... that the segment [d;b] satisfys conditions of corollary 2.2, we now imitate the above proof to finish the corollary Certaintly, the last corollary is a solution for our key questions, in the case ... an index from the element in A .The conception about the shadow of a set was used efficiently by many mathematicians as: Sperner, Kruskal, Katona, Clement, ? We shall study here the shadow of ... IS(c)} to be the union of two consecutive segments Therefore,it is a segment In the case nk−1 < M − 1, apply the corollary 2.1 ( if nk−1 = M − 2) or the corollary 2.3 (if nk−1 < M − ) to the segment...
... convention about replacing (E(α) )n by E(α) q n,q In this paper we study the weighted q-Bernstein polynomials to express the fermionic q-integral on ℤp and investigate some new identities onthe ... http://www.journalofinequalitiesandapplications.com/content/2011/1/64 Page of Theorem is important to study the relations between q-Bernstein polynomials and the weighted q-Euler number in the next section Weighted q-Euler numbers concerning ... Applications 2011, 2011:64 http://www.journalofinequalitiesandapplications.com/content/2011/1/64 Page of By comparing the coefficients onthe both sides of (19) and (20), we obtain the following theorem...
... if A ≤L C and B ≤L D, then A + B≤L C + D A direct consideration is to see whether the star ordering has the same property And the solution is given in the following ∗ ∗ Theorem Let A, B, C, D ... ∗ ≤ CD Proof In view of (1.4), according to the assumptions, we have ∗ AB ∗ AB = AB CD Onthe other hand, on account of (1.4), from the conditions A* ≤ C and B* ≤ D, we have R(A) ⊆ R(C) and ... Applications 2011, 2011:54 http://www.journalofinequalitiesandapplications.com/content/2011/1/54 Page of implication may be not true The following theorem shows that when the implication is true Theorem...
... integral equations of p-adic q-integrals on Zp First, we derive some interesting equations of p-adic q-integrals on Zp From these equations, we give some interesting formulae for the higher-order ... Thus, one obtains the following theorem Theorem 2.9 For h ∈ Z and n ∈ Z , one has h,1 βn,q −n x ∞ qhm x x m n−1 q h−1 1−q m ∞ q h−1 m x m n q 2.40 m From the definition of p-adic q-integral on Zp ... 288–299, 2002 14 V Kurt, “A further symmetric relation onthe analogue of the Apostol-Bernoulli and the analogue of the Apostol-Genocchi polynomials,” Applied Mathematical Sciences, vol 3, no...
... presented also in this section The third one is devoted to prove some auxiliary results which are used for the proof of Main Theorem The proof of Main Theorem is in the fourth section Backgrounds 2.1 ... the introduction the paper contains three sections In the second section we recall some backgrounds concerning Lf (α, ∞)-spaces and D3 (f ) and D4 (f ) properties Some results of Apiola in [1] ... = q2 y} and p1 (x, y) = x, p2 (x, y) = y are the canonical projections By the Proposition 3.2 the second Pham Hien Bang 146 row splits Thus we have the following diagram with exact rows and columns...
... following result Some Results onthe Relation Between 277 Theorem 3.1 Let p be a non-constant holomorphic function on Cm \ S, where S is a hypersurface in Cm and f is a continuous function on a domain ... fz1 on D2 Thus f = f on D1 × D2 and the proof for the case N = is completed Now we assume that the conclusion of the theorem holds for N − ≥ Put k = k1 + · · · + kN From the hypothesis there ... function satisfying the followings: (i) For every z1 ∈ D1 the function fz1 (z2 ) = f(z1 , z2 ) is continuous on D2 (ii) For every z2 ∈ D2 the function f z2 (z1 ) = f(z1 , z2 ) is continuous on...
... and Theorem imply the condition 3d ≤ qn Theorem shows that inequality (1) cannot improve this condition (ii) Let u = and use (2) If q is even then 3d ≤ qn follows again If q is odd then the stronger ... determined in all these cases The final theorem gives at least a lower bound on PqL (u) According to Theorem 5, it is sufficent to consider only odd values of q The following convention is used Extending ... Lemma 1, and Theorem completes the proof If u is considerable greater than q, the Plotkin bound is usually weak and other well known upper bounds, e.g the Hamming bound, give stronger results...
... subset of the covariates to fit/interpret the data There are two main goals of variable selection, one is model identification, the other is regression estimation The former aims at identifying the true ... speaking, the LoRP consists in the so-called loss rank of a model defined as the number of other (fictitious) data that fit the model better than the actual data, and the model selected is the one with the ... dependencies on x The goal of regression/classification is to find a function fD ∈ F ⊂ X →Y “close” to ftrue based onthe past observations D with F some class of functions Or phrased in another way:...
... (F2 ⊗A P5 )GL5 Based onthe results in [23, 24], we have the following Theorem 1.3 Let n be as in Theorem 1.2 Then, we have (F2 ⊗A P5 )GL = n Obviously, Theorem 1.3 implies Theorem 1.2 Note that ... identify the vector space QPk (ω) with QPkω ⊂ QPk We note that the weight vector of a monomial is invariant under the permutation of the generators xi , hence QPk (ω) has an action of the symmetric ... that if µ(n) k, then there exists uniquely a minimal spike of degree n in Pk The following is a criterion for the hit monomials in Pk Theorem 2.4 (Singer [17]) Suppose x ∈ Pk is a monomial of degree...
... interaction in the target language The introduction of authentic texts into the learning situation The provision of opportunities for learners to focus, not only on language but also onthe learning ... effect onthe vocabulary teaching From these, some recommendations were suggested Design of the study The research includes three parts The first part is Introduction, in which the rationale, ... Communication was established onthe 16th January 1962 onthe basis of the mergence of three institutes: the Nguyen Ai Quoc Institute, the Institute of Communication and Education, and the People’s...
... before the test day Strong physical preparation will determine whether you will hit the high score I hope that you will find these insights helpful to you If you have any questions, don’t hesitate ... that you will find these insights helpful to you If you have any questions, don’t hesitate to contact me at neosystem@hn.vnn Good luck and happy scoring! ...
... If, onthe other hand, the question of processing is to be ignored in deciding what is to be viewed as input data, then another consideration must be taken into account It is the following: the ... algorithm, such as is the case in the approach this author has taken, the question of whether the grammar constitutes input data can then be viewed as follows: while the grammar does not constitute a separate ... constant algorithm turns out to be illusory, since the proponents of this concept of simplicity admit that it applies only when the rules are held to the same format Another point raised in connection...
... q-Euler polynomials J Physics A: Math Theor 43, 11 (2010) 255201 12 Kurt, V: further symmetric relation onthe analogue of the Apostol-Bernoulli and the analogue of the Apostol-Genocchi polynomials ... CS, Kim, YH: A numericla investigation onthe structure of the roots of the twisted q-Euler polynomials Adv Stud Contemp Math 19, 131–141 (2009) 15 Ryoo, CS: Onthe generalized Barnes’ type multiple ... benefit from: Convenient online submission Rigorous peer review Immediate publication on acceptance Open access: articles freely available online High visibility within the field Retaining the copyright...
... convergence, convergence in probability, or almost sure convergence is called the Shannon-McMillan theorem or the entropy theorem or the asymptotic equipartition property AEP in information theory ... theory The Shannon-McMillan theorem onthe Markov chain has been studied extensively see 2, In the recent years, with the development of the information theory scholars get to study the Shannon-McMillan ... give a definition of Markov chain fields onthe tree T by using the cylinder distribution directly, which is a natural extension of the classical definition of Markov chains see Definition 1.2 Let...