The Kolmogorov–Riesz compactness theorem

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.     

Primordial <Superscript>4</Superscript>He Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value

We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial ⁴He abundance (Y _P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial ⁴He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v ₀ denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .     

Dextramabs: A Novel Format of Antibody-Drug Conjugates Featuring a Multivalent Polysaccharide Scaffold

Antibody-drug conjugates (ADCs) are multicomponent biomolecules that have emerged as a powerful tool for targeted tumor therapy. Combining specific binding of an immunoglobulin with toxic properties of a payload, they however often suffer from poor hydrophilicity when loaded with a high amount of toxins. To address these issues simultaneously, we developed dextramabs, a novel class of hybrid antibody-drug conjugates. In these architectures, the therapeutic antibody trastuzumab is equipped with a multivalent dextran polysaccharide that enables efficient loading with a potent toxin in a controllable fashion. Our modular chemoenzymatic approach provides an access to synthetic dextramabs bearing monomethyl auristatin as releasable cytotoxic cargo. They possess high drug-to-antibody ratios, remarkable hydrophilicity, and high toxicity in vitro.     

Specht Modules and Simple Modules for Centralizer Algebras of the Symmetric Group

Let Σ_n be the symmetric group on n letters. For l ≤ n identify Σ_l with a subgroup of Σ_n in the natural way. Let k be an algebraically closed field of characteristic p. This article begins to develop a theory for modules over the centralizer algebras kΣ_n^Σ_l that is analogous to James's theory of permutation modules, Specht modules, and simple modules over kΣ_n. We make a conjecture about how to construct all simple kΣ_n^Σ_l-modules, we develop tools to test the conjecture, and we prove that it is correct for all n when l < p.     

Self-Dual Noncommutative {\phi^4} -Theory in Four Dimensions is a Non-Perturbatively Solvable and Non-Trivial Quantum Field Theory

We study quartic matrix models with partition function \({\mathcal{Z}[E, J] = \int dM}\) exp(trace \({(JM - EM^{2} - \frac{\lambda}{4} M^4)}\) ). The integral is over the space of Hermitean \({\mathcal{N} \times \mathcal{N}}\) -matrices, the external matrix E encodes the dynamics, \({\lambda > 0}\) is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing β-function. As the main application we prove that Euclidean \({\phi^4}\) -quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for \({\mathcal{N} \to \infty}\) the same spectrum as the Laplace operator in four dimensions. Using the theory of singular integral equations of Carleman type we compute (for \({\mathcal{N} \to \infty}\) and after renormalisation of \({E, \lambda}\) ) the free energy density (1/volume) log \({(\mathcal{Z}[E, J]/\mathcal{Z}[E, 0])}\) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which in subsequent work is verified for coupling constants \({\lambda \leq 0}\) .     

Radiative spectra of thermal electromagnetic noise induced by planar realistic dielectrics

Spectral characteristics of stochastic fields and their spatial derivatives in various planar structures composed by lossy materials described by realistic dielectric functions are numerically calculated based on solutions to the problems of multipolar electromagnetic fields in a plane layered geometry. A displacement of the maximum of the spectral power densities for spatial derivatives of fluctuating fields to the high-frequency domain, a resonant increase in the density of states of the fluctuating fields at the frequencies of interface excitations and interference modes for the radiative part of the spectra, the influence of geometry on the density of states, and other peculiarities are found by numerical calculations and graphically demonstrated. Interpretations of the above effects are provided.     

Halton-type sequences from global function fields

For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.     

Understanding the Mechanocatalytic Conversion of Biomass: A Low‐Energy One‐Step Reaction Mechanism by Applying Mechanical Force

On the way to establishing biomass as a renewable and environmentally friendly source to cover the ever‐increasing global demand on energy and chemicals, one great challenge is the efficient depolymerization of cellulose. Enhanced conversion rates have been discovered in ball‐milling experiments, thus opening a mechanocatalytic approach. However, an understanding of the impact of mechanical forces on the acid‐catalyzed cleavage of glycosidic bonds at the molecular level is still missing. Herein, we contribute such fundamental insight based on atomistic modeling. Mechanically stressing the macromolecular backbone radically changes the depolymerization pathway from a complex high‐barrier reaction upon thermal activation to a low‐energy single‐step mechanocatalytic process. In addition to revealing a regioselective increase in basicity under a mechanical force, our results provide molecular‐level explanations of the experimental findings and might therefore guide rational ways to improve such mechanocatalytic processes.     

Synthesis and Structure of Monomeric,Trimeric, and Mixed Phenylcyanamides

In a new synthetic approach phenylcyanamide (Hpca) was synthesized by methylation of phenylthiourea followed by a basic work‐up. All products along the synthetic route have been fully characterized by means of NMR, IR, and X‐ray studies. The first structural report of neutral mixed crystals of phenylcyanamide containing monomeric and trimeric Hpca is presented. Examination of these intriguing mixed crystals revealed the formation of distinct layers of monomeric and trimeric Hpca. These layers are interconnected by weak hydrogen bonds. The trimer represents triphenylisomelamine, which readily isomerizes to the triphenylmelamine in the melt, in accord with computations at the B3LYP level, indicating an exothermic process (ΔH=?49.4 kcal mol^?1). Pure trimeric Hpca (triphenylisomelamine) was obtained either by recrystallization of the mixed crystals from boiling water or by trimerization of monomeric Hpca in isopropanol for 12 h under reflux conditions. For comparison tritylcyanamide (Htca) and potassium phenylcyanamide as an [18]crown‐6 complex [K([18]crown‐6)pca] have been synthesized, and the solid‐state structures were determined using X‐ray diffraction techniques. The thermal behavior was studied by thermo‐analytical experiments. In agreement with the experimental results, computations predict an exothermic cyclotrimerization process for Hpca (ΔH=?41.3 kcal mol^?1).