Second Type Of Solution Research Articles

Russia’s Purposes in Its War with Ukraine: From a Regime Change, Conquest, to Territorial Consolidation

This paper investigates the endeavors to solve the Donbas Conflict typologically. The first and most consistent policy was the Minsk Accord belonging to the category of federalization. As has been the case with other post-Soviet secession conflicts, federalization was a hopeless policy, which produced serious commitment problems, while contradicting the real interests of both the parent state (Ukraine) and the secession polities (the DPR and LPR). In the context of the Donbas War none proposed the second type of solution, that is, land-for-peace. Ineffective diplomatic endeavors induced both Ukraine, Russia, and the DPR/LPR to solve the situation in a military way. Azerbaijan’s victory in the Second Karabakh War in 2020 disposed Ukraine for a coercive solution of the Donbas problem (the reconquest policy). The Russian political and military leadership split into two groups: one supporting the policy to make the secession polities (the DPR and LPR) Russia’s protectorates and another supporting the policy to destroy the parent state (Ukraine). The unsatisfactory results of Russia’s choice in 2008 of the protectorate policy vis-à-vis South Ossetia and Abkhazia and underestimation of Kyiv’s defense capacity made the Russian leaders opt for the destruction of Ukraine itself.

Electron and muon g−2 anomalies in general flavor conserving two-Higgs-doublet models

In general two Higgs doublet models (2HDMs) without scalar flavour changing neutral couplings (SFCNC) in the lepton sector, the electron, muon and tau interactions can be decoupled in a robust framework, stable under renormalization group evolution. In this framework, the breaking of lepton flavour universality (LFU) goes beyond the mass proportionality, opening the possibility to accommodate a different behaviour among charged leptons. We analyze the electron and muon $(g-2)$ anomalies in the context of these general flavour conserving models in the leptonic sector (g$\ell$FC). We consider two different models, I-g$\ell$FC and II-g$\ell$FC, in which the quark Yukawa couplings coincide, respectively, with the ones in type I and in type II 2HDMs. We find two types of solutions that fully reproduce both $(g-2)$ anomalies, and which are compatible with experimental constraints from LEP and LHC, from LFU, from flavour and electroweak physics, and with theoretical constraints in the scalar sector. In the first type of solution, all the new scalars have masses in the 1--2.5 TeV range, the vacuum expectation values (vevs) of both doublets are quite similar in magnitude, and both anomalies are dominated by two loop Barr-Zee contributions. This solution appears in both models. In a second type of solution, one loop contributions are dominant in the muon anomaly, all new scalars have masses below 1 TeV, and the ratio of vevs is in the range 10--100. The second neutral scalar $H$ is the lighter among the new scalars, with a mass in the 210--390 GeV range while the pseudoscalar $A$ is the heavier, with a mass in the range 400--900 GeV. The new charged scalar $H^\pm$ is almost degenerate either with the scalar or with the pseudoscalar. This second type of solution only appears in the I-g$\ell$FC model. Both solutions require the soft breaking of the $\mathbb{Z}_{2}$ symmetry of the Higgs potential.

Automatic cyber security risk assessment based on fuzzy fractional ordinary differential equations

Real-time network security risk detection is of great significance to the research of dynamic network security, and it is one of the current research hotspots of network security. Based on the idea of artificial immune, a dynamic network intrusion detection and prediction model based on fuzzy fractional ordinary differential equations is proposed. The uniqueness of the solution is studied in the square integrable equation space using the principle of compression operator, and then the second type of solution is proposed. The differential-type piecewise Taylor series expansion method of the linear Fredholm integral equation is used to obtain the approximate solution expressions and perform convergence and error estimation. The process of network attack detection, antibody concentration calculation method and risk prediction process based on time series autoregressive moving average model are given. The experimental results show that the model can quantitatively analyze the current security situation of the network in real time and make predictions about the risks faced by the network. The prediction effect of catastrophe network risk is better than the GM (1, 1) model, and it is close to the actual risk situation, with high prediction accuracy.

Bright soliton solutions to a nonlocal nonlinear Schrödinger equation of reverse-time type

Two types of multiple bright soliton solutions for a focusing nonlocal reverse-time nonlinear Schrodinger equation are derived by using the Hirota’s bilinear method and the Kadomtsev–Petviashvili hierarchy reduction. Compared with the case of the local Manakov system, both types of soliton solutions are restricted to ones with even numbers. For the first type of solution, the fundamental paired soliton exhibits two paralleled line solitons along with the time axis and the special breathing soliton. For the second type of solution, the fundamental paired soliton only allows head-on collisions with the same velocity, in which the collision with spatial interferences and the degenerate soliton with position shifts can be realized with certain parameters. General higher-order soliton solutions of two types describe the superposition of the fundamental paired soliton, which show a few interesting dynamical behaviors such as the superposed breathing solitons, the interaction of two paired soliton bound states, the interaction of two degenerate solitons with position shifts and the breathing soliton with position shifts.

Barycentric Solutions of Linear Almost Periodic Equations: Baire Class and Almost Automorphy

When the Favard separation condition fails, a linear almost periodic equation possessing bounded solutions may have no almost periodic solutions, or equivalently, no continuous solutions in hull. Almost automorphic solutions are however known to persist and, in the scalar case, the same happens to semi-continuous solutions in the hull. The aim of the present paper is twofold: extending the second type of solutions to higher dimensions, via the notion of barycenter, and fully understanding the relationships with the first type of solutions. Semi-continuity has to be replaced by some Baire class and the scalar connection with almost automorphy breaks down in an unrecoverable way: a not negligible effort is devoted to restore it at deeper level of generality.

Mixed soliton solutions of the defocusing nonlocal nonlinear Schrödinger equation

By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrödinger equation. We reveal that the first type of solution can display a large variety of interactions among two exponential solitons and two rational solitons, in which the standard elastic interaction properties are preserved and each soliton could be either the dark or antidark type. By developing the asymptotic analysis method, we also find that the second type of solution can exhibit the elastic interactions among four mixed asymptotic solitons. But in sharp contrast to the common solitons, the mixed asymptotic solitons have the t-dependent velocities and their phase shifts before and after interaction also grow with |t| in the logarithmical manner. In addition, we discuss the degenerate cases for such two types of mixed soliton solutions when the four-soliton interaction reduces to a three-soliton or two-soliton interaction.

Numerical Simulation of Plasma Near the Cathode Spot of Vacuum Arc

Kinetic numerical simulation of plasma near the cathode spot (CS) was performed. Two types of possible solutions for the self-sustained CS on copper cathode were found. The firs type of solutions is valid for quasi-stationary spot with radius of about $100~\mu \text{m}$ . Stationary solution in this case is possible with cathode temperature 4.2–4.5 kK, current density $\sim 10^{6}$ A/cm2, and applied voltage 20–25 V. The second type of solution is obtained for the spot with radius of $1~\mu \text{m}$ and spherical geometry of plasma expansion. Possible solutions were obtained for the cathode temperature of above 6.2 kK, current density of about $10^{8}$ A/cm2 and applied voltage of 15–25 V. Transient simulations of the near-cathode plasma expansion have shown that if current density remains less than $10^{9}$ A/cm2 then the plasma expansion has a “quiet” self-similar character. At higher current density the plasma expansion has an essentially nonstationary character. The high-density current leads first to the development of Buneman instability and second to the plasma rupture with the creation of conditions for collective acceleration of ions toward the cathode and toward the anode. The accelerated ions create an additional powerful heat flux to the cathode, which should facilitate the reproduction of the CSs in the spark stage of vacuum discharge.

The isothermal Euler equations for ideal gas with source term: Product solutions, flow reversal and no blow up

The one-dimensional isothermal Euler equations are a well-known model for the flow of gas through a pipe. An essential part of the model is the source term that models the influence of gravity and friction on the flow. In general the solutions of hyperbolic balance laws can blow-up in finite time. We show the existence of initial data with arbitrarily large C1-norm of the logarithmic derivative where no blow up in finite time occurs. The proof is based upon the explicit construction of product solutions. Often it is desirable to have such analytical solutions for a system described by partial differential equations, for example to validate numerical algorithms, to improve the understanding of the system and to study the effect of simplifications of the model. We present solutions of different types: In the first type of solutions, both the flow rate and the density are increasing functions of time. We also present a second type of solutions where on a certain time interval, both the flow rate and the pressure decrease. In pipeline networks, the bi-directional use of the pipelines is sometimes desirable. In this paper we present a classical solution of the isothermal Euler equations where the direction of the gas flow changes. In the solution, at the time before the direction of the flow is reversed, the gas flow rate is zero everywhere in the pipe.

A Survey of Enabling Technologies of Low Power and Long Range Machine-to-Machine Communications

Low power and long range machine-to-machine (M2M) communication techniques are expected to provide ubiquitous connections for the wireless devices. In this paper, three major low power and long range M2M solutions are surveyed. The first type of solutions is referred to as the low power wide area (LPWA) network. The design of the LPWA techniques features low cost, low data rate, long communication range, and low power consumption. The second type of solutions is the IEEE 802.11ah which features higher data rates using a wider bandwidth than the LPWA-based solutions. The third type of solutions is operated under the cellular network infrastructure. Based on the analysis of the pros and cons of the enabling technologies of the surveyed M2M solutions, as well as the corresponding deployment strategies, the gaps in knowledge are identified. The paper also presents a summary of the research directions for improving the performance of the surveyed low power and long range M2M communication technologies.

A puzzle about death’s badness: Can death be bad for the paradise-bound?

Since at least the time of Epicurus, philosophers have debated whether (and how) death could be bad for the one who has died, since (it is typically assumed) death is a permanent experiential blank. But a different (and hitherto unexplored) puzzle about death’s badness arises when we consider the death of a person who is paradise-bound. The first purpose of this paper is to develop this puzzle. The second purpose of this paper is to suggest and evaluate several potential attempts to solve the puzzle. After rejecting two seemingly attractive suggestions, I argue that there are two types of solution to the puzzle that can succeed. The first type of solution simply denies that death can be bad for the paradise-bound. I argue that the main worry for this type of solution, namely that it gives up (with respect to the paradise-bound) the common-sense view about death’s badness, is only a prima facie worry. The second type of solution maintains that death can be bad for the paradise-bound because it can deprive her of certain goods, which allows those who are attracted to this type of solution to adopt the deprivation account of death’s badness. I consider three views of the relation between the paradise-bound and paradise that are consistent with the deprivation account, connecting my discussion of paradise with the extant literature on death’s badness.

Gravity of a noncanonical global monopole: conical topology and compactification

We obtain solutions of Einstein's equations describing gravitational field outside a noncanonical global monopole with cosmological constant. In particular, we consider two models of k-monopoles: the Dirac-Born-Infeld (DBI) and the power-law types, and study their corresponding exterior gravitational fields. For each model we found two types of solutions. The first of which are global k-monopole black hole with conical global topology. These are generalizations of the Barriola-Vilenkin solution of global monopole. The appearance of noncanonical kinetic terms does not modify the critical symmetry-breaking scale, $\eta_{crit}$, but it does affect the corresponding horizon(s). The second type of solution is compactification, whose topology is a product of two $2$-dimensional spaces with constant curvatures; ${\mathcal Y}_4\rightarrow {\mathcal Z}_2\times S^2$, with ${\mathcal Y}, {\mathcal Z}$ can be de Sitter, Minkowski, or Anti-de Sitter, and $S^2$ is the $2$-sphere. We investigate all possible compactifications and show that the nonlinearity of kinetic terms opens up new channels which are otherwise non-existent. For $\Lambda=0$ four-dimensional geometry, we conjecture that these compactification channels are their (possible) non-static super-critical states, right before they undergo topological inflation.

IFROWANN: Imbalanced Fuzzy-Rough Ordered Weighted Average Nearest Neighbor Classification

Imbalanced classification deals with learning from data with a disproportional number of samples in its classes. Traditional classifiers exhibit poor behavior when facing this kind of data because they do not take into account the imbalanced class distribution. Four main kinds of solutions exist to solve this problem: modifying the data distribution, modifying the learning algorithm for considering the imbalance representation, including the use of costs for data samples, and ensemble methods. In this paper, we adopt the second type of solution and introduce a classification algorithm for imbalanced data that uses fuzzy rough set theory and ordered weighted average aggregation. The proposal considers different strategies to build a weight vector to take into account data imbalance. Our methods are validated by an extensive experimental study, showing statistically better results than 13 other state-of-the-art methods.

Weiss mean-field approximation for multicomponent stochastic spatially extended systems.

We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972)] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978)] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975)]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997)]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density for the order parameter to the unimodal one.

Limits of global growth, stagnation, creativity and international stability

Arising restrictions of global economic growth due to limited natural resources and capacity of the biosphere adversely affect on people level of life and future expectation. That leads to mass depression and social instability. To consider this problem, psycho-physiological model of onward hedonist in consumer society is developed and investigated. This model is based on the fact that human nature generates a growing desire, needs to progress. After reaching the limits of growth, member of consumer society feel persistent negative emotions and dissatisfaction. It results to socio-economic stagnation, social and international instability. The first type of possible solutions to this problem is based on the global expansion of the limits of growth (e.g., increasing of macroeconomic demand as a result of new Kondratieff technological cycle). The second type of solutions refers to local limits extension of growth within one or more countries, by means of their economic, political or military expansion in the world. But such solutions lead to international instability. The third type of solutions corresponds to periodical decreasing of the macroeconomic consumption followed by its growth (e.g., global financial crisis, decay of states and their unions, national and military conflicts, wars and so on). Such solution also leads to social and international instability. Humanistic solution consists in creativity development of people (especially middle class of developed countries) to focus on spiritual development. So rising desires of these people in spiritual realm can be satisfied under limits of global economic growth.

How can we model selectively neutral density dependence in evolutionary games

The problem of density dependence appears in all approaches to the modelling of population dynamics. It is pertinent to classic models (i.e., Lotka–Volterra’s), and also population genetics and game theoretical models related to the replicator dynamics. There is no density dependence in the classic formulation of replicator dynamics, which means that population size may grow to infinity. Therefore the question arises: How is unlimited population growth suppressed in frequency-dependent models? Two categories of solutions can be found in the literature. In the first, replicator dynamics is independent of background fitness. In the second type of solution, a multiplicative suppression coefficient is used, as in a logistic equation. Both approaches have disadvantages. The first one is incompatible with the methods of life history theory and basic probabilistic intuitions. The logistic type of suppression of per capita growth rate stops trajectories of selection when population size reaches the maximal value (carrying capacity); hence this method does not satisfy selective neutrality. To overcome these difficulties, we must explicitly consider turn-over of individuals dependent on mortality rate. This new approach leads to two interesting predictions. First, the equilibrium value of population size is lower than carrying capacity and depends on the mortality rate. Second, although the phase portrait of selection trajectories is the same as in density-independent replicator dynamics, pace of selection slows down when population size approaches equilibrium, and then remains constant and dependent on the rate of turn-over of individuals.

Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model

In this paper, we reconsider the merits of unfolding solutions based on loss functions involving a normalization on the variance per subject. In the literature, solutions based on Stress-2 are often diagnosed to be degenerate in the majority of cases. Here, the focus lies on two frequently occurring types of degeneracies. The first type typically locates some subject points far away from a compact cluster of the other points. In the second type of solution, the object points lie on a circle. In this paper, we argue that these degenerate solutions are well fitting and informative. To reveal the information, we introduce mixtures of plots based on the ideal point model of unfolding, the vector model, and on the signed distance model. In addition to a different representation, we provide a new iterative majorization algorithm to optimize the average squared correlation between the distances in the configuration and the transformed data per individual. It is shown that this approach is equivalent to minimizing Kruskal’s Stress-2.

The second harmonic generation in the symmetric well containing a rectangular barrier

The problem of determination of the maximum of second harmonic generation in the potential well containing a rectangular barrier is considered. It is shown that, in general, the problem of finding the ensemble of structures with equidistant first three levels has two types of solutions. For the first type the second and third energy levels are located above a rectangular barrier, and for the second type the third level is located above the barrier only. It is also shown, that generation corresponding to the second type of solution always is less than generation for the first one. Taking into account the effective mass changes the problem of finding the generation maximum for a finite depth well is exactly solved.

Relativistic wave equation for the bound states of a system of interacting particles

A method for obtaining the relativistic wave equation for the bound states of a system of interacting charged particles without consideration of spin is proposed. An expansion of the wave function of the system in a complete basis of orthonormal wave functions of vacuum states for each type of particle is used in this equation. It is shown that this equation contains two types of solutions for a proton + electron system. The first type corresponds to Bohr bound states. Exact expressions are obtained for the energy and Bohr radius of the ground state with consideration of the finite mass of the particles. An influence of the energy of translational motion of the system as a whole on the structure of the atomic levels in the laboratory frame is predicted. This effect is due to the finite value of m/M, and leads to removal of the degeneracy of the levels with respect to orbital angular momentum l, and partial removal of the degeneracy with respect to its projection. The second type of solution represents states of the system with binding energy \(E_b = M + m - \sqrt {|M^2 - m^2 |} \) and an exponential wave function damping radius equal to the Compton wavelength of the electron. A complete description of this state requires consideration of the electronic vacuum polarization.

The bath-plug vortex

Steady flow with constant circulation into a vertical drain is considered. The precise details of the outflow are simplified by assuming that the drain is equivalent to a distributed volume sink, into which the fluid flows with uniform downward speed. It is shown that a maximum outflow rate exists, corresponding to no fluid circulation and vertical entry into the drain hole. Numerical solutions to the full nonlinear problem are computed, using the method of fundamental solutions. An approximate analysis, based on the use of the shallow-water equations, is presented for flows in which the free surface enters the drain. There is, in addition, a second type of solution, having a stagnation point at the free surface and no fluid circulation. These flows are also computed numerically, and results are presented.

RECENT DEVELOPMENTS IN NEURODYNAMICS AND THEIR IMPACT ON THE DESIGN OF NEURO-CHIPS

Neurons can be modeled either by equations or differential equations. For the latter, a low-pass filter must be added to the analog function blocks associated with the McCullogh and Pitts type of static neuron in order to provide the time-dependent neuron solution. The low-pass filter enhances stability and enables a time-continuous analog implementation much more compact than that attained with time-discrete analog or pure digital design. A few examples of equations as well as differential equations are known for that part of learning. However, much less than for the recall mode, it is clear how to design learning neuro-chips for temporal pattern processing. It is shown here that a partial differential equation can be used to provide a unified description of both the recall and learning dynamics of a neural network as well as to investigate systematically the VLSI potential for analog time-continuous neuro-chips. It turns out that the recall and learning dynamics can be divided into causal as well as noncausal solutions. The first type of solution includes oscillating or spiking neurons. The second type of solution allows for a much simpler signal representation but leads to the problem of storing the temporal signal of each neuron for as long a time as a single pattern lasts. As this is prohibitive for larger networks and time-varying patterns, the analog VLSI implementation of causal neuron models is suggested.