On the Fattorini Criterion for Approximate Controllability and Stabilizability of Parabolic Systems

In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type $y'=A y+Bu$. We precise the result proved by H. O. Fattorini in \cite{Fattorini1966} for bounded input $B$, in the case where $B$ can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini's criterion is satisfied and if the set of geometric multiplicities of $A$ is bounded then approximate controllability can be achieved with finite dimensional controls. An important consequence of this result consists in using the Fattorini's criterion to obtain the feedback stabilizability of linear and nonlinear parabolic systems with feedback controls in a finite dimensional space. In particular, for systems described by partial differential equations, such a criterion reduces to a unique continuation theorem for a stationary system. We illustrate such a method by tackling some coupled Navier-Stokes type equations (MHD system and micropolar fluid system) and we sketch a systematic procedure relying on Fattorini's criterion for checking stabilizability of such nonlinear systems. In that case, the unique continuation theorems rely on local Carleman inequalities for stationary Stokes type systems

COMPUTING THE FROBENIUS NUMBER

17 pagesInternational audienceAbstract.The Frobenius number $g(A)$ of a finite subset $A\subset \N$ such that $\gcd(A)=1$ is the largest integer which cannot be expressed as $\sum_{a\in A}ax_{a}$ with non-negative integers $x_a$. We present an algorithm for the computation of $g(A)$. Without loss of generality we suppose that there exist $a,b\in A$ such that $\gcd(a,b)=1$. We give a formula for $g(A)$ in the particular case that for all $c,d\in A$, $c+d$ can be written in the form $c+d=xa+yb$ with $x,y\geq 0$ (e.g. $c+d>ab-a-b$). Using Euler polynomials we give a formula for $g(A)$ in the case that $A=\{a,b,c\}$

Frobenius number of a linear Diophantine equation

Commutative ring theory and applications (Fez, 2001), 23--36, Lecture Notes in Pure and Appl. Math., 231, Dekker, New York, 2003International audienceWe denote by N₀ the set of nonnegative integers. Let d≥1 and A={a₁,...,a_{d}} a set of positive integers. For every n∈N₀, we write s(n) for the number of solutions (x₁,...,x_{d})∈N₀^{d} of the equation a₁x₁+⋯+a_{d}x_{d}=n. We set g(A)=sup{n∣s(n)=0}∪{-1} the Frobenius number of A. Let S(A) be the subsemigroup of (N₀,+) generated by A. We set S′(A)=N₀\S(A), N′(A)= CardS′(A) and N(A)= Card S(A)∩{0,1,..,g(A)}. Let p be a multiple of lcm(A) and F_{p}(t)=∏_{i=1}^{d}∑_{j=0}^{(p/(a_{i}))-1}t^{ja_{i}}. We give an upper bound for g(A) and reduction formulas for g(A),N′(A) and N(A). Characterizations of these invariants as well as numerical symmetric and pseudo-symmetric semigroups in terms of F_{p}(t), are also obtained

PREDIKSI KEBANGKRUTAN MENGGUNAKAN MODEL ALTMAN Z-SCORE, SPRINGATE DAN ZMIJEWSKI (Pada Perusahaan Food and Beverage yang Terdaftar di Bursa Efek Indonesia Tahun 2013-2016)

Penelitian ini bertujuan untuk mengetahui perbedaan secara statistik antara prediksi kebangkrutan model Altman Z-score, Springate,dan Zmijewski. Penelitian dilakukan pada perusahaan Food and Beverage terdaftar di Bursa Efek Indonesia periode 2013-2016 dengan sampel sebanyak 13 perusahaan yang di ambil dengan metode purposive sampling. Penelitian ini menggunakan metode kuantitatif dengan data sekunder berupa laporan keuangan sampel yang dipilih. Teknik analisis data dalam penelitian ini menggunakan formulasi prediksi kebangkrutan model Altman Zscore, Springate, dan Zmijewski yang diolah dengan bantuan aplikasi Ms. Excel. Uji hipotesis, menggunakan Kruskal-Wallis Test melalui aplikasi SPSS pada taraf signifikasi =0,05, dimana Ha diterima jika < . Hasil penelitian menunjukan berdasarkan perhitungan rata-rata selama empat tahun prediksi kebangkrutan model Altman Z-score, perusahaan yang berpotensi mengalami kebangkrutan yaitu ALTO, INDF, ROTI, pada grey area yaitu ICBP, MYOR, PSDN, SKBM, SKLT dan ULTJ, perusahaan yang diprediksi sehat yaitu CEKA, DLTA, MLBI. Berdasarkan prediksi kebangkrutan model Springate, ALTO dan PSDN yang berpotensi mengalami kebangkrutan. Berdasarkan prediksi kebangkrutan model Zmijewski hanya MLBI yang berpotensi mengalami kebangkrutan. Hasil uji hipotesis menunjukan terdapat perbedaan yang signifikan antra prediksi kebangkrutan model Altman Z-score, Springate dan Zmijewski (0,000 < 0,05)

Regulatory and legislative monitoring for better management and decision-making

International audienceThis paper deals with regulatory and normative monitoring which is considered as a crucial issue for exporting companies that require developing their economic activities according to international expectations. After reviewing the main support and experiences that aim to alert decision makers about regulatory and normative changes, we examine the "Alert export" service developed by the institutes of standardization to improve monitoring practices and focuses on the Tunisian expertise. How can this service improve decision-making? What is its real impact on the local economic intelligence? And what are the futures challenges? The results of a case study presented in this paper answer these questions and show the specificity of Alert export service in the Tunisian context. The discussion about the study case leads us to suggest some improvement to support performing enterprise management and permit better integration of the local economic intelligence at an international scale

Case Base Mining for Adaptation Knowledge Acquisition

In case-based reasoning, the adaptation of a source case in order to solve the target problem is at the same time crucial and difficult to implement. The reason for this difficulty is that, in general, adaptation strongly depends on domain-dependent knowledge. This fact motivates research on adaptation knowledge acquisition (AKA). This paper presents an approach to AKA based on the principles and techniques of knowledge discovery from databases and data-mining. It is implemented in CABAMAKA, a system that explores the variations within the case base to elicit adaptation knowledge. This system has been successfully tested in an application of case-based reasoning to decision support in the domain of breast cancer treatment