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According to the definition of the German medicine law (AMG 2001), pharmaceuticals are, amongst other things, intended to heal, to mitigate or prevent in their application in the human or animal body, diseases, suffering, body damage or pathological burdens. The undisputed positive purpose of pharmaceuticals and the question of cost budgeting has, in the recent past, limited the room to critically consider, from an environmental perspective, the possible unwanted side effects arising from medicament consumption in Germany. In the German Federal state in 1999 alone the five most important and available pain and rheumatism drugs had approximately 39 tonnes of active substances which, in pharmaceuticals for humans, contained 2.1 tonnes of active antibiotic substances (Abbas and Kratz 2000; BLAC 2001). These biologically high-activity materials are partly converted after intake in the human body and separated afterwards into original and converted forms (BLAC 2001). Within the sewage waters, these residues arrive at the sewage treatment plant, at which point they are often undesirably, incompletely mitigated or held back in surface waters (BLAC 2001).

Eigenvalue problems for symplectic difference systems are considered. The main result of the paper, an oscillation theorem, relates the number of eigenvalues to the number of generalized zeros of solutions.

We extend recently established two-sided or O-Tauberian results concerning the summability method D θ , a based on the Dirichlet series Σa n e - θ n x to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which D θ , a -summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high index case we even obtain a new result for such methods. Our method of proof uses asymptotic properties of the Dirichlet series subject to the assumption that an and An can be interpolated by smooth functions. In addition we develop refined Vijayaraghavan-type results which enable us to infer the boundedness of sequences from the boundedness of their D θ , a -means and the one-sided Tauberian conditions.

Les donnees de chute de litiere, essentiellement des chutes d'aiguilles, etaient disponibles pour 64 sites le long d'un transect depuis le cercle polaire en Scandinavie (41 sites) jusqu'au Sud de l'Espagne (22 sites supplementaires en Europe continentale) et un site dans le mid-ouest americain. Les donnees proviennent de huit especes de Pin. Des regressions ont ete calculees principalement pour la chute d'aiguilles et dans certains cas pour la chute totale de litiere. Il existe une relation lineaire hautement significative entre la chute des aiguilles et la latitude (R 2 adj = 0.285; n = 58; p < 0,001) lorsque l'ensemble des donnees pour toutes les especes sont utilisees. La combinaison des sites en climat boreal et atlantique donne un R 2 adj de 0.732 pour n = 45 (p < 0,001). Une relation lineaire multiple, utilisant l'âge du peuplement, la latitude et la surface terriere est hautement significative et donne un R 2 adj de 0.412 (n = 54; p < 0.001). La meilleure relation lineaire, pour les retours d'aiguilles chez le Pin sylvestre en Scandinavie a ete obtenue en utilisant comme variables predictives l'indice de fertilite stationnelle « H 100 » (R 2 adj = 0.349), la latitude (R 2 adj = 0.331), et la surface terriere (R 2 adj = 0.324) alors que la regression sur les variables altitudes et âge des peuplements etait significative seulement a p < 0,01. Une fonction X 2 pour l'âge du peuplement ameliore la relation avec l'âge, R 2 adj = 0,243. Les relations multiples entre la chute des aiguilles et la latitude associee a la surface terriere et celle associee a la surface terriere plus l'âge, pour les sites Scandinaves, sont hautement significatives (R 2 adj = 0,605 et R 2 adj = 0,661, respectivement, avec n = 41). La procedure de regression progressive sur les donnees des memes sites, combinaisons des variables latitude, indice de fertilite, surface terriere et âge du peuplement permet d'expliquer 78 % de la variation de la chute des aiguilles. Des relations hautement significatives ont ete calculees sur les donnees des retours totaux de litiere, utilisant la meme methodologie sur 32 des sites. Elles demontrent que la quantite des chutes des seules aiguilles peut etre utilisee comme indice pour la chute totale de la litiere.

A general introduction of the bait-lamina test has been made in this article. This article has an introductional character for other articles dealing with the bait-lamina test method and gives the experimental data. The test was first introduced by Torne in 1990 to measure the biological activity of soil. It enables the monitoring of biotic (microbial and zootic) processes in the soil within a short period of time, and detailed investigations. The test system is based on visual assessment of feeding on small portions of thin laminated bait substrate exposed to edaphic processes. The test system has found its application mainly in Germany but in the meanwhile also in Portugal, Switzerland and in the Netherlands in laboratories of soil ecology and soil ecotoxicology. At present there are only few publications in the international literature, but the interest in this method is growing. During the past years two workshops on the subject have been organized in Germany to summarize experiences with and to evaluate the test system and optimize the standard procedure.

V tomto clanku studujeme spektralni a oscilacni vlastnosti symplektických systemů na casových skalach s Dirichletovými okrajovými podminkami. Zaměřujeme se na odvozeni tzv. oscilacnich vět pro tyto systemy, ktere davaji do souvislosti pocet vlastnich hodnot teto okrajove ulohy a pocet (zobecněných) fokalnich bodů hlavniho řeseni systemu. Tento ukol zahrnuje definovani stěžejnich pojmů vlastnich hodnot a zobecněných fokalnich bodů v teorii na casových skalach. Odvozujeme take tradicni geometricke vlastnosti vlastnich hodnot, ktere jsou znamy pro samoadjungovane linearni systemy. V praci nepředpokladame kontrolovatelnost ci normalitu uvažovaneho systemu.

The principle underlying all methods of blood purification for the treatment of uremia is based on the assumption that most symptoms of uremia depend on the concentrations of dialysable substances which are the end products of metabolism normally eliminated by the kidney. Therefore, dialysis therapy can only be effective if the concentrations of these endogenous substances remain below toxic limits.

Given semi-normsf andg on ℝ n and a real number μ>0. Then the successive minima off under the constraintg≤μ are defined by λ j : = inf {λ: there existj linear independent vectors inZ n withf≤λ andg≤μ}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ℝ n (without constraints) coincide with the λ j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.

For a certain class of discrete approximation operators Bnf defined on an interval I and including, e.g., the Bernstein polynomials, we prove that for all f ϵ C(I), the ordinary moduli of continuity of Bnf and f satisfy ω(Bnf; h) ⩽ cω(f; h), n = 1,2,…, 0 < h < ∞, with a universal constant c > 0. A similar result is shown to hold for a different modulus of continuity which is suitable for functions of polynomial growth on unbounded intervals. Some special operators are discussed in this connection.

In this paper the following limit theorem is obtained: If A A and B B are ( n , n ) (n,n) -matrices with rank ( A T , B T ) = n , A T B = B T A {\text {rank}}({A^T},{B^T}) = n,\;{A^T}B = {B^T}A , then A ( A + S B ) − 1 S → 0 A{(A + SB)^{ - 1}}S \to 0 as S → 0 + , i .e . S → 0 S \to 0 + ,\;{\text {i}}{\text {.e}}{\text {.}}\;{\text {S}} \to {\text {0}} where S S is symmetric and positive definite. Some applications of this result are given to linear algebra (the behavior of ( A + λ B ) − 1 {(A + \lambda B)^{ - 1}} as λ → 0 ) \lambda \to 0) and to differential equations (the asymptotic behavior of Hamiltonian systems and of selfadjoint differential equations of even order).

The following limit theorem on Hamiltonian systems (resp. corresponding Riccati matrix equations) is shown: Given(N, N)-matrices,A, B, C andn ∈ {1,…, N} with the following properties:A and kemelB(x) are constant, rank(I, A, …, An−1) B(x)≠N,B(x)∈Cn(R), andB(x)(AT)j-1C(x)∈Cn-j(R) forj=1, …, n. Then\(\mathop {\lim }\limits_{x \to x_0 } \eta _1^T \left( x \right)V\left( x \right)U^{ - 1} \left( x \right)\eta _2 \left( x \right) = d_1^T \left( {x_0 } \right)U\left( {x_0 } \right)d_2 \) forx0∈R, whenever the matricesU(x), V(x) are a conjoined basis of the differential systemU′=AU + BV, V′=CU−ATV, and whenever ηi(x)∈RN satisfy ηi(x0)=U(x0)di ∈ imageU(x0) η′i-Aηni(x) ∈ imageB(x),B(x)(η′i(x)-Aηi(x)) ∈Cn-1R fori=1,2.

Soit {p n } une suite de nombres non negatifs avec p 0 >0, et P n :×∑ k×0 n p k →∞, p(x):=∑ n=0 ∞ p u x n

For given 2n×2n matricesS13,S24 with rank(S13,S24)=2n\(S_{13} \bar S_{24}^T = S_{24} \bar S_{13}^T \) we consider the eigenvalue problem:u′=A(x)u+B(x)v,v′=C1(x;λ)u-AT(x)v with $$S_{13} \left( {_{u\left( b \right)}^{ - u\left( a \right)} } \right) + S_{24} \left( {_{\upsilon \left( b \right)}^{\upsilon \left( a \right)} } \right) = 0,{\text{ }}a< b;$$ where we assume that then×n matrices,A, B, C1 satisfy:A, B, C1, ∂/∂λC1 are continuous on IR resp. IR2;B, C1 are Hermitian;B, −∂/∂λC1 are non-negative definite; and we assume the crucial normality-condition: for any solutionu, v (λ∈IR arbitrary) ∂/∂λC1u≡0 on some interval always impliesu≡v≡0. Then, the main result of the paper (Theorem 2) is the following oscillation result: For any conjoined basisU1(x; λ),V1(x; λ) of the differential system with fixed (with respect to λ) initial valuesU1(a), V1(a), we haven1(λ)+n2(λ)=n3(λ)+n1+n2 for λ ∈ IR with regularU1(b; λ); where\(n_i = \mathop {lim}\limits_{\lambda \to \infty } \);ni(λ),i=1,2;n1(λ) denotes number of focal points of 3U1 in [a, b);n3(λ) denotes the number of eigenvalues which are ≤λ; andn2(λ) denotes the number of negative eigenvalues of a certain Hermitian 3n×3n matrixM(λ). Moreover, it is shown how classical results (e.g. Rayleigh's principle, existence theorem) can be derived from this oscillation theorem via a generalized Picone identity (which yields also the matrixM(λ) above).

We consider time-dependent linear systems of the form x = Ax + Bu , y = Cx with state x ∈ Rn, control (input) u ∈ Rm, and output y ∈ Rp. The main results are local characterizations of observability and strong observability (or observability with unknown inputs) of (A, C) and (A, B, C). These criteria are pointwise rank conditions on a certain matrix, which is explicitly built up from the first n − 2 derivatives of A and B and the first n − 1 derivatives of C. The results generalize well-known theorems for time-invariant systems. The proofs lead also to observers (with and without the input), and the main tool is a generalized product rule for the differentiation of a product of matrices, where only one factor and the product itself are known to be differentiable.

We prove Tauberian theorems for Jp-summability methods of power series type with respect to ordinary convergence. Under a o-Tauberian condition on the underlying sequence our Tauberian conclusion is valid for all Jp-methods. Relaxing the Tauberian assumption to a O-type condition, a related result is shown for methods with “moderate” weight sequences.

Given a symmetric m × m matrix function Q ( t ) which decreases on some interval (0, e], e > 0 [i.e., Q ( t 1 )− Q ( t 2 ) is nonnegative definite for t 1 ⩽ t 2 ] and which admits a factorization of the form Q ( t )= U ( t ) X −1 ( t ), where U ( t )→ U , X ( t )= X as t →0 + with rank( U T , X T ) = m . Then it is shown that lim t→0+ X T Q(t)X=U T X , and lim t→0+ c T Q(t)c=∞ for all c ∉ Im X . Moreover, any monotone matrix function can be factorized as above.

In the first part inequalities for solutions of Riccati matrix difference equations are obtained which correspond to the linear Hamiltonian difference system[formula]whereAk, Bk, Ck, Xk, Ukaren × n-matrices with symmetricBkandCk. If the matricesXkare invertible, then the matricesQk = UkX−1ksolve the Riccati matrix difference equation[formula]In contrast to some recent papers dealing with these equations we do not assume that the matricesBkare invertible. The second part of the paper deals with the asymptotic behaviour of solutionsQk(λ), as|λ| → ∞, of the special Riccati matrix difference equation which corresponds to the Sturm–Liouville equation[formula]of even order 2nwith constant coefficientsr0,…,rn.

In this paper we consider discrete Sturm–Liouville eigenvalue problems of the form L(y) k :=∑ n μ=0 (−Δ) μ r μ (k)Δ μ y k+1−μ =λy k+1 for 0⩽k⩽N−n with y 1−n =⋯=y 0 =y N+2−n =⋯=y N+1 =0 , where N and n are integers with 1⩽n⩽N and under the assumption that r n (k)≠0 for all k . These problems correspond to eigenvalue problems for symmetric, banded matrices A ∈ R (N+1−n)×(N+1−n) with bandwidth 2n+1 . We present the following results: 1. an inversion formula, which shows that every symmetric, banded matrix corresponds uniquely to a Sturm–Liouville eigenvalue problem of the above form; 2. a formula for the characteristic polynomial of A , which yields a recursion for its calculation; 3. an oscillation theorem, which generalizes well-known results on tridiagonal matrices. These new results can be used to treat numerically the algebraic eigenvalue problem for symmetric, banded matrices without reduction to tridiagonal form.

Patients who undergo extensive plasma exchanges using albumin replacement may be more susceptible to infection because they develop significant hypogammaglobulinemia. Substitution of IgG in these patients could be beneficial. A model to calculate the individual amount of IgG required is described. The course of IgG during chronic intermittent membrane plasma separation (MPS) therapy was simulated using an one-pool model. Three modes of substitution were considered for their efficacy: infusion after MPS infusion after discarding an equivalent plasma quantity after termination of MPS, and plasma exchange at the end of MPS against an IgG solution. Mode B was shown to be most economical and was subsequently used to check the validity of the substitution model in a prospective test. The difference between predicted and measured IgG levels was 5% both for simulations from one MPS to the next and for the long-term prediction. The data prove that replacement of IgG after plasma separation is practicable. The substitution model allows to fix in advance any plasma limit value for indication and target of the substitution therapy. Thus it permits to give therapeutic recommendations for individual IgG substitution therapy of secondary antibody deficiency after MPS.

The knowledge of plasma volume (PV) is a basic requirement for the standardization of plasma exchange therapy. PV has to be determined by calculation, as the measurement of PV before every plasma exchange is too cost- and time consuming. A known correlation with measured values results from calculation of plasma volume by means of patient's height and weight. But the present equations are only reliable at normal hematocrit. For this reason we modified the Retzlaff-equations and compared the validity of plasma volume predictions, calculated by these and own equations, with plasma volume measured by the 51Cr-method in 59 patients with pathological hematocrit. The correlation coefficient was 0.82 for men and 0.81 for women (2 0.001) with the modified Retzlaff-equations. On the average the relative error was -1.5% for all and 2.8% for fat and thin men. No significant improvement of accuracy was achieved with other equations. Thus, plasma volume can accurately be calculated from height, weight, and hematocrit with our modified Retzlaff-equations in patients with pathological hematocrit, even if they are very fat or thin. Nomograms for men and women were constructed in order to facilitate the calculation.