discrete mathematics for computer scientists solution manual pdf
Tài liệu Discrete Math for Computer Science Students doc
... original formula for q. Recall that our proof of the formula we had inExercise 1.4-5 did not explain why the product of three factorials appeared in the denominator,it simply proved the formula ... distinct elements. There are n choices for the first number in the list. For each way of choosing the first element, there are n −1choices for the second. For each choiceof the first two elements, ... theproduct in the denominator of the formula in Exercise 1.4-5 for the number of labellings withthree labels is what it is, and could generalize this formula to four or more labels.Equivalence...
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Mathematics for Computer Science pot
... possible, and so the totalscore for the game is 1(1 − 1)/2 = 0. Therefore, P(1) is true.Inductive step: Now we must show that P (1), . , P (n − 1) imply P (n) for all n ≥ 2. Soassume that P ... 1) for all n ∈ N.By the principle of induction, P (n) is true for all n ∈ N, which proves the claim.This proof would look quite mysterious to anyone not privy to the scratchwork we didbeforehand. ... divisibility hold.1. If a | b, then a | bc for all c.2. If a | b and b | c, then a | c.3. If a | b and a | c, then a | sb + tc for all s and t.4. For all c = 0, a | b if and only if ca | cb.Proof....
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 8B) pdf
... acid or dilute basic solution. When adjusting the wwpH ofa buffer solution, make sure to wait until the solution reaches equilibriumafter adding additional acid or base before measuring the ... samplesolutions are filtered and/or centrifuged; the use of a 0.2- or 0.45-µm-pore-sizefilter is generally recommend for removal of particulates [15]. Filtration as apreventive maintenance tool for ... it will also significantly decrease the peak width (especially for the late eluting analytes), thus increasing the resolution. This resolutionincrease obtained with a linear gradient often outweights...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 8C) pdf
... The experiments for wwpH 2–4 were performed on day1, and those for wwpH 5–7 were performed on day 2 (≈36 hr after initial prepa-ration).A further investigation was performed by preparing ... requirement for injectionprecision, sensitivity, standard accuracy (if for an assay method), and retentiontime of the target analyte. Sometimes, a resolution requirement is added for a critical ... “chromatographer’s toolbox”allows for the development of rugged and reproducible methods.8.5.6 Case Study 3: Method Development for a Diprotic Basic CompoundA case study is presented for the method development...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 8D) pdf
... Figure 8-40A for thesample stored in the acidic diluent for 4 days at room temperature shows somedegradation compared to Figure 8-40B for the sample stored in the acidicdiluent for one day ... Flow rate for all four runs was 0.8 mL/min.determine the resolution map for the active and impurity 11 eluting close tothe main component (Figure 8-46). In a similar fashion, a resolution map ... analyte pKashift) for both basic ionization centers. Therefore this cor-relates with a sspKaof 2.7 for pyridinal nitrogen (i.e., 3.3 − 0.6 = 2.7) and withasspKaof 4.7 for the morpholinal...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 4B) pdf
... Similar parameters have been determined for this family of compounds for methanol/water mixtures [80]. Using theseparameters for each family of compounds for a particular type of organic, theasand ... same critical distance (D) needed for ion-pair formation, a solvent with ahigh dielectric constant such as water (∼80) will be less favorable for ion-pairformation compared to a solvent that ... obtain the acid analyte in its fully neutral form?Step 1. First account for the upward pKashift for the acidic analyte upon addi-tion of organic. For every 10 v/v% increase in acetonitrile...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 4C) pdf
... might be obtained for the basic analyte in its neutral form.The advan-tages of employing chaotropic mobile-phase additives at a pH where the basicanalyte is in its fully protonated form provides ... mobile-phase pHadjustment. A chaotropic approach could be used for the separation of verypolar basic compounds as a fast screening method for the resolution of closelyeluting basic species without resorting ... chromatographicmethods for the determination of adsorption and solution isotherms, J. Chro-matogr. 58 (1971), 137–158.182. H. L. Wang, J. L. Duda, and C. J. Radke, Solution adsorption from...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 5) pdf
... the triangleformed by MTBE, dichloromethane, and chloroform defines the selectivitydomain in which the optimum mobile-phase composition will be found. Next,separations are performed with three ... reliable for less polar solvents and solute molecules on alumina or silica stationary phasesonly. Neither of the models is entirely satisfactory in the forms presented, par-ticularly for predicting ... zirconia for normal phase chromatography, J. Chromatogr. A691 (1995), 205–212.22. U. Trüdinger, G. Müller, and K. K. Unger, Porous zirconia and titania as packingmaterials for high-performance...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 11) pdf
... chro-matographic peaks for a given sample will be hard to predict, and thereforethe footprint for fraction collection will be difficult to predict. Experience hasshown that it is not uncommon for 5–10 fractions ... solid-phase and solution- phase synthesis of discretes [27–31].Both solution- phase and solid-phase parallel synthesis permits the productionof large numbers as well as large quantities of these discrete ... by Xu et al. was used for assessing the time-coursemetabolic stability (four time-points in triplicate) for hits identified fromscreening of lead generation libraries. For each compound, a total...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 18) pdf
... eluent for reversed-phase high performance liquid chromatography, Anal. Commun. 33 (1996),327–329.57. R. M. Smith and R. J. Burgess, Superheated water as an eluent for reversed-phasehigh performance ... reversed-phase high-performance liquid chromato-graphy, J. Chromatogr. A 499 (1990), 79–88.85. J.A.Whatley, Chiral resolution of protein-kinase inhibitors by reversed-phase high-performance liquid ... Zirconia stationary phases for extreme separations, Anal. Chem. 73 (2001), 598A–607A.49. J. Li and P.W. Carr,Effect of temperature on the thermodynamic properties, kineticperformance, and stability...
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Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 20) pdf
... oxidized forms of hyperforin by HPLC-NMR andHPLC-MSn, Phytochem. Anal. 14 (2003), 290–297.94. J. K. Roberts and R. J. Smith, Use of liquid chromatography–Nuclear magneticresonance spectroscopy for ... method for theproduction and analysis of large natural product library for drug discovery, Anal.Chem. 74 (2002), 3963–3971.105. M. Careri and A. Mangia, Multidimensional detection methods for ... room for improvement for LC-MS-NMR,and the next decade will define the areas where this hyphenated technique isbest suited.LC-MS-NMR cannot replace LC-MS, LC-NMR or even NMR techniques for the...
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Tài liệu Prolog Experiments in Discrete Mathematics, Logic, and Computability pdf
... applied to arguments is called an atomic formula Atomic formulas are the building blocks of Prolog programs. For example, the following expressions are atomic formulas. p(a, b, X), capital_of(salem, ... a statement taking one of the forms head. or head :- body. where head is an atomic formula and body is a sequence of atomic formulas separated by commas. For example, the following statements ... head is true if all of the atomic formulas in the body are true. The procedural meaning is that for head to succeed, each atomic formula in the body must succeed. For example, suppose we have the...
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