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We consider two eigenvalue problems, associated with a continuous function and with his approximation through a simple (step) function. We prove that their corresponding eigenvalues have very different properties. [ABSTRACT FROM AUTHOR]

In this paper, we derive some results of second order differential subordination involving linear operator, we estimate some of the interesiting property in would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In the paper, smooth functions with non-degenerate critical points on a smooth compact surface with boundary are considered. Firstly, it is shown that these functions are topologically equivalent to m-functions. The equipped Reeb graph is used to describe their topological structure. Secondly, the authors characterize the topological structure of all simple functions with at most 5 critical points. And finally, a formula for the genus of the surface based on the equipped Reeb graph is obtained. [ABSTRACT FROM AUTHOR]

Reactions to other people who get desirable outcomes should be a simple function of how much one desires those outcomes. Four studies (N= 4,978) suggest that one's reactions depend on the temporal location of outcome acquisition: Observers care more (e.g., feel more envy) right before, versus right after, other people have identical experiences (Studies 1, 2a, and 2b). For example, participants' envy in February rose as Valentine's Day approached (as a peer's enviable date loomed in the future) but abruptly plateaued come February 15 onward (after the date occurred). Further, the passing of time specifically assuaged the pain of comparison (whereas positive reactions, such as feeling inspired, remained high; Studies 3a, 3b, and 3c); therefore, taking a past perspective can be used to regulate negative emotions in the present (Study 4). Time asymmetrically shapes the experience of upward comparison, despite other people's desirable outcomes indeed being achieved. Other people's good lives sting less if they have already lived them. [ABSTRACT FROM AUTHOR]

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k -modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functors. In particular, if k is a field and if F is a correspondence functor, then F is finitely generated if and only if the dimension of F ( X ) grows exponentially in terms of the cardinality of the finite set X . Moreover, in such a case, F has actually finite length. Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated. [ABSTRACT FROM AUTHOR]

We show that the use of Sudakov variables greatly simplifies the study of the solutions to the scattering equations in the Cachazo-He-Yuan formalism. We work in the center-of-mass frame for the two incoming particles, which partially fixes the SL(2, ℂ) redundancy in the integrand defining the scattering amplitudes, the remaining freedom translates into a global shift in the azimuthal angle of the outgoing particles. Studying four- and five-particle amplitudes, we see how an appropriate choice of this phase allows for algebraic simplifications when finding solutions to the scattering equations, as well as in the expression of the scattering amplitudes in terms of the locations of the punctures in the sphere. These punctures themselves are remarkably simple functions of the Sudakov parameters. [ABSTRACT FROM AUTHOR]

In the present paper, new subclasses of bi-univalent functions of complex order associated with the (p,q)-derivative are introduced. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of functions belonging to these classes. [ABSTRACT FROM AUTHOR]

Dynamic systems are becoming steadily more important with the profusion of mobile and distributed computing devices. Coincidentally incremental computation is a natural approach to deal with ongoing changes. We explore incremental computation in the parameterized complexity setting and show that incrementalization leads to non-trivial complexity classifications. Interestingly, some incremental versions of hard problems become tractable, while others remain hard. Moreover tractability or intractability is not a simple function of the problem's static complexity, every level of the W-hierarchy exhibits complete problems with both tractable and intractable incrementalizations. For problems that are already tractable in their static form, we also show that incrementalization can lead to interesting algorithms, improving upon the trivial approach of using the static algorithm at each step. [ABSTRACT FROM AUTHOR]

For a computable measure space with computable σ-finite measure we study computability on the space of measurable functions. First we prove that for a natural multi-representation finite union and intersection and countable union are computable. We introduce a natural multi-representation of the measurable functions to a computable topological space and prove that composition with continuous functions is computable. Canonically, for a computable metric space the associated computable topological space has a basis of balls B(a, s) with center from the dense set and rational radius. From a given sequence (μk)k of finite Borel measures we can compute a dense sequence (rj)j of radii such that μk(S) = 0 for all k and all spheres S = S(a, rj ) with a from the dense set and j ∈ N. For measurable functions to computable compact computable metric spaces the natural multi-representation is equivalent to a multi-representation via fast uniformly converging sequences of simple functions. For non-negative measurable numerical functions the sequences can be chosen to be non-decreasing. Some results on integration are added. [ABSTRACT FROM AUTHOR]

Characteristics of isolated substorms selected by variations in the 1-min values of the AL index are analyzed. The substorms were divided into several types with respect to the behavior of the Bz component of the interplanetary magnetic field (IMF) during the expansion phase. The probability of observations of substorms associated with the northward turn of the Bz component of IMF was ~19%, while the substorms taking place at Bz < 0 were observed in 53% of cases. A substantial number of events in which no substorm magnetic activity was observed in the auroral zone after a long (>30 min) period of the southward IMF and a following sharp turn of the Bz component of IMF before the north was detected. The data suggest that a northward IMF turn is neither a necessary nor sufficient condition for generating substorms. It has been shown for substorms of the both types that the average duration of the southward IMF to moment T and the average intensity of the magnetic perturbation in the maximum are approximately the same and amount to ~80 min and-650 nT, respectively. However, for substorms at Bz < 0, their mean duration, including the expansive and recovery phases, is on average 30 min longer than that at a northward turn of IMF. Correlations between the loading-unloading processes in the magnetosphere in the periods of magnetospheric substorms were investigated with different functions that determine the efficiency of the energy transfer from the solar wind to the magnetosphere. It has been shown that the highest correlation coefficient ( r = 0.84) is observed when the function suggested by Newell et al. (2007) is used. It has been detected that a simple function VB yields a high correlation coefficient ( r = 0.75). [ABSTRACT FROM AUTHOR]

We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these combinatorial Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their f-vectors. We also use characters to give a generalization of Stanley's (-1)-color theorem. A q-analogue version of this family of characters is also studied. [ABSTRACT FROM AUTHOR]

Dimensional analysis is combined with computer simulations to identify a useful dimensionless measure for adhesion in contacts of nominally flat surfaces. The measure is a simple function of a few mostly local, well-defined parameters and allows one to estimate how adhesion alters the true contact area in unsticky contacts. For these contacts, we find that the range of adhesion barely affects the gross features of the contact geometry – at a given relative contact area. However, short-range adhesion compactifies contact patches, changes various microscopic distribution functions qualitatively and boosts dissipation when a generalized Tabor coefficient is of order one or greater. [ABSTRACT FROM AUTHOR]

Loss functions describe the economical consequences of the deviations from the target values. In recent years they have been used in wide range of application including process safety assessment. This paper provides a novel analysis to assess potential loss due to process deviation. The assessed losses help to better estimate process economic risk, which in turn assist in effective process system design and operational decision-making. The analysis is presented in four different development stages: (i) loss functions focusing on simple functions; (ii) loss functions with estimated maximum loss; (iii) loss functions focusing on probability distributions; and (iv) loss functions in which both distributions of variables and their dependencies are considered (i.e., hierarchical Bayesian based loss functions). Details discussion on development stages three and four are presented with case studies. First case study demonstrates application of inverted probability distribution and while second case study provides application of the hierarchical Bayesian loss functions. Advantage and disadvantages of different types of loss functions are also discussed. Finally, future research directions have been proposed. [ABSTRACT FROM AUTHOR]

In this article we are going to give a description of a simple p -permutation functor S 1 , C . We can prove the existence of an isomorphism between this functor and the functor which sends a group to the image of the Cartan homomorphism. This fact allows us to link the evaluation of S 1 , C with the image of the Cartan matrix of Comack k ( G ) , and gives us an explicit formula for the dimension of this evaluation. [ABSTRACT FROM AUTHOR]

In this paper we use a result of Nunokawa to extend some results on univalent functions given by Miller and Mocanu. As a consequence, we get several sufficient conditions for starlikeness over the expression $f(z)f''(z)/f^{\prime2}(z)$. [ABSTRACT FROM AUTHOR]

MUSIC is a popular algorithm for estimating the direction of arrival (DOA) in array signal processing applications. In this paper, we analyze the performance of the MUSIC algorithm for a single source system, in the presence of noisy and missing data (when only a random subset of the entries in the data matrix are observed). We prove consistency of the DOA estimate when signal from a single source is impinging on low coherence arrays, and derive an analytic expression for the mean-squared-error (MSE) performance of MUSIC for the case of uniform linear arrays, in the large array and relatively large sample setting. Our analysis is mathematically justified in both the sample rich and deficient regimes. The expression for the MSE is a simple function of array geometry, signal-to-noise ratio (SNR), the fraction of entries observed, and the ratio of the number of sensors to number of snapshots. We derive a phase transition threshold which separates a regime where MUSIC is consistent from a regime where MUSIC is inconsistent. This threshold depends upon the SNR, the probability of observing entries in the data matrix, and number of sensors and snapshots in a simple manner which we make explicit. [ABSTRACT FROM AUTHOR]

Every BPMS must have some facilities for transforming its process definition language to the form directly executable by its execution engine. The paper discusses the situation when different domain specific process languages need to be transformed to one target environment. A new approach based on domain specific mappings is proposed. First, the concept of virtual functional view on target metamodel is introduced which permits to describe the creation of target model elements at a higher level of abstraction by simple functions. Then mapping rule definition based on the virtual view is presented which provides in most cases a simple description how source model elements must be passed to these functions. [ABSTRACT FROM AUTHOR]

Abstract: For external electromagnetic perturbations with dimensionless frequency we consider, respectively, the polarization for a class of Right-Handed material and its corresponding Left-Handed metamaterial. Analytically and numerically they are interrelated through a simple functional form subordinated to the frequency value. Further, magnetization variables are also connected in an analogous way. Both interrelated materials have, concerning the polarization and magnetization, opposite signs inside the window region defined around . [Copyright &y& Elsevier]

Abstract: An algorithm for constructing primitive adjoint-invariant functions on a complex simple Lie algebra is presented. The construction is intrinsic in the sense that it does not resort to any representation. A primitive invariant function on the whole Lie algebra is obtained by lifting a coordinate function on a Kostant slice of the Lie algebra. Such an intrinsic construction of invariant functions is most useful for the bigger exceptional Lie algebras such as the Eʼs. The Maple implementation of this algorithm is outlined at the end and will be applied to these exceptional Lie algebras in a future work. [Copyright &y& Elsevier]

Highlights: [•] We express the relative efficiency of a flat plate heater as ηR = α − Aε − B. [•] We then derive a figure of merit for the heater, FM= α − Aε. [•] We show that A can be expressed as a simple function of inlet water temperature, A =0.0073Tin . [•] For a fixed water temperature, e.g. 60°C, FM is extremely simple: FM= α −0.44ε. [ABSTRACT FROM AUTHOR]

Highlights: [•] An adaptable expert system based time series forecasting method. [•] Decision trees and genetic algorithms are used to optimize the forecasting. [•] Simple functions can be used to forcast non linear time series. [•] Human understandable forecasting process. [ABSTRACT FROM AUTHOR]

Abstract: For a measure space denote by the set of all -integrable simple functions . For a bijection we consider the functional , where is the support of . One of the results says that if the measure has values in and in , the function is monotonic and satisfies the inequality then is a power function. Some characterizations of the functions in two remaining cases when either or are given. The subadditivity of , i.e. a generalization of the Minkowski inequality, is also considered. [Copyright &y& Elsevier]

We extend the work of Ioffe and Lewis [A. Ioffe and A. Lewis,Critical points of simple functions, Optimization, 57 (2008), pp. 3–16] and relate it to the previous work of Morse [M. Morse,Topologically non-degenerate functions in a compact n-manifold, J. Anal. Math. 7 (1959), p. 243]. We show that the concept of regularity for piecewise linear functions can be explained in geometric topological terms and this explanation leads to a unified view of several concepts of regularity for such functions. [ABSTRACT FROM PUBLISHER]

Abstract: We conducted theoretical investigation of long lasting pulses of cosmic-ray electrons and gamma-ray radiation, which are often observed during thunderstorms by particle detectors at high altitude cosmic-ray stations. These thunderstorm ground enhancements (TGEs) last several minutes, during which the flux of electrons and gamma-quants can surpass a few hundred percent over background level. We developed theoretical model and derived energetic spectrums of electrons and gamma-quants at given value of thunderstorm electric field. The model considers two following mechanisms, which can change the flux of electrons in electric field: (i) transformation of the spectrum of cosmic-ray electrons and (ii) formation of electron avalanche. Due to (i) the number of low (few MeV) energy electrons decreases and small abundance (<5% of total flux of cosmic rays) of cosmic-ray electrons with energies >10MeV emerges. The spectral fluxes of two electron components – avalanche and cosmic-ray electrons are derived, which shows that contribution of cosmic-ray electrons in total abundance of electrons is small. Consequently, the contribution of gamma ray radiation, produced by the abundance of cosmic-ray electrons is small as well. We derived the exact equations for the spectrums of these two components of gamma ray radiation and showed that spectral curve of avalanche gamma-quants can be approximated by a simple function exp(−E/E 0)/E up to ∼40MeV. At higher energies gamma-ray radiation is produced by the abundance of cosmic-ray electrons and it has approximately power-law spectrum. [Copyright &y& Elsevier]

This study considers an air-filled heavy geomembrane tube section on a rigid horizontal foundation. All quantities are normalized to obtain similarity solutions. Integral terms of the semianalytic solutions are evaluated analytically, resulting in closed-form solutions. The closed-form solutions are expressed as simple functions of the pressure parameter. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes. [ABSTRACT FROM AUTHOR]

A complex-valued functions that are univalent and sense preserving in the unit disk U can be written in the form f (z) = h(z) + g(z) , where U(z) and g(z) are analytic in. We will introduced the operator Dn which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(α,γ, n) by generalized derivative operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(α,γ, n). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points. [ABSTRACT FROM AUTHOR]

The article discusses the solving of additive functions by adding a simple mathematical condition where the solution to the theorem has the form of f (x) = cx.