Necessaryand Sufficient Conditions Research Articles

Proposal of a facet-to-facet multiple flow direction algorithm based on geometrical and mathematical analysis of physical dispersion over triangle facet

Flow direction algorithms have been widely used to extract crucial terrain attributes of great hydrological and geomorphological significance. However, essential distinctions between the empirically-designed strategies of typical algorithms and the natural rules of physical dispersions bring various problems (e.g. parallel channel, artificial dispersion), leading to the low size and extent precisions of estimated results. In this work, geometrical and mathematical analysis is conducted on the inherent characteristics of physical dispersions along slope lines on local terrains. On each 3 × 3 window of digital elevation model (DEM), center pixel is divided into eight non-overlapping sub-facets. Necessary and sufficient (NS) conditions of size relationships between the elevations of adjacent pixels are summarized to directly identify the receiving facets of a sub-facet. Then, strict mathematical relations are derived between slope direction of a sub-facet and flow proportions allocated to receiving facets. A strategy is designed to re-adjust receiving facets and flow proportions for the boundary flow of adjacent facets. Lastly, a multiple-flow-direction algorithm called TFGA is proposed with the NS condition of size relationships, mathematical relation of slope direction with flow proportion, and adjustment strategy of boundary flow. Case studies are conducted for investigating the total contributing areas (TCA) and specific contributing areas (SCA) estimated by TFGA. Results reveal all-side superiorities of TFGA to typical algorithms in spatial patterns, error indicators and statistic characteristics of estimated TCAs and SCAs. Particularly, TFGA improves size precision of estimated results by approximately one order of magnitude. In a conclusion, we highly recommend TFGA for digital elevation analysis.

Well-Rounded ideal lattices of cyclic cubic and quartic fields

In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic quartic fields which have well-rounded ideals and explicitly construct their minimal bases. In addition, for a given prime number $p$, if a cyclic quartic field has a unique prime ideal above $p$, then we provide the necessary and sufficient conditions for that ideal to be well-rounded. Moreover, in cyclic quartic fields, we provide the prime decomposition of all odd prime numbers and construct an explicit integral basis for every prime ideal.

Solving the Team Allocation Problem in Crowdsourcing via Group Multirole Assignment

In mass crowdsourcing, a platform is used for task allocation. Large complex tasks may be assigned to teams directly. To ensure the rapid accomplishment of tasks, we need to assign a task to multiple teams, while a team is composed of at least one worker. On the other hand, in order to ensure the enthusiasm and income of workers, the platform allows one worker to participate in a limited number of teams. Thereby, a team may undertake multiple but limited tasks. It is obvious that task allocation needs to avoid each worker being overloaded as well as prevent information leakage, which is caused by a task assigned to different teams at the same time. Therefore, different teams being assigned to a certain task cannot include the same workers. Such a scenario forms a many-to-many (M2M) assignment problem [or group multirole assignment (GMRA)] under high-order cardinality (HC) constraints, while the platform wants to choose appropriate and excellent teams for all the tasks in a specific time window. In order to solve this problem, this article studies and formalizes the above problem by introducing HC and conflicting agents on roles (CAR) constraints to GMRA. The main contributions of this article include: 1) the first formalization of the team allocation problem (TAP) in crowdsourcing through extending GMRA and the creation of a composition matrix to express HC constraints of agents and conflict avoiding constraints; 2) theoretical proofs of the theorems of the formalized problem, such as a necessary and sufficient condition (NSC), which confines the solution space of the problem; and 3) a practice solution to the proposed problem based on the IBM ILOG CPLEX optimization package (CPLEX). All the proposed approaches are verified by simulation experiments, which demonstrates that the proposed approaches are efficient, feasible, and practicable.

Finite Gabor systems and uncertainty principle for block sliding discrete fourier transform

In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual finite Gabor tight frame using discrete time Zak transform is given. Also, a method to calculate the coefficients of the finite Gabor system expansion in the case of oversampling and a necessary and sufficient condition for the existence of biorthogonal pair of Riesz basis in l2(ZL) is given. Further, we introduce the notion of block sliding discrete Fourier transform (BSDFT) which reduces the computational complexity and give uncertainty principle for BSDFT. An uncertainty principle for two finite Parseval Gabor frames in terms of sparse representations is given. Finally, using the notion of numerical sparsity, an uncertainty principle for finite Gabor frames is given.

Vector-valued nonuniform multiresolution analysis associated with linear canonical transform domain

A generalization of Mallat?s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis associated with linear canonical transform (LCT-VNUMRA) where the associated subspace V?0 of the function space L2 (R,CM) has an orthonormal basis of the form {?(x ? ?)e? ??A B (t2??2)} ??? where ? = {0, r/N} + 2Z,N ? 1 is an integer and r is an odd integer such that r and N are relatively prime. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of vector-valued nonuniform multiresolution analysis starting from a vector refinement mask with appropriate conditions

L₁-Gain Controller Design for 2-D Markov Jump Positive Systems With Directional Delays

This article is concerned with the stochastic stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain control of two-dimensional (2-D) positive Markov jump systems (PMJSs) with directional delays based on the Roesser model. First, necessary and sufficient conditions (NSCs) for the stochastic stability of the addressed system are established by constructing a deterministic “equivalent” system and applying a stochastic copositive Lyapunov function. This reveals that the stochastic stability of 2-D PMJSs with delays is affected by the size of directional delays, the transition matrix, and system matrices. Second, the exact <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain index is calculated and NSCs in the form of linear programming (LP) are established for the addressed system. Systematic methods for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain controller design are proposed so that the closed-loop system (CLS) is positive and stochastically stable and has an optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain performance, which is achieved using an iterative algorithm and an analytical calculation method for a single-input case. Finally, the potency and accuracy of the theoretical results are verified using two examples.

Mixed [formula omitted] fault detection observer design for delayed 2D positive systems in FM LSS Models

This study is concerned with the problem of the mixed l1/l− fault detection (FD) observer for delayed two-dimensional (2D) positive systems (PSs). The necessary and sufficient conditions (NSCs) are derived under which the residual error system is asymptotically stable (AS) and has the prescribed performance level. The conservatism is greatly reduced compared to the existing results. A new performance analysis method and the mixed l1/l− FD observer design are presented. Firstly, the calculation of l1/l− index for delayed 2D PSs is proposed by establishing the equivalence between the delayed system and the higher dimensional delay-free system in sense of l1 and l− indexes. Secondly, NSCs are developed such that the delayed 2D PS is AS with a desired mixed l1/l− performance. Thirdly, the sufficient conditions of the observer design are further developed based on linear programming. An iterative algorithm is formulated to minimize and maximize the impact of system disturbances and faults on the output signal, respectively. Finally, we present two examples to verify the superiority of the obtained results.

Study of European style options under Itô-McKean Brownian motion with Azzalini skew-normal distribution

In this article, we deal European style option, with arbitrary payoff which includes both put and call options, on an asset whose price evolves as It?-McKean skew Brownian motion with Azzalini skew-normal distribution. Initially, we investigate a condition which leads the It?-McKean skew Brownian motion to be a martingale. Next, we price the option and show that if the payoff function is convex then so is the price function. After this, we show if the payoff is finite then the price function satisfies a partial differential equation with respect to time. Further, we provide a necessary and sufficient condition for the price function to satisfy Feymann-Kac type equation. Next, we study Black-Scholes type equation and give expressions for the delta hedge. Finally, we study the particular case of an European call option in order to compare some of our results with the existing literature. Our results can be used to investigate the optimal exercise boundary, discrete time hedging strategies etc. of the option.

Optimal Attack Strategy Against Fault Detectors for Linear Cyber-Physical Systems

This paper is concerned with the design of false data injection attacks (FDIAs) against fault detectors (FD) for linear cyber-physical systems (CPSs). The purpose of the attacker is to design an stealthy attack scheme such that the defenders cannot detect the faults in time or fail to detect the faults, and at the same time the robustness of the CPS is deteriorated. Unlike the existing optimal attack strategies (OASs) that are established based on sufficient conditions, necessary and sufficient conditions (NASCs) are established to maximize the degradation of the FD performance and robustness of CPS while maintaining stealth. Subsequently, an OAS is constructed by solving coupled backward recursive Riccati difference equations (RDEs). Finally, two simulation examples are employed to show the effectiveness of the designed attack scheme.

The minus order for projections

Let B(H)Id be the set of all projections on a Hilbert space H. The necessary and sufficient conditions are presented for the existence of the supremum, as well as the infimum, of two arbitrary projections in B(H)Id with respect to the minus order ?. For a projection Q in B(H)Id; the properties of the sets {P : P is an orthogonal projection on H and Q ? P} and {P : P is an orthogonal projection on H and P ? Q} are further explored.

Various formulations of inequivalent Leggett–Garg inequalities

In two-party, two-input and two-output measurement scenario only relevant Bell’s inequality is the Clauser–Horne–Shimony–Holt (CHSH) form. They also provide the necessary and sufficient conditions (NSCs) for local realism. Any other form, such as, Clauser–Horne and Wigner forms reduce to the CHSH one. The standard Leggett–Garg inequalities, proposed for testing incompatibility between macrorealism and quantum theory, are often considered to be the temporal analog of CHSH inequalities. However, they do not provide the NSCs for macrorealism. There is thus scope of formulating new macrorealist inequalities inequivalent and stronger than the standard Leggett–Garg inequalities. In this paper, we propose two different classes of macrorealistic inequalities. A class of inequalities which are equivalent to the standard ones in macrorealist model but inequivalent and stronger in quantum theory, and the other class of inequalities are inequivalent to the all the other formulations of Leggett–Garg inequalities both in macrorealist model and in quantum theory. The latter class of macrorealist inequalities reveals the incompatibility between macrorealism and quantum theory for specific cases even when any other formulation of Leggett–Garg inequalities fails to do so. We extend the formulations of inequivalent Leggett–Garg inequalities to the four-time and two-time measurement scenarios. Further, we provide a brief discussion about the alternative formulation of macrorealism known as the no-signaling in time (NSIT) conditions.

Exploiting Virtual Elasticity of Production Systems for Respecting OTD-Part 1: Post-Optimality Conditions for Ergodic Order Arrivals in Fixed Capacity Regimes

Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing speed of throughput reveals a latent capacity, which allows arrival orders above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

This paper considers the reduced-order H ∞ filtering problem for singular Markovian jump systems (SMJSs) with incomplete transition rates (ITRs) by using augmented system method. The considered conditions in this paper are necessary and sufficient (NS), whereas the existing conditions are mainly sufficient. To be concrete, by extracting system matrices in the considered system from augmented system, NS condition for the existence of the full-order H ∞ filtering is provided in terms of linear matrix inequalities (LMIs). However, it is hard to extend the condition to the existence of the reduced-order H ∞ filtering. Thus, by fixing augmented system matrices, NS condition for the existence of the reduced-order one is presented to guarantee the desired filtering error system to be stochastically admissible with H ∞ performance level. Furthermore, there are neither complicated matrix transformation nor equality/rank constraints in this paper. One numerical and one practical examples are illustrated to demonstrate the effectiveness of the achieved results.

Sharp multidimensional numerical integration for strongly convex functions on convex polytopes

This paper introduces and studies a new class of multidimensional numerical integration, which we call ?strongly positive definite cubature formulas?. We establish, among others, a characterization theorem providing necessary and sufficient conditions for the approximation error (based on such cubature formulas) to be bounded by the approximation error of the quadratic function. This result is derived as a consequence of two characterization results, which are of independent interest, for linear functionals obtained in a more general seeting. Thus, this paper extends some result previously reported in [2, 3] when convexity in the classical sense is only assumed. We also show that the centroidal Voronoi Tesselations provide an efficient way for constructing a class of optimal of cubature formulas. Numerical results for the two-dimensional test functions are given to illustrate the efficiency of our resulting cubature formulas.

Optimality conditions for higher order polyhedral discrete and differential inclusions

The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.

Positive operators on extended second order cones

A positive operator on a cone is a linear operator that maps the cone to a subcone of itself. The extended second order cones were introduced by Nemeth and Zhang [17] as a working tool to solve mixed complementarity problems. Sznajder [23] determined the automorphism group and the Lyapunov (or bilinearity) ranks of these cones. Ferreira and Nemeth [9] reduced the problem of projecting onto the second order cone to a piecewise linear equation. Nemeth and Xiao [16] solved linear complementarity problems on the extended second order cone (motivated by portfolio optimization models) by reducing them to mixed complementarity problems with respect to the nonnegative orthant. As an extension of Sznajder's results, this paper aims to be a first work about finding necessary conditions and sufficient conditions for a linear operator to be a positive operator (which extends the notion of an automorphism) on an extended second order cone. Although, in the particular case of second order cones a necessary and sufficient condition is known, for extended second order cone such a condition is very difficult to find without restricting the structure of the linear operator. If the matrix of the linear operator is block-diagonal, we give such a necessary and sufficient condition.

Some connections between various classes of analytic functions associated with the power series distribution

The primary motivation of the paper is to investigate the power series distribution (Pascal model) for the analytic function classes TG, TGS and TGC. Furthermore, we give necessary and sufficient conditions for the Pascal distribution series belonging to these classes.

On the mixed-type generalized inverses of the products of two operators

Let A, B and be closed range operators. The explicit matrix expressions for various generalized inverses are obtained by using block operator matrix methods. Some subtle relationships between the properties of sub-blocks in operator matrices A, B and their range relations are built. New necessary and sufficient conditions for the equivalent relations, inclusion relations and mixed-type generalized inverses relations are presented. Some recent mixed-type reverse-order laws results are covered and many new mixed-type generalized inverses relations are established by using this block-operator matrix technique.

Generalised distances of sequences II: B-distances with weight sequences

In this paper, we investigate the weighted B-distances of infinite sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Zn), and the theory was recently extended for application to sequences. By assigning various weights to the elements of the sequences the concept is further generalized. An algorithm is presented which provides a shortest path between two sequences. Formula is also provided to calculate the weighted B-distance of any two sequences with a neighbourhood sequence B and a weight sequence. There are several neighbourhood sequences, which do not generate metrics. We prove a necessary and sufficient condition for a B-distance to define a generalized metric space above the sequences. Moreover, our results can be applied if the elements of the sequences used with various weights. In case of weight functions used B-distances we present also the metric conditions.

The geometry of contact pseudo-slant submanifolds of a Sasakian manifold

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We verify some properties of the components of the tensor field acting on that kind of submanifold and find out the necessary and sufficient conditions for them to be parallel. Also, necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, contact pseudo-slant product, D?, D? and mixed-geodesic in Sasakian manifold.