In this case, the ordered data plot and the dex scatter plot clearly show two dominant points. This feature would not be obvious if we had generated only the dex mean plot. Interpretation-wise, the most important factor X2 (solute) will, on the average, change the light intensity by about[r]
Now let us proceed to produce an algorithm to solve this task. It will help to visual- ize the problem in very concrete terms. Suppose the list of numbers is so long that it takes a book to list them all. This is in fact how invalid credit card numbers are distrib- uted to stores that[r]
Abstract: The purpose of this article is to show that there exists a smooth real hypersurface germ M p , of D'Angelo infinite type in 2 such that it does not admit any (singular)[r]
p is avoidable on some finite alphabet if Z n avoids p, where words Z n are defined recursively by Z 1 = 1 Z n+1 = Z n (n + 1)Z n , n ∈ IN. Thus the pattern abcacb is a pattern over a 3 letter alphabet, and is avoided by Z 3 = 1213121. It follows that abcacb is avoidable[r]
− x − 3 . Calculate lim x →∞ 2 x 2 x − 1 − x − 3 . SOLUTION Both the numerator and the denominator of this fraction are growing without bound, but the denominator grows much more rapidly than the numerator. (Try this out numerically on your calculator for very large x .) For x very l[r]
• Thời gian này cũng đó cú nhiều kết quả mới về thuật toỏn giải cỏc bài toỏn riờng biệt của qui hoạch tuyến tớnh, như “phương phỏp thu hep chớnh tắc” giải bài toỏn vận tải; “phương phỏp thế vị” giải bài toỏn phõn phối (dạng mởrộng bài toỏn vận tải), vận tải theo tiờu chuẩn thời gian, thuật toỏn phõn[r]
Note two important solutions to equation 2: i In the general case, equation 2 admits steady-state solutions_ζ_ =_ζ__x_.. Arbitrary functions depend on the ratio of the unknowns.[r]
3 A combinatorial proof We give a combinatorial proof of Theorem 2.2 in the present section. Recall that elements of S n +1 can be obtained by inserting n + 1 to elements of S n . Let σ = σ 1 · · · σ n ∈ S n . Denote by σ + k = σ 1 · · · σ k (n + 1)σ k +1 · · ·[r]
References 1 M. Cenkci, Y. Simsek, and V. Kurt, “Further remarks on multiple p -adic q - L -function of two variables,” Advanced Studies in Contemporary Mathematics, vol. 14, no. 1, pp. 49–68, 2007. 2 L.-C. Jang, “On a q -analogue of the p -adic generalized twisted L -
2 Linear Domino Arrangements A well known problem of elementary combinatorics asks for the number of ways to place k indistinguishable non-overlapping dominos on the numbers 1 , 2 , . . . , n , arranged in a row, where a domino is a rectangular pi[r]
Under the stairs is another space that is often under-utilized. With proper lighting, it could become your new office space. Shelving could be installed under the lowest part so you don't bump your head on it. You may have a spare bedroom you could utilize -- or even a sma[r]
where K λµ is a Kostka number, that is, the number of semistandard tableaux of shape λ and content µ , see [3, 2.8.5], [7, § 2.11]. We will deal with two kinds of products of characters: Let l , m be non-negative integers, and let n = l + m . Let χ 1 be a
The purpose of this article is to show that there exists a smooth real hypersurface germ (M p), of D''Angelo infinite type in C2 such that it does not admit any (singular) holomorphic curve that has infinite order contact with M at p .
TRANG 1 A NOTE ON AN IDENTITY OF ANDREWS ZHIZHENG ZHANG _∗_ Department of Mathematics, Luoyang Teachers’ College, Luoyang 471022, P.. In this short note, again using the_q_-exponential o[r]
ϕ ( i ) as the integrand corresponding to the N i -process. The process G i is (see comment after (49)) the discounted amount invested in the portfolio corresponding to the bonds with maturity T i . The main problem in this section is to give conditions that guarantee completeness of the bo[r]
[21] C. S. Yarur, Existence of continuous and singular ground states for semilinear elliptic systems, Elec- tronic Journal of Di ff erential Equations 1998 (1998), no. 1, 1–27. Lingyun Qiu: Department of Mathematics, Tianjin University, Tianjin 300072, China Current address[r]
calculations. Comparison Formulas A comparison formula combines numeric operands — numeric constants, functions that return numeric results, and fields or items that contain numeric values — with special operators to compare one operand with another. A comparison formula[r]
28 Q.-M. Luo and H. M. Srivastava, “Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials,” Journal of Mathematical Analysis and Applications, vol. 308, no. 1, pp. 290–302, 2005. 29 H. Ozden, I. N. Cangul, and Y. Simsek, “Multivariate interpolation[r]
Various kinds of the q -analogue of the Genocchi numbers and polynomials, recently, have been studied by many mathematicians. In this paper, we use Kim’s 14 – 16 methods. By using p -adic q -Vokenborn integral 6 , Kim 2 , 7 – 9 , 14 – 18 constructed many kind of g[r]
4. Higher-order -Euler numbers and polynomials In this section we also assume that with 1 1. Now we study on higher-order -Euler numbers and polynomials and sums of products of -Euler numbers. First, we try to consider the multivariate fermionic -adic, -integ[r]