Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established

Chandrasekhar equations for infinite dimensional systems. II. Unbounded input and output case

AbstractA set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant systems defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, we derive the Chandrasekhar equations and establish the existence, uniqueness, and regularity results of their solutions

Mathematical Musings of a Urologist

The derivatives with respect to the variable $r$ of $\pi r^2$ and $\frac{4}{3}\pi r^3$ are $2\pi r$ and $4\pi r^2$, respectively. This relates, through the derivative, the area enclosed in a circle to the length of that circle and, likewise, the volume of a sphere to the surface area of that sphere. The reasons why this works are basic to a first course in calculus. In this brief article, we expand on these ideas to shapes other than circles and spheres. Our approach is with the first year calculus student in mind

Metabolomics Analysis Identifies D-Alanine-D-alanine Ligase as the Primary Lethal Target of D-cycloserine in Mycobacteria

D-cycloserine is an effective second line antibiotic used as a last resort to treat multi (MDR)- and extensively (XDR)- drug resistant strains of Mycobacterium tuberculosis. D-cycloserine interferes with the formation of peptidoglycan biosynthesis by competitive inhibition of Alanine racemase (Alr) and D-Alanine-D-alanine ligase (Ddl). Although, the two enzymes are known to be inhibited, the in vivo lethal target is still unknown. Our NMR metabolomics work has revealed that Ddl is the primary target of DCS, as cell growth is inhibited when the production of D-alanyl-Dalanine is halted. It is shown that inhibition of Alr may contribute indirectly by lowering the levels of D-alanine thus allowing DCS to outcompete D-alanine for Ddl binding. The NMR data also supports the possibility of a transamination reaction to produce D-alanine from pyruvate and glutamate, thereby bypassing Alr inhibition. Furthermore, the inhibition of peptidoglycan synthesis results in a cascading effect on cellular metabolism as there is a shift toward the catabolic routes to compensate for accumulation of peptidoglycan precursors

Metabolomics Analysis Identifies D-Alanine-D-alanine Ligase as the Primary Lethal Target of D-cycloserine in Mycobacteria

D-cycloserine is an effective second line antibiotic used as a last resort to treat multi (MDR)- and extensively (XDR)- drug resistant strains of Mycobacterium tuberculosis. D-cycloserine interferes with the formation of peptidoglycan biosynthesis by competitive inhibition of Alanine racemase (Alr) and D-Alanine-D-alanine ligase (Ddl). Although, the two enzymes are known to be inhibited, the in vivo lethal target is still unknown. Our NMR metabolomics work has revealed that Ddl is the primary target of DCS, as cell growth is inhibited when the production of D-alanyl-Dalanine is halted. It is shown that inhibition of Alr may contribute indirectly by lowering the levels of D-alanine thus allowing DCS to outcompete D-alanine for Ddl binding. The NMR data also supports the possibility of a transamination reaction to produce D-alanine from pyruvate and glutamate, thereby bypassing Alr inhibition. Furthermore, the inhibition of peptidoglycan synthesis results in a cascading effect on cellular metabolism as there is a shift toward the catabolic routes to compensate for accumulation of peptidoglycan precursors

Assessment of metabolic changes in \u3ci\u3eMycobacterium smegmatis\u3c/i\u3e wild type and \u3ci\u3ealr\u3c/i\u3e mutant strains: evidence for a new pathway of D-alanine biosynthesis.

In mycobacteria, D-alanine is an essential precursor for peptidoglycan biosynthesis. The only confirmed enzymatic pathway to form D-alanine is through the racemization of L-alanine by alanine racemase (Alr, EC 5.1.1.1). Nevertheless, the essentiality of Alr in Mycobacterium tuberculosis and Mycobacterium smegmatis for cell survivability in the absence of D-alanine has been a point of controversy with contradictory results reported in the literature. To address this issue, we examined the effects of alr inactivation on the cellular metabolism of M. smegmatis. The M. smegmatis alr insertion mutant TAM23 exhibited essentially identical growth to wild type mc2155 in the absence of D-alanine. NMR metabolomics revealed drastically distinct phenotypes between mc2155 and TAM23. A metabolic switch was observed for TAM23 as a function of supplemented D-alanine. In the absence of D-alanine, the metabolic response directed carbon through an unidentified transaminase to provide the essential D-alanine required for survival. The process is reversed when D-alanine is available, in which the D-alanine is directed to peptidoglycan biosynthesis. Our results provide further support for the hypothesis that Alr is not an essential function of M. smegmatis, and that specific Alr inhibitors will have no bactericidal action

Flett's mean value theorem in topological vector spaces

We prove some generalizations of Flett's mean value theorem for a class of Gateaux differentiable functions f:X→Y, where X and Y are topological vector spaces

Presence of 5-hydroxyguaiacyl units as native lignin constituents in plants as seen by Py-GC/MS

Instituto de Recursos Naturales y Agrobiología de Sevilla, CSIC, P.O. Box 1052, 41080-Seville, Spain 2Centro de Investigaciones Biológicas, CSIC, Ramiro de Maeztu 9, E-28040 Madrid, Spain E-mail address: [email protected] (J.C. del Río)The presence of 5-hydroxyguaiacyl moieties in the lignin from several plants has been assessed by Py-GC/MS. Different woody (eucalypt) and nonwoody (flax, hemp, kenaf, jute, sisal and abaca) angiosperms were selected for this study. The pyrolysis of whole fibers released lignin-derived products with p-hydroxyphenyl, guaiacyl and syringyl structures. Indeed, a series of compounds having a 5-hydroxyguaiacyl nuclei, including 3-methoxycatechol, 5-vinyl-3-methoxycatechol and 5-propenyl-3-methoxycatechol, were detected and identified in all samples, although in lower amounts than the normal guaiacyl and syringyl compounds. The analysis of the lignins isolated from the same plants also indicated the presence of 5-hydroxyguaiacyl moieties in the isolated lignins. These compounds are supposed to arise from the pyrolysis of 5-hydroxyguaiacyl moieties, which are supposed to be native constituents of lignin in plants forming benzodioxane substructures.This study has been supported by the Spanish Ministerio de Ciencia y Tecnología (MCyT) and FEDER funds (project AGL2005-01748) and the EU project BIORENEW (NMP2-CT-2006-026456). We thank CELESA S.A. (Tortosa, Spain) for providing the nonwoody plant samples, and ENCE for providing the eucalypt wood sample.Peer reviewe

Fitting Age-Period-Cohort Models Using the Intrinsic Estimator: Assumptions and Misapplications

We thank Demography’s editorial office for the opportunity to respond to te Grotenhuis et al.’s commentary regarding the methods used and the results presented in our earlier paper (Masters et al. 2014). In this response, we briefly reply to three general themes raised in the commentary: (1) the presentation and discussion of APC results, (2) the fitting of full APC models to data for which a simpler model holds, and (3) the variation in the estimated age, period, and cohort coefficients produced by the intrinsic estimator (IE) (i.e., the “non-uniqueness property” of the IE, as referred to by Pelzer et al. (2015))