In this paper, by using the variational method, a sufficient condition for the unique existence of the stationary solution of the reaction-diffusion ecosystem is obtained, which directly leads to the global asymptotic stability of the unique equilibrium point. Moreover, delayed feedback ecosystem with reaction-diffusion item is considered, and utilizing impulse control results in the globally exponential stability criterion of the delayed ecosystem. It is worth mentioning that the Neumann zero-boundary value that the infected and the susceptible people or animals should be controlled in the epidemic prevention area and not allowed to cross the border, which is a good simulation of the actual situation of epidemic prevention. And numerical examples illuminate the effectiveness of impulse control, which has a certain enlightening effect on the actual epidemic prevention work . That is, in the face of the epidemic situation, taking a certain frequency of positive and effective epidemic prevention measures is conducive to the stability and control of the epidemic situation. Particularly, the newly-obtained theorems quantifies this feasible step. Besides, utilizing Laplacian semigroup derives the $p$th moment stability criterion for the impulsive ecosystem.

We study the atom-field interaction at finite temperature and in the dispersive regime. We show that the master equation for this sytem may be solved with the use of superoperator techniques. We calculate the linear entropy in case the field is initially in a coherent state and the atom in a superposition of its ground and excited states.

This work reports a characterization of crystallographic phases and chemical composition of hercynite-spinel (FeAl2O4) natural long crystals and their powders using X-ray Diffraction, Scanning Electron Microscopy, Inductively Coupled Plasma mass spectrometry, and mineralographic/petrographic analysis. The samples studied show a high content of hercynite with Neumann bands/Widmanstätten patterns, coexisting with other crystallographic phases such as corundum, spinel (MgAl2O4), esseneite, kamacite, hedenbergite, pseudobrookite, and ulvospinel. The diffractograms of two of the samples examined exhibit an extraordinary sharpness of the diffraction peaks that determines a high degree of crystallinity, which is hard to obtain in hercynite synthesized by artificial methods. In addition, the hercynite natural samples are less porous than the artificially synthesized hercynite. The x-ray diffraction pattern of one of the pulverized crystalline samples allowed us to estimate the percentage of the main phases present. The crystallographic existent phases with the highest participation in one of the spinel samples were hercynite (43.4%), corundum (18.7%), spinel (18.4%), esseneite (17.2%), and kamacite with a 2.3 %. These results contribute to the structural characterization of this unique material widely used in many technological applications.

The notion of quantum-mechanics-free subsystem (QMFS) was introduced by Tsang and Caves in 2012. They showed that it is possible to design the dynamics of coupled quantum systems in such a way that one can construct a subsystem in which a given classical dynamics is realized, thus avoiding the measurement back-action of quantum mechanics. Although they mention that the Heisenberg picture equations of motion for QMFS was first proposed by Koopman in 1931 as a formulation of classical Hamiltonian dynamics in Hilbert space, in fact the connection between QMFS and Koopmann-von Neumann mechanics is deeper. Namely, quantum-mechanics-free subsystem is nothing but the realization of Sudarshan's perspective on the Koopman-von Neumann mechanics.

A variant of the von Neumann-Wigner Interpretation is proposed. Problems arising from the quantum Zeno effect are addressed as we have described previously. We do, however, offer some new, and perhaps unexpected observations. We are accustomed to thinking of wave function collapse as occurring consequent to laboratory measurements. We speculate that, whatever physical correlate of consciousness exists within the brain, it is quantum mechanical in the sense that a brain, left to itself, would eventually decohere into a state no longer compatible with its conscious functioning. Wave function collapse returns it to a state compatible with consciousness. Indeed, this may be its important reason for occurring. A universe without it simply could not play host to conscious brains. The fact that it also prevents us from encountering "absurd" situations in the laboratory is merely a fortunate dividend. Whenever a quantum measurement is made the universe's future history splits into a number of possibilities. This number may be very large or infinite. And we believe consciousness plays a vital role in this happening. A "conscious" universe where quantum measurements are being made allows for an enormous number of equally acceptable world-histories. An "unconscious" one, always evolving in a unitary fashion, allows for only one. If we assume that the decision as to which worldhistory is the real one (i.e. this one) is made at random we see that the universe is overwhelmingly more likely to be "conscious" than not.

In a previous work by the author it was shown that the Koopman-von Neumann formulation of classical mechanics (KvN) exhibits quantum interference. As such it was there claimed that KvN ought to be considered as a proper quantum mechanical theory in a similar sense as ordinary non-relativistic quantum mechanics (OQM) is. In this article this claim is made manifest by showing that KvN and OQM can be taken as merely inequivalent representations resulting from one and the same quantization scheme. Of course, as the typical notion of quantization necessitates the canonical commutation relations (CCR) to hold, which they do not in KvN, the concept needs to be properly revised. To justify such a revision the typical reasons for necessitation the CCR, reductionism and quantization as 'turning brackets to commutators', are examined and found insufficient.

Current-quark masses are compared to the rest masses allowed by the Helmholtz equation in a polar model. Within the uncertainty of the current u quark mass determination, the current quark mass coincides with the rest mass allowed by the Helmholtz equation in the polar model in accordance with the second root of the zero Neumann function. Current d quark mass coincides with the rest mass calculated in accordance with the third root of the Bessel zero function. On the basis of a comparison of these results with the results obtained earlier for ordinary real particles u and d quarks stability is discussed.

Extension of a derivation on a universally reversible JC-algebra A⊆B(H)_{sa} to the C*-algebra [A] generated by A in B(H) was studied by Upmier [20, Theorem 2.5]. In this article we study the extension of a Jordan derivation on a universally JC-algebra A to its universal enveloping real and complex C*-algebras R and U, respectively. Also, we establish the relationship between local derivations (resp., 2-local derivations, weak local derivations, weak-2-local derivations) of a universally JC-algebra A and the corresponding maps on its universal enveloping real and complex C*-algebras R and A, respectively.

In this article, we have tried to extend the Neumann–Kopp law concerning the heat capacity of solid compounds to other physical observables for materials represented as mixtures of chemical compounds, alloys, and ceramics. The main goal of this study is to find the intervals of external or internal parameters for a solid compound, within which its physical observable - the magnetic transition temperature for this work, can be expressed in terms of the atomic or molar weighted sum of the magnetic transition temperatures of the constituent elements of a compound. Outside these intervals, we tried to figure out the structure of the variable by which the weighted sum should be multiplied. Thus, for USb–x(ThSb) mixtures with a mole fraction x from 0.36 to 0.55, the magnetic transition temperature of this mixture is expressed in term of the molar weighted sum of the temperature of uranium structural transition associated with a change in the magnetic properties of uranium and of the temperature at which the nature of the magnetic susceptibility of antimony changes. For the magnetic Laves phase compounds Er(Fe_0.8–xMn_0.2–yCo_x+y)₂, the Curie temperature of the compound is equal to the weighted sum of the Curie temperatures of all elements of the compound, except for Mn, at x = 0.1, y = 0 and y = 0.1. For the paramagnetic Curie temperature of intercalated dichalcogenides Cr_xМоSe₂, it can be expressed in terms of the weighted Neel temperature of chromium multiplied by a variable depending on x, on the atomic numbers of all elements of the compound, and on a parameter proportional to the derivatives with respect to x of the dichalcogenide’s crystal lattice parameters.

This article proposes a novel formulation of quantization, which considers the Koopman-von Neumann formulation (KvN) and ordinary non-relativistic quantum mechanics (OQM) as unitarily inequivalent representations of the same underlying structure. The approach is grounded in the notion that contextuality, rather than occurrence if Plank's constant, is the fundamental aspect of quantum mechanics. The motivation for this novel view arises from the limitations of traditional approaches to quantization, combined with previous research demonstrating contextuality in KvN. Using a representation-theoretic approach, both KvN and OQM are regarded as valid quantum theories, separated by a superselection rule.

Fourier expansions by the polyharmonic-Neumann eigenfunctions showed improved convergence compared to the Fourier expansions by the classical trigonometric system due to the rapid decay of the corresponding Fourier coefficients. Based on this evidence, we investigate interpolations on a finite interval that are exact for the polyharmonic-Neumann eigenfunctions and show the same benefits. Further, we improve the convergence of the interpolations by applying the idea of quasi-periodicity, where the basis functions are periodic on a slightly extended interval. We show that those interpolations have much better convergence rates away from the endpoints of the approximation interval. Moreover, the interpolations are more accurate on the entire interval. We prove those properties for a specific case of the polyharmonic-Neumann eigenfunctions known as the modified Fourier system. For other basis functions, we provide evidence based on the results of numerical experiments.

Let $m$ and $n$ be the fixed positive integers. Suppose $\mathcal{A}$ is a von Neuman algebra with no central summands of type $I_{1}$ and $L_{m}$ be a Lie type higher derivation i.e., an additive (linear) map $L_{m} :\mathcal{A}\to \mathcal{A}$ such that \begin{equation}\label{def2} \[L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\] %L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\nonumber \end{equation} for all $\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}\in \mathcal{A}$. In the present paper, we study Lie type higher derivations on von Neuman algebras and prove that every additive Lie type higher derivation on $\mathcal{A}$ has a standard form at zero product as well as at projection product. Further, we discuss some more related results.

We refute a recently proposed thought experiment namely the Dead-Alive Physicist (DAP) whose authors claim it to be the falsification of the von Neumann interpretation in Quantum Mechanics. We discover major flaws in their model and our justification serves the purpose of disregarding further claims and assertions made in the paper at various stages. Thus, in a yet another situation, it is proven that the formalism advanced by von Neumann is non-trivial and non-falsifiable.

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

The basic challenges of this work are twofold: demonstrating the dependence between the functional and topological qualities of partition networks and finding the simplest—with respect to algorithmic complexity—network elements. The study of these problems is based on finding the solution to an appropriate antagonistic vertex game. The results of the numerical simulations of antagonistic partition games demonstrate that the winner’s graphs are “almost always” dense and hyperenergetic compared to the loser’s graphs. These observations reveal that successful evolutionary mechanisms can be realized, in principle, by the simplest objects (such as viruses).

We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the denition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.

Neuromorphic computing, a brain inspired non-Von Neumann computing system, addresses the challenges posed by the Moore’s law memory wall phenomenon. It has the capability to increasingly enhance performance while maintaining power efficiency. Neuromorphic chip architecture requirements vary depending on the application and optimizing it for large-scale applications remains to be a challenge. Neuromorphic chips are programmed using spiking neural networks which provide them with important properties such as parallelism, asynchronism, and on-device learning. Widely used spiking neuron models include the Hodgkin-Huxley Model, Izhikevich model, integrate-and-fire model and spike response model. Hardware implementation platforms of the chip follow three approaches: analog, digital, or a combination of both. Each platform can be implemented using various memory topologies which interconnects with the learning mechanism. Current neuromorphic computing systems typically use the unsupervised learning spike timing-dependent plasticity algorithms. However, algorithms such as voltage-dependent synaptic plasticity have the potential to enhance performance. This review summarizes the potential neuromorphic chip architecture specifications and highlights which applications they are suitable for.

The development of small scale hydroelectric power plants in Norway is determined by natural conditions, policies, attitudes and property rights. The owner of the river is the central decision maker. It is he who decides whether he will develop the power plant himself, Whether he wants to enter into a contract with an external investor and let him develop the power plant, whether he will sell his property rights or postpone the decisions. All available choices will involve risk. In order for him to make the best choice he must find the certainty equivalent to each of the choices and choose the one with the highest certainty equivalent. This is the first time the utility theory of John von Neumann and Oskar Morgenstern has been applied to decision makers in the hydro power industry in Norway.

This paper introduces a new adaptation of the enthalpic lattice Boltzmann method (LBM) tailored to simulate the intricate dynamics of conjugate heat transfer in non-homogeneous media, showcasing considerable potential for enhancing heat exchanger designs. This approach expands upon the conventional enthalpic LBM framework by seamlessly incorporating tailored source terms, enabling precise representation of local and transient variations in the medium’s thermophysical properties. The resulting LBM model comprehensively captures the energy conservation equation, with exceptions made only for flow compressibility and viscous dissipation, thereby significantly augmenting its versatility in analyzing heat exchanger configurations. Verification tests, comprising assessments of both transient and steady-state solutions, unequivocally validate the accuracy of the proposed model, further bolstering its reliability for analyzing heat exchange processes within intricate heat exchanger geometries. To demonstrate its efficacy, simulations of conjugate heat transfer processes involving fluid natural convection within structured cavities were performed, imposing both Dirichlet and Neumann boundary conditions to emulate scenarios encountered in practical heat exchanger operations. The findings yield compelling insights, particularly in the transient regime, revealing the beneficial impact of structured cavities on enhancing heat transfer processes. These insights inform potential design optimizations for heat exchangers. The results emphasize the potential of the modified enthalpic LBM approach to elucidate complex heat transfer phenomena in non-homogeneous media and structured geometries, offering valuable implications for heat exchanger engineering and optimization.

This paper presents a discrete compartmental Susceptible-Exposed-Infected-Recovered/Dead (SEIR/D) model to address the expansion of Covid-19 pandemic. When time passes, the status of the cells is determined by binary rules that update following both a neighbourhood and a delay pattern. The model assumes the environmental parameters have a crucial impact on the expansion of the disease so a grid is assigned to each parameter to model the single effect caused by this parameter. The expansion is then the weighted sum of all the grids. This proposal shows how the grid architecture, along with an update rule and a neighbourhood pattern is a valuable tool to model the pandemic expansion. This model has already been analyzed in previous works and compared with the corresponding continuous models solved by ordinary differential equations (ODE), coming to find the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the illness. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both the peak of Infected and the Recovery/Death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and in the case of plant pests.

In this work, we propose a transition wave equation from quantum to classical regime in the framework of the von Neumann formalism for ensembles and then obtain an equivalent scaled equation. This leads us to develop a scaled statistical theory following the well-known Wigner-Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in-between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities including probability density plots, scaled trajectories and arrival times are analyzed.

: In the last years, materializations of neuromorphic circuits based on nanophotonic arrangements have been proposed, which contain complete optical circuits, laser, photodetectors, photonic crystals, optical fibers, flat waveguides, and other passive optical elements of nanostructured materials, which eliminate the time of simultaneous processing of big groups of data, taking advantage of the quantum perspective and thus highly increasing the potentials of contemporary intelligent computational systems. This article is an effort to record and study the research that has been conducted concerning the methods of development and materialization of neuromorphic circuits of Neural Networks of nanophotonic arrangements. In particular, an investigative study of the methods of developing nanophotonic neuromorphic processors, their originality in neuronic architectural structure, their training methods and their optimization has been realized along with the study of special issues such as optical activation functions and cost functions.

It is claimed that classical mechanics (CM) in terms of its equivalent Koopman-von Neumann formulation (KvN) is indeed a ’real’ quantum theory since the formalism of quantum mechanics (FQM) does not, nor need it, exclude it as a such. This claim is made manifest by suggesting a common structure of which both KvN and ordinary quantum mechanics (OQM) correspond to unitary representations of, although unitarily inequivalent such. It is shown that OQM is obtained by enforcing the extra physical condition of quantized energy levels, which by itself does not constitute the ’quantum mystery’. It is furthermore shown that KvN in a physically realizable sense contain the hallmark quantum behavior of quantum interference. It is hence concluded that both CM and OQM are subjected to the same foundational issues. As the central part of both KvN and OQM is the introduction of probabilities via FQM it is suggested that the foundational issues regarding FQM are less about FQM itself and more about the concept of probability.

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e. with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e. the concept of neutron's (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle's dynamics from the quantum dynamics of the scatterer---a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, 'which-path detection' versus interference, von Neumann measurement, Week Values, etc.) new observable effects may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. 7

The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.

We mathematically derived a comprehensive theoretic framework “Asymmetry Theory”, based solely on the well-established principle of “the constancy of the velocity of light” without any other assumptions, like the ether. This paper proves that Asymmetry Theory encompasses all results of Special Relativity (STR) as a special case when the observer moves perpendicularly to the “source-observer” line. It explains everything STR does but extends beyond it, offering novel and groundbreaking insights. The longstanding controversies surrounding STR arise from its application outside its intended special case, hence, they are all resolved in Asymmetry Theory. Asymmetry Theory is supported by all experiments supporting STR, like Kaufmann, Ives-Stilwell, muon lifetime, nuclear reaction…., and those contradicting STR, like the Lunar range and GPS tests of light speed and the lack of transverse Doppler shift. Despite its mathematical rigorousness and all experimental evidence, we propose two new experiments to decisively test predictions from both theories.The mathematically derived Asymmetry Theory is a more comprehensive theoretical framework covering STR as a special case. It is self-consistent and theoretically proved by Maxwell’s equations. It does not contradict any established physical observations but instead resolves century-old controversies by providing a unified, mathematical and paradox-free explanation of key phenomena. Furthermore, its groundbreaking results offer a unified perspective across various distinct laws of physics, including: A formula for light velocity mathematically explains the Sagnac effect, one-way light speed, stellar aberration, Michelson-Morley, Hafele-Keating and Optic clocks. Electrodynamics formulas encompass particle acceleration, Mass-Energy and matter wave. A unified formula for all cases of classical and transverse Doppler effects covers time-varying Doppler effect, cosmological redshift, and Cherenkov radiation. A generalized form of Maxwell's equations for moving observers directly derives the formulas for light speed, Doppler effect and Sagnac effect.