An integral-free representation of the Dyson series using divided differences by Amir Kalev, Itay Hen

“…Using the mathematical tool of divided differences, we introduce an alternative representation for the series that is entirely free from both time ordering and integrals. In this new formalism, the Dyson expansion is given as a sum of efficiently-computable divided differences of the exponential function, considerably simplifying the calculation of the Dyson expansion terms, while also allowing for time-dependent perturbation calculations to be performed directly in the Schrödinger-picture. …”
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Analytical expressions for pulse profile of neutron stars in plasma environments by Gastón Briozzo, Emanuel Gallo

“…We also show how to use the new formalism to model the flux coming from different emission caps, not necessarily circular or antipodal and including the case of ring-shaped hot spots. …”
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A two-stream formalism for the convective Urca process by Lesaffre, P, Podsiadlowski, P, Tout, C

“…We derive a new formalism for convective motions involving two radial flows. …”

Variable-Barrier Quantum Coulomb Blockade Effect in Nanoscale Transistors by Pooja Yadav, Soumya Chakraborty, Daniel Moraru, Arup Samanta

“…We qualitatively replicate the experimental results with numerical calculation using this formalism for two and three energy levels participated in the tunneling transport. The new formalism supports the features of most of the small-scaled SET devices.…”
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Inclusive production of small radius jets in heavy-ion collisions by Zhong-Bo Kang, Felix Ringer, Ivan Vitev

“…We develop a new formalism to describe the inclusive production of small radius jets in heavy-ion collisions, which is consistent with jet calculations in the simpler proton–proton system. …”
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Resilience for Goal-Based Agents: Formalism, Metrics, and Case Studies by Jennifer Leaf, Julie A. Adams, Matthias Scheutz, Michael A. Goodrich

“…This manuscript proposes a new formalism of resilience as a computational construct that accounts for an agent’s sensors, effectors, communication channels, and computational resources. …”
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Tool for Behavioral Analysis of Well-Structured Transition Systems by L. V. Dworzanski, V. E. Mikhaylov

“…It makes the description of new formalisms very close to the formal definition. Therefore, it is easy to introduce and modify new formalisms as well as conduct analysis of the behavioural properties without much programming efforts. …”
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Potential Momentum and the equilibration of short Charney waves by Pablo Zurita-Gotor, Richard S. Lindzen

“…This paper proposes a new formalism for studying the extratropical circulation, based on the concept of potential momentum. …”
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Reduced density matrix and combined dynamics of electrons and nuclei by Zhao, Yang, Yokojima, Satoshi, Chen, Guan Hua

“…The single electron reduced density matrices and the Glauber coherent states are used for the electronic and nuclear degrees of freedom, respectively. The new formalism is applicable to simulate the dynamics of large molecular systems. …”
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Parton Distribution Functions at the high precision LHC by Bailey, S

“…We focus on the key concept of gauge dependency, which is highly relevant for this new formalism.</p> …”

Photon regions and umbilic conditions in stationary axisymmetric spacetimes by K. V. Kobialko, D. V. Gal’tsov

“…Here we suggest geometric description of PR in generic stationary axisymmetric spacetimes, showing that PR can be foliated by partially umbilic hypersurfaces, such that the umbilic condition holds for classes of orbits defined by the foliation parameter. New formalism opens a way of analytic description of PR in stationary axisymmetric spacetimes with non-separable geodesic equations.…”
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Anomalous Diffusion and Surface Effects on the Electric Response of Electrolytic Cells by Antonio M. Scarfone, Giovanni Barbero, Luiz R. Evangelista, Ervin K. Lenzi

“…We establish, in general terms, the conservation laws connected to a modified displacement current entering the fractional approach formulation of the Poisson–Nernst–Planck (PNP) model. In this new formalism, we obtain analytical expressions for the electrical impedance for the case of blocking electrodes and in the presence of general integrodifferential boundary conditions including time-fractional derivatives of distributed order. …”
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The Montevideo Interpretation: How the Inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem by Rodolfo Gambini, Jorge Pullin

“…These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. …”
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Causal and compositional structure of unitary transformations by Lorenz, R, Barrett, J

“…To address this, we introduce a new formalism of `extended circuit diagrams', which goes beyond what is expressible with quantum circuits, with the core new feature being the ability to represent direct sum structures in addition to sequential and tensor product composition. …”

The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations by Sayantan Choudhury

“…We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in primordial cosmology. …”
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High precision calculation of generic extreme mass ratio inspirals by Throwe, William (William Thomas)

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Indefinite causal orders in thermodynamics and from time superpositions by Felce, D

“…Finally, the possibility for ICOs to arise from superpositions in time is considered. A new formalism, developed to analyse such superpositions, is applied to the case of two events which have a quantum uncertainty associated with their times. …”

Model for the overall phase-space acceptance in a Zeeman decelerator by Dulitz, K, Vanhaecke, N, Softley, T

“…We present a new formalism to calculate phase-space acceptance in a Zeeman decelerator. …”

Analysis of the Equilibrium Distribution of Ligands in Heterogeneous Media–Approaches and Pitfalls by Maria João Moreno, Luís M. S. Loura, Jorge Martins, Armindo Salvador, Adrian Velazquez-Campoy

“…Systems of increasing complexity are considered, from proteins with single to multiple binding sites, from ligands interacting with proteins only to biomembranes containing lipid bilayers and membrane proteins. A new formalism is proposed, in which ligand binding is treated as a partition process, while considering the saturation of protein binding sites. …”
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Sequential Monte Carlo with cross-validated neural networks for complexity of hyperbolic black hole solutions in 4D by Armin Hatefi, Ehsan Hatefi

“…The solutions stay invariant under the combination of space-time dilation with internal SL(2,R) transformations. We develop a new formalism based on Sequential Monte Carlo (SMC) and artificial neural networks (NNs) to estimate the self-similar solutions to the equations of motion in the hyperbolic class in four dimensions. …”
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