Complex Equilibrium Research Articles

Natural Compounds for Preventing Ear, Nose, and Throat-Related Oral Infections.

Oral health is an essential element in maintaining general well-being. By preserving the complex equilibrium within the oral microbial community, commensal microorganisms can protect against extrinsic pathogenic threats. However, when an imbalance occurs, the organism is susceptible to a broad range of infections. Synthetic drugs can be administered to help the body fight against the fungal, bacterial, or viral burden. Nonetheless, they may produce undesirable consequences such as toxicity, adverse effects, and drug resistance. In this respect, research has focused on finding safer and more efficient alternatives. Particularly, increasing attention has been drawn towards developing novel formulations based on natural compounds. This paper reviews the plant-based, algae-based, and beehive products investigated for their antimicrobial properties, aiming to thoroughly present the state of the art on oral infection prevention in the ear, nose, and throat (ENT) field.

Population genomics of transposable element activation in the highly repressive genome of an agricultural pathogen.

The activity of transposable elements (TEs) can be an important driver of genetic diversity with TE-mediated mutations having a wide range of fitness consequences. To avoid deleterious effects of TE activity, some fungi have evolved highly sophisticated genomic defences to reduce TE proliferation across the genome. Repeat-induced point mutation (RIP) is a fungal-specific TE defence mechanism efficiently targeting duplicated sequences. The rapid accumulation of RIPs is expected to deactivate TEs over the course of a few generations. The evolutionary dynamics of TEs at the population level in a species with highly repressive genome defences is poorly understood. Here, we analyse 366 whole-genome sequences of Parastagonospora nodorum, a fungal pathogen of wheat with efficient RIP. A global population genomics analysis revealed high levels of genetic diversity and signs of frequent sexual recombination. Contrary to expectations for a species with RIP, we identified recent TE activity in multiple populations. The TE composition and copy numbers showed little divergence among global populations regardless of the demographic history. Miniature inverted-repeat transposable elements (MITEs) and terminal repeat retrotransposons in miniature (TRIMs) were largely underlying recent intra-species TE expansions. We inferred RIP footprints in individual TE families and found that recently active, high-copy TEs have possibly evaded genomic defences. We find no evidence that recent positive selection acted on TE-mediated mutations rather that purifying selection maintained new TE insertions at low insertion frequencies in populations. Our findings highlight the complex evolutionary equilibria established by the joint action of TE activity, selection and genomic repression.

Post-buckling path and free vibration of a symmetric laminated plate vertically coupled with fluid under in-plane load

In this paper, the effect of compressive in-plane load on the equilibrium paths and vibration characteristics of a vertical symmetric laminated plate coupled with fluid is studied theoretically both in the pre- and post-buckling state. The Third-order shear deformation theory and von Karman nonlinear strain displacement relationship are utilized to describe the nonlinear deformation of the plate consists of a number of fiber-reinforced layers. The Hamilton's principle is introduced to formulate the plate-fluid coupled governing equations. A two-step theoretical approach is developed. Firstly, based on the Cylindrical arc-length method, we solve the nonlinear static equations to trace the snap-back behavior and pass the limit points along the complex equilibrium paths obtaining the stable buckling deflection. Then the coupled vibration characteristics are calculated using the tangent stiffness at the stable positions. The present theoretical results are validated by the numerical results. The effects of added mass and hydrostatic load are compared and analyzed. It is noted that, in the post-buckling state, the number of limit points along the static unstable equilibrium path increases with the compressive in-plane load getting larger. The variation trends of the natural frequencies and modes under different in-plane loads in pre- and post-buckling state are investigated.

Dynamic Modeling for Temperature Prediction in a Fluidized Bed Biomass Gasification Process

A long short-term memory (LSTM) based artificial neural network (ANN) model is developed to predict the temperatures of the fluidized bed and freeboard as well as of the outlet gas temperature during the fluidized bed biomass gasification process. The various available equilibrium models and the kinetic models to simulate this process are often found impractical at a large scale due to the assumptions on which these models are framed. Instead of solving complex kinetic and equilibrium models, this study explores the potential of utilizing an LSTM model for the dynamic modeling of a fluidized bed biomass gasifier. The influence of various hyperparameters on LSTM model performance are also studied. Among many tested activation functions, tanh has the lowest mean squared error overall. Adagrad and SGD are identified as the most suitable optimizers for our LSTM model. Single and two layered LSTM models are compared. The LSTM model is validated with the spatio-temporally resolved experimental data of the pilot plant fluidized bed gasifier. The LSTM model is further examined for temperature predictions at three future points (1 min, 3 min, and 5 min ahead). Overall, the LSTM model offers a sufficiently accurate alternative for temperature prediction in fluidized bed biomass gasifier.

Characterization of Oral Microbiota in Cats: Novel Insights on the Potential Role of Fungi in Feline Chronic Gingivostomatitis.

Previous studies have suggested the involvement of viral and bacterial components in the initiation and progression of feline chronic gingivostomatitis (FCGS), but the role of fungi remains entirely unknown. This pilot study aimed to investigate the bacteriome and mycobiome in feline oral health and disease. Physical exams, including oral health assessment, of privately owned, clinically healthy (CH) cats (n = 14) and cats affected by FCGS (n = 14) were performed. Using a sterile swab, oral tissue surfaces of CH and FCGS cats were sampled and submitted for 16S rRNA and ITS-2 next-generation DNA sequencing. A high number of fungal species (n = 186) was detected, with Malassezia restricta, Malassezia arunalokei, Cladosporium penidielloides/salinae, and Aspergillaceae sp. being significantly enriched in FCGS samples, and Saccharomyces cerevisiae in CH samples. The bacteriome was significantly distinct between groups, and significant inter-kingdom interactions were documented. Bergeyella zoohelcum was identified as a potential biomarker of a healthy feline oral microbiome. These data suggest that fungi might play a role in the etiology and pathogenesis of FCGS, and that oral health should not simply be regarded as the absence of microbial infections. Instead, it may be viewed as the biological interactions between bacterial and fungal populations that coexist to preserve a complex equilibrium in the microenvironment of the mouth. Additional investigations are needed to improve our understanding of the feline oral ecosystem and the potential interactions between viruses, bacteria, and fungi in FCGS.

Compliance With Vaccination Recommendations Among Patients With Multiple Myeloma: A Real World Experience.

Compliance With Vaccination Recommendations Among Patients With Multiple Myeloma: A Real World Experience.

A Machine Learning Approach to Study Demographic Alterations in Honeybee Colonies Using SDS-PAGE Fingerprinting.

Simple SummaryHoneybees are vital pollinators for the human food chain. Colony depopulation is a serious threat to Apis mellifera populations and unfortunately it is also one of the most elusive and difficult to study. This research deals with the problem at its foundation: population imbalances. The proposed method allows to discriminate, with remarkably good performances, precocious foragers from proper aged ones using SDS-PAGE patterns of haemolymph proteins. Implications and future perspectives are discussed.Honeybees, as social insects, live in highly organised colonies where tasks reflect the age of individuals. As is widely known, in this context, emergent properties arise from interactions between them. The accelerated maturation of nurses into foragers, stimulated by many negative factors, may disrupt this complex equilibrium. This complexity needs a paradigm shift: from the study of a single stressor to the study of the effects exerted by multiple stressors on colony homeostasis. The aim of this research is, therefore, to study colony population disturbances by discriminating overaged nurses from proper aged nurses and precocious foragers from proper aged foragers using SDS-PAGE patterns of haemolymph proteins and a machine-learning algorithm. The KNN (K Nearest Neighbours) model fitted on the forager dataset showed remarkably good performances (accuracy 0.93, sensitivity 0.88, specificity 1.00) in discriminating precocious foragers from proper aged ones. The main strength of this innovative approach lies in the possibility of it being deployed as a preventive tool. Depopulation is an elusive syndrome in bee pathology and early detection with the method described could shed more light on the phenomenon. In addition, it enables countermeasures to revert this vicious circle.

Hydrogen Based Compounds as Energetic Catalysts for Liquid Rocket Engines: Implications and Applications

In the current scenario of space propulsion, liquid propellants have significantly proved useful in the upper stage rocket engines. Over the past couple decades, the world had inclined positively towards cryogenic fuel(s) viz., liquid oxygen and liquid hydrogen due to their high specific impulse. A higher specific impulse implies lower duration to achieve design cruise velocity for a given rocket initial and instantaneous mass. Liquid hydrogen and liquid oxygen as fuel and oxidizer can generate one of the highest enthalpy release in combustion, producing a specific impulse of up to 450 seconds at an effective exhaust velocity of 4.4 kilometres per second. Whereas, selected disadvantages are encountered in the form of storage and production. This indicates overdependence on cryogenic propellants and has necessitated the active research effort for better alternatives. As an interesting alternative, the combination of Dinitrogen Tetroxide (N2O4) and Monomethyl Hydrazine (MMH) have been used for many space applications owing to an extreme storage stability and hypergolic nature. Present study aims to express the effect of hydrogen-based compounds on the rocket performance. Four distinctive compounds from two groups of hydrogen-based compounds are tested with the varying oxidizer and fuel proportions to obtain a new, cost-effective and user-friendly composition that can be prepared at room temperature. The investigation attempt and explains the effect of hydrogen based energetic propellants using N2O4 and MMH as the base composition for upper stage performance. The work is motivated by the need of efficient space operations with attractive propulsive alternatives to minimize over-dependence on cryogenics, which will ultimately result in cost effectiveness. Various energetic materials were tested with the base composition by using standard NASA-CEA complex chemical equilibrium model. The performance was evaluated in terms of variation in specific impulse and characteristic velocity both of which are significant parameters. To, validate the practical utility, the role of chamber pressure, supersonic area ratio and optimal Oxidizer to fuel ratio (O/F) was determined. The work led to two interesting findings, a composition of beryllium hydride with base composition for high performance of rockets and the negative impact of hydrogen on liquid propellants.

Electrocoagulation/oxidation/flotation by direct pulsed current applied to the removal of antibiotics from Brazilian WWTP effluents

Emerging contaminants such as pharmaceutical residue brings harmful effects to the environment and human health as well. In Brazil, wastewater treatment plants (WWTPs) for influents and effluents do not remove efficiently that kind of residue due to the conventional biological-like treatment. In this context, alternative treatments, such as electrocoagulation can be used to achieve better removal efficiency based on electrolytic treatment. In this work, electrocoagulation processes (ECOF) were applied to remove antibiotics, such as trimethoprim (TMP) and amoxicillin (AMX) using a direct pulsed current (DPC). The electrocoagulation process was conducted using different anodes (304 and 316L steel electrodes and 1050 aluminum electrodes), and were evaluated experimental parameters such as corrosion rate, pH of the working solution and operational costs. In comparison with other electrodes, the 1050 aluminum electrode showed the larger corrosion rate, longer service life and smaller operational costs (energy and electrode consumptions). In addition, using of the pulsed direct current reduced the consumption energy of the electrocoagulation process by 30% when compared to the same process using direct current. During electrocoagulation process, the electrodes showed a complex hydrolysis equilibrium due to charge density transfer of the electrodes themselves which resulted in an acid-base equilibrium between hydrolysis products and AMX/TMP molecules. For 1050 aluminum electrodes, the pH of the electrolyte during electrocoagulation process changed from 3.0 to 5.5, and the cationic equilibrium containing Al3+ and Al(OH)2+ along the studied molecules was proposed. The same equilibrium approach was used in iron present in the steel electrodes: once the pH ranged from 3.0 to 7.0, the proposed equilibrium for this system evolves Fe3+, Fe(OH)2 and Fe(OH)3 compounds. To investigate the reactivity between AMX/TMP molecules and the electrodic surfaces, DFT calculations were conducted, and the analysis of molecular parameters in the experimental processes showed a passivation effect of AMX and TMP molecules towards 1050 aluminum electrode while AMX presented a corrosion effect in steel electrodes. Therefore, the 1050 aluminum electrode presented the best efficiency over steel electrodes in electrocoagulation process for AMX and TMP removal in wastewater, having potential to be applied in large scale application in a WWTP.

Game Theory in Practice, on the (Non) Discovery of Social Equilibria

What follows is an attempt to view (elementary) game theory through the prism of recent developments in philosophy of mathematics. In particular, if a model (in the sense of model theory)on an appropriate domain can be constructed from a formal theory and it can be established that homomorphic mappings between model structures are possible then such a maneuver undermines the Realistic case for solution concepts since it makes the denotation of such concepts problematic since the denotation ceases to be unique. This creates philosophical problems within the Philosophy of mathematics which affects communities of mathematicians working in particular mathematical areas. (Groups, Rings, Vector Spaces, Graphs and so on) However when it comes to game theory, problematic denotation affects not only Professionals (mathematicians, economists, game theorists) but also ‘ordinary’ people in the real world who interact with each other in social contexts amenable to game theoretic analysis I note briefly that Game theory has difficulties, still, with equilibrium selection and simple 2X2 games fail to predict and these problems have triggered extensive debates. I do not specify any specific causal connection between referential failure and any given issue within game theory I do however suggest that there is clearly a need to supplement the semantics of equilibrium concepts (here the minimax theorem) and I note that even simple 2X2 games typically come with labels, prisoner, husband-wife, hawk and so on. These perhaps provide hooks into more comprehensive semantics. I also briefly discuss conventions as an additional mechanism. Finally I suggest that if this analysis is on the right lines it might be extended to include more complex social equilibrium mechanisms like Nash equilibrium or general economic equilibrium in micro economics. The style is deliberately informal.

The structure and stability of faecal pigment-Zinc(II) complexes

This work presents an in-depth study on the nature of the faecal pigment-zinc(II) complexes using spectroscopic, thermodynamic and computational studies towards a molecular level understanding regarding its structure, complexation and stability. The analysis of faecal pigments (FPs), specifically urobilin (UB) and stercobilin (SB), is often carried out using Schlesinger's test, that uses the zinc complexation induced enhancement of FPs fluorescence. It was observed that in addition to the expected 1:1 stoichiometry, FP-Zn(II) complex with 1:2 stoichiometry also form. This was confirmed by the ESI-MS mass spectral fragmentation patterns. A rigorous benchmarking process towards using optimized basis set and functionals for molecular orbital TD-DFT calculations on UB-Zn(II) complex suggested the use of B3LYP hybrid functional and LANL2DZ basis set as the optimized combination. Molecular geometries and transition energies predicted from MO calculations corroborated well with FTIR and mass spectrometric results. FP-Zn(II) complexation equilibria in aqueous media involve disaggregation of higher FPs followed by metal-ligand complexation. The binding constant values of FP-Zn(II) complexes were estimated to be 101 M−1 & 22 M−1 for 1:1 and 1:2 stoichiometries of SB-Zn(II) complexes and 105 M−1 & 11 M−1 for 1:1 and 1:2 stoichiometries of UB-Zn(II) complexes in aqueous media. For the 1:1 complexes, the enthalpy (∆H0) and entropy (∆S0) values for SB-Zn(II) are 65 k J mol−1 and 269 J K−1 mol−1, respectively. Similarly, enthalpy (∆H0) and entropy (∆S0) for UB-Zn(II) complexes are 69 kJ mol−1 and 256 J K−1 mol−1, respectively. This understanding of the structure and thermodynamics of FP-Zn(II) complex is expected to aid in developing aqueous phase analytical strategies towards the fluorescence-based analysis of FPs, an important component of water quality analysis.

Programmable quantum simulations of spin systems with trapped ions

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated to produce long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields, in a prototypical example of a quantum simulator. Here we review the theoretical mapping of atomic ions to interacting spin systems, the preparation of complex equilibrium states, the study of dynamical processes in these many-body interacting quantum systems, and the use of this platform for optimization and other tasks. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on the behavior of interacting quantum systems that cannot be modeled with conventional computers.

Speciation study involving mononuclear binary transition metal (CoII, NiII and CuII) complexes of L-methionine in non-ionic micellar medium

The present work aims to evaluate the binding capacities of binary complexes of L-Methionine with transition metal ions CoII, NiII and CuII in Triton X 100-water mixtures, a non-ionic micellar media of different compositions (0.0–2.5% (v/v)), investigated under the experimental conditions of 0.16 mol/dm3 ionic strength using NaNO3 at a temperature of 303.0 ± 0.1 K Potentiometrically. The potentiometric data was assessed by Irving-Rossotti pH metric technique with the least-squares method of MINIQUAD75, a computer program. The selectivity of the best fit model obtained by continuous exhaustive chemical modelling studies and the accuracy of the results is assessed based on statistical parameters. MLH, ML and ML2 are the identified species for the three M(CoII, NiII and CuII) - Met systems. The shift in the equilibrium of binary metal-methionine complexes with variation in composition (0.0–2.5%) of the solvent can be explained by electrostatic together with non-electrostatic forces contributed by the interaction of solute with solvent.

Equilibrium of bi-stable flexural-tensegrity segmental beams

One dimensional discrete systems composed of a simple chain of bi-stable springs, with nearest neighbor interaction, have been used to interpret the complex equilibrium states of materials supporting multiple crystallographic phases, foldable macromolecules and biological structures. A discrete system is here proposed for bending within the broad class of flexural-tensegrity beams, which consist of segments in unilateral contact, with tailored-shaped contact surfaces, pre-stressed by an unbonded tendon. Any contact joint shows a bi-stable response to its relative rotation such as a snap-spring hinge, thanks to the internal carving of the segments that increases the mobility of the tendon within them. The constitutive response is nonlocal, because the tendon is free to slide within well lubricated sheaths. The case of pure bending, representing the counterpart of uniaxial tension in the one-dimensional lattice chain, shows that the system can support stable and metastable configurations, possibly containing one snap-spring hinge in the spinodal part of the energy landscape. Remarkably, not only the maximum hysteresis paths, but also the Maxwell paths, are strain-hardening in type. This is due to the nonlocal effect from the unbonded tendon: the rotation of any contact joint stiffens all the other joints, so that the orderly snaps of the spring-hinges occur at an increasing bending moment. An experimental program has been conducted on 3D printed physical models either in a hard or soft device. Symmetric and non-symmetric equilibrium configurations are obtained that are in perfect agreement with the theoretical predictions. Possible applications are envisaged, but they are yet to be fully appreciated.

Academic Reminiscences and Thermodynamics-Kinetics of Thermo-Barometry-Chronology

This article has three major components that include, in addition to the technical aspects, reminiscences of my academic upbringing, my move to the USA from India, and my professional career. I have recounted many stories that I hope convey some sense of time, especially in these two countries with vastly different cultures, my personal journey with its ups and downs and how I made the transition to an academic career path in USA even though that was not in my future plan as a young man. The development of the field of thermobarometry and its integration with diffusion and crystal kinetic modelling of compositional zoning (or lack thereof) and cation ordering in minerals have led to important quantitative constraints on the pressure-temperature-time evolution of terrestrial rocks and meteorites. I review the historical developments in these areas and a segment of my own research spanning the period of 1964-2021. The foundational works of the thermometry of metamorphic rocks and palaeothermometry were laid at the University of Chicago around 1950. Subsequently, the synergetic growth of thermodynamics and experimental studies in petrology in the 1960s and 1970s, along with the introduction of electron microprobe as a nondestructive analytical tool with micron scale resolution, gave a major boost to the field of thermobarometry. There were also significant new developments in the field of thermodynamics of solid solutions in the petrology community and demonstration from observational data, countering strong scepticism, that the principles of classical thermodynamics were applicable to “complex natural systems”. The section on thermodynamic basis of thermobarometry concludes with a discussion of the thermodynamics of trace element and single mineral thermometry. I further deal with the experimental protocols, along with selected examples, for phase equilibrium studies that provide the bedrock foundation for the field of thermobarometry based on elemental compositions of coexisting minerals in a rock. It is followed by an account of the controversies and international meetings relating to the aluminum silicate and peridotite phase diagrams that play crucial roles in the thermobarometry of metamorphic rocks and mantle xenoliths, respectively. The construction of quantitative petrogenetic grids to display stability relations of minerals in multicomponent–multiphase systems came into play in the field of metamorphic petrology in the mid-1960s and early 1970s. Augmented by experimental data, these petrogenetic grids led to important discoveries about the P-T-<em>f</em>(O<sub>2</sub>) and bulk compositional controls on the stability of certain “index” minerals that are used to define metamorphic isograds and different types of regional metamorphism; one such grid also opened up a new field that came to be known as ultra-high temperature metamorphism. The construction of petrogenetic grids has now evolved to computer based calculations of complex equilibrium P-T phase diagrams, commonly referred to as “pseudosections”, by minimisation of Gibbs free energy of a system with fixed bulk composition. I discuss these historical developments and modern advancements. Subsequently I highlight some aspects of thermobarometry and diffusion kinetic modelling of selected natural samples along with their broader implications and present a critical discussion of different protocols for thermobarometry of natural assemblages. Following up on the introductory historical perspective of development of palaeothermometry, I discuss the modern advancements using density functional theory (DFT). Examples of DFT based calculations have been shown for hydrogen isotope fractionation in mineral-water/hydrogen systems and “clumped isotope” thermometry. The hydrogen isotope fractionation data led the development of new low temperature palaeothermometers using serpentine-talc/brucite mineral pairs. These results enable simultaneous solutions of both temperature and source of fluid in the serpentinisation process of rocks. The final section is devoted to high temperature thermochronology dealing with the problems of closure temperature of decay systems in minerals and the use of bulk and spatial resetting of mineral age according to a specific decay system to determine cooling rates of the host rocks. Complications arise in the interpretation of mineral ages determined by such decay systems as <sup>176</sup>Lu-<sup>176</sup>Hf or the short- lived system <sup>53</sup>Mn-<sup>53</sup>Cr in which the parent nuclide has a much lower closure temperature than the corresponding daughter product. Numerical simulations help explain the discrepancy between the <sup>176</sup>Lu-<sup>176</sup>Hf and <sup>147</sup>Sm-<sup>143</sup>Nd ages of garnets in metamorphic rocks and enable construction of the entire T-t cycle from the discrepant ages and some additional constraints.

Long-run market equilibria in coupled energy sectors: A study of uniqueness

We propose an equilibrium model for coupled markets of multiple energy sectors. The agents in our model are operators of sector-specific production and sector-coupling technologies, as well as price-sensitive consumers with varying demand. We analyze long-run investment in production capacity in each sector and investment in coupling capacity between sectors, as well as production decisions determined at repeated spot markets. We show that in our multi-sector model, multiplicity of equilibria may occur, even if all assumptions hold that would be sufficient for uniqueness in a single-sector model. We then contribute to the literature by deriving sufficient conditions for the uniqueness of short- and long-run market equilibrium in coupled markets of multiple energy sectors. We illustrate via simple examples that these conditions are indeed required to guarantee uniqueness in general. The uniqueness result is an important step to be able to incorporate the proposed market equilibrium problem in more complex computational multilevel equilibrium models, in which uniqueness of lower levels is a prerequisite for obtaining meaningful solutions. Our analysis also paves the way to understand and analyze more complex sector coupling models in the future.

The pH and mercury ion stimuli-responsive supramolecular assemblies of cucurbit[7]uril and Hoechst 33342

In the present work, we have investigated the effect of pH and mercury ions on the host–guest complex formed between cucurbit[7]uril (Q[7]) and Hoechst 33342 (H33342). 1H NMR, UV–vis and fluorescence spectroscopy revealed that acid/base stimulation could change the binding stoichiometry between Q[7] and H33342. The results suggest that two complexation equilibria (1:1 and 2:1) may exist between H33342 and Q[7] at pH 2.0 and 4.5, respectively. However, a 1:1 host–guest complex was formed between H33342 and Q[7] at pH 7.0 and 10.0. Q[7] shows differential affinities for the protonated and neutral forms of H33342 dye. Moreover, the switching between H33342∙2H+@2Q[7](1:2) at pH 4.5 and H33342∙H+@Q[7](1:1) at pH 7.0 was reversible. Furthermore, as a metal stimulus, Hg2+ ions could push (i) Q[7] from the piperazine ring to the benzimidazole position with a 1:1 guest–host ratio and (ii) a second Q[7] onto the ethyl position with a 1:2 guest–host stoichiometry. This stimulus response system will have potential applications in the field of molecular switch design.

A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics

This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by extrapolating the solutions from two previously converged load steps. The extrapolation is a linear combination of the previous solutions; therefore, it is simple and inexpensive. Additionally, the proposed extrapolated predictor also serves as a means for identifying the forward movement along the equilibrium path without the need for any sophisticated techniques commonly employed for explicit tracking. The ability of the proposed technique to successfully compute complex equilibrium paths in static structural mechanics problems is demonstrated using seven numerical examples involving truss, beam-column and shell models. The computed numerical results are in excellent agreement with the reference solutions. The present approach does not require prohibitively small increments for its success.

Occupational harmony: Embracing the complexity of occupational balance

ABSTRACT Occupational balance is a central concept in occupational science, but it is complex and lacks an agreed-upon definition. Further, the concept has not been given significant attention by scholars outside Western societies. Building upon traditional Chinese culture and Chinese scholars’ Human Complex System Theory, this article presents a proposed Model of Occupational Harmony, offering an Eastern understanding of how the orchestration of everyday occupations relates to health and well-being. The notion of occupational harmony highlights harmonious human-environment transactions as the essence of the phenomenon and integrates multiple perspectives in previous occupational balance literature, including activity patterns, time use, occupational characteristics, need satisfaction, and biological rhythms. It is asserted that occupational harmony can be characterized as complex equilibria among three pairs of two-sided occupational characteristics and achieved via harmony among five dimensions of occupational engagement and coherence across multiple levels of human-environment transactions. This article is a beginning theoretical conceptualization of occupational harmony, allowing occupational scientists to embrace the complexity of the orchestration of occupational engagement.

Ligand‐Directed Approach in Polyoxometalate Synthesis: Formation of a New Divacant Lacunary Polyoxomolybdate [γ‐PMo10O36]7−

AbstractPolyoxometalates (POMs) have received increasing attention over the last decades for extending their application and properties that originate from novel structures. For the synthesis of a variety of POM structures, multivacant lacunary POMs are key precursors, which are typically synthesized by empirically controlling the complex equilibrium in aqueous solvents. Unfortunately, despite the excellent catalytic and electrochemical properties of “polyoxomolybdates”, only one multivacant lacunary species, i.e., [A‐α‐PMo9O34]9−, has been identified and isolated because multivacant lacunary polyoxomolybdates are typically unstable. Here we report a ligand‐directed approach for the selective formation of an unprecedented lacunary polyoxomolybdate in organic solvents. By structure transformation of a pyridine‐coordinated [A‐α‐PMo9O34]9−, a new γ‐Keggin‐type divacant lacunary polyoxomolybdate [γ‐PMo10O36]7− was obtained, which can be further used as a precursor for synthesizing a POM–organic hybrid.