Infinite Values Research Articles

Efficient Multistate Route Computation

A multi-state graph is defined as a graph where each edge is associated with a stochastic, rather than fixed, value. For cases where the stochastic value is discrete and represents a distance or time, an algorithm is presented which efficiently finds the single-source shortest paths and distances for all combinations of edge values. Infinite and negative weight values are allowed as long as there are no negative weight cycles. Efficiency is achieved by both leveraging dynamic programming and only finding solutions for the set of dominant states that correctly cover any possible edge metric setting for the graph. Although the method has exponential complexity in the worst case, some samples and example graphs are used to illustrate the savings over a brute-force combinatoric approach. Furthermore by leveraging some real-world assumptions, a pseudo-polynomial version is presented that can be applied to larger scale problems. The results of the method are then shown to enable the computation of most-likely shortest paths .

A new metric of absolute percentage error for intermittent demand forecasts

The mean absolute percentage error (MAPE) is one of the most widely used measures of forecast accuracy, due to its advantages of scale-independency and interpretability. However, MAPE has the significant disadvantage that it produces infinite or undefined values for zero or close-to-zero actual values. In order to address this issue in MAPE, we propose a new measure of forecast accuracy called the mean arctangent absolute percentage error (MAAPE). MAAPE has been developed through looking at MAPE from a different angle. In essence, MAAPE is a slope as an angle, while MAPE is a slope as a ratio, considering a triangle with adjacent and opposite sides that are equal to an actual value and the difference between the actual and forecast values, respectively. MAAPE inherently preserves the philosophy of MAPE, overcoming the problem of division by zero by using bounded influences for outliers in a fundamental manner through considering the ratio as an angle instead of a slope. The theoretical properties of MAAPE are investigated, and the practical advantages are demonstrated using both simulated and real-life data.

Elucidation of molecular interactions between a DBU based protic ionic liquid and organic solvents: thermophysical and computational studies

Energy profile of 1,8-diazabicyclo[5.4.0]undec-7-en-8-ium trifluoroacetate [DBUTFA].

Limiting activity coefficient measurements in binary mixtures of dichloromethane and 1-alkanols (C1–C4)

Limiting activity coefficients γ∞ in binary mixtures of dichloromethane with four lower 1-alkanols (C1–C4) were experimentally determined employing alternatively the techniques of inert gas stripping, comparative ebulliometry, Rayleigh distillation, and differential distillation. For each case, the suitable technique was chosen on the basis of the limiting relative volatility of the solute and/or volatility of the solvent. The measurements yielding data of good accuracy (relative standard uncertainty of γ∞ from 0.01 to 0.03) were carried out at several temperatures in the range from (283–333) K. The variation of limiting activity coefficients with temperature was fitted by a suitable two- or three-parameter equation and compared with available literature information on both limiting activity coefficients and calorimetric partial molar excess enthalpies at infinite dilution. The performance of the leading prediction method Modified UNIFAC was further examined using these new data. Concentration dependences of activity coefficients calculated from their infinite dilution values using van Laar equation were found to agree well with those inferred from reliable VLE data from the literature. The occurrence of an azeotropic point was tested for the systems under study and the temperature dependence of the azeotropic composition was estimated for mixtures of dichloromethane with methanol and ethanol.

Generalized differentiation of piecewise linear functions in second-order variational analysis

The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to optimization and stability. This class consists of lower semicontinuous functions with possibly infinite values on finite-dimensional spaces, which are labeled as “piecewise linear” ones and can be equivalently described via the convexity of their epigraphs. In this paper we calculate the second-order subdifferentials (generalized Hessians) of arbitrary convex piecewise linear functions, together with the corresponding geometric objects, entirely in terms of their initial data. The obtained formulas allow us, in particular, to justify a new exact (equality-type) second-order sum rule for such functions in the general nonsmooth setting.

Symmetric -charts: Sensitivity to nonnormality and control-limit estimation

ABSTRACTWe study the classical symmetric -chart with control limits set k standard deviations from the known in-control mean. The standard deviation is estimated with in-control data, in what we refer to as Phase-I. We consider three performance measures: the average run length (ARL), the standard deviation of the conditional average run length (SDARL), and the corresponding coefficient of variation. Modeling the data as independent and identically distributed, with marginal distributions chosen from the Johnson family, we investigate in-control and out-of-control sensitivities to three factors: the third and fourth standardized moments of the data distribution and the number of Phase-I observations. Considering both bounded and unbounded data distributions, our analytical, numerical, and Monte Carlo simulation results show that nonnormality has a substantial effect on all three performance measures; and the effects are nonmonotonic in both skewness and kurtosis. We show that all three performance measures are flawed when estimating the standard deviation. In particular, we show that ARL and SDARL values increase, eventually becoming infinite, as the number of Phase-I observations decreases, even in cases where run length is finite with probability one. We show analytically that, for bounded data distributions with any finite shift, estimating the standard deviation sometimes results in infinite ARL and SDARL values.

Team Optimal Control of Stochastically Switched Systems With Local Parameter Knowledge

This paper considers the optimal decentralized control of linear systems with stochastically switched cost and system matrices depending on local parameters. Two types of dynamic switched problems are considered, with partially nested and one-step delayed sharing information structures. For the former case, parameters and measurements follow a partially nested structure with the parameters possibly being correlated across all stages. For the latter case, parameters are assumed to be Markov processes, with their values along with measurements available instantaneously to local controllers, but with a one time step delay to others. The solution to both these problems rely on the optimal solution to a static (one-stage) stochastic-parameter problem with local type dependent Gaussian measurements, and for this purpose the static quadratic team problem is examined in some generality. Using an operator theoretic framework, it is shown that the sequential update scheme always converges to the team optimal strategy for general static quadratic team setups. This, when applied to the static stochastic-parameter problem, yields the team optimal strategy. The corresponding strategy is affine in the measurements with the parameter dependent coefficients obtained by solving a set of linear equations. These equations are immediately solvable when the total number of parameter values is finite. However, for the case of infinite parameter values, the update scheme also provides a mechanism to determine an approximation to the team optimal strategy.

Instability of α boson vacuum in highly compressed baryonic matter

Within the relativistic mean-field (RMF) method we investigate the behavior of boson complex scalar fields associated with 4He () nuclei and () antinuclei and the conditions that make possible the generation of (, ) pairs due to the vacuum instability in highly compressed baryonic systems consisting of nucleons (with baryon number B = 1) and/or particles (B = 4). The first part of the paper discusses infinite systems under the assumption that the Lagrangian describing the relativistic field of and particles also comprises a quartic self-interaction term. A wide set of RMF parametrizations is used and we establish in each case the conditions for the onset of vacuum instability. We consider both compressed standard baryonic matter with small admixtures of particles and, vice versa, systems comprising nuclei that are gradually doped with symmetric nuclear matter, and calculate the energy of the mode as a function of baryon density and particle density for both particle and antiparticle sectors. In the second part of the paper we focus on finite-sized baryonic systems. We illustrate this case with a schematic model consisting of a short-range potential where the strengths of the meson fields are prescribed by the infinite matter values and derive the spectrum of bound states for both particles and antiparticles.

Volumetric properties for binary and ternary mixtures of allyl alcohol, 1,3-dichloro-2-propanol and 1-ethyl-3-methyl imidazolium ethyl sulfate [Emim][EtSO4] from T = 298.15 to 318.15 K at ambient pressure

Based on density measurements, volumetric properties including excess molar volumes, partial molar volumes, partial molar excess volumes and their infinite dilution values, for binary and ternary solutions of allyl alcohol, 1,3-dichloro-2-propanol and 1-ethyl -3-methyl imidazolium ethyl sulfate [Emim][EtSO4] have been determined. Entire range of composition and temperatures from T=(298.15–318.15)K at ambient pressure (0.087MPa) have been considered. The excess molar volumes were negative for two binary mixtures including allyl alcohol whereas were positive for solutions of ionic liquid+1,3-dichloro-2-propanol. These quantities, for all binary mixtures, showed decrease by increasing temperatures which are explained based on intermolecular interactions and steric effects. Thermal expansion coefficients and their excess values have also been appraised for binary mixtures. The excess thermal expansion coefficients were negative for all binary mixtures and increased by raising temperature. The excess molar volumes have been modeled by Redlich–Kister equation for binary solutions and by Singh, Nagata–Tamura and Cibulka equations for ternary mixture.

Cusp summations and cusp relations of simple quad lenses

We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the other one that describes the deviation from the circular lens. In our recent work, we have found that the cusp and the fold summations are not equal to 0, when a point source infinitely approaches a cusp or a fold from inner side of the caustic. Based on the magnification invariant theory, which states that the sum of signed magnifications of the total images of a given source is a constant, we calculate the cusp summations for the five lens models. We find that the cusp summations are always larger than 0 for source on the major cusps, while can be larger or smaller than 0 for source on the minor cusps. We also find that if these lenses tend to the circular lens, the major and minor cusp summations will have infinite values, and with positive and negative signs respectively. The cusp summations do not change significantly if the sources are slightly deviated from the cusps. In addition, through the magnification invariants, we also derive the analytical signed cusp relations on the axes for three lens models. We find that both on the major and the minor axes the larger the lenses deviated from the circular lens, the larger the signed cusp relations. The major cusp relations are usually larger than the absolute minor cusp relations, but for some lens models with very large deviation from circular lens, the minor cusp relations can be larger than the major cusp relations.

Study of thermodynamic and transport properties of aqueous system containing poly(ethylene glycol) dimethyl ether 2000 and poly(propylene glycol) 400

Mixture of {poly(ethylene glycol) dimethyl ether 2000 (PEGDME2000)+poly(propylene glycol) 400 (PPG400)+water} forms an aqueous two phase system. For this system the binodal curves were measured at two temperatures from which the single phase region was obtained. The density, speed of sound and viscosity measurements were performed in the single phase region for {poly(ethylene glycol) dimethyl ether 2000 (PEGDME2000)+poly(propylene glycol) 400 (PPG400)+water} system and the corresponding binary ((PPG400)+water) solutions at T=(293.15, 298.15, 303.15, 308.15, and 313.15)K. From these measurements, values of the excess molar volume (VmE) and isentropic compressibility deviation (ΔKS) were calculated and correlated to the modified Wilson and polymer NRTL models. The viscosity values of binary and ternary solutions were correlated by the Eyring-modified Wilson and Eyring-NRTL models. From the density data for the binary and ternary solutions at dilute range, the apparent specific volumes at infinite dilution values were also determined. Some information regarding the segment–solvent and segment–segment interactions is obtained from these values.

Energy multiplication and fissile fuel breeding limits of accelerator-driven systems with uranium and thorium targets

The study analyses the integral 233U and 239Pu breeding rates, neutron multiplication ratio through (n,xn)- and fission-reactions, heat release, energy multiplication and consequently the energy gain factor in infinite size thorium and uranium as breeder material in an accelerator driven systems (ADS), irradiated by a 1-GeV proton source. Energy gain factor has been calculated as Menergy = 1.67, 4.03 and 5.45 for thorium, depleted uranium (100% 238U) and natural uranium, respectively, where the infinite criticality values are k∞ = 0.40, 0.752 and 0.816. Fissile fuel material production is calculated as 53 232Th(n,γ)233U, 80.24 and 90.65 238U(n,γ)239Pu atoms per incident proton, respectively.The neutron spectrum maximum is by ∼1 MeV. Lower energy neutrons E < 1 MeV have major contribution on fissile fuel material breeding (>97.5%), whereas their share on energy multiplication is negligible (0.2%) for thorium, depleted uranium. Major fission events occur in the energy interval 1MeV < E < 50 MeV.

Thermodynamic Insights in the Separation of Cellulose/Hemicellulose Components from Lignocellulosic Biomass Using Ionic Liquids

This work reports on the ionic liquid (IL) based separation of cellulose/hemicellulose from lignocellulosic biomass, by means of macroscale predictions using the COnductor like Screening MOdel for Real Solvents (COSMO-RS) model that is based on a statistical mechanical framework. For the benchmarking studies the experimental infinite dilution activity coefficient values for 13 components were predicted in 1-alkyl-3-methylimidazolium bis{(trifluoromethyl)sulphonyl}imide with an average absolute deviation (%AAD) of 15 %. Further, the solid–liquid equilibria of glucose, fructose, galactose, and xylose in [EMIM][EtSO4] and Aliquat®336 were predicted successfully with 15 % root-mean-square deviation. Afterwards, the selectivities were predicted at infinite dilution for cellulose/hemicellulose in 1,156 ILs with a combination of 34 cations and 34 anions. Based on these values, the ammonium-based ILs 1-methyl-4-aminotriazolium hexafluorophosphate [14MATAZ][PF6] and 4-aminotriazolium bis(oxalato(2)borate) [4ATAZ][BOB] were found to be good candidates for cellulose and hemicellulose extraction, respectively. The ILs selected using the COSMO-RS methodology were then studied qualitatively in terms of interaction energies and HOMO–LUMO energy gap. The binding energy for [1-methyl-4-aminotriazolium][PF6] + cellulose and [4-aminotriazolium][BOB] + cellulose systems are higher as compared with IL + cellulose + hemicellulose, indicating greater stability.

Regular Gleason Measures and Generalized Effect Algebras

We study measures, finitely additive measures, regular measures, and σ-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be studied in the frame of generalized effect algebras.

The Power of Linear Programming for General-Valued CSPs

Let $D$, called the domain, be a fixed finite set and let $\Gamma$, called the valued constraint language, be a fixed set of functions of the form $f:D^m\to\mathbb{Q}\cup\{\infty\}$, where different functions might have different arity $m$. We study the valued constraint satisfaction problem parametrized by $\Gamma$, denoted by VCSP$(\Gamma)$. These are minimization problems given by $n$ variables and the objective function given by a sum of functions from $\Gamma$, each depending on a subset of the $n$ variables. For example, if $D=\{0,1\}$ and $\Gamma$ contains all ternary $\{0,\infty\}$-valued functions, VCSP($\Gamma$) corresponds to 3-SAT. More generally, if $\Gamma$ contains only $\{0,\infty\}$-valued functions, VCSP($\Gamma$) corresponds to CSP($\Gamma$). If $D=\{0,1\}$ and $\Gamma$ contains all ternary $\{0,1\}$-valued functions, VCSP($\Gamma$) corresponds to Min-3-SAT, in which the goal is to minimize the number of unsatisfied clauses in a 3-CNF instance. Finite-valued constraint languages contain functions that take on only rational values and not infinite values. Our main result is a precise algebraic characterization of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a valued constraint language $\Gamma$, BLP is a decision procedure for $\Gamma$ if and only if $\Gamma$ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language $\Gamma$, BLP is a decision procedure if and only if $\Gamma$ admits a symmetric fractional polymorphism of some arity, or equivalently, if $\Gamma$ admits a symmetric fractional polymorphism of arity 2. Using these results, we obtain tractability of several novel classes of problems, including problems over valued constraint languages that are (1) submodular on arbitrary lattices; (2) $k$-submodular on arbitrary finite domains; (3) weakly (and hence strongly) tree submodular on arbitrary trees.

Interleaving data and effects

AbstractThe study of programming with and reasoning about inductive datatypes such as lists and trees has benefited from the simple categorical principle of initial algebras. In initial algebra semantics, each inductive datatype is represented by an initial f-algebra for an appropriate functor f. The initial algebra principle then supports the straightforward derivation of definitional principles and proof principles for these datatypes. This technique has been expanded to a whole methodology of structured functional programming, often called origami programming.In this article we show how to extend initial algebra semantics from pure inductive datatypes to inductive datatypes interleaved with computational effects. Inductive datatypes interleaved with effects arise naturally in many computational settings. For example, incrementally reading characters from a file generates a list of characters interleaved with input/output actions, and lazily constructed infinite values can be represented by pure data interleaved with the possibility of non-terminating computation. Straightforward application of initial algebra techniques to effectful datatypes leads either to unsound conclusions if we ignore the possibility of effects, or to unnecessarily complicated reasoning because the pure and effectful concerns must be considered simultaneously. We show how pure and effectful concerns can be separated using the abstraction of initial f-and-m-algebras, where the functor f describes the pure part of a datatype and the monad m describes the interleaved effects. Because initial f-and-m-algebras are the analogue for the effectful setting of initial f-algebras, they support the extension of the standard definitional and proof principles to the effectful setting.Initial f-and-m-algebras are originally due to Filinski and Støvring, who studied them in the category Cpo. They were subsequently generalised to arbitrary categories by Atkey, Ghani, Jacobs, and Johann in a FoSSaCS 2012 paper. In this article we aim to introduce the general concept of initial f-and-m-algebras to a general functional programming audience.

Application of the boundary layer flow and heat transfer over a flat plate using collocation method

The aim of this article is to apply the collocation method for boundary layer in unbounded domain. The solution for velocity and temperature are computed by applying the collocation method. It does not need any perturbation, linearization, or small parameter versus homotopy perturbation method and parameter perturbation method. Also the determination of the auxiliary parameter and auxiliary function versus homotopy analysis method is not necessary. The use of a special technique to obtain solutions that are very close to the exact solution of the equation has been attempted. The idea is to transform the equations and boundary conditions into another set of variables. In comparison with previous studies, the solution shows that the results of the present method are in excellent agreement with those of the numerical methods. As an important result, it is depicted that approximation of the physical quantities f ′′(0) and θ′(0) are more accurate in comparison with those obtained using homotopy perturbation method. Also, the results reveal that this method is more suitable for solution of boundary layer problems with infinite boundary values.

Ehrenfest scheme for complex thermodynamic systems in full phase space

For a thermodynamic system with multiple pairs of intensive/extensive variables and the thermodynamical coefficients attain finite or infinite values on the phase boundary, we obtain the two classes of Ehrenfest equations in the full phase space, and find that the rank of the matrix for these equations can tell us the dimensions of the phase boundary. We also apply this treatment to the RN-AdS black hole.

Rothe method for parabolic variational–hemivariational inequalities

The paper deals with the convergence analysis of the semidiscrete Rothe scheme for the parabolic variational–hemivariational inequality with the nonlinear pseudomonotone elliptic operator. The problem involves both a discontinuous and nonmonotone multivalued term as well as a monotone term with potentials which assume infinite values and hence are not locally Lipschitz. We prove the existence of a solution and establish a convergence result of a numerical semidiscrete scheme. The proof can be viewed both as the proof of solution existence as well as the proof of the convergence of a numerical semidiscrete scheme. The numerical simulations to present the rate of convergence with respect to space and time for piecewise linear finite elements are presented as well.

Electromagnetic scattering by approximately cloaked cylindrical bodies with nonhomogeneous anisotropic cloaking material

In cloaking, a body is hidden from detection by surrounding it by a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point (3D or spherical configuration) or a line (2D or cylindrical configuration). Some components of the electrical parameters of the cloaking material are required to have infinite or zero value at the boundary of the hidden object. Approximate cloaking can be achieved by transforming the cylindrical bodies (dielectric and conducting) virtually into a small cylinder rather than a line, which eliminates the zero or infinite values of the electrical parameters but produces scattering. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. In this work, the scattering pattern and the back-scattering cross-section against the frequency for cloaked conducting and dielectric cylinders are studied for both transverse magnetic (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii.