5fundamentals on functions with complex variables

... Divisibility of anticyclotomic L -functions and theta functions with complex multiplication By Tobias Finis Introduction The divisibility properties of Dirichlet L -functions in infinite families of characters ... denominator of bb K ¯ with (β) = bb−1 Weil representation and theta functions To construct theta functions in the adelic setting we use the Weil representation By the Stone-von Neumann theorem ... connecting theta functions with complex multiplication to special values of Hecke L -functions of anticyclotomic characters Yang considers a different model (V, ρ, ω) for the Weil representation,...

Ngày tải lên: 06/03/2014, 08:21

... varieties of dimension d with complex multiplication by a a CM field (i.e a totally complex number field endowed with an involution which becomes complex conjugation in any complex embedding) whose ... The definition of ωY , the definition of the L fact that the harmonic forms on A(C) are precisely the translation invariant ON THE PERIODS OF MOTIVES WITH COMPLEX MULTIPLICATION 749 ones, imply ... link between Lerch ζ -functions and Dirichlet L -functions It follows from the functional equation of Dirichlet L -functions when the character is primitive Recall that by definition (see before Theorem...

Ngày tải lên: 14/03/2014, 22:20

... integration operation Hence, the IHMPT is appropriate for the parameters estimation of multicomponent CPS Furthermore, from the analysis above, we can see that the IHMPT requires only onedimensional ... algorithm of ship target based on the IHMPT is discussed in Section 4; the results for simulated and measured data are given in Section 5; Section is the conclusion for the paper = A0 exp j 4π ... section, we use the numerical example to demonstrate the effectiveness of IHMPT in the suppression of cross-terms for multicomponent CPS For convenience, we assume that the simulated signal consists...

Ngày tải lên: 21/06/2014, 05:20

... numbers, and let f be a convex function on I If a, b, c, d ∈ I such that c, d ∈ a, b and pa qb pc qd, 2.4 then qf b ≥ pf c pf a qf d 2.5 Lemma 2.3 Let f be a convex function on I, and let x1 , x2 ... Inequalities and Applications with equality for ··· a2 a1 ··· , ak ak−1 ak ··· Qi / Qi Rk an , R / Qi Rk ak k 2.12 Using Corollary 2.5, we can prove the propositions below Proposition 2.6 Let < a1 ≤ ... Jensen’s difference Δ f, p, x is minimal when x1 ··· x2 xi−1 xi 2.7 Lemma 2.4 Let f be a convex function on I, and let x1 , x2 , , xn ∈ I (n ≥ 3) such that x1 ≤ x2 ≤ · · · ≤ xn 2.8 For fixed...

Ngày tải lên: 21/06/2014, 07:20

... class Em,p q, γ of analytic functions with negative coefficients Let us consider the functions f given by ∞ zp f z ak zk A.1 k p which are analytic in U For such a function f, we say that f ∈ Gn q, ... Re 1/γ p−q A.13 Consequently, the function f defined by the above is the extremal function for the class n Gn q, γ But our class Em,p q, γ is defined with analytic functions f with negative 1,p ... and S Ponnusanny, Eds., “Open problems,” World Scientific, 1990, Conference on New Trends in Geometric Function Theory and Applications S Owa and G S S˘ l˘ gean, “Starlike or convex of complex...

Ngày tải lên: 21/06/2014, 17:20

... gj,n z yn , as required n Convolution and convex combination k In this section, we show that the class MHSs j, m, α is invariant under convolution and convex combination of its member ∞ n −1 j ... sufficient condition for functions f h g, where h and k g given by 1.3 to be in the class MHSs j, m, α Indeed, it is shown that this coefficient k condition is also necessary for functions to be ... “Harmonic meromorphic starlike functions, ” Bulletin of the Korean Mathematical Society, vol 37, no 2, pp 291–301, 2000 K Al-Shaqsi and M Darus, On subclass of harmonic starlike functions with...

Ngày tải lên: 22/06/2014, 02:20

... is generalized to nonlinear terms: ϕ1 u s, t and ϕ2 u s, t Our strategy is to monotonize functions ϕi s with other two nondecreasing ones such that one has stronger monotonicity than the other ... J→R are all continuous functions such that α β 0 Obviously, the estimation obtained in 11 cannot be applied to 3.2 We first give an estimation for solutions of 3.2 under the condition F x, y, u, ... is a nonnegative and nondecreasing function on x0 , X × J Then, 2.11 is equivalent to u x, y ≤ ψ −1 η x, y ∀ x, y ∈ x0 , Y × J 2.13 By the fact that b x ≤ x for x ∈ x0 , X and the monotonicity...

Ngày tải lên: 22/06/2014, 03:20

... matrices associated with graph G Here n is the number of vertices of graph G, I is identity matrix and A(G) is the adjacency matrix of this graph Consider two functions of graph G based on these classes: ... Boston, MA [2] V Dobrynin, On the function “sandwiched” between α(G) and χ(G), Electron J Combinat., 4, R19 (1997), 3pp [3] V Dobrynin, On the rank of a matrix associated with a graph, Discrete Mathematics, ... the following question: can we use the functions θ(G), r(G) and d(G) in (1) instead of r+ (G)? In the common case the answer is negative The proof is based on the following lemmas Lemma If α(G)...

Ngày tải lên: 07/08/2014, 08:20

... association of clinical response with overall survival after the treatment with a definitive 5-FU/CDDP-based CRT in 49 patients with ESCC The survival depended on the response, i.e., CR or non-CR ... patients with a complete response (CR, N = 23), dotted line: patients not with a complete response (non-CR, N = 26) The survival depended on the response (P = 0.001, Log-rank test) Discussion Originally, ... might affect the association of the plasma concentrations of 5-FU with long-term survival Conclusions Japanese ESCC patients were followed up for years after treatment with a definitive 5-FU/CDDP-based...

Ngày tải lên: 10/08/2014, 10:21

... See Chapter 10, “Conditional Formatting,” for additional tips on using the MOD function 172 Chapter Use the SUBTOTAL function to perform several operations The SUBTOTAL function can be used to ... function to return the integer portion of a division The opposite of PRODUCT, which was used in the previous tip, is QUOTIENT This function calculates the integer portion of a division operation ... Mathematical Functions 165 Use the PRODUCT function to multiply conditional values In this example, values are listed in columns A and B Excel should calculate the product of each value in a row but only...

Ngày tải lên: 14/08/2014, 08:22

... convex functions we have f (t) + (i − 1)f (s) ≥ f (y1 ) + f (y2 ) + · · · + f (yi ) Adding this inequality to Jensen’s inequality for the convex function pf (z) + (1 − p)f (s) ≥ f (t), the conclusion ... (1 + k)f (s) with the more restrictive condition: f (x) ≤ f (y) for any x, y ∈ I such that x≤s≤y and x + ky = (1 + k)s To prove this assertion, we have to show that this condition implies f (x) ... Theorem 1.11 to the function f (u) = g(eu ) In addition, we set s = 0, S = ln r, and replace x with ln x, y with ln y, and each xi with ln Remark 1.19 If f is differentiable on (0, ∞), then Corollary...

Ngày tải lên: 15/08/2014, 16:55

... proof ε(x) = −8x2 − R EFERENCES [1] V CÎRTOAJE, On some inequalities with power-exponential functions, J Inequal Pure Appl Math., 10(1) (2009), Art 21 [ONLINE: http://jipam.vu.edu.au/article.php?sid=1077] ... proof of the necessary condition We prove the sufficient condition Put a = − x and b = + x, where < x < Since the desired inequality is true for x = and for x = 1, we only need to show that (2.3) ... Art 72, pp 1+x 1−x + (1 + x)r(1−x) r 1−x − r ln(1 + x) 1+x http://jipam.vu.edu.au/ S OLUTION O F O NE C ONJECTURE The inequality ϕ (x) < is equivalent to (2.4) r 1+x 1−x 1−x − ln(1 + x) 1+x 1+x...

Ngày tải lên: 15/08/2014, 16:55

... S ⊂ C ∪ {∞} and f and g be two non-constant meromorphic (entire) functions If Ef (S) = Eg (S) implies f = g for any two non-constant meromorphic (entire) functions f, g, then S is called a unique ... f = g for any pair of non-constant meromorphic (entire) functions A set S ⊂ C ∪ {∞} is called a URSM≤m (URSE≤m ) if for any two non-constant meromorphic (entire) functions f, g, Ef≤m (S) = Eg≤m ... nomial for meromorphic (entire) functions, if P (f ) = cP (g) implies f = g for any two non-constant meromorphic (entire) functions f and g , and any nonzero constant c ∈ C We sayP is a SUPM...

Ngày tải lên: 12/10/2015, 16:18

... continuous functions on K Assume that u : U → R ∪ +∞ is a continuous function function on U satisfying the following conditions: (a) inf U u > −∞; 13 (b) fj < u on K, inf K fj ≥ −M for some constant ... for functions of the form log |f | but also for continuous plurisubharmonic function on U Since every continuous plurisubharmonic ˆ U may be continued to a continuous plurisubharmonic on a small ... locally bounded on Ω ˜ such that Ω Ω ˜ U and that holomor(iii) For every pseudoconvex domain Ω ˜ by holomorphic functions ˜ can be approximated uniformly on Ω phic functions on Ω on U we have ˜...

Ngày tải lên: 14/10/2015, 07:59

... complete 3.3 Integration of non-periodic functions The problem of the optimal numerical integration of non-periodic functions is more involved The cubature formula below is a modification of (3.2) involving ... of functions with bounded mixed difference, Mat Sb, 183(7), 1992; English transl in Mat Sb, 76:283–292, 1993 24 [7] D D˜ ung Approximation of functions of several variables on a torus by trigonometric ... contribution [4]) We will first focus on periodic functions and extend the results later to the non-periodic situation 3.1 Integration of periodic functions We are going to prove the theorem...

Ngày tải lên: 14/10/2015, 15:32

... David, Dissabled Village Children, The Hesperian Foundation Edition 1996 Werner David, Wgere thre is no doctor The Hesperian Foundation, P.O.Box, 1692, Palo Alto CA,94302, USA,1992,506 pages ... tr khỏc li c ng thỏi quỏ Mt na s tr b bi nóo cú chm phỏt trin tinh thn 4.8 Ri lon nghe v nhỡn Mt s tr cú ri lon nghe v nhỡn Nu khụng phỏt hin iu ny, nờn mt s b m s cho rng tr thiu thụng minh ... 75 Bi nóo - U nóo: gõy tn thong nóo v gõy cỏc du chng nh bi nóo, song tin trin cng ngy cng xu i Lõm sng 4.1 Du hiu sm - Lỳc sinh : ngi mm nhn Tr...

Ngày tải lên: 25/10/2012, 11:22

... regimen for unresectable ESCC with T4 or M1a [5,6] A long-term evaluation of efficacy and toxicity with 139 patients resulted in a complete response (CR) rate of 56%, along with a 5-year survival rate ... Figure A course consisted of continuous infusion of 5-FU at 400 or 500-550 mg/m2/day for days 1-5 and 8-12, infusion of CDDP at 40 mg/m2/day on days and 8, and radiation at Gy/day on days to 5, ... study was conducted with the authorization of the institutional review board and followed the medical research council guidelines of Kobe University Determination of Plasma Concentration of 5-FU...

Ngày tải lên: 26/10/2012, 09:39

... Physical and Virtual Memory Addressing and Indirection Functions with Multiple Outputs Arrays and Pointer Arithmetic Strings String Utility Functions Searching and Sorting Algorithms Linear Search ... segmentation faults, other difficult-to-identify errors • What happens if we dereference ppi now? 11 Functions with multiple outputs • Consider the Extended Euclidean algorithm ext_euclid(a,b) function ... Physical and Virtual Memory Addressing and Indirection Functions with Multiple Outputs Arrays and Pointer Arithmetic Strings String Utility Functions Searching and Sorting Algorithms Linear Search...

Ngày tải lên: 25/04/2013, 08:07

... vừa xuống canh sợi vải Khi có 3-4 mũi kim, rút kim lên vuốt theo đường khâu cho phẳng * Khi khâu xong cần lại mũi (khâu thêm đến mũi) mũi cuối, xuống kim sang mặt trái, vòng chỉ, tết nút trước cắt ... 0,5 cm, mặt phải vải lên mũi nhỏ nằm ngang cách * GV theo dõi uốn nắn thao tác cho HS * Khi học xong mũi khâu nhà số em khéo tay phụ gia đình vắt lai, vá số quần áo Những HS nam tự may phù hiệu ... bút chì - Xâu vào kim - Vẽ gút đầu - Khâu từ phải sang trái - Lên kim từ mặt trái vải - Khi khâu xong cần lại mũi Khâu mũi đột mau: -Vạch đường thẳng mảnh vải theo chiều dài bút chì -Lên kim mũi...

Ngày tải lên: 03/06/2013, 01:25

... ngun tử chứa proton nơtron 2) số proton ngun tử ln ln nhỏ số nơtron ngun tử 3) số proton ngun tử ln ln số electron ngun tử Chọn phát biểu : A có B C có D 1,2,3 Câu 27: Trong ngun tử X, tổng ... muối cacbonat, nhận định sau ? A.Tất muối cacbonat tan nước B Tất muối cacbonat bị nhiệt phân , trừ muối cacbonat kim loại kiềm C Tất muối cacbonat bị nhiệt phân tạo oxit kim loại cacbon dioxit ... có phân lớp electron ngồi 3p4 Hãy câu sai sau nói ngun tử X : A Lớp ngồi ngun tử X có electron B Hạt nhân ngun tử X có 16 proton C Trong bảng tuần hồn , X nằm chu kỳ D Trong bảng tuần hồn...

Ngày tải lên: 29/06/2013, 01:27