A mathematical study of the plasticity effects in muscle contraction

Hill's three-element model of contracting muscle is expanded by replacing the series and the parallel elastic elements with elastoplastic elements. The contractile element is structurally described making use of the sliding filament theory. The resulting mathematical model is formulated in terms of an evolution variational inequality for a nonlinear and nonlocal transport-type operator. The existence and uniqueness of the solution are described along with a numerical approach.This work was supported by M.P.I. (fondi per la ricerca scientifica) and by I.A.N. of C.N.R. Pavia.     

A theoretical and numerical approach to some free boundary problems

Summary In this paper some free boundary problems related to the flow of fluids in porous media are studied. Using a method due to Baiocchi, for these problems we not only establish theoretical results (existence and uniqueness theorems for the solution) but at the same time develop an algorithm for the numerical approach of the solution. Such an algorithm is rigorous from a mathematical point of view and it competes very well with the ones already known both in simplicity of programming and in speed of execution. Entrata in Redazione il 18 luglio 1973. ? Laboratorio di Analisi Numerica del C.N.R. di Pavia ? and ? Università di Pavia ?. This work was supported by C.N.R. in the frame of L.A.N. at Pavia.     

On the solvability of implicit differential inclusions

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are applied to the investigation of differential inclusions unsolved for the unknown function. The statements on solvability, solution estimates, and well-posedness of these inclusions are derived.     

Reactivity of monoenic and conjugated diene systems present in unsaturated olefin terpolymers—II. Reactions with methyl radicals

The experimental rate constants for the reactions of methyl radicals with model compounds simulating ethylidene-norbornene (ENB), methylene-norbornene (MNB) and isopropylidene-dicyclopentadiene (IPDCP) units in EPDM and EPTM elastomers are reported. These constants, as well as others reported in a previous paper or derived from the literature, have been used to perform a kinetic analysis of the grafting of styrene onto EPM, EP-ENB or EP-IPDCP in inert solvent. The systems of kinetic differential equations have been solved by numerical integration without steady state approximation. Valuable information has been obtained on the role of the nature of radical initiators and the sensitivity of the results to change with constants in the various steps.     

Exploring the Bile Stress Response of Lactobacillus mucosae LM1 through Exoproteome Analysis

Lactobacillus sp. have long been studied for their great potential in probiotic applications. Recently, proteomics analysis has become a useful tool for studies on potential lactobacilli probiotics. Specifically, proteomics has helped determine and describe the physiological changes that lactic acid bacteria undergo in specific conditions, especially in the host gut. In particular, the extracellular proteome, or exoproteome, of lactobacilli contains proteins specific to host– or environment–microbe interactions. Using gel-free, label-free ultra-high performance liquid chromatography tandem mass spectrometry, we explored the exoproteome of the probiotic candidate Lactobacillus mucosae LM1 subjected to bile treatment, to determine the proteins it may use against bile stress in the gut. Bile stress increased the size of the LM1 exoproteome, secreting ribosomal proteins (50S ribosomal protein L27 and L16) and metabolic proteins (lactate dehydrogenase, phosphoglycerate kinase, glyceraldehyde-3-phosphate dehydrogenase and pyruvate dehydrogenases, among others) that might have moonlighting functions in the LM1 bile stress response. Interestingly, membrane-associated proteins (transporters, peptidase, ligase and cell division protein ftsH) were among the key proteins whose secretion were induced by the LM1 bile stress response. These specific proteins from LM1 exoproteome will be useful in observing the proposed bile response mechanisms via in vitro experiments. Our data also reveal the possible beneficial effects of LM1 to the host gut.     

Parametric stability in Robe’s problem

In this work we have given a Hamiltonian formulation to Robe’s problem, obtaining again the classic results. We have computed the resonances existing in the circular case and obtained some information with regard to the linear stability of the central equilibrium of Robe’s problem in the elliptic case. In some critical cases we have constructed, in the parameter plane, the boundary curves that separate the regions of stability and instability.     

Sufficient Optimality Conditions for Optimal Control Problems with State Constraints

It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.     

Un risultato relativo a disequazioni variazionali d’evoluzione per operatori del primo ordine int con termini di ritardo

Résumé On donne en utilisant la méthode de pénalisation un théorème d’existence et d’unicité de la solution des inequations variationelles d’évolution pour les opérateurs du 1. er ordre en t à argument retardé.

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Lavoro eseguito in parte mentre l’autore fruiva di una Borsa del C.N.R. presso l’Università di Parigi e in parte presso il Laboratorio di Analisi Numerica del C.N.R. in Pavia.

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Entrata in Redazione il 12 novembre 1970.