientation estimates, which are unavailable ** in ** sLORETA solutions Discussion and conclusion ** In ** ** EEG ** ** source ** analysis, ** the ** ** inverse ** problem...

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... ** source ** configurations are needed A ** review ** ** on ** ** solving ** ** the ** inverse ** problem ** is given ** in ** [3] ** In ** this ** review ** article several aspects of ** solving ** ** the ** ** forward ** ** problem ** ** in ** ** EEG ** ** source ** localization will be discussed ... configuration ** The ** inverse ** problem ** attempts to find ** the ** electrical ** source ** which generates a measured ** EEG ** By ** solving ** ** the ** inverse ** problem,** repeated solutions of ** the ** ** forward ** ** problem ** for different ** source ** configurations ... ** the ** probe at ** the ** top, at ** the ** probe ** in ** ** the ** middle ** the ** incoming inhibitory action potential is measured and shown ** The ** neuron processes ** the ** incoming potentials: ** the ** excitatory action potentials are...

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... 360 ** The ** ** Cauchy ** ** characteristic ** ** problem ** ** Global ** solvability ** of ** ** the ** ** problem ** Consider ** the ** case ** for ** f (u) = −λ|u| p u, where λ = and p > are ** the ** given real numbers In this case (1.1) takes ** the ** form ... to ** the ** limit as m → ∞, we obtain (2.4) Thus ** the ** lemma is proved Remark 2.5 Before passing to ** the ** question ** on ** ** the ** solvability ** of ** ** the ** nonlinear ** problem ** (2.1), (2.2), we consider this question ** for ** ... will, more so, be ** the ** strong generalized continuous solution ** of ** ** problem ** (3.9) There◦ fore, taking into account that G ∈ C(DT ,ST ), by Lemma 3.2, ** for ** ** the ** function u ** the ** integral representation u(x,t)...

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... ** DEVELOPMENT ** ** OF ** ** SOME ** ** LOCAL ** ** SEARCH ** ** METHODS ** ** FOR ** ** SOLVING ** ** THE ** ** VEHICLE ** ** ROUTING ** ** PROBLEM ** ZENG LING (B.ENG, DUT) A THESIS SUBMITTED ** FOR ** ** THE ** DEGREE ** OF ** MASTER ** OF ** ENGINEERING DEPARTMENT ** OF ** INDUSTRIAL ... traversed by ** the ** ** vehicle;** • ** The ** costs associated with ** the ** utilization ** of ** ** the ** ** vehicle;** • ** The ** capacity ** of ** ** the ** ** vehicle,** expressed as ** the ** maximum weight or volume ** the ** ** vehicle ** can load; • ** The ** devices ... studied type ** of ** ** the ** VRP family Set covering based algorithms One ** of ** ** the ** exact ** methods ** ** for ** ** solving ** ** the ** VRP is based on a set covering formulation ** of ** ** the ** ** problem ** Let ** the ** index set ** of ** all feasible...

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... ** linear ** ** functional-** diﬀerential ** equations,** Arch Math (Brno) 33 (1997), no 3, 197–212 , ** Boundary ** ** Value ** Problems ** for ** Systems of ** Linear ** ** Functional ** Diﬀerential ** Equations,** Folia Facultatis Scientiarium ... Kiguradze and B Puˇ ** a,** ** On ** ** boundary ** ** value ** problems ** for ** systems of ** linear ** ** functional-** diﬀerential ** equations,** Czechoslovak Math J 47(122) (1997), no 2, 341–373 , ** On ** ** periodic ** solutions of systems of ** linear ** ... Scientiarium Naturalium Universitatis Masarykianae Brunensis Mathematica, vol 12, Masaryk University, Brno, 2003 I T Kiguradze and B L Shekhter, Singular ** boundary ** ** value ** problems ** for ** ** second-order ** ordinary...

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... real-valued function, ** the ** functions Q : R × R → R and G : R × R × R → R are continuous In ** the ** process, ** the ** authors used ** Fixed ** ** Point ** ** Theory ** ** for ** ** the ** ** Functional ** ** Diﬀerential ** ** Equations ** ** with ** ** Finite ** ** Delay ** ... (v(t), vt )| < t∈[0,∞) (5.4) ** Fixed ** ** Point ** ** Theory ** ** for ** ** the ** ** Functional ** ** Diﬀerential ** ** Equations ** ** with ** ** Finite ** ** Delay ** 59 Finally, we need only ** to ** prove that ** for ** each h ** with ** ||h|| < , ** the ** following equation has ... need ** to ** show that b = n (2.12) ** Fixed ** ** Point ** ** Theory ** ** for ** ** the ** ** Functional ** ** Diﬀerential ** ** Equations ** ** with ** ** Finite ** ** Delay ** 51 We suppose by contradiction that b < n Since g is locally Lipschitzian in ** the ** second...

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... contains a forest ** of ** given ** size ** Lemma (i) An r-uniform hypergraph with at least r!(t − 1)r edges contains a forest with t edges (ii) Let F be a 3-uniform hypergraph Then either (a) F contains a forest ... complete ** hypergraphs ** should also have the highest ** Tur´n ** density a among all ** hypergraphs ** with the same number ** of ** edges Were this true de Caen’s bound would give π(F ) < − Ω(f −(r−1)/r ) ** for ** an r-uniform ... [5] conjectured that ** for ** any t there is a o constant C so that any r-uniform hypergraph with C r edges contains a sunﬂower with t edges We can obtain a bound ** of ** this form ** for ** forests, indeed, we...

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... Lemma with n = ** and ** s = **27 ** ** and ** get ki ≤ **58 ** 8k5 + 15k6 + 22k7 + 29 **(8)** i **8 ** Multiplication with 3/22 ** and ** rounding oﬀ yields Lemma ** the ** electronic journal of combinatorics 14 (20 **07)** , #R **27 ** Some preliminaries ... that i **8 ** ki > holds From F) follows i **8 ** ki ≤ If equality holds, then by **(8)** k5 = k6 = k7 = ** and ** thus k5 +2k6 +3 i **7 ** ki = contradicting F) If i **8 ** ki = 1, then by **(8)** we have 8k5 + 15k6 + 22k7 ≤ 29 ... + 3|L **7 ** | by |B ∩ L| ≤ ** for ** L ∈ L≥5 ≤ 4(k5 + 2k6 + by (2) ki ) i **7 ** ≤ **28 ** by Lemma ** and ** (13) follows by ( **18)** ** the ** electronic journal of combinatorics 14 (20 **07)** , #R **27 ** Proof of Theorem Let C ⊂ F7 be...

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... present ** a ** feasible solution ** for ** ** the ** ** dual ** ** problem ** with exactly this objective value ** For ** ** a ** ** binary ** matrix ** A,** ** the ** set ** of ** variables in RSP-Relax corresponds to ** the ** set ** of ** rectangles that are completely ... parallel to ** the ** x-axis and ** the ** y-axis are called horizontal and vertical, respectively We associate ** a ** bipartite graph G = (H ∪ V, E) with P ** The ** vertex sets H and V are ** the ** sets ** of ** horizontal ... such that x1 + · · · + xt is minimal ** The ** integral ** problem ** RSP can be formulated in ** a ** geometric setup as follows We associate ** A ** with ** a ** rectangular m×n-array ** of ** unit squares in ** the ** plane ** The ** set...

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... trivially ** on ** each F ∈ FR ** The ** information which goes undetected by FR is thus complicated indeed **ON ** ** THE ** ** CLASSIFICATION ** ** PROBLEM ** ** FOR ** ** NUCLEAR ** ** C ** ∗ ** **** -ALGEBRAS ** 1041 Some remarks ** on ** ** the ** classiﬁcation ** problem ** ... Annals of Mathematics, 167 (2008), 1029–1044 ** On ** ** the ** classiﬁcation ** problem ** ** for ** ** nuclear ** ** C ** ** ****-algebras ** By Andrew S Toms Abstract We exhibit a counterexample to Elliott’s classiﬁcation conjecture ** for ** simple, ... precisely that ˜ of [V1] ** The ** reason ** for ** ** the ** speci **c ** choice of point evaluations will be made clear shortly.) Straightforward calculation shows that ** the ** projection pi ∈ Bi corresponds to a complex...

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... ** equations,** diagonal systems and variational integrals Manuscripta Math 55, 467–486 (1986) doi:10.1007/BF01186659 Rutkauskas, S: ** On ** ** the ** ** first ** ** boundary ** ** value ** ** problem ** ** for ** ** the ** class ** of ** ** elliptic ** systems ... degenerating ** at ** an inner point Math Model Anal 6(1), 147–155 (2001) Rutkauskas, S: ** On ** ** the ** Dirichlet ** problem ** ** for ** ** a ** ** system ** ** of ** ** degenerate ** ** at ** ** a ** point ** elliptic ** ** equations ** in ** the ** class ** of ** bounded functions ... ** problem ** ** for ** ** a ** ** system ** ** of ** ** elliptic ** ** equations ** ** that ** ** strongly ** ** degenerate ** ** at ** ** a ** point ** Boundary ** ** Value ** Problems 2011 2011:16 Submit your manuscript to ** a ** journal and beneﬁt from: Convenient online submission...

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... article as: Hung et al.: ** On ** ** the ** ** regularity ** ** of ** ** the ** ** solution ** ** for ** ** the ** ** second ** ** initial ** ** boundary ** ** value ** ** problem ** ** for ** ** hyperbolic ** ** systems ** ** in ** ** domains ** ** with ** ** conical ** points ** Boundary ** ** Value ** Problems 2011 2011:17 ... NT: ** The ** ** initial-** ** boundary ** ** value ** problems ** for ** parabolic equations ** in ** ** domains ** ** with ** ** conical ** points ** In:** Albert, R, Baswell (eds.) Advances ** in ** Mathematics Research, vol 10, Nova Science Publishers, Inc, ... results ** on ** ** the ** ** regularity ** ** of ** solutions ** of ** elliptic ** boundary ** problems ** in ** smooth ** domains ** (see, e.g., [12]), we have Hung et al ** Boundary ** ** Value ** Problems 2011, 2011:17 http://www.boundaryvalueproblems.com/content/2011/1/17...

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... ** Spectral ** analysis of ** the ** ** problem ** ** on ** ** the ** half-line was studied by Fulton 22 Also, physical application of ** the ** ** problem ** ** with ** ** the ** linear ** spectral ** ** parameter ** appearing ** in ** ** the ** ** boundary ** conditions ** on ** ** the ** ... Section 2, ** the ** ** scattering ** data ** for ** ** the ** ** boundary ** value ** problem ** 1.1 – 1.3 are deﬁned ** In ** Section 3, ** the ** fundamental ** equation ** ** for ** ** the ** ** inverse ** ** problem ** is obtained and ** the ** continuity of ** the ** ** scattering ** ... of ** scattering ** theory ** for ** ** the ** ** boundary ** value ** problem ** 1.1 – 1.3 ** in ** ** the ** special case was studied ** in ** 14 When ρ x ≡ ** in ** 1.1 ** with ** ** the ** ** spectral ** ** parameter ** appearing ** in ** ** the ** ** boundary ** conditions, ** the ** inverse...

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