Sum identities

Luận văn nhằm trình bày một số kết quả nghiên cứu gần đây (xem Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions, Journal of Integer Sequences, Vol. 14 (2011)) về một bài toán cổ điển liên quan đến công thức biểu diễn tổng các hàm phần nguyên. Trong bài báo đó, tác giả giới thiệu phương pháp tạo ra bất đẳng thức, một vài đồng nhất thức với tổng nâng lên lũy thừa hàm sàn, hàm trần và hàm tròn, đồng thời áp dụng phương pháp này vào dãy các số nguyên không âm, biến chúng được trở thành dãy có chu kỳ.

39p capheviahe26 02-02-2021 36 3   Download

Sums of products of two Gaussian q -binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.

10p danhdanh27 07-01-2019 18 2   Download

We present a novel hierarchy of AKNS integrable couplings based on a specific semidirect sum of Lie algebras associated with sl. By applying the variational identity, we derive a bi-Hamiltonian structure of the resulting coupling systems, thereby showing their Liouville integrability.

10p danhdanh27 07-01-2019 15 1   Download

This paper describes some fusion techniques for achieving high accuracy species identification from images of different plant organs. Given a series of different image organs such as branch, entire, flower, or leaf, we firstly extract confidence scores for each single organ using a deep convolutional neural network.

15p mat_vang1 14-01-2019 28 1   Download

Stable laws { also called -stable or Levy-stable { are a rich family of probability distributions that allow skewness and heavy tails and have many interesting mathematical properties. They appear in the context of the Generalized Central Limit Theorem which states that the only possible non-trivial limit of normalized sums of independent identically distributed variables is -stable. The Standard Central Limit Theorem states that the limit of normalized sums of independent identically distributed terms with nite variance is Gaussian (-stable with  = 2).

175p thuymonguyen88 07-05-2013 65 17   Download

The most basic yet comprehensive component of a strong institutional image is a unified visual presentation. Collectively, all elements of the University of Kentucky must present to the world a consistent image that reflects our quality, professionalism and mission. The University of Kentucky name carries heavy responsibility. It stands as the sum of the institution’s many parts and embodies the authentic, recognizable essence of this institution. It must reinforce to many diverse audiences a definitive and unique impression.

13p seketnoi 29-04-2013 73 8   Download

Accounting relationships state definite facts about the world in relational terms. In particular, the national income identity (which simply states that total expenditure is the sum of its components) 8 implies, without need for further proof, that there is a reciprocal, offsetting relationship between public deficits and private savings. To be precise, the financial balance of the private sector (the excess of domestic saving over domestic investment) must always just equal the sum of the government budget deficit and the net export surplus.

14p loginnhanh 22-04-2013 68 2   Download

We prove the strong Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a geometric reformulation, we show that the Dolbeault cohomology H q (X; Ωp ) of the loop Grassmannian X is freely generated by de Rham’s forms on the disk coupled to the indecomposables of H • (BG). Equating the two Euler characteristics gives an identity, independently known to Macdonald [M], which generalises Ramanujan’s 1 ψ1 sum. For simply laced root systems at level 1, we also find a ‘strong form’ of Bailey’s 4 ψ4 sum. ...

47p dontetvui 17-01-2013 59 7   Download

A simple q-analogue of the sum of cubes is given. This answers a question posed in this journal by Garrett and Hummel.In their paper Garrett and Hummel commiserate the fact that (1) is not as simple as one might have hoped, and ask for a simpler sum of q-cubes. In response to this I propose the identity

2p thulanh5 12-09-2011 52 2   Download

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: COMPOSITION SUM IDENTITIES RELATED TO THE DISTRIBUTION OF COORDINATE VALUES IN A DISCRETE SIMPLEX.

14p thulanh4 10-09-2011 52 5   Download

Chapter 4 LOCAL LIMIT THEOREMS § 1. Formulation of the problem Suppose that the independent, identically distributed random variables X1 , X2 ,. . . . have a lattice distribution with interval h, so that the sum Zn = X1 + X2 + . . . + X„ takes values in the arithmetic progression {na + kh ; k = 0, ± 1, . . . } .

19p dalatngaymua 30-09-2010 83 8   Download