Complete Set Of Solutions Research Articles

Entropy calculation for networks with determined values of flows in nodes

The paper analyses a network with given input and output flows in each of its nodes. The basis of this analysis is the algorithm for determining the set of solutions of the linear equations system, using the Gaussian method. The power of the set determines the structural entropy of the system. By introducing uncertainty into the value of part of the information flows, the deviation of the network from its equilibrium state is simulated. The set of potential solutions, as a part of the total set of the system solutions, determines the statistical entropy of the system. The probability entropy is calculated for a network with four nodes and a total flow of 10 erlangs with a sampling step of 1 erlang. Calculated entropy values for 1, 2, 3, and 4 uncertain flows out of a total of 16 flows that are transmitted between nodes of the fully connected network. As a result of the conducted statistical analysis of entropy values, the optimal number of statistical intervals for entropy values is determined: 4, 11, 24, and 43 intervals for 1, 2, 3, and 4 uncertain flows, respectively. This makes it possible to highlight the set of flows in the system that have the greatest influence on the entropy value in the system. The obtained results are of practical importance, as they enable the detection of deviations of the network from its equilibrium state by monitoring the passage of traffic on individual branches of a complex telecommunication network. Since, as shown in our previous works, the task of determining the complete set of solutions of the system for the number of nodes greater than 4 has a significant computational complexity, the application of the algorithm to such networks requires an increase in the discretization step of the values of information flows in the network. Another way to reduce computational complexity can be to reduce the set of analysed solutions to a subset of solutions close to the equilibrium state of the system.

Searching Mass-Balance Analysis to Find the Composition of Martian Blueberries: Database of Complete Solution Sets

Searching Mass-Balance Analysis to Find the Composition of Martian Blueberries: Database of Complete Solution Sets

Approximate multi-objective optimization for integrated bus route design and service frequency setting

This paper focuses on the transit network design and frequency setting problem for bus transit systems, where solutions are simultaneously generated in favor of the passengers and operator. While multi-objective solutions exist in the literature, simplifications and inconsistent assumptions make them hard to compare. For example; researchers have proposed solutions that report on a minimal fleet size without considering the service frequencies that guide the passenger’s travel options, as a result, logical choices made by all passengers would cause the buses in the transit system to be overcrowded. To address this issue, we have developed a mathematical model which couples service frequencies and passenger assignment reflective of available choice options a passenger can take in the network. This approach can achieve lower operating costs while still ensuring that passengers can reach their destination at no detriment to journey times. We have constructed a complete set of multi-objective solutions, and compared them with those in the literature. The experiments demonstrate that our current solutions generally dominate those in the literature.

Semiclassical constant-density spheres in a regularized Polyakov approximation

We provide an exhaustive analysis of the complete set of solutions of the equations of stellar equilibrium under semiclassical effects. As classical matter we use a perfect fluid of constant density; as the semiclassical source we use the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field in the Boulware vacuum (the only vacuum consistent with asymptotic flatness and staticity). For the RSET we use a regularized version of the Polyakov approximation. We present a complete catalogue of the semiclassical self-consistent solutions which incorporates regular as well as singular solutions, showing that the semiclassical corrections are highly relevant in scenarios of high compactness. Semiclassical corrections allow the existence of ultra-compact equilibrium configurations which have bounded pressures and masses up to a central core of Planckian radius, precisely where the regularized Polyakov approximation is not accurate. Our analysis strongly suggests the absence of a Buchdahl limit in semiclasical gravity, while indicating that the regularized Polyakov approximation used here must be improved to describe equilibrium configurations of arbitrary compactness that remain regular at the center of spherical symmetry.

Flow routing aiming load balancing and path length in multi-hop networks with different link qualities

This paper considers an exact bi-objective approach for simultaneously minimizing the total cost of flow routing and the network bottleneck when link qualities and flow weights are relevant. This is useful for wireless multi-hop networks with long-term TCP (Transmission Control Protocol) flows. The introduced proposal can generate a minimal complete set of Pareto-optimal solutions. Our proposal is evaluated through simulation in which are explored different parameter settings and metrics.

Floquet–Bloch eigenwaves and bandgaps in a di-periodic potential

We present general solutions to the Schrödinger equation for a di-periodic potential composed of two frequencies, thus generalizing the standard sinusoidal potential. The Schrödinger equation with a di-periodic potential becomes a three-term Whittaker–Hill equation that is solved by two different approaches. The first is applying the central equation formalism, which allows determining the Floquet–Bloch eigenwaves and band structure as a function of the potential parameters. In the second approach, we transform the Whittaker–Hill equation into an Ince equation with a suitable change of variable. In this case, we get a complete set of orthogonal solutions described by Ince functions. The well-known Mathieu functions obtained with purely sinusoidal potentials are a special case of Ince functions.

Solving max-Archimedean t-norm interval-valued fuzzy relation equations

This paper discusses a new method for finding the complete set of tolerable solutions of max-Archimedean interval-valued fuzzy relation equations. According to the literature, three types of solution sets, namely; tolerable solution set, united solution set and controllable solution set can be identified with interval-valued fuzzy relation equations. The structure and the properties of the tolerable solution set are studied. The complete set of tolerable solutions can be characterized by one maximum solution and finitely many minimal solutions. An efficient method based on the concept of covering is proposed which computes all minimal solutions. The concept of covering is useful for large size problems in terms of computation. The proposed method is illustrated with some examples.

Cold-heat adaptive control for cross-season based on bi-salt composite sorbent

<p indent=0mm>Efficient utilization of solar energy and industrial waste heat has become an important research topic in heat recovery. The sorption continuous cool-heat storage method can be used for cross-season cold-heat adaptive control owing to its advantages of high cooling and heating storage density, long-term and stable storage, and adjustable output temperature. However, this method involves the screening and synthesis of novel sorbents and optimal design of the cross-season combined cold-heat storage system. To solve the problems of low heat storage rate, high heat dissipation in the storage process, intermittent output of cold-heat, and uncontrollable temperature output in the process of adaptive control of industrial waste heat in an industrial area, a high-performance bi-salt consolidated composite sorbent is synthesized and screened in this work. Moreover, an optimized cross-season cold-heat adaptive control system is developed. Additionally, we investigate the sorption/desorption characteristics of the composite sorbent and then test the cold-hot storage/output effect of the seasonal cold-heat adaptive control system. The method adopted in the strategy mainly focuses on the efficient utilization and critical requirements of low-grade energy, such as solar energy and industrial waste heat. From the aspects of material synthesis and screening, sample performance characterization test, construction optimization, and performance evaluation of cold-heat adaptive control system, a complete set of technical solutions for the reasonable seasonal distribution of low-grade thermal energy is proposed. It provides insights for seasonal cold-heat combined storage/output.

A computational algebraic geometry technique for determining nonlinear normal modes of structural systems

A computational algebraic geometry technique is developed for determining nonlinear normal modes (NNMs) of multi-degree-of-freedom (MDOF) nonlinear dynamic systems. Specifically, resorting to computational algebraic geometry concepts and tools, such as Gröbner basis, it is shown that the complete solution set of a nonlinear algebraic system of coupled multivariate polynomial equations is determined exactly, even for a relatively large number of unknowns. Herein, these unknowns represent expansion coefficients for approximating NNMs of nonlinear dynamic systems. In this regard, the exact nature of the determined coefficient vector, which is one the significant advantages of the technique, implies increased confidence in approximating NNMs more accurately by utilizing higher-order expansions with additional terms. Several numerical examples referring to various MDOF nonlinear dynamic systems are considered for demonstrating the efficacy and potential of the solution technique. Also, note that although the technique is developed herein by relying on the classical Shaw–Pierre definition of NNMs, this is not necessarily a restriction of the methodology. In fact, the proposed computational algebraic geometry solution framework can be potentially used, in a rather straightforward manner, in conjunction with alternative NNM definitions and problem formulations requiring the solution of nonlinear algebraic equations of polynomial form.

Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization

In this article, we study a novel computational technique for the efficient numerical solution of the inverse boundary identification problem with uncertain data in two dimensions. The method essentially relies on a posteriori error indicators consisting of the Tikhonov regularized solutions obtained by the method of fundamental solutions (MFS) and the given data for the problem in hand. For a desired accuracy, the a posteriori error estimator chooses the best possible combination of a complete set of fundamental solutions determined by the location of the sources that are arranged in a particular manner on a pseudo-boundary at each iteration. Also, since we are interested in a stable solution, an adaptive stochastic optimization strategy based on an error-balancing criterion is used, so as to avoid unstable regions where the stability contributions may be relatively large. These ideas are applied to two benchmark problems and are found to produce efficient and accurate results.

Systematic description of wind-driven protoplanetary discs

Aims. Planet-forming discs are believed to be very weakly turbulent in the regions outside of 1 AU. For this reason, it is now believed that magnetised winds could be the dominant mechanism driving accretion in these systems. However, currently, no self-consistent approach can describe discs that are subject to a magnetised wind in a way similar to the α disc model. In this article, I explore the parameter space of wind-driven protoplanetary discs in a systematic manner and present scaling laws that can be used in reduced models in a similar way to α disc models. Methods. I computed a series of self-similar wind solutions, assuming that the disc is dominated by ambipolar and Ohmic diffusion. These solution were obtained by searching for stationary solutions in the finite-volume code PLUTO using a relaxation method and continuation. Results. Self-similar solutions are obtained for values of plasma β ranging from 102 to 108 for several Ohmic and ambipolar diffusion strengths. Mass accretion rates of about 10−8 M⊙ yr−1 are obtained for the poloidal field strength β = O(104) or equivalently, 1 mG at 10 AU. In addition, the ejection efficiency is always close to 1, implying that wind mass-loss rate can be higher than the inner mass accretion rate when the wind-emitting region is large. The resulting magnetic lever arms are typically lower than 2, possibly reaching 1.5 in the weakest field cases. Remarkably, the mean transport properties (accretion rate and mass-loss rate) mostly depend on the field strength and much less on the disc diffusivities or surface density. The disc internal structure is nevertheless strongly affected by Ohmic resistivity, strongly resistive discs being subject to accretion at the surface while ambipolar only models lead to mid-plane accretion. Finally, I provide a complete set of scaling laws and semi-analytical wind solutions, which can be used to fit and interpret observations. Conclusions. Magnetised winds are unavoidable in protoplanetary discs as soon as they are embedded in an ambient poloidal magnetic field. Very detailed disc microphysics are not always needed to describe them, and simplified models such as self-similar solutions can capture most of the physics seen in full 3D simulations. The remaining difficulty to set up a complete theory of wind-driven accretion lies in the transport of the large-scale field, which remains poorly constrained and is not well understood.

Reissner–Nordström geometry counterpart in semiclassical gravity

We compute the renormalized stress–energy tensor (RSET) of a massless minimally coupled scalar field in the regularized Polyakov approximation, as well as its backreaction, on the classical Reissner–Nordström spacetime. The complete set of solutions of the semiclassical self-consistent equations is obtained and compared with their classical counterparts. The semiclassical Reissner–Nordström family involves three kinds of geometries that arise depending on the charge-to-mass ratio of the spacetime. In the under-charged regime, the geometry has its external horizon replaced by a wormhole neck that leads to a singular asymptotic region at finite proper distance. The over-charged regime reveals a naked singularity surrounded by a cloud of (infinite) mass coming from the quantized field. Between both behaviours there is a separatrix solution reminiscent of the extremal black hole classical geometry. As the RSET over an extremal horizon is finite, the semiclassical backreaction does not get rid of the horizon. Nonetheless, we show that the resulting horizon is singular.

Wall and interfacial shear stresses in laminar two-phase stratified flow in pipes

Exact solutions for separated two-phase flows are useful as a benchmark for numerical codes and for testing closure relations for simplified 1D Two-Fluid models. In particular, the correct representation of the wall and interfacial shear stresses is essential for the modeling of these flows. In this study, a complete set of exact solutions for laminar stratified two-phase flows in inclined pipes is used to explore the wall and interfacial shear stresses. We examine all possible configurations with concave and convex interfaces, which are related to the contact angle of the phases with the pipe surface. A closed-form analytical expression for the average interfacial shear stress was obtained for all cases of stratified two-phase flow. The limiting behavior of the local shear stresses at the triple-point (TP) region, where the interface meets the pipe wall, is determined by residue calculus. It is shown that the shear stresses behavior upon approaching the TP is determined by the fluid's viscosity ratio and the contact angle. The combinations of those parameters that result in convergence or divergence of the shear stresses at the TP are identified. The usefulness of the analytical expressions obtained for correctly predicting the shear stresses variation upon approaching the TP is demonstrated and discussed.

Cage Solitons

The theoretical framework of the Haus master equation of passive mode-locking is revisited. Reformulating the equation in the frequency domain as coupled ordinary differential equations, the complete set of fundamental soliton solutions is surveyed. For large values of anomalous dispersion, this leads to the well known bell-shaped solutions originally found by inverse scattering. Closer to zero dispersion, mode-locked spectra are affected by the available gain bandwidth, and solitons with Bessel-like temporal profiles are found. These spectrally caged solitons match previously unexplained pulse characterization measurements of few-cycle oscillators and mode-locked fiber lasers in the normal dispersion regime. Moreover, the frequency domain formalism suggests that a phase lock between the modes can even be established in the absence of saturable absorption. This finding may explain numerous mysterious experimental reports of mode-locking or comb formation in passive microring resonators and semiconductor lasers. Therefore our frequency-domain approach sheds new light into soliton physics from a completely different perspective.

Exploring the Cultural, Managerial and Organizational Implications on Mergers and Acquisitions Outcomes

Abstract Background/Purpose: This work is focused on the variables that influence the outcomes of mergers and acquisitions, by learning from past mistakes, adopt better strategies and make wiser decisions to enhance the outcomes of their mergers and acquisitions. Using a qualitative approach, this research contributes to existing knowledge on mergers and acquisitions performance by exploring the cultural, managerial and organizational factors dimensions through an integrative approach using multiple perspectives. Methodology: Fifteen interviews were conducted with experienced professionals in multiple areas of mergers and acquisitions. Content analysis was used to interpret the results. This enabled to achieve a more complete set of answers and potential solutions while comparing opinions on the same problems from slightly different angles. Results: Results show the existence of managerial hubris, emotional attachment and over-optimism in mergers and acquisitions. There was a relative support towards standardizing the process of mergers and acquisitions deals, but respondents advise to keep some creativity and flexibility. Conclusion: The article concludes by addressing key issues for mergers and acquisitions performance: capabilities and experience; organizational communication; internal coordination; and, key issues for decision-making.

Radiation of twisted photons from charged particles moving in cholesterics

The radiation of twisted photons by charged particles traversing a cholesteric plate is studied in the framework of quantum electrodynamics in an anisotropic inhomogeneous dispersive medium. The complete set of solutions to the Maxwell equations in the cholesteric plate is constructed in the paraxial and small anisotropy approximations. The explicit expressions for the average numbers of plane-wave and twisted photons created by a charged point particle crossing the cholesteric plate are derived. The selection rules for the twisted photons radiated at the harmonic n ∈ ℤ are established. In the paraxial regime, the projection of the orbital angular momentum of a radiated twisted photon obeys the selection rule l = ± (2n + 1). In the approximation of a small anisotropy of the permittivity tensor, the selection rule becomes m = ± 2n, where m is the projection of the total angular momentum of a radiated twisted photon. The sign “±” in these selection rules is related to the choice of the forward or reflected waves in the cholesteric and is realized at the different energies of radiated photons. As the examples, the radiation of optical twisted photons by electrons with the Lorentz factors γ = 235 and γ = 500 and by uranium nuclei with γ = 2 are considered. It is shown that charged particles traversing normally a cholesteric plate can be used as a pure source of twisted photons. These results can be employed for elaboration of compact flexible sources of twisted photons, new particle detectors, and for diagnostics of the structure of liquid crystals.

Interval Solution to Fuzzy Relation Inequality With Application in P2P Educational Information Resource Sharing Systems

Max-min fuzzy relation inequalities have recently been introduced to describe the peer-to-peer (P2P) educational information resource sharing systems. It is well known that the complete solution set of the max-min fuzzy relation system is fully determined by its minimal solutions. However, solving all the minimal solutions has been proven to be equivalent to the set-covering problem, which is NP-hard. Without solving the complete solution set, some specific solutions can be obtained through the corresponding fuzzy relation optimization problems. However, these solutions are usually unstable and fragile. Any minor fluctuations to the components of these specific solutions will cause them to be no longer feasible. In this work, we define and study the widest interval solution of a max-min fuzzy relation inequality system for the first time. The interval solution allows the solution to fluctuate within some range. The fluctuation range is determined by the width of the interval solution. We propose a novel resolution method for searching for the widest interval solution. The resolution method is carried out by detailed procedures and illustrated by a numerical example.

Innovative approaches to the formation of competitive tourism products (services): foreign and domestic experience

Purpose. The aim of the article is systematization of innovative approaches to the formation of competitive tourism products (services), provided by foreign and domestic experience. Methodology of research. The following methods are used to achieve the above goal: a systematic approach – to establish a complete set of innovative solutions; generalizations and unifications that allow to establish the most optimal and acceptable approaches to the formation of competitive tourism products (services). Findings. Based on the study of domestic and foreign experience in the formation of competitive tourism products (services) systematization of innovative approaches in this area: the approach associated with the formation of tourism products (services) depending on their connection with certain values, opportunities to solve problems as internal nature (at the level of tour operators) and external (socially significant); an approach based on the orientation of products (services) on international tourist cultural routes; institutional innovative approach related to the focus on the involvement of institutions, objects of different infrastructure for the creation and provision of competitive tourism products (services); approach to the creation of products (services) in the tourism industry, based on the virtualization of travel (virtualized approach); virtualized approach based on visualization and virtualization of travel (virtualized visualized approach). It is determined that the given universal systematization can be adapted to modern conditions of development in this sphere, in particular, challenges and threats of epidemiological character which have arisen in the beginning of 2020 in the world. It is proved that the virtualized visualized approach proposed in the study can be implemented for a wide range of types of tourism, but its implementation requires the development of new knowledge, skills, strong potential to attract new consumers who are focused on purchasing travel remotely. Originality. For the first time, promising areas for the development of competitive positions of tourism entities, tourism industries, based on the current realities of the spread of epidemiological threats; possible features of management of creation and the organization of introduction of tourist products (services) developed in the context of the virtualized visualized approach are formulated. Practical value. The results of the study can be used by domestic tourism entities to find and implement innovative approaches to the formation of products (services) in terms of the impact of the spread of epidemiological threats. Key words: innovative approaches, tourist products (services), competitive positions, threats of epidemiological character, virtualized visualized approach, remote mode, values, international tourist cultural routes.

Research on the Cave Exploration Technology of Overhead Transmission Line Tower Foundation

Overhead transmission lines are the main form of high-voltage and UHV long-distance transmission. When the line path passes through limestone areas, mining areas and others, the possible existence of karst caves and mined-out areas under the tower base will have a greater impact on the stability of the foundation. According to previous detection experience, different underground cave forms and detection requirements need to choose suitable detection technology to obtain better detection results. This paper will explain the different detection technologies, combine multiple overhead line engineering practices, study the detection technology of underground caves, and guide the subsequent exploration of the tower foundation underground caves. Finally, carry out three-dimensional geological modeling of the exploration data, and study the application of three-dimensional data processing and display technology in the exploration of the line tower base cave. Through the above summary, analysis and experimental research, a complete set of technical solutions for the exploration of tower foundation caves on overhead transmission lines has been completed, laying the foundation for the further development of subsequent detection technologies.

Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces

We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method.