Complete Set Of Solutions Research Articles

Salesforce.org launches new software suite for nonprofits

Salesforce.org, the philanthropic arm of Salesforce.org, has launched a new suite of services aimed at helping nonprofits with impact measurement. According to the company, the Salesforce.org Nonprofit Cloud offers a complete solution set that enables nonprofits to track and measure programs in real time and raise more funds by unlocking data with artificial intelligence–driven insights.

Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations

In this paper we present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem. We contribute a generating algorithm that will, without supervision, generate the entire non-dominated set for any number of objectives. To our knowledge, this is the first generating method for general discrete multi-objective problems that uses a variant of the Tchebychev norm. In a computational study, our algorithm’s running times are comparable to previously proposed algorithms.

A complete set of integrals and solutions to the Szekeres system

The Szekeres system is an ODE system arising from the Szekeres cosmological model. The paper presents the way to solve it using its four global independent first integrals. It also contains the complete set of its solutions in the particular cases, related to the set where the integrals are indefinite.

Multiple solutions for a nonconvex variational problem with double‐well potentials

SummaryIn this paper, we present a set of complete solutions for a nonconvex variational problem with double‐well potentials in higher dimensions. Based on the canonical duality theory, the corresponding nonlinear Euler‐Lagrange equation with Neumann boundary condition can be converted into an algebraic equation, which can be solved analytically to obtain the solutions of the dual problem. Correspondingly, local extrema of the primal problem can be identified by the pure complementary energy principle.

Generation of Alternative Solutions in the Redundancy Management Problem for Hardware Complexes

We consider the problem of finding a set of alternative configurations of redundant complexes for onboard equipment and give an analytic solution. The redundancy problem is solved by finding admissible values of the “integration” matrix that contains the connections between input and output interfaces of individual components of the complex. For the case of a structured set of “integration” matrices, the set of nominal matrices and additions to them yields a complete set of solutions. We also give an illustrative example.

Pareto-based branch and bound algorithm for multiobjective optimization of a safety transformer

PurposeThis paper aims to propose a multiobjective branch and bound (MOBB) algorithm with a new criteria for the branching and discarding of nodes based on Pareto dominance and contribution metric.Design/methodology/approachA multiobjective branch and bound (MOBB) method is presented and applied to the bi-objective combinatorial optimization of a safety transformer. A comparison with exhaustive enumeration and non-dominated sorting genetic algorithm (NSGA2) confirms the solutions.FindingsIt appears that MOBB and NSGA2 are both sensitive to their control parameters. The parameters for the MOBB algorithm are the number of starting points and the number of solutions on the relaxed Pareto front. The parameters of NSGA2 are the population size and the number of generations.Originality/valueThe comparison with exhaustive enumeration confirms that the proposed algorithm is able to find the complete set of non-dominated solutions in about 235 times fewer evaluations. As this last method is exact, its confidence level is higher.

Towards the appropriate synthesis of the four-bar linkage

Uncertainties are an inherent element in all mechanisms, arising from the manufacturing and assembly process or even from the operation of the device. In terms of synthesis routines for mechanisms, uncertainties are generally neglected since they are difficult to account for. In this work, the concept of appropriate design is utilized to develop routines that can more easily account for uncertainties in the geometrical parameters. These routines have been developed for linkages, specifically the four-bar linkage, and are capable of synthesizing the complete set of design solutions, referred to as allowable regions, for a set of desired coupler curve characteristics. The description of the desired coupler curve may contain any number of precision points and (or) trajectories. Several problems are solved in this work, including obtaining a representation of the coupler curve corresponding to a set of design parameters containing uncertainties, and synthesizing the appropriate designs for multiple descriptions of desired coupler curves. The results are quite promising and show great potential for using the appropriate design methodology for linkage synthesis.

The Researches on Cycle-Changeable Generation Settlement Method

Through the analysis of the business characteristics and problems of price adjustment, a cycle-changeable generation settlement method is proposed to support any time cycle settlement, and put forward a complete set of solutions, including the creation of settlement tasks, time power dismantle, generating fixed cycle of electricity, net energy split. At the same time, the overall design flow of cycle-changeable settlement is given. This method supports multiple price adjustments during the month, and also is an effective solution to the cost reduction of month-after price adjustment.

Dealing with residual energy when transmitting data in energy-constrained capacitated networks

This paper addresses several problems relating to the energy available after the transmission of a given amount of data in a capacitated network. The arcs have an associated parameter representing the energy consumed during the transmission along the arc and the nodes have limited power to transmit data. In the first part of the paper, we consider the problem of designing a path which maximizes the minimum of the residual energy remaining at the nodes. After formulating the problem and proving the main theoretical results, a polynomial time algorithm is proposed based on computing maxmin paths in a sequence of non-capacitated networks. In the second part of the paper, the problem of obtaining a quickest path in this context is analyzed. First, the bi-objective variant of this problem is considered in which we aim to minimize the transmission time and to maximize the minimum residual energy. An exact polynomial time algorithm is proposed to find a minimal complete set of efficient solutions which amounts to solving shortest path problems. Second, the problem of computing an energy-constrained quickest path which guarantees at least a given residual energy at the nodes is reformulated as a variant of the energy-constrained quickest path problem. The algorithms are tested on a set of benchmark problems providing the optimal solution or the Pareto front within reasonable computing times.

The Differential Counting Polynomial

The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common generalization of the dimension polynomial and the (algebraic) counting polynomial. Under mild additional assumptions, the differential counting polynomial decides whether a given set of solutions of a system of differential equations is the complete set of solutions.

Travelling-wave amplitudes as solutions of the phase-field crystal equation.

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the [Formula: see text] method (Malfliet & Hereman 1996 Phys. Scr.15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput.154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general [Formula: see text] solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general [Formula: see text] solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

Lexicographic Maximum Solution of Min-Product Fuzzy Relation Inequalities for Modeling the Optimal Pricing With Fixed Priority Grade in Supply Chain

Fuzzy relation inequalities composed by the min-product operation are established to model the pricing relation in a supply chain system. Basic properties of the min-product fuzzy relation inequalities are presented first, based on which the complete solution set could be characterized and obtained. In fact, each solution of the corresponding fuzzy relation inequalities is exactly a feasible price scheduling. Considering the fixed priority grade of the suppliers, the concept of lexicographic maximum solution is introduced and investigated, as an optimal price scheduling that maximizes the benefits. A detailed algorithm is developed to search the unique lexicographic maximum solution with a numerical illustrative example.

Implications of the Fermi-LAT Pass 8 Galactic Center excess on supersymmetric dark matter

The Fermi Collaboration has recently updated their analysis of gamma rays from the center of the Galaxy. They reconfirm the presence of an unexplained emission feature which is most prominent in the region of 1–10 GeV, known as the Galactic Center GeV excess (GCE). Although the GCE is now firmly detected, an interpretation of this emission as a signal of self-annihilating dark matter (DM) particles is not unambiguously possible due to systematic effects in the gamma-ray modeling estimated in the Galactic Plane. In this paper we build a covariance matrix, collecting different systematic uncertainties investigated in the Fermi Collaboration's paper that affect the GCE spectrum. We show that models where part of the GCE is due to annihilating DM is still consistent with the new data. We also re-evaluate the parameter space regions of the minimal supersymmetric Standard Model (MSSM) that can contribute dominantly to the GCE via neutralino DM annihilation. All recent constraints from DM direct detection experiments such as PICO, LUX, PandaX and Xenon1T, limits on the annihilation cross section from dwarf spheroidal galaxies and the Large Hadron Collider limits are considered in this analysis. Due to a slight shift in the energy spectrum of the GC excess with respect to the previous Fermi analysis, and the recent limits from direct detection experiments, we find a slightly shifted parameter region of the MSSM, compared to our previous analysis, that is consistent with the GCE. Neutralinos with a mass between 85–220 GeV can describe the excess via annihilation into a pair of W-bosons or top quarks. Remarkably, there are models with low fine-tuning among the regions that we have found. The complete set of solutions will be probed by upcoming direct detection experiments and with dedicated searches in the upcoming data of the Large Hadron Collider.

The effect of variation of soil conditions along the pipeline in the fault-crossing zone

In the paper, buried steel pipelines crossing strike-slip and normal-slip faults are considered within analytical and numerical approaches. The effect of variation of the backfill soil properties along the pipeline in the fault-crossing zone on the stress-strain state of the pipeline is analyzed.The analytical model developed in the previous publications is substantially reworked to take into account the variation of soil conditions along the pipeline length and the effect of internal pressure on the deformed pipe geometry. A complete set of analytical solutions for the axial pipeline-soil interaction force taking into account two zones along the pipeline length with different soil conditions, plastic behavior of the pipeline and soil, initial stress in the pipeline has been derived and introduced into the model.The effect of special (loose sand) backfill segment length on the pipeline response under strike-slip and normal-slip fault actions is studied. It is shown that the extension of the special backfill length has an advantageous effect in case of substantial axial fault displacement component. In this case, the reduction of soil constraining effect on a larger distance substantially reduces the maximal tensile strains in the pipeline. In contrast, under bending-dominant behavior of the pipeline, the elongation of the special backfill zone has no positive effect on the maximal strains.

On the Solution Set of the Admissible Bounded Control Problem via Orthogonal Polynomials

The complete set of solutions to the admissible bounded control problem of the Brunovsky control system of dimension $m$ for $m\geq 2$ via orthogonal polynomials on $[0,T]$ and their second kind polynomials is obtained. For $m\geq 2$ given an initial position $x_0$ and a time $T$ greater than the optimal time $t_{\min}$ , we prove that there are only two bang-bang controls with $m$ switchings that steer the state trajectory to the origin exactly at time $T$ .

Conformal basis for flat space amplitudes

We study solutions of the Klein-Gordon, Maxwell, and linearized Einstein equations in $\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primaries under the Lorentz group $SO(1,d+1)$. Such solutions, called conformal primary wavefunctions, are labeled by a conformal dimension $\Delta$ and a point in $\mathbb{R}^d$, rather than an on-shell $(d+2)$-dimensional momentum. We show that the continuum of scalar conformal primary wavefunctions on the principal continuous series $\Delta\in \frac d2+ i\mathbb{R}$ of $SO(1,d+1)$ spans a complete set of normalizable solutions to the wave equation. In the massless case, with or without spin, the transition from momentum space to conformal primary wavefunctions is implemented by a Mellin transform. As a consequence of this construction, scattering amplitudes in this basis transform covariantly under $SO(1,d+1)$ as $d$-dimensional conformal correlators.

Estimation of mass outflow rates from dissipative accretion disc around rotating black holes

We study the properties of the dissipative accretion flow around rotating black holes in presence of mass loss. We obtain the complete set of global inflow-outflow solutions in the steady state by solving the underlying conservation equations self-consistently. We observe that global inflow-outflow solutions are not the isolated solution, instead such solutions are possible for wide range of inflow parameters. Accordingly, we identify the boundary of the parameter space for outflows, spanned by the angular momentum ($\lambda_{\rm in}$) and the energy (${\cal E}_{\rm in}$) at the inner sonic point ($x_{\rm in}$), as function of the dissipation parameters and find that parameter space gradually shrinks with the increase of dissipation rates. Further, we examine the properties of the outflow rate $R_{\dot m}$ (defined as the ratio of outflow to inflow mass flux) and ascertain that dissipative processes play the decisive role in determining the outflow rates. We calculate the limits on the maximum outflow rate ($R_{\dot{m}}^{\rm max}$) in terms of viscosity parameter ($\alpha$) as well as black hole spin ($a_k$) and obtain the limiting range as $3\% \le R_{\dot{m}}^{\rm max} \le 19\%$. Moreover, we calculate the viable range of $\alpha$ that admits the coupled inflow-outflow solutions and find that $\alpha \lesssim 0.25$ for $R_{\dot m} \ne 0$. Finally, we discuss the observational implication of our formalism to infer the spin of the black holes. Towards this, considering the highest observed QPO frequency of black hole source GRO J1655-40 ($\sim 450$ Hz), we constrain the spin value of the source as $a_k \ge 0.57$.

Phase transitions in thick branes endorsed by entropic information

The so-called configurational entropy (CE) framework has proved to be an efficient instrument to study nonlinear scalar field models featuring solutions with spatially-localised energy, since its proposal by Gleiser and Stamapoulos. Therefore, in this work, we apply this new physical quantity in order to investigate the properties of degenerate Bloch branes. We show that it is possible to construct a configurational entropy measure in functional space from the field configurations, where a complete set of exact solutions for the model studied displays both double and single-kink configurations. Our study shows a rich internal structure of the configurations, where we observe that the field configurations undergo a quick phase transition, which is endorsed by information entropy. Furthermore, the Bloch configurational entropy is employed to demonstrate a high organisational degree in the structure of the configurations of the system, stating that there is a best ordering for the solutions.

Microscale Gaseous Slip Flow in the Insect Trachea and Tracheoles

An analytical investigation into compressible gas flow with slight rarefactions through the insect trachea and tracheoles during the closed spiracle phase is undertaken, and a complete set of asymptotic analytical solutions is presented. We first obtain estimates of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver respiratory gases to the cells, by comparing the magnitude of the different forces in the compressible gas flow. The 2D Navier-Stokes equations with a slip boundary condition are used to investigate compressibility and rarefied effects in the trachea and tracheoles. Expressions for the velocity components, pressure gradients and net flow inside the trachea are then presented. Numerical simulations of the tracheal compressible flow are performed to validate the analytical results from this study. This work extends previous work of Arkilic et al. (J Microelectromech Syst 6(2):167-178, 1997) on compressible flows through a microchannel. Novel devices for microfluidic compressible flow transport may be invented from results obtained in this study.

Baikov-Lee representations of cut Feynman integrals

We develop a general framework for the evaluation of d-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy’s residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.