Behavior of Hilbert networks under perturbations of their elements

We study the behavior of a Hilbert network (i.e., a finite or countably infinite network whose variables are in a Hilbert space and in which the associated total energy is finite) whose elements are affected by perturbations. More specifically, we will give estimates for a change of the current distribution caused by (a) perturbations of the elements of the nominal network when the voltage sources are fixed, and (b) a change of voltage sources in a network whose elements are perturbed. The conditions given in our theorems imply insensitivity and robust stability of the nominal network. The applications of the results are illustrated by an example of an infinite network.This research was supported by the NSF Grant #DMS-9102910.     

Multi-sensor inline measurements of crystal size and shape distributions during high shear wet milling of crystal slurries

Size and shape distributions are among critical quality attributes of particulate products and their inline measurement is crucial for monitoring and control of particle manufacturing processes. This requires advanced tools that can estimate particle size and shape distributions from multi-sensor data captured in situ across various processing steps.In this work, we study changes in size and shape distributions, as well as number of particles during high shear wet milling, which is increasingly being employed for size reduction in crystalline slurries in pharmaceutical processing. Saturated suspensions of benzoic acid, paracetamol and metformin hydrochloride were used in this study. We employ our recently developed tools for estimating particle aspect ratio and particle size distributions from chord length distribution (CLD) measurements and imaging. We also compare estimated particle size distributions from CLD and imaging with corresponding estimates from offline instruments.The results show that these tools are capable of quantitatively capturing changes in particle sizes and shape during wet milling inline. This is the first time that such a capability has been reported in the literature. The ability to quantitatively monitor particle size and shape distributions in real time will enable development of more realistic and accurate population balance models of wet milling and crystallisation, and aid more efficient control of crystallisation processes.     

Ultrathin Hierarchical Porous Carbon Nanosheets for High‐Performance Supercapacitors and Redox Electrolyte Energy Storage

The design of advanced high‐energy‐density supercapacitors requires the design of unique materials that combine hierarchical nanoporous structures with high surface area to facilitate ion transport and excellent electrolyte permeability. Here, shape‐controlled 2D nanoporous carbon sheets (NPSs) with graphitic wall structure through the pyrolysis of metal–organic frameworks (MOFs) are developed. As a proof‐of‐concept application, the obtained NPSs are used as the electrode material for a supercapacitor. The carbon‐sheet‐based symmetric cell shows an ultrahigh Brunauer–Emmett–Teller (BET)‐area‐normalized capacitance of 21.4 µF cm^?2 (233 F g^?1), exceeding other carbon‐based supercapacitors. The addition of potassium iodide as redox‐active species in a sulfuric acid (supporting electrolyte) leads to the ground‐breaking enhancement in the energy density up to 90 Wh kg^?1, which is higher than commercial aqueous rechargeable batteries, maintaining its superior power density. Thus, the new material provides a double profits strategy such as battery‐level energy and capacitor‐level power density.     

Nanoporous Nitrogen‐Doped Graphene Oxide/Nickel Sulfide Composite Sheets Derived from a Metal‐Organic Framework as an Efficient Electrocatalyst for Hydrogen and Oxygen Evolution

Engineering of controlled hybrid nanocomposites creates one of the most exciting applications in the fields of energy materials and environmental science. The rational design and in situ synthesis of hierarchical porous nanocomposite sheets of nitrogen‐doped graphene oxide (NGO) and nickel sulfide (Ni₇S₆) derived from a hybrid of a well‐known nickel‐based metal‐organic framework (NiMOF‐74) using thiourea as a sulfur source are reported here. The nanoporous NGO/MOF composite is prepared through a solvothermal process in which Ni(II) metal centers of the MOF structure are chelated with nitrogen and oxygen functional groups of NGO. NGO/Ni₇S₆ exhibits bifunctional activity, capable of catalyzing both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) with excellent stability in alkaline electrolytes, due to its high surface area, high pore volume, and tailored reaction interface enabling the availability of active nickel sites, mass transport, and gas release. Depending on the nitrogen doping level, the properties of graphene oxide can be tuned toward, e.g., enhanced stability of the composite compared to commonly used RuO₂ under OER conditions. Hence, this work opens the door for the development of effective OER/HER electrocatalysts based on hierarchical porous graphene oxide composites with metal chalcogenides, which may replace expensive commercial catalysts such as RuO₂ and IrO₂.     

Some results on the invertibility of nonlinear operators

The objective of this paper is to present certain conditions guaranteeing invertibility of a nonlinear operator between normed linear spaces. The idea is to approximate the given operator by an invertible, possibly linear operator, and reduce the problem to the contraction mapping principle. Several theorems of this kind are given, which appear as generalizations of some early results by I.W. Sandberg, and estimates for an approximate inverse are established. Finally, introducing certain invertibility indices, further sufficient and necessary conditions for invertibility are given.     

Lipid Nanoparticles for Broad-Spectrum Nucleic Acid Delivery

Lipid nanoparticles (LNPs) are the most advanced nonviral modality for nucleic acid (NA) delivery, and have recently gained enormous attention in the fields of RNA therapeutics and vaccine development. Here, ionizable adamantane-based lipidoids named XMaNs, which circumvent the usual need for laborious optimization of LNP components for highly diverse types of NAs, are described. The non-toxic XMaN6 lipidoid is highly versatile in entrapment and delivery of siRNA, mRNA, plasmid DNA, and a cyclic dinucleotide. XMaN6-based LNPs efficiently deliver: 1) siRNA into human primary hepatocytes and cell lines that are hard-to-transfect; 2) mRNA into mouse liver; 3) plasmid DNA; 4) 2′,3′-cGAMP into cells and activated the cGAS-STING pathway three orders of magnitude more efficiently than 2′,3′-cGAMP alone. To our knowledge, such universality in delivering different NA types has not been previously described and can accelerate translation of LNPs into the clinic.     

Production of sophorose lipids byTorulopsis bombicola from safflower oil and glucose

The production of sophorose lipids increased with increasing concentrations of both safflower oil and glucose, and was profoundly influenced by the concentration of yeast extract. A high concentration of sophorose lipids (about 135 g/L) was obtained (in a 1-L Bellco stirred reactor) when the medium consisted of 10% glucose, 10.5% safflower oil, 0.1% urea, and 0.25–0.3% yeast extract. A similar yield of sophorose lipids also was obtained in a 20-L bioreactor. About 50% of the apolar sophorose lipid 1′,4″-lactone 6′,6″-diacetate (SL-1) was found in the mixture of sophorose lipids produced under these conditions.     

A new approach to line and line segment clipping in homogeneous coordinates

The clipping operation is still the bottleneck of the graphics pipeline in spite of the latest developments in graphical hardware and a significant increase in performance. Algorithms for line and line segment clipping have been studied for a long time and many research papers have been published so far. This paper presents a new robust approach to line and line segment clipping using a rectangular window. A simple extension for the case of convex polygon clipping is presented as well. The presented approach does not require a division operation and uses homogeneous coordinates for input and output point representation. The proposed algorithms can take advantage of operations supported by vector–vector hardware. The main contribution of this paper is a new approach to intersection computations applied to line and line segment clipping. This approach leads to algorithms that are simpler, robust, and easy to implement.     

Robust stability and sensitivity of input-output systems over extended spaces

This paper is the second part of [6] which is concerned with the sensitivity of general input-output systems over extended spaces. It is assumed that such systems, which need not be of feedback type, are governed by nonlinear operator equations relating the input, the state, and the output. These equations depend on a parameterA that can vary in a neighborhood of a nominal valueA ₀. Essentially, a system is called insensitive if any truncation of its output depends continuously onA provided the input is fixed. The theorems derived provide sufficient conditions for insensitivity. A control system of a feedback-feedforward type and a dynamical system described by a linear vector differential equation on [0, ) are discussed as examples.