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This paper introduces strong bisimulation for continuous-time Markov decision processes (CTMDPs), a stochastic model which allows for a nondeterministic choice between exponential distributions, and shows that bisimulation preserves the validity of CSL. To that end, we interpret the semantics of CSL - a stochastic variant of CTL for continuous-time Markov chains - on CTMDPs and show its measure theoretic soundness. The main challenge faced in this paper is the proof of logical preservation that is substantially based on measure theory.

In this paper, several characterizations for s-closed spaces are obtained using regular semiclosed sets and some sets having two properties of near openness and near closedness in the same time. Images of s-closed spaces under some noncontinuous mappings are investigated. The relations between s-closedness and near compactness, co-compactness, almost co-compactness, light compactness, mild compactness are obtained. S-closed subsets relative to a semi-T2-spaces are also discussed. في هذا البحث بعض الخواص الجديدة لفراغات س - المغلقة التي قدمها طومسون عام 1967 ، وذلك باستخدام بعض المجموعات التي لها خاصية قريبة الانفتاح وقريبة الانغلاق في آن واحد ، كما تم مناقشة صور الفراغات س - المغلقة تحت تأثير بعض الرواسم غير المتصلة ، كما تضمن البحث دراسة عن علاقة الانغلاق السيني ببعض أنواع الأصماط ، واحتوى البحث كذلك على مناقشة للمجموعات الجزئية السينية المغلقة بالنسبة لفراغ T2 النصفي .

Shor's factoring algorithm (SFA) finds the prime factors of a number, $N=p_1 p_2$, exponentially faster than the best known classical algorithm. Responsible for the speed-up is a subroutine called the quantum order finding algorithm (QOFA) which calculates the order -- the smallest integer, $r$, satisfying $a^r \mod N =1$, where $a$ is a randomly chosen integer coprime to $N$ (meaning their greatest common divisor is one, $\gcd(a, N) =1$). Given $r$, and with probability not less than $1/2$, the factors are given by $p_1 = \gcd (a^{\frac{r}{2}} - 1, N)$ and $p_2 = \gcd (a^{\frac{r}{2}} + 1, N)$. For odd $r$ it is assumed the factors cannot be found (since $a^{\frac{r}{2}}$ is not generally integer) and the QOFA is relaunched with a different value of $a$. But a recent paper [E. Martin-Lopez: Nat Photon {\bf 6}, 773 (2012)] noted that the factors can sometimes be found from odd orders if the coprime is square. This raises the question of improving SFA's success probability by considering odd orders. We show that an improvement is possible, though it is small. We present two techniques for retrieving the order from apparently useless runs of the QOFA: not discarding odd orders; and looking out for new order finding relations in the case of failure. In terms of efficiency, using our techniques is equivalent to avoiding square coprimes and disregarding odd orders, which is simpler in practice. Even still, our techniques may be useful in the near future, while demonstrations are restricted to factoring small numbers. The most convincing demonstrations of the QOFA are those that return a non-power-of-two order, making odd orders that lead to the factors attractive to experimentalists.

Bergstra, Bethke and Ponse proposed an axiomatization for Basic Process Algebra extended with (binary) iteration. In this paper, we prove that this axiomatization is complete with respect to strong bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based on the axioms, and prove that this term rewriting system is terminating, and that bisimilar normal forms are syntactically equal modulo commutativity and associativity of the +.

International audience; In this paper, we propose a rigorous derivation of the expression of the projected Generalized Stein Unbiased Risk Estimator ($\GSURE$) for the estimation of the (projected) risk associated to regularized ill-posed linear inverse problems using sparsity-promoting L1 penalty. The projected GSURE is an unbiased estimator of the recovery risk on the vector projected on the orthogonal of the degradation operator kernel. Our framework can handle many well-known regularizations including sparse synthesis- (e.g. wavelet) and analysis-type priors (e.g. total variation). A distinctive novelty of this work is that, unlike previously proposed L1 risk estimators, we have a closed-form expression that can be implemented efficiently once the solution of the inverse problem is computed. To support our claims, numerical examples on ill-posed inverse problems with analysis and synthesis regularizations are reported where our GSURE estimates are used to tune the regularization parameter.

International audience; Mathematical morphology can process the binary and grayscale image successfully. This theory cannot be extended to the color image directly. In color space, a vector represents a pixel, so in order to compare vectors, vectoriel orderings must be defined first. This paper addresses the question of the extension of morphological operator to the case of color images. The proposed method used the order by bit mixing to replace the conditional order. Our order is based on a combination of reduced and bit mixing ordering of the underlying data. Additionally it is a total ordering. Since it not only solves the problems of false color generated by the marginal order but also those of multiple extrema generated by reduced order. The performance of the introduced operators is illustrated by means of different applications: color gradients for segmenting, image smoothing (noise suppression) by median filter operator and Laplacian operators. Examples of natural color images and synthetic color images are given. Experimental results show the improvement brought by this new method.

Relations are very important mathematical objects in different fields of theory and applications. In many real applications, for which gradation of relations is immanent, the classical relations are not adequate. Interpolative relations (I-relations) (as fuzzy relations) are the generalization of classical relations so that the value (intensity) of a relation is an element from a real interval [0, 1] and not only from {0, 1} as in the classical case. The theory of I-relations is crucially different from the theory of fuzzy relations. I-relations are consistent generalizations of classical relations and, contrary to fuzzy relations, all laws of classical relations (set-theoretical laws) are preserved in general case. In this paper, the main characteristics of I-relations are illustrated on the interpolative preference structures (I-preference structures) as consistent generalization of classical preference structures.

In this paper, we establish some new inequalities of Hermite-Hadamard type for the strongly-generalized nonconvex function by using the generalized fractional integral operator. Some new results as special cases are provided as well. At the end, some applications to special mean are obtained. © 2020 Natural Sciences Publishing.

As a space-filling method, Voronoi Treemaps are used for showcasing hierarchies. Previously presented algorithms are limited to visualize nonspatial data. The approach of spatial Voronoi Treemaps is proposed in this paper to eliminate these problems by enabling the subdivisions for points, lines, and polygons with spatial coordinates and references. The digital distance transformation is recursively used to generate nested raster Voronoi polygons while the raster to vector conversion is used to create a vector-based Treemap visualization in a GIS (geographic information system) environment. The objective is to establish a spatial data model to better visualize and understand the hierarchies in the geographic field.

In this paper, the modified variational iteration method (MVIM) is reintroduced with the enhancement of Padé approximants to lengthen the interval of convergence of VIM or MVIM when used alone in solving nonlinear problems. KdV, mKdV, Burger's and Lax's equations are used as examples to illustrate the effectiveness and convenience of the proposed technique.

In this paper we study the saddle point optimality conditions and Lagrange duality in multiobjective optimization for generalized subconvex-like functions. We obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solutions which will be adequately defined. We also define a new dual problem for the multiobjective programming problem with the special property of being a scalar programming problem.

This is an expository paper, which provides a first approach to nearly Kenmotsu manifolds. The purpose of this paper is to focus on nearly Kenmotsu manifolds and get some new results from it. We prove that for a nearly Kenmotsu manifold is locally isometric to warped product of real line and nearly K\"ahler manifold. Finally, we prove that there exist no nearly Kenmotsu hypersurface of nearly K\"ahler manifold. It is shown that a normal nearly Kenmotsu manifold is Kenmotsu manifold.

A Gabor system in $L^2(\mathbb{R})$, generated by a window $g\in L^2(\mathbb{R})$ and associated with a sequence of times and frequencies $\Gamma\subset\mathbb{R}^2$, is a set formed by translations in time and modulations of $g$. In this paper we consider the case when $g$ is the Gaussian function and $\Gamma$ is a sequence whose associated Gabor system $\mathcal{G}_\Gamma$ is complete and minimal in $L^2(\mathbb{R})$. We consider two main cases: that of the lattice without one point and that of the sequence constructed by Ascensi, Lyubarskii and Seip lying on the union of the coordinate axes of the time-frequency space. We study the stability problem for these two systems. More precisely, we describe the perturbations of $\Gamma$ such that the associated Gabor systems remain to be complete and minimal. Our method of proof is based essentially on estimates of some infinite products.

International audience; In this paper, we propose some efficient and robust numerical methods to compute the ground states anddynamics of Fractional Schrödinger Equation (FSE) with a rotation term and nonlocal nonlinear interactions.In particular, a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal interactionevaluation [33]. To compute the ground states, we integrate the preconditioned Krylov subspace pseudospectralmethod [5] and the GauSum solver. For the dynamics simulation, using the rotating Lagrangiancoordinates transform [16], we first reformulate the FSE into a new equation without rotation. Then, atime-splitting pseudo-spectral scheme incorporated with the GauSum solver is proposed to simulate the newFSE. In parallel to the numerical schemes, we also prove some existence and nonexistence results for theground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentumand the center of mass, are stated. The ground states properties with respect to the fractional orderand/or rotating frequencies, dynamics involving decoherence and turbulence together with some interestingphenomena are reported.

An elastic-perfectly plastic discretized structure subjected to given proportional loads, undergoes displacements, some of which are measured. On the basis of this experimental data the yield limits and the hardening coefficients are sought, whereas the elastic properties are known. A number of possible ways of tackling this inverse problem are outlined and discussed. The present paper contains results on the sensitivity analysis for elastoplastic problems in the case of discrete structures modeled by finite elements. This formulation covers situations where inaccuracies of practical significance with known statistical properties affect both the measurements and the modeling of the real system.

We mainly introduce some weak versions of the $M_{1}$-spaces, and study some properties about these spaces. The mainly results are that: (1) If $X$ is a compact scattered space and $i(X)\leq 3$, then $X$ is an $s$-$m_{1}$-space; (2) If $X$ is a strongly monotonically normal space, then $X$ is an $s$-$m_{2}$-space; (3) If $X$ is a $\sigma$-$m_{3}$ space, then $t(X)\leq c(X)$, which extends a result of P.M. Gartside in \cite{CP}. Moreover, some questions are posed in the paper., Comment: 8 pages

International audience; This paper is devoted to the comparison of three two-fluid models in steam-water applications involving phase transition and shock waves. The three models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all models and to more complex Equations Of State. Particular attention is paid to the verification of every step of the method so that convergence studies can be carried out. Afterwards, models are compared with each other and with experimental data in two different cases of steam-water transients. The first one is Simpson water-hammer experiment and the second one is a rapid depressurization with flashing studied in Canon experiment.

This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time. Orienteering problems occur in logistic situations were an optimal combination of locations needs to be selected and the routing between the selected locations needs to be optimized. In the time-dependent variant, the travel time between two locations depends on the departure time at the first location. Next to a mathematical formulation of the TD-OP, the main contribution of this paper is the design of a fast and effective algorithm to tackle this problem. This algorithm combines the principles of an ant colony system (ACS) with a time-dependent local search procedure equipped with a local evaluation metric. Additionally, realistic benchmark instances with varying size and properties are constructed. The average score gap with the known optimal solution on these test instances is only 1.4% with an average computation time of 0.5 seconds. An extensive sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in its parameter settings. publisher: Elsevier articletitle: A fast solution method for the time-dependent orienteering problem journaltitle: European Journal of Operational Research articlelink: http://dx.doi.org/10.1016/j.ejor.2013.11.038 content_type: article copyright: Copyright © 2013 Elsevier B.V. All rights reserved. ispartof: European Journal of Operational Research vol:236 issue:2 pages:419-432 status: published

International audience; In typical applications, chromatic indices are calculated as linear combinations of the normalized r-, g-and bchannels and used as features for a later classification based on chromatic appearance. But the variety of indices used in the literature is very limited. Furthermore is the choice of which index to use justified either empirically, based on false mathematical assumptions or not justified at all. The reason for the lack of mathematical justification is that so far no formal definition of chromatic indices existed. Such a definition is provided in this paper. An experimental classification with 180 different index combinations shows that the index choice has a significant impact on the classification. The results stand in sharp contrast to the very limited variety of indices used in the literature. The results imply the need for deterministic methods to estimate ideal indices for a given application, for which we hope the provided formalization might be useful.

In broadcast fading channel, channel variations can be exploited through what is referred to as multi-user diversity and opportunistic scheduling for improving system performance. To achieve the gains promised by this kind of diversity, the transmitter has to accurately track the channel variations of the various receivers, which consumes resources (time, energy, bandwidth), and thus reduces the resources remaining for effective data transmissions. The transmitter may decide not to acquire or probe the channel conditions of certain receivers, either because these receivers are presumably experiencing severe fading, or because the transmitter wishes to spare resources for data transmissions. It may also decide to transmit to a receiver without probing its channel; in such cases, the transmitter guesses the channel state, which often results in a reduction of the transmission rate compared to when the transmitter knows the channel state. Ultimately, the transmitter has to decide to which receiver it should transmit. In this paper, we identifying the joint probing and transmission strategies realizing the optimal trade-off between the channel state acquisition and the effective data transmission. The objective is to maximize the system throughput. Finally, we propose several extensions of the proposed strategy, including a scheme to maximize the system utility and a scheme to ensure the system stability., 10.1109/78.845940, © IEEE

The manuscript of the preceding article was kindly sent to me by the author so that I could state my position in regard to it. Mrs. Ehrenfest-Afanassjewa (1) has presented in this paper a very satisfactory and general treatment of the conditions which must be fulfilled if a set of physical equations are to be homogeneous with respect to a given transformation, that is, if they are to remain unchanged when each of the quantities of a particular kind Yi occurring in the equations is multiplied by a factor Ei.

Capacity definition recognises that only traverse point or uniform section of roadway capacity can be estimated. Since midblock median U-turn opening is a nonuniform infrastructure, a novel capacity estimation method is needed. The paper proposes sectioning models for estimating U-turn capacity based on dynamics and regression theory. Surveyed U-turn roadway was divided into three sections (entry, middle curve, and exit). Traffic data for each section and adjoining priority traffic stream were collected continually for eight weeks. After modifying passenger car values, ensuing traffic flows and computed densities were used to develop capacity model for entry and middle curve. Regression models where traffic flows from the exit section were taken as the dependent variables and flows from the priority stream were taken as independent variable were used to model capacity for the exit section. Sensitivity analysis shows that the proposed models can produce reliable and accurate results. Results reveal that that traffic capacity at entry (1221 pcu/h) and exit (about 350 pcu/h) sections differs significantly. The paper concluded that U-turn roadway capacity cannot be generalized because the structure is nonuniform.