... listening many times For example, if you have an audio book, listen to the first chapter 30 times before you go to the second chapter You could listen to the first chapter times each day, for 10 days ... much improved because of you, and also my understanding of native speakers is much better than before So I would like to say thank you very very much!!” Mao Sokha Deep Learning Of English Grammar ... Listen to the Audio of this text Learn it deeply • Listen and read it at the same time Do this 10 times • • Listen only to the audio Do this 10 times Review new or difficult phrases Put them in...
... of Hong Kong and the Area of Excellence Scheme ofthe University Grants Committee (Hong Kong) for their support We are grateful forthe support from a Hong Kong RGC grant (BQ -44 5) and Hong Kong ... Martin, M.E & Beaumont, C (2002) Expression ofthe two mRNA isoforms ofthe iron transporter Nrmap2/DMTI in mice and function ofthe iron responsive element Biochem J 363, 44 9 45 5 12 Su, M.A., ... H-bonds between Val17 and Leu21 were not detected in any ofthe 16 conformers, while the H-bonds between Asp 14 and Phe18 were missing in the majority ofthe 16 conformers, indicating that the...
... denotes the number of rows in the parity check matrix ofthe code, uk is the number of nonzero elements in the kth row ofthe parity check matrix and niter is the number of iterations ofthe optimization ... the phase offset ofthe channel The proposed method of blind estimation ofthe phase offset is based on a MAP approach in the sense of maximizing the probability that a phase θ corresponds to the ... that can be adjusted and i is the number ofthe current iteration The xi reached at the final iteration ofthe Gradient descent algorithm is the solution ofthe optimization problem In our case, we...
... solutions ofthe considered problem must be modified Moreover the truncations that have to be made in the nonlinear part ofthe problem 1. 14 , forthe continuous case, and in 1.19 , forthe Carath´ ... odory one, must be extended to e the nonlinear boundary conditions This new truncation onthe boundary conditions must satisfy similar properties to the ones ofthe nonlinear part ofthe equation, ... derive the existence of a solution a growth condition onthe nonlinear part ofthe equation with respect to the dependence onthe first derivative is imposed The most usual condition is the so-called...
... duration, the PHICH is also mapped into the first OFDM symbol ofthe first slot of each subframe Onthe other hand, forthe extended CP duration, the PHICH is mapped to the first OFDM symbols ofthe ... mapping The size ofthe REG varies depending onthe OFDM symbol number and antenna configuration [1] The PCFICH is always mapped into the first OFDM symbol ofthe first slot of each subframe Forthe ... In the second OFDM symbol, the number of REGs available per PRB will befor single- or two-transmit antennas, and for four-transmit antennas This paper focuses onthe performance analyses of the...
... discussing the analogues ofthe notion of convex function in n variables However, the roots ofthe research in this area can be traced long before him In a long time, the subject of multiplicative convexity ... multiplicatively convex function if and only if log f x is a convex function of log x Modulo this characterization, the class of all multiplicatively convex functions was first considered by Motel , in a beautiful ... multiplicatively concave on a, b × a, b Lemmas and the Proof of Theorem 1.6 Forthe sake of readability, we first introduce and establish several lemmas which will be used to predigest the proof of Theorem...
... estimation algorithm should be considered as a natural choice for hemodynamic data assimilation studies Onthe other hand, the nonlinear particle filter solution to the problem introduces some other ... concentrate mainly onthe transient behavior associated with the start up ofthe system Furthermore, this is a nonautonomous system where the functions ofthe observables depend explicitly on ... increase in neural activity, and the consumption of oxygen and the amount of dHb increase Consequently, as compensation, an abrupt increase Nonlinear Joint Estimation We addressed this nonlinear...
... mappings,” Information Sciences, vol 178, no 19, pp 3791–3798, 2008 17 D H Hyers, Onthe stability ofthe linear functional equation,” Proceedings ofthe National Academy of Sciences ofthe United ... point theorem ofthe alternative, for contractions on a generalized complete metric space,” Bulletin ofthe American Mathematical Society, vol 74, pp 305–309, 1968 22 D Mihet and V Radu, Onthe ... general function The aim of this section is to give an alternative proof for that result in 15, Section , based onthe fixed point method Also, our method even provides a better estimation Theorem 3.1...
... are based onthe asymptotic analysis of solutions of 1.1 However, this approach requires the sign restriction ofthe sequence ck and additional assumptions onthe convergence divergence of certain ... called the minimal solution of 2.1 If w is the distinguished solution of 2.1 , then the associated solution of 1.1 given by the formula k−1 Φ−1 xk j m wj rj is said to bethe recessive solution of ... where summation characterizations of recessive solutions of 1.1 are investigated using the asymptotic analysis ofthe solution space of 1.1 Proposition 2.1 Let x be a solution of 1.1 i Suppose...
... for −∞ < r < s < t < ∞, Λt−r f ≤ Λt−s f Λs−r f s r t Proof As in the proof of Theorem 2.1, we use Theorem 1 .4 instead of Theorem 1.3 2.17 Journal of Inequalities and Applications Theorem 2 .4 ... 1.2 For extension of Theorem 1.1 see cf Popoviciu 6–8 , 9, pages 2 14- 215 has proved the following results Theorem 1.3 Let φ : a, b → R be convex and f : 0, → R be continuous, increasing, and convex ... positive One has that Γs f is log-convex and the following inequality holds for −∞ < r < s < t < ∞, Γt−r f ≤ Γt−s f Γs−r f s r t 2 .46 Proof As in the proof of Theorem 2.1, we use Theorem 1 .4 instead...
... = 0, then A has at least one fixed point in U (5.5) Richard Avery et al The proof ofthe following generalization of Theorem 4. 1 to multivalued maps is essentially the same asthe proof of Theorem ... ,U,Q(α,r) = 1, (4. 9) therefore by the solution property (G6) ofthe fixed point index, the operator A has a fixed point x ∈ U The argument in the proof of Theorem 4. 1 immediately guarantees the following ... (2.5) is continuous and for all x, y ∈ P and t ∈ [0,1] Let α and ψ be nonnegative continuous concave functionals on P and let β be a nonnegative continuous convex functional on P; then, for positive...
... Section 4, we consider two bifurcation problems related to 1.8 , 1.9 , and use the global bifurcation theorems from Section to analyze the global behavior ofthe components of nodal solutions of ... see that as f has two zeros s1 , s2 : s2 < < s1 , the bifurcation structure ofthe nodal solutions of 1.8 , 1.9 becomes more complicated: the component ofthe solutions of 1.8 , 1.9 from the trivial ... that 4. 3 and 4.4 are the same, and each of them is equivalent to 1.8 , 1.9 The results of Lemma 3.3 for4. 3 can be stated as follows: for each integer k ≥ 1, ν ∈ { , −}, there exists a continuum...
... sufficient conditions forthe existence of a λ0 ∈ R \{0} for which 1.8 and 1.9 are satisfied Second, we prove the existence ofthe limit z ∞ and give a limit formula for z ∞ under the condition only ... in Section 4, including an interesting nonconvolution equation This example shows the significance ofthe middle sum in 1.3 , since only this term contributes to the limit ofthe solution of 1.1 ... equation ofthe form 3.1 by using the transformation λ−n x ϕ n , z n n∈Z 5 .43 Lemma 5.5 Under the conditions of Theorem 3.3, the sequence z : Z →R defined by 5 .43 satisfies 3.1 , where the sequences...
... when applied to concrete difference equations, but additional difficulties appear, because among other things, we need to get explicit formulas forthe solution ofthe equation to be studied We study ... but the most interesting application concerns with partial difference equations In fact, the homogeneous equation associated to 1.2 corresponds to the best discretization ofthe wave equation cf ... section we first give a geometrical link between the best discretization 1.2 and the equations ofthe form Δ2 xn Axn k fn , x0 x1 0, k ∈ {0, 1, 2} 3.1 The motivation comes from the recent article of...
... The node belonging to the flow’s path one hop way from the receiver, which we denote asthe last forwarding node, is responsible for sending the proofs to the gateway, which contain information ... information onthe path(s) ofthe flow When receiving the proofs, the gateway sends them to the authentication and accounting server to verify the truthfulness ofthe information, through the cryptographic ... present the delay and jitter for each traffic profile The objective of these tests is to evaluate the impact of multicast routing in the traffic for different configurations ofthe testbed when the network...
... = 0, then A has at least one fixed point in U (5.5) Richard Avery et al The proof ofthe following generalization of Theorem 4. 1 to multivalued maps is essentially the same asthe proof of Theorem ... ,U,Q(α,r) = 1, (4. 9) therefore by the solution property (G6) ofthe fixed point index, the operator A has a fixed point x ∈ U The argument in the proof of Theorem 4. 1 immediately guarantees the following ... (2.5) is continuous and for all x, y ∈ P and t ∈ [0,1] Let α and ψ be nonnegative continuous concave functionals on P and let β be a nonnegative continuous convex functional on P; then, for positive...
... that the set M is closed subset ofthe space Ꮿ((0,1]L2 ([0, ∞))) (for the proof see Lemma A.1 in the appendix of this paper) Therefore (1 ) has unique nontrivial solution in the set M Let u bethe ... uniformly continuous function for x ∈ [0, ∞) (for u ∈ M L(u)(r) is uniformly continuous function for r ∈ [0, ∞) because L(u)(r) ∈ Ꮿ([0, ∞)) and as in the proof of Theorem 3.1 (after we use the ... Blow up ofthe solutions of homogeneous Cauchy problem (1), (2) Let v(t) bethe same function as in Theorem 3.1 Theorem 3.2 Let n ≥ be fixed, let h1 (r), h2 (r) fixed, which satisfy the conditions...
... along the corresponding branches ofthe MS in the image acquired at the end ofthe interval so that the distance between the CPs on each branch remains uniform This simulates the growth ofthe ... Control points onthe boundary ofthe hypha computed during the elongation process plus control points selected onthe boundary ofthe conidium These points allow us to reconstruct the image of ... in control points xi The functions are called radial asthe value of each basis function φi depends only onthe distance from its center xi The properties ofthe transformation f depend on the...
... 84. 45 0.1212 94. 92 84. 45 0.1103 95. 04 84. 45 0.11 14 Table 5: Squared biases for simulated data: equal covariance model The squared biases are in 10 4 unit, the same as deviation variances N Classifier ... relative increase in deviation dispersion Given a sample set S, we use the following notations for classification errors Forthe exact mathematical formulae ofthe cross-validation errors, please refer ... since the meansquared error of an error estimator equals the sum ofthe variance and the squared bias, one might ask whether feature selection has a significant impact onthe bias Given that the...
... Page Why Classify? 36 Classification of Expenditure 37 Control of Expenditure 39 35 CLASSIFICATION OF EXPENDITURE WHY CLASSIFY? Whenever the business spends money it has an impact onthe model ... increase operating profits increase Earnings increase Dividends retain additional profit and so the process continues THE BUSINESS FINANCIAL MODEL COMMON MISCONCEPTIONS ‘At the year-end the Retained ... whatever remains after all these costs have been met belongs to the shareholders and will either be: - paid out as a Dividend, or - ploughed back as Retained Profit p16 Retained Profits THE BUSINESS...