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Project Gutenberg’s Philosophy and Fun of Algebra, by Mary Everest Boole This eBook is for the use pdf
... Commandments and a few other old standard formularies by heart, and repeat them every now and then And say to yourself, “If I really am doing my algebra quite rightly, this (the standard formularies) ... swing of rhythmic beats is good for all people, but more good for the people of Isra¨l e than for anybody else; and that wandering off into irregular un-rhythmic freaks is more bad for the people of ... stretch of body and mind by going to the boundless fairyland of your subject Think how the great mathematicians can weigh the earth and measure the stars, and reveal the laws of the universe; and...
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Báo cáo toán học: " Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann boundary conditions" ppt
... ), (H2 ) and the following conditions hold true: (b+ ) b(t) ≥ for t ≥ (f+ ) f (x, t) ≥ for x ∈ Ω and t ≥ (g+ ) g(x, t) ≥ for x ∈ ∂Ω and t ≥ (f2 )+ There exist an open subset Ω0 of Ω and r1 > ... (x) for x ∈ Ω and lim inf t→0 |F (x,t)| |t|r1 (x) < +∞ uniformly for x ∈ Ω ¯ (g5 ) There exists r2 ∈ C (Ω) such that < r2 (x) < p∗ (x) for x ∈ ∂Ω and lim inf t→0 |G(x,t)| |t|r2 (x) < +∞ uniformly ... exist an open subset Ω0 of Ω and r1 > such that lim inf t→0 F (x,t) |t|r1 >0 uniformly for x ∈ Ω0 (g2 ) There exists r2 > such that lim inf t→0 G(x,t) |t|r2 > uniformly for x ∈ ∂Ω (H2 ) β2 r1...
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báo cáo hóa học:" Existence and multiplicity of solutions for a fourth-order elliptic equation" potx
... R and a.e x in Ω, where a(x) ∈ Lq (Ω), b ∈ R and < p < N +4 N −4 if N > and < p < ∞ if N ≤ and q + p = 1; (H4) f (x, t) = o(|t|) as t → uniformly for x ∈ Ω ; (H5) There exists a constant Θ > and ... Existence and multiplicity of solutions for a fourth-order elliptic equation Fanglei Wang∗1 and Yukun An2 College Department of Science, Hohai University, Nanjing, 210098, P R China of Mathematics, ... (4) and (H5) Hence, I(tϕ1 ) ≤ l2 t2 ϕ1 2 − tΘ ϕ1 Θ Θ + C4 → −∞ as t → +∞ and part is proved Proof of Theorem 2.1 From Lemmas 2.2 and 2.3, it is clear to see that I(u) satisfies the hypotheses of...
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Báo cáo hóa học: "Research Article On the Nonexistence and Existence of Solutions for a Fourth-Order Discrete Boundary Value Problem" doc
... Therefore, we have reduced the problem of finding a solution of 1.5 to that of seeking a critical point of the functional J defined on Rk In order to obtain the existence of critical points of J ... nonexistence of nontrivial solutions of BVP 1.5 Finally, in Section 4, we provide various sets of sufficient conditions on the existence of solutions of BVP 1.5 when f is superlinear, sublinear, and Lipschitz ... Moreover, in a special case of f we obtain a necessary and sufficient condition for the existence of unique solutions of BVP 1.5 To conclude the introduction, we refer to 21, 22 for the general background...
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Báo cáo hóa học: "Research Article Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems" ppt
... Ge, and X Lin, “Existence of solutions for a class of third-order nonlinear boundary value problems,” Journal of Mathematical Analysis and Applications, vol 294, no 1, pp 104–112, 2004 Y Feng and ... now formulate and prove our main results on the existence and uniqueness of solutions for nth-order three point boundary value problem 1.1 , 1.2 Theorem 3.1 Assume that i there exist lower and ... Hence x1 t is a solution of BVP 1.1 , 1.2 and satisfies 3.3 Now we give a uniqueness theorem by assuming additionally the differentiability for functions f, g and h, and a kind of estimating condition...
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Báo cáo hóa học: " Research Article Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary Value Problems" pptx
... solution of 4.5 , then y i is a solutionn of 1.2 Proof Since we remark that x i is a solution of 4.5 , if and only if T K i, j λF j n − 1, T x j , Tx i x i n−1 , for ≤ i ≤ T 4.6 j Let y i for ≤ ... of 3.5 , then y t is a solution of 1.1 Further, if y t is a solution of 1.1 , imply that x t is a solution of 3.5 Let P {x ∈ C 0, | x t ≥ 0, for all t ∈ 0, } Obviously, P is a normal cone of ... 0, ∞ is continuous and nondecreasing; h : 0, ∞ → 0, ∞ is continuous and nonincreasing, and h may be singular at y Next, we consider the existence and uniqueness of solutions for the following...
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Báo cáo hóa học: " Research Article Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary " doc
... solution of 4.5 , then y i is a solutionn of 1.2 Proof Since we remark that x i is a solution of 4.5 , if and only if T K i, j λF j n − 1, T x j , Tx i x i n−1 , for ≤ i ≤ T 4.6 j Let y i for ≤ ... of 3.5 , then y t is a solution of 1.1 Further, if y t is a solution of 1.1 , imply that x t is a solution of 3.5 Let P {x ∈ C 0, | x t ≥ 0, for all t ∈ 0, } Obviously, P is a normal cone of ... 0, ∞ is continuous and nondecreasing; h : 0, ∞ → 0, ∞ is continuous and nonincreasing, and h may be singular at y Next, we consider the existence and uniqueness of solutions for the following...
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Báo cáo hóa học: " Stretching and immobilization of DNA for studies of protein–DNA interactions at the single-molecule level" ppt
... of force, namely gradient and scattering forces, are produced since the laser light can be both transmitted and reflected from the particle The gradient force is proportional to the gradient of ... 2:185–201 base sequence information from a single-stranded template and synthesizes the complimentary strand The differences between DNAP and RNAP include (1) catalyzing of addition of a new deoxyribonucleotide ... growing chain of DNA for DNAP while RNAP catalyzes the addition of NTP to the growing chain of RNA; and (2) DNAP requires a primer (a short piece of ssDNA annealed to the template strand) to initiate...
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Báo cáo hóa học: "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR SOME THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS" pptx
... BVP (1.1λ ) X Xian and D O’Regan Proof Let z0 (t) = for t ∈ [0,1], and zλ (t) = λg(Rλ + 1)(Lτ z0 )(t) for t ∈ [0,1] Since L0 is increasing and g is nonincreasing, then we have for any n ∈ N, xn ... contradiction Therefore, β(t) ≥ un,λ (t) for t ∈ [0,1] Similarly, we can show that α(t) ≤ un,λ (t) for t ∈ [0,1] Thus, un,λ (t) is a positive solution of (2.1λ ) The proof is complete n Proof of the main ... (1.1λ ) has at least one positive solution The proof is complete Lemma 2.13 Let α(t) and β(t) be lower and upper solutions of (2.1λ ) for some n ∈ N and n λ > 0, ≤ α(t) ≤ β(t) Then (2.1λ ) has at...
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Báo cáo hóa học: "BOUNDEDNESS AND VANISHING OF SOLUTIONS FOR A FORCED DELAY DYNAMIC EQUATION" pot
... behavior of solutions of (1.1) Theorem 3.1 If (H1), (H2), (H3) hold, then every solution of (1.1) goes to zero in the limit Proof If x is a nonoscillatory solution of (1.1), assume without loss of ... as n → ∞ By the choice of Xn , the solution x of (1.1) satisfies limt→∞ x(t) = Douglas R Anderson 15 Corollary 3.2 If (H1) and (H3) hold, then every solution of the unforced equation xΔ (t) + ... equations, Journal of Mathematical Analysis and Applications 234 (1999), no 1, 77–90 [13] C Qian and Y Sun, Global attractivity of solutions of nonlinear delay differential equations with a forcing term,...
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Báo cáo hóa học: "CONVERGENCE AND PERIODICITY OF SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS" potx
... u ≤ σ, f (u) = −1 if u > σ, for some constant σ ∈ R The aim of this paper is to investigate the convergence and periodicity of solutions for system (1.1) as f is of the digital nature (1.2), ... input-output relation of a neuron For simplicity, let N denote the set of all nonnegative integers, and define N(m) = {m,m + 1,m + 2, }, N(m,n) = {m,m + 1, ,n} for any m,n ∈ N and m ≤ n Moreover, ... I33 (1.10) By a solution of the system (1.1), we mean a sequence {(xn , yn )} of points in R2 that is defined for all n ∈ N(1) and satisfies (1.1) for n ∈ N(1) Clearly, for any (x0 , y0 ) ∈ R2 ,...
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Báo cáo hóa học: "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUPERLINEAR p-LAPLACIAN EQUATIONS" potx
... Foundation of China (No 10471113) and by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China References [1] A Ambrosetti and P H ... ) = +∞ uniformly in a.e x ∈ Ω, where a ∈ L∞ (Ω) satisfies a(x) ≤ λ1 for all x ∈ Ω and a(x) < λ1 on some Ω ⊂ Ω with |Ω | > 0, λ1 is the first eigenvalue of −Δ p and |Ω | is the measure of Ω Then ... [6] for p = 2, and recently by Liu and Li in [9] for general p > We can easily prove that Assumption 1.2 is equivalent to Assumption 1.1 when θ = and Assumption 1.2 gives some general sense of...
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THERMODYNAMIC MODELING, ENERGY EQUIPARTITION, AND NONCONSERVATION OF ENTROPY FOR DISCRETE-TIME pptx
... (M) and ᏺ(M) for the range space and the null space of a matrix M, respectively, spec(M) for the spectrum of the square matrix M, rank(M) for the rank of the matrix M, ind(M) for the index of ... (E), E ∈ R+ (4.8) Proof The proof is identical to the proofs of Theorems 3.5 and 3.11 For the statement of the next result, recall the definition of p = [1/β1 , ,1/βq ]T and define P diag[β1 , ... Furthermore, equalities hold in (4.1) and (4.2) if and only if ∆Ei = and βi Ei = β j E j , i, j = 1, , q, i = j Proof The proof is identical to the proofs of Propositions 3.3 and 3.9 Note that with the...
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modeling and pricing of swaps for financial and energy markets with st
... By Black and Scholes (1973), Dupire (1994), Derman and Kani (1994) April 17, 2013 15:36 8660: Modeling and Pricing of Swaps ws-book975x65 Modeling and Pricing of Swaps for Financial and Energy ... framework for an analysis of option pricing, discrete-time models are ideal for the statistical and descriptive analysis of the patterns of daily price changes Volatility clustering, periods of high and ... 2013 15:36 10 8660: Modeling and Pricing of Swaps ws-book975x65 Modeling and Pricing of Swaps for Financial and Energy Markets Swishchuk, A (2009a) Pricing of variance and volatility swaps with...
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Báo cáo khoa học: " Comparisons of Sampling Procedures and Time of Sampling for the Detection of Salmonella in Danish Infected Chicken Flocks Raised in Floor Systems" pptx
... Comparison of results of sampling of 26 Salmonella infected broiler flocks at weeks of age, and at slaughter age by pairs of sock samples No of Salmonella positive samples at slaughter age No of Salmonella ... samples for Salmonella In both of these flocks S EnteriActa vet scand vol 43 no 1, 2002 26 K Gradel et al Table Statistics used for, and results of comparisons between three sample types for the ... weeks of age 10 2 16 Numbers in the table show the number of flocks Acta vet scand vol 43 no 1, 2002 1 10 26 Procedures for detection of Salmonella in chicken Table Statistics used for, and results...
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Báo cáo khoa học: "Case mix, outcome and length of stay for admissions to adult, general critical care units in England, Wales and Northern Ireland: the Intensive" pptx
... and are confirmed by the participating units Analyses Performance of the CMPD against the DoCDat criteria The CMPD was rated on a scale of to for each of the 10 DoCDat criteria for coverage and ... collected on the source of admission to the CMP unit and the location immediately prior to the source of admission For admissions for whom either of these locations is theatre and recovery in the ... Directory of Clinical Databases’ criteria for assessing the coverage and accuracy of a clinical database (adapted from [3,4]) R100 (DoCDat) was established to inform researchers and clinicians of what...
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Báo cáo sinh học: "Assessment of methods and analysis of outcomes for comprehensive optimization of nucleofection" pptx
... cell lines Nucleofection is an emerging technology for intracellular molecular delivery It is typically used in a single-cuvette format for delivery of nucleic acids such as plasmids and siRNA, and ... point was first standardized by subtracting the mean of the data set from each data point and then dividing by the standard deviation of the data set Standardized and raw data for the secondary ... 96-well nucleofection plate was loaded with 20 μL of one of the three nucleofection solutions (approximately 275,000 cells) and the plate was loaded into the Amaxa 96-well Shuttle for nucleofection...
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A research to assess community ecotourism and suggestions of solutions for sustainable tourism development in Van Don District, Quang Ninh province
... consultation of local and national managers and professors in tourism The structure of thesis Apart from the introduction (7 pages), conclusion (4 pages), list of abbreviations, list of tables, list of ... environment of plants and animals, air quality, water quality and soil environment had unbeneficial changes with the life of plants and animals and humans because of tourist activities Therefore, the ... managers; Implementing training on tourism profession and tourism management for staff performing management of tourism, culture and information; Implementing professional occupation training courses...
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