Roxana Mihaela
email: roxana.nicolai@gmail.com

Nicolai

Dan Tiba
email: dan.tiba@imar.ro

Implicit parametrizations and applications

Keywords: implicit systems, local parametrization, shape optimization, boundary observation

We discuss recent constructive parametrizations approaches for implicit systems, via systems of ordinary differential equations. We also present the notion of generalized solution, in the critical case and indicate some numerical examples in dimension two and three, using Mat-Lab. In shape optimizations problems, using this method, we introduce general optimal control formulations in the boundary observation case. This extends previous work of the authors on optimal design problems with distributed cost functional.

Introduction

The implicit function theorem or the inverse function theorem ensure as well the local existence of implicit parametrizations for the solution of implicit systems, under classical assumptions, [START_REF] Dontchev | Implicit functions and solution mappings[END_REF], [START_REF] Krantz | The implicit functions theorem[END_REF]. Recently, in authors' papers, [START_REF] Nicolai | Implicit functions and parametrizations in dimension three: generalized solution[END_REF], [START_REF] Tiba | The implicit functions theorem and implicit parametrizations[END_REF], explicit constructions (via iterated ordinary differential equations) of implicit parametrizations, in dimensions two and three, have been discussed. A possible extension of such constructions to arbitrary dimension is investigated in the preprint [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF]. Moreover, this new approach allows the introduction of the notion of generalized solution, solving implicit systems under C 1 hypotheses, in the critical case.

Such considerations have impact in shape optimization problems (fixed domain methods) where implicit representations of domains play an essential role. The aim is to obtain a general method to solve optimal design problems via optimal control theory. In the case of Dirichlet boundary conditions, a theoretical analysis together with numerical experiments are reported in [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF], [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems[END_REF]. For a general background, we quote [START_REF] Neittaanmäki | Optimization of Elliptic Systems. Theory and Applications[END_REF]. Notice that this method is essentially different from the level set method (for instance, no Hamilton-Jacobi equation is necessary in [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF], [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems[END_REF]).

This paper is organized as follows. In Section 2, we recall briefly the implicit parametrization approach. Some numerical examples in the critical case, in dimension two and three are outlined in Section 3. The last section discusses possible applications in shape optimization.

Implicit Parametrizations and Generalized Solution

We limit the presentation to the case of one implicit equation in dimension three:

f (x, y, z) = 0, in Ω ⊂ R 3 , (1)
Ω an open connected subset. We assume that f ∈ C 1 (Ω) and there is (x 0 , y 0 , z 0 ) ∈ Ω such that (1) is satisfied. We also impose, for the moment, that (x 0 , y 0 , z 0 ) is noncritical for f , i.e. ∇f (x 0 , y 0 , z 0 ) = 0. To fix ideas, we assume:

f x (x 0 , y 0 , z 0 ) = 0. (2)
Later, we shall remove this hypothesis and discuss the critical case. For the general situation, we quote [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF].

We associate to (1) the following systems of first order partial differential equations (with independent variables t and s) of iterated type:

x (t) = -f y (x(t), y(t), z(t)), t ∈ I 1 , y (t) = f x (x(t), y(t), z(t)), t ∈ I 1 , (3)
z (t) = 0, t ∈ I 1 , x(0) = x 0 , y(0) = y 0 , z(0) = z 0 ; (4)
φ(s, t) = -f z (ϕ(s, t), ψ(s, t), ξ(s, t)), s ∈ I 2 (t), ψ(s, t) = 0, s ∈ I 2 (t), (5) ξ(s, t) = f x (ϕ(s, t), ψ(s, t), ξ(s, t)), s ∈ I 2 (t), ϕ(0, t) = x(t), ψ(0, t) = y(t), ξ(0, t) = z(t), t ∈ I 1 .

The iterated character of the PDE system (3)-( 6) consists in the fact that the coupling between (3)-( 6) is made just via the initial conditions [START_REF] Neittaanmäki | Optimization of Elliptic Systems. Theory and Applications[END_REF]. This very weak coupling, together with the presence of just one derivative in each equation create the possibility to solve (3)-( 6) as ODE systems. Namely, the system (3)-( 4) is indeed of ODE type. The system (5)-( 6) has the t independent variable as a parameter, entering via the initial conditions and may be interpreted as an ODE system with parameters. The existence may be obtained via the Peano theorem since f ∈ C 1 (Ω). Moreover, one may infer via this theorem and some simple calculations that the local existence interval I 2 (t) may be chosen independently of t ∈ I 1 , i.e. I 2 (t) = I 2 . Under slightly stronger regularity assumptions, for instance ∇f locally Lipschitzian, we also obtain uniqueness for (3)- [START_REF] Neittaanmäki | Optimization of Elliptic Systems. Theory and Applications[END_REF]. For very weak assumptions in this sense, see [START_REF] Zuazua | Log-Lipschitz regularity and uniqueness of the flow for a field in [W n/p+1 loc (R n )] n[END_REF] or [START_REF] Diperna | Ordinary differential equations, transport theory and Sobolev spaces[END_REF], since the system (3)-( 6) has divergence free right-hand side.

The fact that (3)-( 6) provides a parametrization of the solution of (1), around (x 0 , y 0 , z 0 ) is stated in the following theorem, proved in [START_REF] Nicolai | Implicit functions and parametrizations in dimension three: generalized solution[END_REF]:

Theorem 1. Assume that f ∈ C 2 (Ω) and I 1 , I 2 are sufficiently small. Then, (ϕ, ψ, ξ) : I 1 × I 2 → Ω is a regular transformation on its image. Remark 1. The systems (3)-( 4), respectively ( 5)-( 6) are of Hamiltonian type, in fact. In dimension two, for the implicit equation g(x, y) = 0, just one Hamiltonian system may be used, to obtain the parametrization (see [START_REF] Thorpe | Elementary topics in differential geometry[END_REF], [START_REF] Tiba | The implicit functions theorem and implicit parametrizations[END_REF]):

a (t) = -g y (a(t), b(t)), t ∈ I 1 , b (t) = g x (a(t), b(t)), t ∈ I 1 , (7)
a(0) = a 0 , b(0) = b 0 ,
In arbitrary dimension, the solution is more involved [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF].

Remark 2. The advantage of Theorem 1 or other implicit parametrization results, is exactly their explicit character. Moreover, the fact that the solution is obtained via systems of ordinary differential equations makes it possible to use maximal solutions. Theorem 1 has a local character, but in applications, the maximal existence intervals I 1 , I 2 may be very large. In many cases, one may obtain even global solutions [START_REF] Nicolai | Implicit functions and parametrizations in dimension three: generalized solution[END_REF]. In comparison with implicit function theorems, removing the restrictive requirement that the solution is in function form, allows to obtain a more complete description of the manifold corresponding to (1).

The above construction provides the basis for the introduction of the generalized solution of (1), in the critical case and we recall it briefly here, for reader's convenience. We remove hypothesis [START_REF] Dontchev | Implicit functions and solution mappings[END_REF], that is the point (x 0 , y 0 , z 0 ) may be critical. We notice that the following weaker property is valid in general: there is (x n , y n , z n ) ∈ Ω such that

(x n , y n , z n ) → (x 0 , y 0 , z 0 ) such that ∇f (x n , y n , z n ) = 0. (8)
If ( 8) is not valid, then ∇f (x 0 , y 0 , z 0 ) = 0 in a neighborhood V of (x 0 , y 0 , z 0 ) and, consequently, f (x, y, z) = 0 in V . This is a trivial situation of no interest. For general implicit systems, a similar property may be stated, expressing the fact that the equations of the system have to be functionally independent [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF].

Due to [START_REF] Nicolai | Implicit functions and parametrizations in dimension three: generalized solution[END_REF], one can construct the solution of ( 3)-( 6) with initial condition in (x n , y n , z n ). We denote by T n ⊂ Ω, the set described by (ϕ n , ψ n , ξ n ) obtained in [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF], in this case. Since f is in C 1 (Ω), T n may be assumed compact. By truncation (or imposing Ω to be bounded), we get {T n } bounded with respect to n. On a subsequence denoted by α, we have:

T n → T α
in the Hausdorff-Pompeiu metric, where T α ⊂ Ω is some compact subset, [START_REF] Neittaanmäki | Optimization of Elliptic Systems. Theory and Applications[END_REF].

Definition 1. In the general (critical) case, we call T = ∪T α to be the generalized solution of [START_REF] Diperna | Ordinary differential equations, transport theory and Sobolev spaces[END_REF], where the union is taken after all the sequences and subsequences as above.

It can be shown that (x 0 , y 0 , z 0 ) ∈ T , any point in T satisfies [START_REF] Diperna | Ordinary differential equations, transport theory and Sobolev spaces[END_REF] and that Definition 1 provides the usual solution in the classical nonsingular case, [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF]. That is, Definition 1 is an extension of the classical notion of solution. If (x 0 , y 0 , z 0 ) is an isolated critical point, then again T coincides (locally) with the solution of (1). Otherwise, T may be just the boundary of the solution set of (1), according to [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF]. A complete description of the level sets (even of positive measure) of a function, may be obtained in this way.

An algorithm for the approximation of generalized solutions is detailed in [START_REF] Nicolai | An algorithm for the computation of the generalized solution for implicit systems[END_REF]. In the next section we indicate some computational examples in this sense.

Numerical Examples

All the examples in this section were performed with MatLab. We consider just the critical case.

Example 1. Let g(x, y) = x 3 -siny, with the critical point (x 0 , y 0 ) = 0, π 2 .

We are in the critical case: g(x 0 , y 0 ) = 0, ∇g(x 0 , y 0 ) = (0, 0). According to Definition 1, we have to solve [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems[END_REF] with approximating initial conditions 0, Example 2. Let f (x, y, z) = xyz, with the initial point (x 0 , y 0 , z 0 ) = (0, 0, 0). solutions of the second system corresponding to all the six approximating initial conditions. In fact, for the initial conditions with negative third coordinate we have used the variant (9) of the system ( 5)-( 6) that avoids y = ct, specific to ( 5)-( 6), and improves the graphical representation. We have intendedly represented, for clarity, just a small number of integral curves. j(y Ω (x), x)dx [START_REF] Philip | A penalization and regularization technique in shape optimization[END_REF] subject to

π 2 + ± 1 100 , ∓ 1 100 , 0, π 2 + ± 1 100 , ± 1
-∆y Ω = f in Ω (11)
y Ω = 0 on ∂Ω [START_REF] Sokolowsky | Introduction to Shape Optimization[END_REF] Here E ⊂ Ω ⊂ D ⊂ R d , d ∈ N, are bounded Lipschitzian domains, with E and D given and Ω unknown, f ∈ L 2 (D), Λ is either E or Ω and j : R × D → R satisfies appropriate measurability and other hypotheses [START_REF] Neittaanmäki | Optimization of Elliptic Systems. Theory and Applications[END_REF]. More general state equation, other boundary conditions may be considered as well. Traditional solution methods are boundary variations, speed method, topological asymptotics, the mapping method, the level set method etc., [START_REF] Sokolowsky | Introduction to Shape Optimization[END_REF], [START_REF] Sethian | Level set methods[END_REF]. In the papers [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF], [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems[END_REF], [START_REF] Philip | A penalization and regularization technique in shape optimization[END_REF] functional variations for domains are introduced and studied. The idea is to assume that the admissible domains for ( 10)-( 12) are defined implicitly by

Ω = Ω g = int{x ∈ D; g ∈ C( D); g(x) ≥ 0} ( 13
)
Here g is in some subset of admissible functions G ad , corresponding to the family of admissible domains Ω = Ω g . For instance, since we impose that E ⊂ Ω = Ω g , then we have to require

g(x) ≥ 0, ∀x ∈ E. ( 14
)
Other constraints may be added according to the envisaged applications. Due to the representation [START_REF] Thorpe | Elementary topics in differential geometry[END_REF], one may use the functional variations of Ω, in the direction of h ∈ C( D):

Ω g+λh = int{x ∈ D; g + λh ≥ 0}, ( 15
)
where λ > 0 is a scalar and h satisfies similar conditions as in ( 13), [START_REF] Tiba | The implicit functions theorem and implicit parametrizations[END_REF]. Notice that the variations [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF] of Ω = Ω g may be very complex, combining boundary and topological variations. The function g is a shape (or level) function, but the approach ( 13)-( 15) is not to be confused with the level set method (we have no artificial time in the definition of Ω g or in g, we need no Hamilton-Jacobi equation, etc.). An essential ingredient in using general functional variations in the problem (10)-( 12) is the following approximation of ( 11), [START_REF] Sokolowsky | Introduction to Shape Optimization[END_REF]:

-∆y ε + 1 ε (1 -H ε (g)) y ε = f, in D, (16)
y ε = 0, on ∂D, (17)
where H is the Heaviside function and H ε is some regularization. Such penalization / regularization approaches were used already in [START_REF] Mäkinen | On a fixed domain approach for a shape optimization problem[END_REF]. The basic approximation result in this case, according to [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF], is the following:

Theorem 2. If Ω = Ω g is of class C, then y ε / Ωg → y Ωg weakly in H 1 (Ω g ), on a subsequence.
Domains of class C, roughly speaking, have just continuous boundary. A thorough presentation with applications can be found in [START_REF] Tiba | Domains of class C: properties and applications[END_REF].

Based on Theorem 2, one can approximate the problem ( 10)-( 12) by the problem (10), ( 16), [START_REF] Ziemann | Optimal thickness of a cylindrical shell[END_REF]. If Λ = E, this formulation is already a self-contained optimal control problem with unknown g. If Λ = Ω, then we approximate as well [START_REF] Philip | A penalization and regularization technique in shape optimization[END_REF] by

D H ε (g(x))j(y ε (x), x)dx. ( 18
)
Notice that the formulation ( 16)-( 18) excludes the explicit presence of the unknown geometry of Ω and is in fact an optimal control problem with the control g acting in the coefficients of the lower order terms of state equation [START_REF] Tiba | Domains of class C: properties and applications[END_REF].

Solving for the optimal g ε immediately yields the optimal geometry Ω gε as a level set. In the formulation ( 16)-( 18) one can easily use functional variations as in [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF]. See [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF], [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems[END_REF], [START_REF] Philip | A penalization and regularization technique in shape optimization[END_REF] for numerical examples as well.

The case of boundary observation (cost) needs a special treatment based on the developments from Section 2 and we shall briefly comment on this, just in dimension 2.

We also fix, without loss of generality, some point x 0 = (x 1 0 , x 2 0 ) ∈ D\E ⊂ R 2 such that g(x 0 ) = 0 for any admissible g ∈ C 1 (D). We assume as well that

g(x) = 0 ⇒ ∇g(x) = 0, (19)
g(x) = 0, on ∂D, (20)
to avoid the presence of critical points on ∂Ω g and the corresponding admissible domains will not "touch" ∂D. We shall denote by Λ g , the connected component of ∂Ω g , containing x 0 (the presence of multiply connected domains Ω g is allowed in our setting).

The above setting together with the condition ( 14) defines the set G ad of admissible controls in ( 16)- [START_REF] Zuazua | Log-Lipschitz regularity and uniqueness of the flow for a field in [W n/p+1 loc (R n )] n[END_REF]. It is possible to work without (20), but this would complicate the exposition. Finally, we impose that G ad ⊂ W 3,∞ (D). Notice that the obtained class of admissible geometries remains very rich.

Then, by §2, relation [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems[END_REF], we know that Λ g can be parametrized by the solution of the Hamiltonian system:

x 1 (t) = - ∂g ∂x 2 (x 1 (t), x 2 (t)), t ∈ I g , (21)
x 2 (t) = ∂g ∂x 1 (x 1 (t), x 2 (t)), t ∈ I g , (x 1 (0) , x 2 (0)) = x 0 . (22)
By Proposition 3 in [START_REF] Tiba | The implicit functions theorem and implicit parametrizations[END_REF], due to the boundedness of D and (19), (20) , we may assume that the solution of (21), ( 22) is periodic and Λ g is a closed curve, for any g ∈ G ad . The interval I g may be assumed to start in 0 and have the period length (that can be easily determined numerically in applications).

We comment now the following example:

J(g) = Λg ∂y ε ∂n 2 dσ = Ig ∂y ε ∂n (x 1 (t), x 2 (t)) 2 x 1 (t) 2 + x 2 (t) 2 dt, (23)
which is a typical case in boundary observation problems and y ε solves ( 16), [START_REF] Ziemann | Optimal thickness of a cylindrical shell[END_REF]. By (21), ( 22) and simple computations, we have:

J(g) = Ig [∇y ε (x 1 (t), x 2 (t)) • ∇g(x 1 (t), x 2 (t))] 2 |∇g(x 1 (t), x 2 (t))| -1 dt, (24)
.

Notice that the cost functional in (23)-( 24) makes sense since G ad ⊂ W 3,∞ (D) which ensures the regularity of Λ g . Together with (19), (20) and ( 16), [START_REF] Ziemann | Optimal thickness of a cylindrical shell[END_REF], we have that y ε ∈ H 2 (D). The formulation ( 16), ( 17), (24) again removes any direct reference to the geometric unknowns. Under regularity assumptions, one can consider functional variations [START_REF] Tiba | A Hamiltonian approach to implicit systems, generalized solutions and applications in optimization[END_REF] and compute directional derivatives (by the chain rule). In the case of thickness optimization problems for shells, a numerical approach based on directional derivatives is used in [START_REF] Ziemann | Optimal thickness of a cylindrical shell[END_REF]. A detailed study of shape optimization problems with boundary observation, including the adjoint equation method and computational examples will be performed in a forthcoming paper based on the above approach. The computation of the adjoint equation, in the simpler case of distributed observation in E, is performed in [START_REF] Neittaanmäki | Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions[END_REF].

Remark 3. The advantage of our approach is given by the generality of the admissible variations (combining boundary and topological perturbations without "prescribing" their topological type) and the fact that optimal control theory, in the fixed domain D, may be applied.

  100 . The result is shown in Figure 1. In Figure 2 we perform a zoom around the critical point. The four curves corresponding to these initial conditions cannot be distinguished visually, from each other.

Fig. 1 . 2 )Fig. 2 .

 122 Fig. 1. g(x, y)=x 3 -sin y,(x0, y0)=(0, π 2 ) Fig. 2. zoom around (x0, y0) = (0, π 2 )

Fig. 5 Fig. 6 .

 56 Fig. 5. the initial condition (1/10, 1/10, 9/100) Fig. 6. the solution corresponding to the six initial conditions

Acknowledgments. The work of both authors was supported by Grant 145/2011 of CNCS Romania.

We are in the critical case: f (x 0 , y 0 , z 0 ) = 0 and ∇f (x 0 , y 0 , z 0 ) = 0. Consider the approximating initial conditions In Figure 3 we show the results for the system (3)-(4), the four curves corresponding to the four initial conditions. In Figure 4 we superpose the results, corresponding to each of the previous four curves as initial conditions, obtained for the system ( 5)-( 6) together with the following alternative (see [START_REF] Nicolai | An algorithm for the computation of the generalized solution for implicit systems[END_REF]) system:

The dark colours correspond to the points where both systems produce solutions. Using the symmetry, the result can be extended for z < 0.

Example 3. Let f (x, y, z) = (10x 2 -y 2 -z)(x 2 -10y 2 -z), with the initial point (x 0 , y 0 , z 0 ) = (0, 0, 0).

We are again in the critical case: f (x 0 , y 0 , z 0 ) = 0 and ∇f (x 0 , y 0 , z 0 ) = 0.

Consider the approximating initial conditions

In Figure 5 we represent the solutions of the systems (3)-(4), respectively (5)-( 6) for the initial condition 1 10 , 1 10 , 9 100

. In Figure 6 we have put together the


Łukasz Przysucha
email: lukasz.przysucha@ue.wroc.pl

Content Management Systems based on GNU GPL license as a support of knowledge management in organizations and business

Keywords: 2 CMS, Content Management System, Open Source, GNU GPL, Knowledge Management, Flow of information

Content Management Systems are an increasingly popular form of publishing content on the Internet. Its popularity gained by a large intuitive, rich diversity of graphical representations and great functionality. The author focused on a characterization of free systems based on GNU GPL license which have high prospects for growth and development. The main goal of this article is to find common ground between knowledge management and content management systems. Author believes that area of content management is not sufficiently exploited and would greatly assist the process of knowledge management in organizations. The article includes possible scenarios and development steps of Content Management Systems implementation in area of Knowledge Management. There were also defined the different points of view of knowledge management depending on the assumed perspective. This chapter is divided into 4 areas, which were finally assembled: content management, content management systems, GNU GPL license, knowledge management and implementation of content management systems in area of knowledge management.

Introduction

For several years we have seen higher interest of knowledge management and the use of artificial intelligence in organizations and companies. It is closely related with development of technology and networks that support an information flow. Free solutions quickly become an alternative and competition for paid services. The main goal of this article is to find common ground between knowledge management (KM) and content management systems (CMS). Author believes that area of content management is not exploit enough and would greatly assist the process of knowledge management in organizations. Article focused on Content Management Systems working on GNU GPL license because free systems highly support development and prospects of content management process. The secondary objective is related with popularizing importance, universality and many developments of CMS. This paper explores the place for Content Management Systems available remotely on the network within organizations and business places.

In recent times, it has written several works related with CMS and GNU GPL license. Mainly it was the university work but sometimes business too. Dimitrios Michelinakis from University of Warwick prepared the report "Open Source Content Management Systems: An Argumentative Approach" [START_REF] Michelinakis | Open Source Content Management Systems: An Argumentative Approach[END_REF], submitted for the award of MSc Electronic Business Management. It was one of the first looks at the essence of Web content management. Another thesis, "Content Management Systems -Business effects of an implementation" by Therese Karlsson and Jennie Boije af Gennäs from IT University of Göteborg and Chalmers University of Technology contains analysis of the implementation of system in a business.

First section of this work focused on the importance of content management. There are positive effects of the implementation of content management system with IBM and PPL Energy Company. The second section shows usage of content management systems. There are located technical issues, the differences between dynamic and static pages and financial terms of system implementation. The next part is about GNU GPL license as a tool supporting CMS developing. At this point it shows the positive attributes of open source software and future prospects of development. The last 2 sections are related to knowledge management and Deployment of CMS in Knowledge Management. In the last section author proposed action and vision for further development of content management for supporting knowledge management.

Meaning of content management

At the beginning, it is worth discussing idea of the creation of data and content management working in the network. Content management (CM) is the sum of processes and technologies supporting the management, processing, gathering and publishing information in different forms [2]. In the case of network CM, users manage the electronic form of documents. There are many types of content in CMSs [3]. It is mainly text, graphics, charts, videos, animations, and interface of system. Regardless of display content server has equivalent of the contents displayed, their components, generators and elements of database. Content management is not just about sorting the content, collecting and publishing but on effective content storage, recovery and reuse. Administrator of content management systems can set the connection between CMS and data warehousing for better management of large files and advanced data structure. For the proper management, the user has to elaborate the appropriate rules, instructions and the ways of action for users of the system. Systems that support content definitely raise the awareness of individual employees in the whole structure of the organization, clear the scheme of action and exchange of information, organize and support the organizational hierarchy.

Fig. 1. Content Lifecycle

The entire content management process has many meanings in different perspectives. In business aspects content management can be considered as a goal to increase profits. Preliminary analyses give possibilities to check what system is the most appropriate for tasks carried out in the organization. System for content management reduces the time to provide information as well as the data rate increases which has a direct impact on increasing organizations profit. Content Management can also identify missing information and data, thus strengthen the company's position. The consequence of content management at a higher level is a Business Intelligence, which processes data and provides analysis. It can also be an extension of the system on the network. On the other hand, content management can support structure of company and give the division of labor at different positions. Segregation of work according the granted rank and employee level in the organization hierarchy as well as the possibility of verification by higher levels of employees may support organization structure and identify performed tasks. In many ways systems can have the capability of individual work and development of employees and thus provide autonomy of action for the particular employee. From a conceptual point of view content management is the acquisition of information, management and publication of the final results that have been put to the processes of sorting and modifications. Technically this is the architecture of both the user and the server side. The company is perceived by external organizations mainly based on resources and values. A very large part of information is unstructured. In case of their separation and sorting employees can bring new business value. With the appropriate actions presentation, content can be revived and manipulated. IBM presents examples of content management applications in their offer [4]. PPL Energy Company in the United States decided to introduce a solution that abolished problems associated with processing paper documents, reduced their loosing and improper use as well as reduced access time to files structured and unstructured. That software made it much easier to find data documents. Their selection time was reduced from five days to a few seconds. In addition, about 75% decreased time extracting the data necessary for current projects. Employees also can verify whether the messages inside the company, as well as documents, are properly stored. The second example is related with implementation at Iowa State University. Content management system that was installed by IBM definitely improved the transmission of documents by students and data security also increased. The university saves approx. $ 40,000 per year in print. As you can see CM is widely applicable to companies, underscores the value of their business and reduce fixed costs.

Usage of Content Management Systems

Web CMS is a part of content management systems that can be used in a variety of organizations and enterprises. Currently, most CMSs are dynamic pages. Static pages were popular in the 90's of the last century, but currently they are abandoned as standardization of static websites. Static pages don't change content during displaying by user. If there are any changes on the page, an administrator is forced to overwrite the files manually. HTML-based site has advantages and disadvantages. It's very easy and fast to prepare that kind of site. Preparation of static page does not require much effort, thus it is quite cheap. The biggest applications for this kind of websites are simple web business cards. It doesn't require PHP and MySQL database installed on server. Hosting can also be for free. The biggest drawback is the lack of interaction with users. These pages are intended only to provide information unilaterally without any action on the user-administrator. They are therefore generally less interesting than dynamic. The main difference between static and dynamic Web pages is based on the technology of their production. Each static page being part of a larger website must be prepared by the web creator first. The final shape and structure of such a service must be known at the stage of design and preparation.

Fig. 2. Scheme of a static page

Dynamic pages, as opposed to static pages are generated on the fly by the HTTP server on the basis of variables and parameters provided by the web browser. Resident module or other external program is responsible for generating the above-mentioned page. It interprets the commands contained in the script. The entire code generated in this way is based on HTML (tags). How much help is the technique of dynamically generating web pages, let clearly shows a very simple example. The University wants to have a library website. Book collection consists of tens of thousands of items. In the first case designed site have to consist tens of thousands handwritten pages. Any change is going to force overwrite the particular HTML file. In the case of dynamic pages there is one page which allows user to add contents without obligation of adding new files designed from the outset.

Fig. 3. Scheme of a dynamic page

Once pages are generated in real time in front of the HTML server based on the data provided by the program for browsing the Internet. These sites are dependent on the actions taken by the user is currently browsing them. For example, after adding a comment on the page there is a new entry, date and an author. Sometimes they are also given additional user identification data such as IP, browser and version of system. An administrator can change the contents in two ways -first method, client-side use of scripting languages like JavaScript and ActionScript, which make direct changes to elements (DOM. Document Object Model). The main benefits of this method are shorter response times, much less server load and improved interactive effect of the application. It is not required to interact with database, making it easier when employee want to change the code. The second method is called server-side, using programming languages such as PHP, ASP and Perl. This processing is useful for a contact database and a permanent memory, for example validating the user or data exchange.

There are two types of systems in financial terms. The first are paid systems that are usually created for dedicate projects. Paid, commercial CMSs as opposed to base on open source have a high consistency of the whole system [5]. Technology is created in one company or developer. Work in one place or contact through video conferencing and communicators increases compatibility and professionalism of the program because the code is more consistent. Unfortunately, in this case, developers can draw conclusions only after detecting errors. It's impossible to integrate free plug-ins and templates with pay solutions. In the case where a company goes bankrupt it is uncertain support and reduced safety. Work in one room or in constant contact through programs and video conferencing, communication is of a high standard, which significantly increases efficiency in the future and synchronize the entire final product. Content Management Systems under the GNU GPL license are more attractive. Users don't pay for the system and add-ons available on the Internet. Also many templates resources are public and free of charge. The code is regularly updated in the case of most systems like WordPress or Joomla. A huge community operating on platforms strengthens security against possible attacks from hackers. Systems offer easy migration between servers. Current standards of free CMS allow simple export and import data between servers. User needs just to install the plugin and copy the generated files. Free CMSs have intuitive interface developed by thousands of users. Both the administrative panels as front-end pages have a simple scheme adapted for the standard user. Using the website does not require any advanced programming knowledge.

GNU GPL License as a tool supporting CMS developing

WordPress, Joomla and Drupal operate on public license. GNU General Public License says that the program is free software if it performs 4 assumptions [START_REF] Lindberg | Intellectual Property and Open Source[END_REF]:

1. The freedom to run any program under this license, regardless of the purpose. 2. Freedom to analyze and modify the program for improvement. 3. Freedom to provide a program to help other users. 4. The freedom to improve the program and distribute their own modifications. It refers to the entire community.

Open source code means that the whole system and additional plugins are integral and all users can use without paying money. [7] That greatly reduces cost of ownership by administrator. In the current economic situation, these systems have gained in value. Authors give us the ability to view and modify system code. Therefore, users can fully customize the CMS to their needs. Free Content Management Systems have a high utility and application. The same system can be used simultaneously for simple website, which showcase the individual as well as sophisticated management platform for example at the university. Many different commercial organizations use a free content management services. In most cases, open source CMS means better quality [START_REF] Connor | How To Create A Website For Business Or Personal Use[END_REF]. The code is created by thousands of people [9]. Upgrades improve the code and protect the whole system. Open code creates a new community of developers supporting systems. There is many platforms and boards with support in the Internet. Local user groups provide thousands of free templates, designed for system administrators [START_REF] Boiko | Content Management Bible[END_REF]. Skins are divided thematically, and each user will find something for themselves.

The Not all platforms are constantly updated and supported by developers and the community. Only the most popular have the full support and round the clock help among users and the administration. The intuitive interface developed for several years, with thousands of users. Both panels -administrative side and front-end page have a simple scheme adjusted for the standard user. There is no required advanced programming knowledge.

There is no warranty in case of a breakin and other adverse reactions. The user runs the risk of installation on his own responsibility. In case of problems he must contact with a private companies supporting systems or community trust system. Table 1. Advantages and disadvantages of CMS based on the GNU GPL license Systems based on GNU GPL license have many advantages. Their use is widespread in business. For example, the website of the White House, www.whitehouse.gov regularly use Drupal for manage their website. The most popular news media like The New York Times, CNN, Forbes and Reuters have pages based on the WordPress engine while Joomla applicable on linux.com or cloud.com. However, these systems are used only for publishing content and have a function of transfer and delivery information.

Commercial system

Advantages

Disadvantages

Commercial systems have more niche use in projects where standard solutions are not enough. For a fee, buyer get any desired product.

The user of the system must pay for its acquisition, often for technical support and maintenance. Manufacturers also are demanding fees for additional extensions and plug-ins, as well as a new graphical interfaces. High consistency of all modules. If the system is created by a developer or a single team all the elements are more consistent and matched to one another.

Managing such a system is often more difficult than the free solutions, because it is based on original ideas and assumptions, it is not adapted to the standards.

The creators of commercial solutions have an individual approach to the customer. Larger companies give a warranty on the product and in case of failure the immediate technical support and compensation. User is confident that programmer will verify the problem. Proprietary systems are difficult in personalization. For open source systems user can view available extensions and build a page by adding existing modules. In the case of commercial applications usually tools are written from scratch, and the final result can be seen only after the completion of the order. The user can secure the uniqueness. When paying for an exclusive license, buyer is sure that the graphical user interface or mechanism of action is not used by any other website on the Internet.

For small business systems cannot be fully secure, due to the many possibilities of attack and a small number of computer support system.

Table 2. Advantages and disadvantages of commercial CMS

Deployment of CMS in Knowledge Management

During the implementing of content management system employees have to verify metadata system that is abstract layer supporting the activity of the platform.

Organizational interests of group can be divided into 8 separate entities [ Defining the objectives and requirements is necessary to create the system. In this case they must clearly identify the use of system and its benefits. A goal is something that an organization wants to accomplish. A requirement is a thing that the designed system must do, be, or have to meet organization goals. The requirements and objectives are closely linked and the system design must be specifically defined. In order to determine the objectives and requirements manager downloading the full reports on the functioning of the organization from all locations. Audience's layer defines target audience. The system interface should be adjusted depending on the type of customers/users, its functionality and performance. All the layers are linked to each other and have appeal. It should be noted that the audiences mainly define external users who are merely recipient of system. For example, if the bank's website, in which a group of employees will put information from a particular area of the company, most customers will have read-only attribute information without interfering with them. Publications and content types are an important part of the scheme of the whole content management system. Publishing of content and the way of system managing have a big impact for the functioning of the entire organization. It can be archive old data, exchange of current information and publication of reports or other type of data. The systems are currently compatible with the most of file types including videos, photos, graphics, XML files and so on. The authors are a group of people who have an access to back-end website. They can edit and modify the content in the whole system. Note that the attributes of individual users of the system are different. Team Manager must have more attributes than members of his team to verify and control work. Acquisition sources are needed to provide a source files implemented in the system. An important issue is the compatibility of the external media with hardware and software that supports system. Workflow and staffing -workflow is an event or a sequence of events that are performed in the CMS. It defines a constant user activity or one-time execution of the element. Access structure informs about privileges of users and provides list of users. It also contains relationships between them. Systems allow create the groups of users with broader availability.

Content management systems fully support the idea of knowledge management in companies and organizations. Knowledge management is a modification of tacit knowledge into explicit knowledge and sharing it within the company/organization [START_REF] Mach | Validation as the Integral Part of a Knowledge Management Process[END_REF]. It is an attempt to make the best use of the knowledge that is available in organization, create new knowledge and increase its understanding. Knowledge management can also be regarded as a process which operates the acquired knowledge. This perspective of understanding of knowledge management is described in [13] Knowledge accumulating: known as knowledge acquisition, data mining and machine learning -can be automated for extracting knowledge from relevant documents or simply -database files.

Knowledge creating -knowledge modelling, knowledge representation (in fact, all activities useful in a development process) are phases arising from methods elaborated in "knowledge engineering environments". Knowledge sharing -modern technologies (including intelligent browsers) offer almost unlimited access to knowledge resources from any place. For example: a wellconceived e-commerce application contains knowledge on products and services, is able to explain how to use products in given contexts, how to connect several devices together, etc.

Knowledge application -completing the whole process with practical using knowledge-bases in specific environment. In other words, some patterns how to use knowledge to solve different problems are proposed and implemented.

Therefore, from a technical point of view, knowledge management can also be a process of acquiring knowledge, later processing and sharing and finally implementing. There are also other points of view of term knowledge CMSs increase finding speed of knowledge, organize current scheme the storage and work as a tool for management of information thereby increasing the capacity for knowledge management. Additional functionality like an expert systems built-in content management systems such as WordPress, Joomla, Drupal can support fully the process of knowledge management in the company [START_REF] Tiwana | Knowledge Management Toolkit[END_REF]. Resources are properly stored and delivered with user access levels. Knowledge management is an interdisciplinary field. Operating systems on a network can assist in this process in various aspects. Open CMSs help to operate with data stored in files and repositories. Many plugins can support with decision making and help desk working. Expert systems added as a plugins represent artificial intelligence and advice for users / workers [START_REF] Ruggles | The State of the Notion, Knowledge Management in Practice[END_REF]. -Research what elements of Knowledge Managements can be implemented in Content Management Systems Content Management system is a tool that will be aimed at supporting the process of Knowledge Management. As a preliminary we have to estimate future functionality and usability of system. The prototype of system supporting knowledge management should be based on a specific example. During the implementation in a particular industry or company, we are able to determine the success of the subsequent implementation. After the final installation we can fully understand sense and utility the entire project. Theoretical assumptions can only be the basis for the later creation of the system. The main elements of knowledge management, which can be used in creating a system for an organization, are focused around the use of current knowledge and acquiring new knowledge. We can group them in several areas. The first is about generating and acquiring new knowledge from both organizations as well as from the external environment. The system should encourage contributors to share knowledge and enable information transfer between all of them. Issue what goes hand in hand is related with security of information storage and exchange of knowledge. The administrator must ensure reliability and safety.

In case of the most popular systems based on open source like WordPress there is build-in security and updates. The administrator should ensure compatibility for those who have access to the organization, mainly available in all browsers and operating systems. Getting the information, we need to organize representation of knowledge in documents, databases, external files and software. Success of the system is depending on final product. Last area is focused on measuring the value of knowledge, adequate and reasonable use of knowledge and streamlining the flow of knowledge throughout the system.

-Study what parts of Content Management have common areas in Knowledge Management.

We need to verify what elements supporting knowledge management can be implemented into the system. Some of them such as sorting parts, storage and aggregate elements and expertise systems are already in the early stages of use and can be implemented to create a new system.

2. Development of extensions for systems.

-Create new elements of CMS supporting organization in Knowledge Management like artificial intelligence widgets, plugins and scripts.

The area of knowledge management in content management systems is still undiscovered and there are no designed concepts that can be exploited. The system should be modified in the organization and include intuitive interface for all users. In the initial part of implementation, users will get testers status and the administrator should increase the frequency of database backup.

Ruddy Ruggles prepared a report -The state of the Notion: Knowledge Management in practice, source: [16] saying what are desirable actions during the implementation of projects which can support knowledge management. All tasks were divided into three groups: projects in a company that have already realized and current projects that are currently being implemented in the enterprise, intentions purposes to be carried out and what they should prepare to streamline work. In case of content management systems most of the objectives can be achieved by an appropriate modification of the system. Executives acknowledged that current activities are focused on the implementation of intranet, creating knowledge repositories based on data warehousing, implementing decision-support tools creating groupware to support collaboration. The first one -intranet can be achieved in CMS by setting the system in local server or sharing in the Internet but reserving access relevant rigidities. The platform could serve both assumptions -intranet and extranet but only if a low degree of secrecy of data. Banks and other organizations that store customer data they cannot afford to provide data beyond the walls of the institution. Most of content management systems are prerequisites for data warehouse. Using the database, mainly MYSQL, fulfills this.

Fig. 7. Database location in CMS

The graphic above shows location of database in the interaction between CMS and server. Content Management System consists database, html files which are located mainly in PHP files and other files and multimedia like pictures, PDF files and so on. All these elements are put together and displayed by the server in an intelligible form for the user. System interface supports user and administrator to manage large amounts of data. Media and other external files can be classified as a data. The third project is focused on implementing decision-support tools. Support tool for knowledge is an essential component for organization to begin the process of knowledge management. If there is no specific rules and workflows for decision-making employees have a limited range of help and support. This is detrimental for process of knowledge management. What is interesting executive need to implement mapping sources of internal expertise and establishing new knowledge rules. One of the main tasks in organization enabling effective use of their knowledge is finding and defining a knowledge resources. Knowledge maps help in the future in developing business plans, planning, managing time and tasks, reporting, project management, analysis, preparation offers and many others. Content Management System could be a perfect tool to create such a map. Diagram shows the steps in creation of knowledge map. 3. Testing new ideas for case study in business.

-Test of widgets and plugins installed on the server and cloud.

Business greatly supports and promotes science. Companies and organizations can create and test a case study that will indicate the right way of development of the system. They must provide a layer of practical use both before the implementation and during the testing. Case study can also answer the questions what elements of the company have to virtualize.

4. Implementation of developed solutions in enterprise.

-Analysis of the implemented elements in organization.

The next post-implementation step is related with assessment of compliance with the assumptions. Workers prepare reports and analyze changes in the system.

-Conclusions and improvement.

After the completion of entire cycle designer should apply patches on the system and draw up a final report and conclusions.

Identification of elements that use a knowledge in organizations such as problems, processes and queries Identification of sources of knowledge in the indicated processes Dissemination and standardization of knowledge to make it accessible and understandable to everyone in the organization Creation of graphical interface for users to intuitively navigate through the information. In the second part design a mechanism which allows updating and modifying flow of knowledge

Conclusion

The article presents a role of content management systems in knowledge management. To understand the importance of systems application author defined a content management, cycle of content in organizations and showed the priorities and objectives of the organization from information and data perspective. On theoretical grounds it was created last chapter which contains information how to merge both of areas. Author decided to divide explored issues into the following steps: Development schemes and operating instructions which can be specified between research what elements of Knowledge Managements can be implemented in Content Management Systems and study what parts of Content Management have common areas in Knowledge Management. The next step is focused on extension to the system which includes creating new elements of CMS supporting organization in Knowledge Management like artificial intelligence widgets, plugins and scripts. This is the practical part of the action based on the findings of theoretical. Then testing new ideas for case study in business and implementation of developed solutions in enterprise. These steps include full study of content management systems for knowledge management. Nowadays, managers and directors are increasingly aware that the role of management in the organization is fairly important, how it can positively affect for organizational structure, enterprise profits and performance of employees. From the perspective of a market it could have a positive impact on ahead of the competition.

It is not possible to achieve the organization's objectives without the use of knowledge, technology and employees. It is definitely still undeveloped area which can support knowledge management in the enterprise and pursue its objectives, which are usually improving the organizational structure, increase profits and proper management of information and knowledge.

Fig. 4 .

 4 Fig. 4. What is Knowledge Management (source: Benjamins, V.R., Knowledge Management in Knowledge-Intensive Organizations, 2001)

Fig. 5 . 1 .

 51 Fig. 5. Knowledge Management Disciplines (source: K. Dalkir, Knowledge Management in Theory and Practice, second edition 2011)

Fig. 6 .

 6 Fig. 6. Knowledge Management Disciplines (source: Ruggles R.: The State of the Notion, Knowledge Management in Practice. California Management Review vol. 40 no. 3, Spring 1998)

Fig. 8 .

 8 Fig. 8. Knowledge map creation process.

Fig. 9 .

 9 Fig. 9. Components needed for knowledge management

  following tables compare the advantages and disadvantages of systems based on open source and commercial platform:

	CMS based on open source
	Advantages		Disadvantages
	Users do not pay for the system and	Getting more unwanted messages
	add-ons available on the Internet. High	commonly called spam, such as
	availability of free templates	advertising, system notifications from the
		creators
	The code is updated regularly for the	No custom applications. For individual
	most popular type systems like	processes and mechanisms, an open
	WordPress or Joomla. With a massive	system	may	not	include	such
	community security attacks is high.	functionality.
	Easy migration between servers.
	Current standards of free CMS allow
	import and export database and files to
	another server. User have to install the
	plugin and copy generated files.


Mieczyslaw Owoc
email: mieczyslaw.owoc@ue.wroc.pl

Krzysztof Hauke
email: krzysztof.hauke@ue.wroc.pl

Pawel Weichbroth
email: pawel.weichbroth@zie.pg.gda.pl

Mieczysław Owoc

Paweł Weichbroth

Knowledge-Grid Modelling for Academic Purposes

Keywords: Knowledge Grid, Knowledge Management, Ontology

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

These days, people and machines produce countless volumes of data and information, consciously and intentionally transformed into knowledge. Undoubtedly, the value of the obtained information and knowledge varies from a theoretically low value with a small number of applications to being widely appreciated (new theories and inventions) with a universal usage. In particular, knowledge generated and disseminated in academic and institutional research centres should be considered as an extremely precious resource for civilization.

The crucial quest is how to manage the scientific achievements attained in "knowledge centres" in order to fulfil all knowledge management expectations starting from the capture of knowledge through to its usage. All the steps performed in the broad sense of knowledge management lead to the formulation and maintenance of knowledge structures, therefore a key point is the care of knowledge dynamics including multidimensional aspects of the functioning of knowledge. Exploring the essence of collective intelligence is another key scientific challenge.

In considering a systematic approach to a global vision of a knowledge environment, we focus on collections or "islands" of wisdom -so the very natural concept of a knowledge grid initiated at the beginning of this century by Mario Cannataro and Domenico Talia in Europe and Hai Zhuge in China. In this context, we can say that human imagination, combined with expertise, and internal and external information, may serve as a medium to produce new non-trivial knowledge. Thus, knowledge may be regarded as a product of cognitive processes and is of great importance for solving many complex problems in a variety of domains.

The concept of a knowledge grid as a potential method of knowledge acquisition and management will be presented in the next section. The ultimate goal of broadly understood university knowledge is the performance of all essential activities pertaining to gathering and maintaining knowledge resources.

This chapter is organized as follows. In the next section the state of the art of the knowledge grid and related terms are given. In the third section, the selected domains of university knowledge management are discussed. In the fourth section, the models of university knowledge are depicted and described. The last section provides final conclusions.

Knowledge grid and ontology

The presence of numerous information resources is typical for an information society. We live in a world where countless systems deliver huge amounts of data that is not only necessary for operational management but also for more advanced applications including research and educational purposes. These last two are especially essential and valid in the case of the academic environment. In order to assure access to the results of educational and research activities we need advanced tools that contain knowledge resources, among which we can enumerate the following entities: courses, publications, projects, etc.

All of the aforementioned categories arise in a plethora of different fields thus creating specialized knowledge grids. Without doubt, the development of such a platform is a tremendous challenge, therefore many aspects of knowledge management should be taken into account -additionally, models prepared for this purpose should be multidimensional.

According to general assumptions of a knowledge grid (KG), distributed knowledge resources can be offered as a set of services supporting research, innovation and decision-making processes (compare with [START_REF] Zhuge | The Knowledge Grid. Toward Cyber-Physical Society[END_REF]). Therefore, a KG is an essential tendency in improving endeavours that deal with acquiring and maintaining different forms of collective knowledge and thus is investigated in terms of several important aspects. Generally speaking, three research streams seem to be crucial in the presentation of the related work: surveys on KG process infrastructure, an exploration of KG usability and an inquiry into KG features and effectiveness.

Surveys on knowledge grid processes are focused on an investigation of the components and transformations performed in KG frameworks. There are several papers devoted to one or more processes connected to KG concepts. Knowledge acquisition in a distributed environment is, in particular, one of the hottest topics; there are several authors that study this specific field: Shaw [START_REF] Shaw | A Grid-Based Tool for Knowledge Acquisition: Validation with Multiple Experts[END_REF], Bhatia & Yao [START_REF] Bhatia | A New Approach to Knowledge Acquisition by Repertory Grids[END_REF], Ford & Petry [START_REF] Ford | Knowledge Acquisition from Repertory Grids Using a Logic of Confirmation[END_REF], as well as Talia & Trunfilo [START_REF] Talia | How Distributed Data Mining Tasks can Thrive as Knowledge Services[END_REF], and Goble et al. [START_REF] Goble | ODESGS Framework, Knowledge-based Markup for Semantic Grid Services[END_REF]. All of the aforementioned researchers have dealt with techniques and tools. Other researchers focused on the integration and platforms necessary in KG processing, namely: Mancilla-Amaya et al. [START_REF] Mancilla-Amaya | The E-Decisional Community: An Integrated Knowledge Sharing Platform[END_REF] who stressed the E-decisional community as an integrated knowledge shar-ing platform, and Cannataro & Talia [START_REF] Cannataro | The Knowledge Grid[END_REF], and Berman [START_REF] Berman | From TeraGrid to Knowledge Grid. Integrating distributed resources into cohesive, virtual supercomputers[END_REF] who pictured parallel and distributed knowledge discovery platforms. The lack of proposals on how to model a KG is still challenging for research teams.

Concepts of a knowledge grid can be implemented in many areas. The exploration of KG usability in different sectors, and some individual contextual demands, are critical for successful implementation. Skodras [START_REF] Skodras | GRID Technologies => 'Education' = 'Distance Education[END_REF] checked the technologies that dealt with grid implementation in the educational sector, while Zhuge [START_REF] Zhuge | China's E-Science Knowledge Grid Environment[END_REF][START_REF] Zhuge | Discovery of Knowledge Flow in Science[END_REF] discussed the discovery of knowledge flow in science. Similarly, Qin & Fahringer [START_REF] Qin | A novel domain oriented approach for scientific grid workflow composition[END_REF], and Tofan et al. [START_REF] Tofan | Capturing Tacit Architectural Knowledge Using the Repertory Grid Technique[END_REF] made a survey about a novel domain-oriented approach for scientific purposes (compare with [START_REF] Ćurčin | Discovery Net: Towards a Grid of Knowledge Discovery[END_REF][START_REF] Mangalwede | Context-Aware Intelligent Multi-Agent Technology in Knowledge Grid Environments for E-Learning Systems[END_REF]). In all of these papers, scientific orientation is present in grid visions.

The third research stream refers to grid properties and effectiveness. Zhuge introduced KGOL -a specialised language prepared for making operations on a knowledge grid [START_REF] Zhuge | KGOL: A Knowledge Grid Operating Language[END_REF]. Grid density and attraction, as important properties of stream data clustering, were considered by Tu & Chen [START_REF] Tu | Stream Data Clustering Based on Grid Density and Attraction[END_REF]. The last example of work represents inquires into the discussed topic and refers to effective keyword search [START_REF] Pallis | Effective Keyword Search for Software Resources installed in Large-scale Grid Infrastructures[END_REF].

The topics presented in the discussed papers only partially cover the actual challenges of the KG area. However, the modelling of a knowledge grid for universities was not directly mentioned in any of the aforementioned papers. The special properties and components in such a model should be included in the hereby presented model.

Ontology, a term borrowed from philosophy, has played an essential role in computer science since 1967. According to T.R Gruber an ontology denotes an explicit specification of a conceptualization [START_REF] Gruber | Towards principles for the design of ontologies used for knowledge sharing[END_REF]. The body of knowledge representation is based on the conceptualization of the following categories: objects, concepts, terms and other entities, which by definition are in the area of interest. There are certain relationships among the defined categories which fulfil the picture of the described domain and its parts. In other words, it is an abstract, a phenomenon in which we are able to recognize important concepts. Formality refers to the possibility of processing ontology by a computer system, uniqueness means the definitive (primary) meaning of all concepts, and clarity indicates that their usage should be determined directly.

B. Smith singled out two approaches for the development of ontologies: relevance and reductionism [START_REF] Smith | The Relevance of Philosophical Ontology to Information and Computer Science[END_REF]. The first is the search for taxonomy beings, in line with reality at all levels of aggregation from the micro-world to the cosmological. The second perception of reality takes place through the prism of a privileged being; the ontology is the result of the decomposition of reality into smaller components or the result of a reduction of the multiplicity of types. Thus, generally, in a first approach analysis things lead to a general description of all the entities, and subsequently, only a limited set of them is taken into consideration.

The main questions referring to the representation of crucial knowledge grid components as ontology objects concern the following:

 What kind of categories must be considered in order to cover the main academic activity areas?  Assuming a multidimensional approach to modelling a university knowledge grid, the quest relates to potential aspects of the ontology built.

 The problem of how to present the discovered relationships among identified categories in such organizations is fundamental. In addition is the quest about how to transform the knowledge grid in terms of using operators to generate new pieces of knowledge in order to achieve new generations of this knowledge (a topic partially presented in [START_REF] Owoc | Transformations of the Knowledge Grid. Ontological foundations[END_REF]). The itemised quests will be established as a starting point to create an ontology in the following sections.

3

Selected domains of university knowledge management

Universities identified traditionally as higher education institutions play different roles in modern society. The first aspect of this relates to considering universities as organizations with determined goals and resources. Secondly, the main activity of such educational institutions is to provide facilities for teaching. Thirdly, in order to extend academic knowledge and scientific abilities, research specific for particular areas should be performed. Therefore, any university should deliver the mentioned activities: learning and research using the available resources which are components of the general university infrastructure. Selected aspects of particular knowledge management will be presented in the next section.

In considering any university as an institution with advanced information resources, a need for knowledge management (KM) appears. Therefore, complex IT infrastructures create the fundamentals of knowledge organization including an organizational culture as essential factors of the whole knowledge management process. At the very least the following factors for KM processes (apart from the mentioned organizational culture, IT infrastructure and knowledge organization) should be itemised: knowledge measurement and effective and systematic processes (see [START_REF] Al-Oqaily | Success Factors of Knowledge Management in Universities (A Case Study: Jordanian Private Universities)[END_REF]). To be more precise: there are real interconnections between these factors and, in particular, certain additional impacts can be included, for example: direct influence of qualification levels on knowledge organization and knowledge measurement, years of experience on both the defined factors and finally, searching time and effort connected with systematic processes. All these factors are present in any academic center -the graph in Figure 1 reflects the interconnection between the mentioned factors and determinants.

Fig. 1. Interconnection between KM Success Factors and Determinants

Source: [START_REF] Al-Oqaily | Success Factors of Knowledge Management in Universities (A Case Study: Jordanian Private Universities)[END_REF] Organizational Culture

IT Infrastructures

Knowledge organization

Knowledge measurement

Effective and Systematic processes

Qualification Levels

Experience Years

Searching Time and Effort

The concept of knowledge management needs a discussion about the people involved in particular phases of the process performance. Very often these staff are referred to as knowledge workers (see [START_REF] Mostak | Knowledge Management in Universities: Role of Knowledge Workers[END_REF]). The following roles are defined in order to cover the main domains of university activities (teaching, research and service): analysts, engineers and stewards. All the mentioned staff are responsible for keeping organizational knowledge in universities.

The preparation of an ontology for the whole university can be started from specific areas or aspects. In designing intelligent services for a smart campus, focused on people, infrastructure (including: buildings, rooms, grounds) and other instruments and tools [START_REF] Somsuphaprungyos | Ontology-based Framework of Intelligent Services for a Smart Campus[END_REF]. These categories are essential in an ontology oriented on services.

Considering the assumptions of a smart university model for education, different perspectives and priorities should be included. Coccoli et al. (see: [START_REF] Coccoli | Smarter Universities. A Vision for the Fast Changing Digital Era[END_REF]) focused on opinion collection (supported by data mining algorithms) to generate some visions of teaching. In such an approach, the ontology is limited to standards existing in a university (see Figure 2).

A more global approach is evident in the case of Knowledge Management System (KMS) implementation. Basically, three areas must be included in order to cover all the essential domains of university activities: Research, Education and Management. In M. Oprea's proposal of KMS [START_REF] Oprea | A University Knowledge Management Tool for Academic Research Activity Evaluation[END_REF] these areas are considered as a crucial background for a prepared university portal -see Figure 3.

Fig. 2. The model of a smarter university

Source: [START_REF] Coccoli | Smarter Universities. A Vision for the Fast Changing Digital Era[END_REF] The discussed solutions of university knowledge management components are important in the ontology presented in the next section.

4

Ontology of academic knowledge

Short presentation of Ontorion

The Ontorion Fluent Editor is a comprehensive tool for editing and manipulating complex ontologies, developed in Controlled Natural Language [START_REF] Kapłański | Controlled English interface for knowledge bases[END_REF]. Controlled English is the main built-in feature, which makes this tool more suitable than other XMLbased OWL editors. It is also supported via Predictive Editor, which prohibits one from entering any sentence that is grammatically or morphologically incorrect and actively provides help to the user during sentence writing [START_REF] Seganti | Collaborative Editing of Ontologies Using Fluent Editor and Ontorion[END_REF].

For each edited OWL file, a taxonomy tree is built upon data from this file and all the included ontologies. Each tree can be visualized using a user-friendly palette of colours and divided into four parts: thing (shows "is-a" relations between concepts and instances), nothing (shows concepts that cannot have instances), relation (shows the relations hierarchy between concepts and/or instances) and attribute (shows the attributes hierarchy).

In our opinion, the implementation phase of the creation of an ontology is a straightforward task, because a user just types simple sentences expressing dependencies between things at the assumed level of detail using the editor available in Fluent Fig. 3. The structure of a generic University Knowledge Management System Source: [START_REF] Oprea | A University Knowledge Management Tool for Academic Research Activity Evaluation[END_REF] Editor. The package for the created documents provides automatic and real-time help in several ways, such as: hint box, predicted word list and syntax error markers [START_REF] Kapłański | Cognitum Ontorion: Knowledge Representation and Reasoning System[END_REF].

Models of a university knowledge ontology

In order to present an ontology for knowledge management embracing crucial areas for university purposes three models representing: research, education and management are necessary. All of the models are presented in the form of "Documents" (describing components of each particular area) and "Force Directed Layouts" (visualising relationships coming from the introduced components).

In Figure 4 a partial description of the educational area for university knowledge is presented. Particular statements express categories and relationships among the defined objects including their instances. The presented ontology can be extended through more detailed characteristics of the concrete objects and instances, as well as through the insertion of new elements and rules essential in the domain.

A graphical form of this domain is presented in Figure 5. There are several relations among the defined concepts/instances, determining the roles (be-part-of, teach, taught, participate) or goals of relationships (need, implement). The effects of education can be clarified as acquired knowledge, possessed abilities or social competences.

Fig. 4. Sentences describing educational university knowledge

The next part of the presented ontology concerns the research area of university activities. The following parts constitute the content of the described domain: Researcher, project, source, publication, infrastructure and result -see Figure 6 [START_REF] Owoc | Toward knowledge-grid model for academic purposes[END_REF].

The list of relations proposed for this sector includes the behaviour of concepts (direct, participate) or their functionality (generate, need, provide, received and use). 7 shows interconnections between objects and instances according to their defined roles and functionalities. Some of the presented objects or instances can be divided into smaller parts; for example -"Infrastructure" representing tools, materials, teams and funds necessary for the undertaken projects.

Similarly, the "Source" can be represented in many ways -in particular as the result of external projects or publications. In practice, a large number of interconnections is typical for advanced projects.

The last, managerial, area of the presented knowledge management seems to relate to any institution but some elements are specific for academic purposes. In Figure 8 the particular components represented are not limited just to a list of typical categories: departments, positions, staff, but additionally include more global objects present in previous descriptions such as "Education" and "Research". In the last part of the ontological approach to the description of university knowledge we focus on potential aspects of knowledge perspectives. At least three aspects must be considered: time, space and social. In all previously presented ontologies these aspects can be applied. The document presenting the initial version of this problem is proposed in Figure 10.

The infrastructure of a university is presented as the three previously presented domains: Management, Education and Research, with specific relationships to the category University. Additionally, three aspects are underlined: Time, Area and Social. Special features representing particular domains are subordinated to Management, Education and Research, respectively. In practice these aspects can express the social characteristics of all the domains and the activeness of university staff in the defined areas (Research and Education are selected as examples). The third dimension "Time" denotes versions of the Research, Management and Education solutions through time.

The graphical form of the determined relationships is shown in Figure 11. University, as the three joined domains of Education, Research and Management represents very specialised roles fulfilled in these areas (offered, lead and bemanaged-by, respectively). Concluding, the presented ontology describing university categories can be applied to any educational and research institution at least as an initial framework for the creation of real knowledge management systems.

Conclusions

For such organizations as universities, knowledge has always been the most crucial and prominent asset together with academic scholars and teachers. Previous attempts at the presentation of knowledge management in universities were limited to discussions about essential factors determining successful knowledge management processes in universities, knowledge workers in the educational sector or the presentation of a general infrastructure for the creation of university knowledge systems.

Undoubtedly, academic knowledge represents all features typical for a knowledge grid approach. Especially in the case of presenting the three domains of the university structure: managerial, educational and research. An analysis of KG infrastructures present in universities allowed for the modelling of these three domains and the presentation, on the surface, of relatively autonomous ontologies describing the main categories and relationships for Management, Education and Research. Additionally, an integrated perspective considering three aspects of university knowledge: time, area and social was proposed as a three-dimensional ontology typical for academic centres.

The elaborated version of an academic ontology should be extended through the insertion of dynamic features of the knowledge management process. For example, particular models can be enriched with the validation of knowledge models or with proposals of the implementation of active rules for the defined categories. This way Fig. 11. Sentences describing university knowledge aspects our further research will allow for more advanced solutions in academic knowledge management systems.

Fig. 6 .Fig. 5 .

 65 Fig. 6. Sentences describing research university knowledge

Fig. 7 .

 7 Fig. 7. Graph presenting research university knowledge

Fig. 8 .

 8 Fig. 8. Sentences describing managerial university knowledge

Fig. 9 .

 9 Fig. 9. Diagram presenting managerial university knowledge

Fig. 10 .

 10 Fig. 10. Sentences describing university knowledge aspects