Test Functions, Schur–Agler Classes and Transfer-Function Realizations: The Matrix-Valued Setting

Given a collection of test functions, one defines the associated Schur–Agler class as the intersection of the contractive multipliers over the collection of all positive kernels for which each test function is a contractive multiplier. We indicate extensions of this framework to the case where the test functions, kernel functions, and Schur–Agler-class functions are allowed to be matrix- or operator-valued. We illustrate the general theory with two examples: (1) the matrix-valued Schur class over a finitely-connected planar domain and (2) the matrix-valued version of the constrained Hardy algebra (bounded analytic functions on the unit disk with derivative at the origin constrained to have zero value). Emphasis is on examples where the matrix-valued version is not obtained as a simple tensoring with ${{\mathbb C}^{N}}$ of the scalar-valued version.     

An approximation theory for the identification of nonlinear volterra equations

An abstract approximation framework and convergence theory for Galerkin approximations to inverse problems involving nonlinear Volterra integral equations is developed. The approach relies on the theory of m-accretive operators in Banach spaces. An application to heat flow in materials with memory is also discussed.     

Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces

Two strong convergence theorems for a proximal method for finding common zeroes of maximal monotone operators in reflexive Banach spaces are established. Both theorems take into account possible computational errors.     

Metal‐Mediated Functionalization of Natural Peptides and Proteins: Panning for Bioconjugation Gold

Selective modification of natural proteins is a daunting methodological challenge and a stringent test of selectivity and reaction scope. There is a continued need for new reactivity and new selectivity concepts. Transition metals exhibit a wealth of unique reactivity that is orthogonal to biological reactions and processes. As such, metal‐based methods play an increasingly important role in bioconjugation. This Review examines metal‐based methods as well as their reactivity and selectivity for the functionalization of natural proteins and peptides.     

Parton distributions and new physics searches: the Drell–Yan forward–backward asymmetry as a case study

We present the first unquenched lattice-QCD calculation of the form factors for the decay \(B\rightarrow D^*\ell \nu \) at nonzero recoil. Our analysis includes 15 MILC ensembles with \(N_f=2+1\) flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from \(a\approx 0.15\) fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element \(|V_{cb}|\). We obtain \(\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}\). The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall \(\chi ^2\text {/dof} = 126/84\), which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict \(R(D^*) = 0.265 \pm 0.013\), which confirms the current tension between theory and experiment.

     

Bio‐Inspired Transition Metal–Organic Hydride Conjugates for Catalysis of Transfer Hydrogenation: Experiment and Theory

Taking inspiration from yeast alcohol dehydrogenase (yADH), a benzimidazolium (BI⁺) organic hydride‐acceptor domain has been coupled with a 1,10‐phenanthroline (phen) metal‐binding domain to afford a novel multifunctional ligand ( L ^BI+) with hydride‐carrier capacity ( L ^BI++H^?? L ^BIH). Complexes of the type [Cp*M( L ^BI)Cl][PF₆]₂ (M=Rh, Ir) have been made and fully characterised by cyclic voltammetry, UV/Vis spectroelectrochemistry, and, for the Ir^III congener, X‐ray crystallography. [Cp*Rh( L ^BI)Cl][PF₆]₂ catalyses the transfer hydrogenation of imines by formate ion in very goods yield under conditions where the corresponding [Cp*Ir( L ^BI)Cl][PF₆] and [Cp*M(phen)Cl][PF₆] (M=Rh, Ir) complexes are almost inert as catalysts. Possible alternatives for the catalysis pathway are canvassed, and the free energies of intermediates and transition states determined by DFT calculations. The DFT study supports a mechanism involving formate‐driven Rh?H formation (90 kJ mol^?1 free‐energy barrier), transfer of hydride between the Rh and BI⁺ centres to generate a tethered benzimidazoline (BIH) hydride donor, binding of imine substrate at Rh, back‐transfer of hydride from the BIH organic hydride donor to the Rh‐activated imine substrate (89 kJ mol^?1 barrier), and exergonic protonation of the metal‐bound amide by formic acid with release of amine product to close the catalytic cycle. Parallels with the mechanism of biological hydride transfer in yADH are discussed.     

Two Projection Algorithms for Solving the Split Common Fixed Point Problem

Journal of Optimization Theory and Applications - We study the split common fixed point problem for Bregman relatively nonexpansive operators in real reflexive Banach spaces. Using Bregman...     

An easier proof of the maximal arcs conjecture

It was a long-standing conjecture in finite geometry that a Desarguesian plane of odd order contains no maximal arcs. A rather inaccessible and long proof was given recently by the authors in collaboration with Mazzocca. In this paper a new observation leads to a greatly simplified proof of the conjecture.