The degree of shape preserving weighted polynomial approximation

We analyze the degree of shape preserving weighted polynomial approximation for exponential weights on the whole real line. In particular, we establish a Jackson type estimate.     

Are the degrees of the best (co)convex and unconstrained polynomial approximations the same? II

In Part I of the paper, we have proved that, for every α > 0 and a continuous function f, which is either convex (s = 0) or changes convexity at a finite collection Y _s = {y _i } ^s _i=1 of points y _i ∈ (-1, 1),

A generalized moment problem

Let {λ _n} (n≧0) satisfy (1.1) we are considering the following problems: What are the necessary and sufficient conditions on a sequence {μ_n} (n≧0) in order that it should possess the representation (1.2) wherea(t) is of bounded variation or the representation (1.3) wheref(t) ∈L _M[0, 1] orf(t) is essentially bounded.     

Generalized partial dynamical symmetry in nuclei

We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.     

Shape preserving widths of Sobolev-type classes ofs-monotone functions on a finite interval

LetI be a finite interval andr ∈ ℕ. Denote by △ ₊ ^s L _q the subset of all functionsy ∈L _q such that thes-difference △ _T ^s y(·) is nonnegative onI, ∀τ>0. Further, denote by △ ₊ ^s W _p ^r the class of functionsx onI with the seminorm ‖x ^(r) ‖L _p ≤1, such that △ _T ^s x≥0, τ > 0, τ>0. Fors=3,…,r+1, we obtain two-sided estimates of the shape preserving widths , whereM ⁿ is the set of all linear manifoldsM ⁿ inL _q , dimM ⁿ ≤n, such thatM ⁿ ⋂△ ₊ ^s L _q ≠ 0. Part of this work was done while the first author visited Tel Aviv University in 2001 and part of it while the second author was a member of the Industrial Mathematics Institute (IMI), University of South Carolina.     

Supersymmetric patterns in the pseudospin, spin, and coulomb limits of the dirac equation with scalar and vector potentials

We show that the Dirac equation in (3+1) dimensions gives rise to supersymmetric patterns when the scalar and vector potentials are (i). Coulombic with arbitrary strengths or (ii). when their sum or difference is a constant, leading to relativistic pseudospin and spin symmetries. The conserved quantities and the common intertwining relation responsible for such patterns are discussed.     

Interpolatory Pointwise Estimates for Polynomial Approximation

We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f∈ C[0,1] , by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases. November 16, 1998. Date revised: July 12, 1999. Date accepted: September 13, 1999.     

Trouble-shooting deployment and recovery options for various stationary passive acoustic monitoring devices in both shallow- and deep-water applications

Deployment of any type of measuring device into the ocean, whether to shallow or deeper depths, is accompanied by the hope that this equipment and associated data will be recovered. The ocean is harsh on gear. Salt water corrodes. Currents, tides, surge, storms, and winds collaborate to increase the severity of the conditions that monitoring devices will endure. All ocean-related research has encountered the situations described in this paper. In collating the details of various deployment and recovery scenarios related to stationary passive acoustic monitoring use in the ocean, it is the intent of this paper to share trouble-shooting successes and failures to guide future work with this gear to monitor marine mammal, fish, and ambient (biologic and anthropogenic) sounds in the ocean-in both coastal and open waters.     

Development and Validation of an Innovative Analytical Approach for the Quantitation of Tris(Hydroxymethyl)Aminomethane (TRIS) in Pharmaceutical Formulations by Liquid Chromatography Tandem Mass Spectrometry

A novel COVID-19 vaccine (BriLife^®) has been developed by the Israel Institute for Biological Research (IIBR) to prevent the spread of the SARS-CoV-2 virus throughout the population in Israel. One of the components in the vaccine formulation is tris(hydroxymethyl)aminomethane (tromethamine, TRIS), a buffering agent. TRIS is a commonly used excipient in various approved parenteral medicinal products, including the mRNA COVID-19 vaccines produced by Pfizer/BioNtech and Moderna. TRIS is a hydrophilic basic compound that does not contain any chromophores/fluorophores and hence cannot be retained and detected by reverse-phase liquid chromatography (RPLC)-ultraviolet (UV)/fluorescence methods. Among the few extant methods for TRIS determination, all exhibit a lack of selectivity and/or sensitivity and require laborious sample treatment. In this study, LC–mass spectrometry (MS) with its inherent selectivity and sensitivity in the multiple reaction monitoring (MRM) mode was utilized, for the first time, as an alternative method for TRIS quantitation. Extensive validation of the developed method demonstrated suitable specificity, linearity, precision, accuracy and robustness over the investigated concentration range (1.2–4.8 mg/mL). Specifically, the R² of the standard curve was >0.999, the recovery was >92%, and the coefficient of variance (%CV) was <12% and <6% for repeatability and intermediate precision, respectively. Moreover, the method was validated in accordance with strict Good Manufacturing Practice (GMP) guidelines. The developed method provides valuable tools that pharmaceutical companies can use for TRIS quantitation in vaccines and other pharmaceutical products.