Business Versus Complexity

AbstractAccording to our view, business is an economic category consists of products that are sold in markets that have a significant contribution to a company's business portfolio. At a company's level, businesses have a competitive position in the distribution of its resources to the consumption of inputs. In terms of management decision the allocation of material resources, labor and capital reflects its market position and determine the hierarchy of the various products that have turnover. The cost of the Knowledge of information produced determine the internal complexity of operation at an organization. Complex business models started to be represented everywhere around us the relationships between various entities that adapt and respond to the dynamics of internal and external environment. Most often these models operate in networks. Information system (IS) can be a modern solution to explain the above-mentioned complexity. The information in this case to capture the interactions between production function and the marketing in a subsystem which dialogues between its parts that are found in the interaction within the system to create knowledge and value this knowledge in costs and outcome. This paper focuses on information systems in an organization of great complexity as Google. Inc. its financial accountancy consideration and also the effects measures of Information System (IS) used in Google Inc

Randomized Complexity of Parametric Integration and the Role of Adaption II. Sobolev Spaces

We study the complexity of randomized computation of integrals depending on a parameter, with integrands from Sobolev spaces. That is, for $r,d_1,d_2\in{\mathbb N}$, $1\le p,q\le \infty$, $D_1= [0,1]^{d_1}$, and $D_2= [0,1]^{d_2}$ we are given $f\in W_p^r(D_1\times D_2)$ and we seek to approximate $$Sf=\int_{D_2}f(s,t)dt\quad (s\in D_1),$$ with error measured in the $L_q(D_1)$-norm. Our results extend previous work of Heinrich and Sindambiwe (J.\ Complexity, 15 (1999), 317--341) for $p=q=\infty$ and Wiegand (Shaker Verlag, 2006) for $1\le p=q<\infty$. Wiegand's analysis was carried out under the assumption that $W_p^r(D_1\times D_2)$ is continuously embedded in $C(D_1\times D_2)$ (embedding condition). We also study the case that the embedding condition does not hold. For this purpose a new ingredient is developed -- a stochastic discretization technique. The paper is based on Part I, where vector valued mean computation -- the finite-dimensional counterpart of parametric integration -- was studied. In Part I a basic problem of Information-Based Complexity on the power of adaption for linear problems in the randomized setting was solved. Here a further aspect of this problem is settled.Comment: 32 page

Randomized Complexity of Parametric Integration and the Role of Adaption I. Finite Dimensional Case

We study the randomized $n$-th minimal errors (and hence the complexity) of vector valued mean computation, which is the discrete version of parametric integration. The results of the present paper form the basis for the complexity analysis of parametric integration in Sobolev spaces, which will be presented in Part 2. Altogether this extends previous results of Heinrich and Sindambiwe (J.\ Complexity, 15 (1999), 317--341) and Wiegand (Shaker Verlag, 2006). Moreover, a basic problem of Information-Based Complexity on the power of adaption for linear problems in the randomized setting is solved.Comment: 30 page

Complexity of Initial Value Problems in Banach Spaces

We study the complexity of initial value problems for Banach space valued ordinary differential equations in the randomized setting. The right- hand side is assumed to be r-smooth, the r-th derivatives being ϱ-Hölder continuous. We develop and analyze a randomized algorithm. Furthermore, we prove lower bounds and thus obtain complexity estimates. They are related to the type of the underlying Banach space. We also consider the deterministic setting. The results extend previous ones for the finite dimensional case from [2, 9, 10].Изучается сложность задачи Коши для банаховозначных обыкновенных дифференциальных уравнений с рандомизированными начальными условиями. Правая часть предполагается r-гладкой, а r-е производные ϱ-гельдеровыми. Разрабатывается и анализируется рандомизированный алгоритм. Кроме того, доказываются оценки снизу и, таким образом, получаются оценки сложности. Они связаны с типом основного банахова пространства. Также рассматриваются детерминистические начальные данные. Эти результаты обобщают предыдущие, полученные для конечномерного случая [2, 9, 10]