... from results of 47–49 the conditions of Lemmas 2.3, 2.4, 2.5 at the same time are conditions for stability in probability of the equilibrium point of 2.1 Stability of equilibrium points From ... 3.10 has two pointsof equilibrium x1 3−λ 3−λ 4μ , x2 3−λ− 3−λ 4μ 4.1 In Figure 1, the region where the pointsof equilibrium are absent white region , the region where both pointsof equilibrium ... with σ in the points A, B, C, D of the space of μ, λ Figure In the point A with μ −5, λ −3 both equilibrium points x1 and x2 are unstable In Figure two trajectories of solutions of 3.10 are shown...
... No preposition in 'Let's discuss it.' Prepositions after adjectives characteristic of independent of typical of We hope that the examples will help you find your way around in grammar books so ... relative clauses (They are essential to make the meaning of the sentence clear.) The woman who lives next door is very friendly I know a lot of people who live in Manchester The windows that were ... the basic message of the sentence.) Goethe, who died in 1832, was a famous writer Our car, which is quite old, is still reliable I'd like you to meet our secretaries, some of whom are bilingual...
... result is construction of an isomonodromy action of Zm(n+1)−1 on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)) The (birational) action of certain rank n ... identically equal to I The proof of uniqueness is complete To prove the existence we note, first of all, that it suffices to provide a proof if one of the κi ’s is equal to ±1 and one of the δj ’s is equal ... If the ratios of eigenvalues of A0 are not real then Theorem 3.9, Lemma 4.2, and Proposition 4.4 provide a proof of Theorem 4.5 However, our goal is to provide an independent proof of this theorem,...
... important players in their field of activity: Unicer has the major share of the beer market in Portugal and ACPB is a very well known producer of wine with appellation of origin Vinho Verde BREWERY ... volume of produced beer attain 4.7 m3/m3 (Carlsberg, 2005) but it should be pointed that the wastewater to beer ratio is often 1.2 m3/m3 to m3/ m3 less because part of the water is disposed off ... Another factor is the amount of waste sludge generated from aerobic metabolism, which also needs to be handled and disposed of Both increase the cost of operation of the treatment system Therefore,...
... substantial differences in the correlations across models at this CRA but rather that these differences are the result of the sampling differences 13 Default risk derived from report of odds ratio of ... mean the percentile equivalent of the score generated by a particular model 2.2.3 Correlation across Scoring Models The simplest measure ofsimilarity or differenceof the scores produced by the ... groups of 10% of the sample.14 For example, consumers with VantageScores in the bottom 10% of scores, consumers with scores between the 10th percentile of scores and the 20th percentile of scores,...
... not EXPENSIVE Advertising increases cost of product so the consumers must spend more money to own products Conclusion Advertising has both good and bad points Therefore, consumers should consider ... STRENGTHS They can supply a wide range of products to their customers because customers watch television many times a day so they can easily recognize brand name of the suppliers The customers are ... interested in the purchase of that products because she/he is their idol For example, My Tam Singer advertised for Pepsi so there are many people use Pepsi products instead of Coca cola TELEVISION...
... ultimate goal of finding useful biomarkers of etiology and outcome at different ages Therefore we have included some of the Spitzoid melanocytic neoplasms (as a part of the group of patients age ... levels of expressions of these miRs may contribute to differences in phenotypic and pathologic presentation of melanocytic neoplasms at different ages We performed an exploratory analysis of 666 ... comparative microRNA profiling of the primary melanocytic neoplasms of adults and young adults We observed distinct miRNA profiles in the primary melanocytic neoplasms of adults and young adults...
... 32 c The proof of Theorem is complete Proof of Theorem Due to the same idea of Proof Theorem 1, we omit the proof Proof of Theorem Suppose that f is a transcendental entire solution of finite order ... counting function of zeros of F such that simple zeros F are counted once and multiple zero twice Proof of Theorem Let f be an entire solution of Equation (1.4) Without loss of generality, we ... solution of finite order r of a difference equation of the form H(z, f )P(z, f ) = Q(z, f ), where H (z, f ), P(z, f ), Q(z, f ) are difference polynomials in f such that the total degree of H (z,...
... common fixed point of f and S Since gu = fz, following arguments similar to those given above we conclude that fz is a common fixed point of g and T as well Now we show the uniqueness of fixed point ... corresponding metric space (X, dG) Author details Department of Mathematics, Lahore University of Management Sciences, 54792 Lahore, Pakistan 2Department of Mathematics, Statistics and Physics, Qatar University, ... commutativity and common fixed points Soochow J Math 1(25), 37–42 (1999) doi:10.1186/1687-1812-2011-41 Cite this article as: Abbas et al.: Common fixed pointsof R-weakly commuting maps in generalized...
... generated by (1.5) converges strongly to a common element of the set of fixed pointsof nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone ... http://www.fixedpointtheoryandapplications.com/content/2011/1/47 Page of 13 for all y Î C The set of solutions of the variational inequality is denoted by VI(C, B) A mapping B of C to H is called inverse strongly monotone ... [6], we introduced the following iteration to find some solutions of variational inequality and fixed pointsof countable family of nonexpansive mappings in a Hilbert spaces H: x0 Î C, xn+1 = PC...
... We denote by F(S ) the set of all common fixed pointsof mappings in S (S), i.e., F(S ) := s∈s F(Ts ), where F (Ts) := {x Î C : Tsx = x} is the set of fixed pointsof Ts For any bounded net {xa} ... Page of 14 Proof This is an easy consequence of Proposition 3.4 since μs’ (f (s’)) = μs(f (s’)) = lims f (s’) = a ■ Proposition 3.6 [[12], Proposition 4.1] Let C be a closed convex subset of a ... Research University Project under Thailand’s Office of the Higher Education Commission for financial support Author details Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang...
... problem of finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed pointsof a family of infinitely nonexpansive mappings and the set of solutions of ... common element of the set of solutions of a generalized equilibrium problem, the set of fixed pointsof a family of infinitely nonexpansive mappings, and the set of solutions of the variational ... family of infinitely (finitely) nonexpansive mappings is too completed to use for finding the common element of the set of solutions of problem (1.2) and the set of fixed pointsof a family of infinitely...
... initial data of solutions of certain difference equations Throughout this paper, ℝ denotes the set of real numbers and ℝ+ = [0, ∞), and ℤ denotes the set of integers, while N0 denotes the set of nonnegative ... the study of boundedness, uniqueness, continuous dependence of solutions of certain difference equations Feng et al Advances in Difference Equations 2011, 2011:21 http://www.advancesindifferenceequations.com/content/2011/1/21 ... of integral points in ℝ, where m0, n0 Î ℤ Let := I × I ⊂ Z2 We denote the set of all ℝ-valued functions on Ω by ℘(Ω), and denote the set of all ℝ+-valued functions on Ω by ℘+(Ω) The partial difference...
... θ of the complex root is a rational multiple of π, the system is globally periodic 4.4 Stability of Fixed Points We finish this section with the complete study of the stability of the fixed points ... periodic of prime period We now study the stability of fixed points in some of the cases Recall that a fixed point of our system x∗ , y∗ always verifies y∗ λ for some real eigenvalue λ of the matrix ... attention on three aspects of the dynamics of the system: the boundedness character and asymptotic behavior of its solutions, the existence of periodic orbits in particular, of prime period-two solutions...
... “Approximating fixed pointsof nonexpansive mappings,” International Journal of Mathematics and Mathematical Sciences, vol 24, no 3, pp 173–177, 2000 16 M Maiti and B Saha, “Approximating fixed pointsof nonexpansive ... convergence theorems of fixed points are obtained in a uniformly smooth Banach space; see 10 for more details Very recently, Zegeye and Shahzad 11 studied the common zero problem of a family of m-accretive ... αn JA zn , converges strongly to a solution x∗ of the equation Ax n≥0 3.29 References F E Browder, “Convergence of approximants to fixed pointsof nonexpansive non-linear mappings in Banach spaces,”...
... converges strongly to x∗ The rest of the proof is almost the same as Theorem 3.1 This completes the proof Remark 3.3 Theorems 3.1 and 3.2 improve and generalize Theorem 3.1 of from contractive mapping ... supported by The Key Program of NSFC Grant no 70831005 , the National Natural Science Foundation of China 10671135, 11026063 , and the Open Fund PLN0904 of State Key Laboratory of Oil and Gas Reservoir ... family of nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol 323, no 2, pp 1402–1416, 2006 R Chen and H He, “Viscosity approximation of common fixed points...
... λ, of order p s r Note that, none of the roots of this polynomial are given by dk , k 1, , s or σj , j 1, , p since, from Figures to 3, it is easy to see that none of the eigenvalues of ... same number of evals s l m s l m That is, same number of evals s l m s l m That is, same number of evals s l m s l m That is, same number of evals s l m s l m That is, same number of evals s−1 ... inverse spectral theory of Jacobi operators, provides an alternative factorisation, to that of 10 , of a second-order difference equation, where the factors are adjoints of one another This paper...
... set of fixed pointsof f resp., g is denoted by F f resp., F g A point x ∈ M is a coincidence point common fixed point of f and g if fx gx x fx gx The set of coincidence pointsof f and g is denoted ... have U f U ∪ g 0c0 , 3.19 Journal of Inequalities and Applications then by the definition of f, we can consider U ⊆ 0, Hence closure of U being closed subset of a compact set is compact Also pn ... f k a Journal of Inequalities and Applications a Thus a is a common fixed point of f k and g k and hence of f a contradiction, hence f k a and g Now we establish the uniqueness of a Suppose there...
... inequalities of uniformly convex and uniformly smooth Banach spaces,” Journal of Mathematical Analysis and Applications, vol 157, no 1, pp 189–210, 1991 Z Opial, “Weak convergence of the sequence of successive ... fixed point p of {Tm }, m ∈ {1, 2, } such that p is the unique solution, in F, to the variational inequality f p − p, J y − p ≤ 0, ∀y ∈ F 3.3 Proof Step We prove the uniqueness of the solution ... of T , where p is the unique solution in F T to the following variational inequality: f p − p, j u − p ≤ ∀u ∈ F T 3.19 Acknowledgment A Razani would like to thank the School of Mathematics of...