euler´s generalization of fermat´s little theorem
World Vision’s Little Book of Maternal and Child Health in the Asia Pacific pdf
... before the age of five – three quarters of them before the age of one At the heart of these statistics is malnutrition Only around 15% of children are exclusively breastfed to the age of six months ... effort over 40 years of public healthcare to improve the standards of maternal health has paid off, with Sri Lanka now able to report a maternal death rate around 1/10th of that of countries like ... A total of 98% of births take place in a medical facility However, Sri Lanka’s children suffer from a high level of malnutrition, caused in part by a lack of knowledge on the benefits of breastfeeding...
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Đề tài "A sharp form of Whitney’s extension theorem " ppt
... SHARP FORM OF WHITNEY’S EXTENSION THEOREM 513 The following observation is typical of our repeated applications of Helly’s theorem in the proof of Theorem C Let P denote the vector space of (m−1)rst ... Thus, Theorem C is the heart of the matter In a moment, we sketch some of the ideas in the proof of Theorem C First, however, we make a few remarks on the analogue of Problem with m in place of ... polynomials 15 Proof of Lemmas 9.1 and 5.2 16 A rescaling lemma 17 Proof of Lemma 5.3 18 Proofs of the theorems 19 A bound for k # References *I am grateful to the Courant Institute of Mathematical...
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the 7 irrefutable rules of small business growth - steven s. little
... to realize the full potential of your business PROFIT IS IMPORTANT As I travel the country speaking to groups of entrepreneurs, there’s often one person at the end of my time who wants to play ... talking about profitable growth Profits are a great way to measure success Profits are often the best way to fund organic growth Profits help us measure our performance Profits matter, but not more ... did a little historical research In the early 1990s, Nobel-prize-winning economist Milton Friedman (one of the few economists most of us have ever heard of ) wrote an article for the Journal of...
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Báo cáo toán học: "A Generalization of Gosper’s Algorithm to Bibasic" docx
... multiple of all ¯ P ¯ coefficient-denominators of P , let g denote the greatest common divisor of all coefficients of ¯ ¯, and define z := g/l Then, for P ∗ := z −1 · P , the bibasic monic decomposition of ... actually is a solution of the bibasic hypergeometric telescoping problem (1) This completes the proof of the correctness of Algorithm Telescopep,q the electronic journal of combinatorics (1996), ... uniqueness of the so-called bibasic monic decomposition of a polynomial as shown below 3 the electronic journal of combinatorics (1996), #R19 Example The bibasic monic decompositions of the polynomials...
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Báo cáo toán học: "A generalization of Simion-Schmidt’s bijection for restricted permutations" doc
... (i, j) ∈ Om (π) Proof For any m ≥ 2, let D be the set of all diagram squares of rank at most m − The proof is based on the following procedure First represent the elements of D as white squares ... the set of its diagram squares of rank at most m − 3, and by D2 the set of the remaining diagram squares Now define σ = Φm (π) to be the permutation in Sn whose set of diagram squares of rank ... equal in general to the column indices of the diagram squares of π having rank at least 3.) The construction of σ’s array is completed as described in the proof of Proposition With the notations introduced...
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Báo cáo toán học: "A Schr¨der Generalization of Haglund’s Statistic on o Catalan Paths" pptx
... the rows of length of Π, and also which rows of length are D rows, since the v = iteration of φ creates an N step in section of φ(Π) for every N row of Π of length 0, and a D or E step of φ(Π) ... corresponding to the portion of Π affecting the v = i loop One verifies from the definition of dinv that the number of inversion pairs of Π of the form (x, y) with rowx of length i, rowy of length i + and ... equals the number of inversion pairs of τ involving 2’s and 1’s or 2’s and 0’s Similarly, the number of inversion pairs of Π of the form (x, y) with rowx of length i, rowy of length i + and y...
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Báo cáo toán học: "A quantitative ergodic theory proof of Szemer´di’s e theorem" pot
... inequality This concludes the proof of Proposition 9.1 As a quick corollary of this Proposition we can now prove the d = case, at least, of Theorem 3.3 Proof of Theorem 3.3 when d = Let fU ⊥ , ... scheme, and this explains the large number of variations between the known proofs of Szemer´di e type theorems Also, each of the known proofs finds some parts of the above scheme more difficult than ... The energy incrementation argument The proof of the recurrence theorem (Theorem 3.3) and the structure theorem (Theorem 3.5) relies not only on factors of almost periodic functions, which we constructed...
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Báo cáo toán học: "On a Generalization of Meyniel’s Conjecture on the Cops and Robbers Game" potx
... independence of every (2s + 2)-subset of S, (s′1 , , s′m ) is a permutation of (s1 , , sm ) Therefore, the number of ordered representations of u − v using m members of S is m!, so the number of ... ⊆ Z2 be the set of columns of H It is known that every set of 2s + columns of H is linearly independent over Z2 (c.f., e.g., [1]), hence, in particular, every (2s + 2)-subset of S is linearly ... affect the set of possible moves of the players, and the cop number of a disconnected graph obviously equals the sum of the cop numbers for each connected component For a survey of results on...
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On Euler’s Discretization of Sliding Mode Control Systems with Relative Degree Restriction
... eigenvalues of Bc are zeros of the characteristic equation (5) which is Hurwitz 2.2 Euler’s Discretization We consider the effects of the discrete implementation of the control system (6) by means of the ... circle then every trajectory of the w subsystem converges to a period–2 orbit Bounds for the steady state of the subsystem w are given by Theorem 1: Euler’s Discretization of SMC Systems |w1 | ≤ αh ... n−1 Summarizing, we have the following result: Theorem [7] Let us assume that the eigenvalues of Bc have negative real parts, and that eigenvalues of I + hBc are located within the unit circle...
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Fermat’s Last Theorem
... Fermat’s Last Theorem for a set of exponents of density one However, Fermat’s Last Theorem was still not known to be true for an infinite set of prime exponents In fact, the theorem of Faltings ... results concerning the structure of Hecke algebras: the generalization by Taylor and Wiles of a result of de Shalit, and the generalization by Wiles of a result of Ribet Chapter establishes the ... subgroup of E(Q), and r ≥ is the rank of E over Q Concerning the possible structure of T , there is the following deep result of Mazur, a variant of which also plays a crucial role in the proof of...
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Đề tài " Deligne’s integrality theorem in unequal characteristic and rational points over finite fields " pptx
... codimension of AI in X Since cI ≥ 1, we conclude with Theorem 1.5 i) The proof of Theorem 1.1 and its consequences Proof of Theorem 1.1 We denote by Φ a lifting of Frobenius in the DeligneWeil group of ... eigenvalues of Φ on the right-hand side are (some of) the eigenvalues of F on the left-hand side We apply again Deligne’s integrality theorem [6], loc cit to conclude the proof Proof of Theorem 1.5 ... shows that the number of rational points of Y is congruent to modulo |k| This finishes the proof of Theorem 1.1 Proof of Corollary 1.2 One applies Bloch’s decomposition of the diagonal [2, Appendix...
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Báo cáo hóa học: "Research Article Equivalent Extensions to Caristi-Kirk’s Fixed Point Theorem, Ekeland’s Variational Principle, and Takahashi’s Minimization Theorem" ppt
... beginning with Theorem 3.1, we have established the following results with the proof routes: Theorem 3.2 ⇒ Theorem 3.4 ⇒ Theorem 3.5; Theorem 3.4 ⇒ Theorem 4.1 ⇒ Theorem 5.1; 5.10 Theorem 3.5 ⇒ Theorem ... proof of Theorem 4.2 reduces to g f x From the proof we can further see that the nonemptiness and the closedness of M u imply the existence of v in M u such that M v ⊆ {v} ii If we apply Theorem ... noting that T in the above proof is a multivalued mapping to which Theorem 3.4 is directly applicable, in contrast to 11, Theorem and 16, Theorem From the proof of Theorem 3.5, we see that the...
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Báo cáo toán học: " Derangements and Euler’s difference table for C" potx
... Our proof of the last two theorems is a generalization of that given by Clarke et al [8], where the (k, ) = (0, 1) case of Corollary is proved Note that the (k, , m) = (0, 2, 0) case of (2.6) ... give combinatorial proofs of three remarkable ,n ,n recurrence relations of dm ’s ,n Proof of Theorem Let m and k be integers such that n ≥ m ≥ k ≥ Denote by Gm (k) the set of ,n permutations in ... set of the colored permutations of order n with m k-successions to the product of the set of all the electronic journal of combinatorics 15 (2008), #R65 m-subsets of [n − k] and the set of colored...
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GENERALIZATION OF A THEOREM OF CLIFFORD
... group of T Since the divisibility theory Ω of U −1 S is totally ordered, interchanging the role of G, H and Σ, Ω, respectively, a repetition of the proof of Theorem 3.10 yields, in view of [1] ... problems GENERALIZATION OF A THEOREM OF CLIFFORD (4) If S is a B-monoid such that S \ {0} is the positive cone of a lattice-ordered group G, then S is obviously the factor of the positive cone of the ... ˆ is a refinement of uˆ GENERALIZATION OF A THEOREM OF CLIFFORD and wˆ ˆ a is a common refinement of vˆ for some a ˆ ∈ F (X), then wˆ and wˆ ˆ a are both common refinements of yˆ Therefore by...
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A generalization of cohens theorem
... Faculty of Science, Mahidol University Thesis entitled A GENERALIZATION OF COHEN’S THEOREM was submitted to the Faculty of Graduate Studies, Mahidol University for the degree of Doctor of Philosophy ... Similarly the case of injective modules, we will introduce some characterizations of projective modules by the following theorem Theorem 2.6.5 [36, Theorem 5.3.1] The following properties of a right ... ideal of R is a fully invariant submodule of RR if it is a two-sided ideal of R Definition 2.7.2 A fully invariant submodule X of M is called a prime submodule of M if for any ideal I of S =...
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Tài liệu Báo cáo khoa học: "A GENERALIZATION OF THE OFFLINE PARSABLE GRAMMARS" doc
... f'mite set of symbols, so there is only a finite number of strings of given length L, and it has a finite number of rules, so there is only a finite number of possible parse trees of given depth ... will halt The essential properties of offline parable grammars are these: Theorem It is decidable whether a given unification grammar is offline parsable Proof: It is straightforward to construct ... problem Let C a be the set of pairs [A,B] such that A B by a tree of depth n Clearly C t is the set of pairs [A,B] such that (A ) B) is a rule of G Also, Cn+1 is the set of pairs [A,C] such that...
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Báo cáo khoa học: "A Comparative Study on Generalization of Semantic Roles in FrameNet" ppt
... illustrations of Hyi For the relation types Inchoative of and Causative of, we define role groups in the opposite direction of the hierarchy, parent Hyi = {y|y = yi ∨ y is a parent of yi }, Design of Role ... = yi ∨ y is an ancestor of yi } Hyi We formalize the generalization of semantic roles as the act of grouping several roles into a class We define a role group as a set of role labels grouped by ... roles of Inchoative of and Causative of relations represent more neutral stances or consequential states; for example, Killing::Victim is a parent of Death::Protagonist in the Causative of relation...
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Báo cáo khoa học: "Robustness and Generalization of Role Sets: PropBank vs. VerbNet" doc
... lexical entry of that sense, as opposed of using the arguments that appear in all senses On the Generalization of Role Sets We first seek a basic reference of the comparative performance of the classifier ... conclusions on the robustness and generalization across verbs of the role sets under study In order to study the behavior of both role sets in out of domain data, we made use of the PropBanked Brown corpus ... identify the Destination argument of a proposition governed by the verb send and the Beneficiary argument of the verb compose This fact might compromise generalization of systems trained on PropBank,...
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